Image-based autofocus for optical systems

Abstract

This disclosure describes illumination methods and systems for illumination, as well as methods and systems for autofocusing the systems. The systems can be used, for example, for microscopy and sequencing platforms. The methods and systems of this disclosure can provide fast and accurate autofocus, thereby reducing errors and improving system throughput.

Description

Technical Field

[0001] Cross-reference This application claims the benefit of U.S. Provisional Application No. 63 / 484,723, filed Feb. 13, 2023, which is hereby incorporated by reference in its entirety.

Background Art

[0002] In many fluorescence-based genomic test assays, such as genotyping or nucleic acid sequencing, dye molecules attached to nucleic acid molecules tethered to a substrate are excited using an excitation light source, and the fluorescence signal is generated at spatially localized position(s) on the substrate, and then the fluorescence is imaged onto an image sensor via an optical system. Next, an analysis process is used to analyze the image, find the position of the labeled molecules (or clusters of clonally amplified molecules) on the substrate, and quantify the fluorescence photon signal in terms of wavelength and spatial coordinates. Then, this process can correlate with the extent to which a particular chemical reaction, such as a hybridization event or a base addition event, occurred at a specified location on the substrate. Imaging-based methods provide for large-scale parallel processing and multiplexing capabilities and help reduce the cost and accessibility of such technologies.

Summary of the Invention

[0003] This specification describes methods and systems for autofocusing optical systems, such as optical systems for imaging sequencing reactions, so that the optical signal is focused and acquired, and can be relied upon to produce accurate sequencing analysis results. The systems and methods described herein can conveniently and accurately determine the z-shift for autofocusing the optical system using a single image. The single image can be acquired using the image sensor of the optical system after tilting the sample stage relative to the image sensor, without requiring dedicated hardware such as an autofocus (AF) laser or AF sensor, and these are used solely for the purpose of autofocusing. The image-based autofocus methods and systems described herein offer advantageous savings in machine costs and reduce the complexity of the optical system compared to existing autofocus methods that use AF lasers and / or AF sensors. Furthermore, the methods and systems described herein require only a single image, which reduces time consumption and computational complexity compared to existing autofocus methods that rely on at least two images and / or machine learning algorithms.

[0004] This disclosure provides a method for focusing an optical system, comprising: receiving an image of a substrate of the optical system, wherein a portion but less than all of the image is in focus, and the portion of the focused image is offset from the center of the image; determining the amount of focus misalignment in the image using at least the portion of the focused image and the distance from the center of the image; and adjusting the parameters of the optical system to adjust for the misalignment. In some embodiments, the image is an image of a flow cell, and the substrate is a flow cell. In some embodiments, the adjustment in (c) is an auto-adjustment. In some embodiments, the image is received from an autofocus element. In some embodiments, the determination is made in a maximum of about 600 milliseconds (ms). In some embodiments, the determination is made in a maximum of about 100 ms. In some embodiments, the method further includes imaging the substrate using a light source and a detector to generate an image prior to (a). In some embodiments, the determination is made using the image and without using an additional image. In some embodiments, the image includes a length or width in the range of about 0.1 millimeters (mm) to about 5 centimeters (cm). In some embodiments, the image includes a length or width within the range of about 0.5 mm to about 9 mm. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 400 nanometers (nm). In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 100 nanometers (nm). In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 50 nanometers (nm). In some embodiments, the center of the focused region is determined using an image processing algorithm. In some embodiments, the image processing algorithm includes determining the center of the focused region by separating the image into a predetermined number of regions and using the sum or average intensity of each region to identify the location of the focused region.In some embodiments, image intensity or spatial frequency information of the location of the focused region is used to locate the center of the focused region. In some embodiments, information about the geometric pattern in the image determines the image processing algorithm.

[0005] This disclosure provides a method for focusing an optical system, comprising: imaging a substrate tilted at a certain tilt angle using a detector, such that the image of the substrate includes a focused portion and an out-of-focus portion; determining the focus shift of the optical system using a processor, at least partially based on the tilt angle and the distance from the center of the image of the focused portion; adjusting the substrate to eliminate the tilt angle; and adjusting the substrate by the amount of the focus shift, thereby focusing the optical system. In some embodiments, determining in (b) further includes using a vector from the center of the image of the focused portion. In some embodiments, the method further includes a motor coupled to the substrate configured to impart a tilt angle. In some embodiments, the detector is part of an autofocus element. In some embodiments, the optical system further comprises an additional detector configured to image the substrate. In some embodiments, the method further includes tilting the substrate to the tilt angle before (a). In some embodiments, the method further includes untilting the substrate following (d). In some embodiments, tilting means tilting a plane perpendicular to the optical axis of the optical system. In some embodiments, the tilt angle is approximately 0.01 to approximately 89 degrees. In some embodiments, the tilt angle is approximately 0.05 to approximately 15 degrees. In some embodiments, the angular resolution of the tilt angle is approximately 0.001 to approximately 0.2 degrees. In some embodiments, the angular resolution of the tilt angle is approximately 0.01 to approximately 0.1 degrees. In some embodiments, the angular resolution of the tilt angle is approximately 0.01 to approximately 0.08 degrees. In some embodiments, the determination is performed using an image and without the use of additional images.In some embodiments, the substrate includes a flow cell comprising one or more surfaces, at least one hydrophilic polymer coating layer, a plurality of oligonucleotide molecules attached to the at least one hydrophilic polymer coating layer, and a plurality of clone-amplified nucleic acid molecules immobilized on the attached plurality of oligonucleotide molecules, wherein the plurality of immobilized clone-amplified sample nucleic acid molecules are located at a distance of less than λ / (2*NA), where λ is the central wavelength of the excitation energy source and NA is the numerical aperture of the optical system. In some embodiments, the substrate includes a bead-like flow cell. In some embodiments, the bead-like flow cell includes a surface containing fluorescent beads chemically immobilized on the substrate. In some embodiments, the fluorescent beads are randomly distributed on the surface. In some embodiments, the fluorescent beads include at least about four different types of beads configured to emit different colors in response to excitation from a laser. In some embodiments, the error from the distance from the focal plane to the true distance from the focal plane is at most about 400 nanometers (nm). In some embodiments, the error between the distance from the focal plane and the true distance from the focal plane is at most about 100 nanometers (nm). In some embodiments, the error between the distance from the focal plane and the true distance from the focal plane is at most about 50 nanometers (nm). In some embodiments, (d) occurs before the optical system images the nucleic acid molecules immobilized on the substrate in the first flow cycle. In some embodiments, the method further includes repeating (a) to (d) to refocus the optical system for the second flow cycle.

[0006] This disclosure provides a method for focusing an optical system, comprising: imaging a substrate using a detector tilted at a certain tilt angle, such that the image of the substrate includes a focused portion and an out-of-focus portion; determining the misfocus of the optical system using a processor, at least partially based on the tilt angle and the distance from the center of the image of the focused portion; and adjusting the substrate by the misfocus amount, thereby focusing the optical system. In some embodiments, the method further includes adjusting the substrate by the misfocus amount, thereby bringing the substrate into focus. In some embodiments, the method further includes tilting the detector to the tilt angle before (a). In some embodiments, the method further includes untilting the detector after (c). In some embodiments, tilting is tilting a plane perpendicular to the optical axis of the optical system. In some embodiments, the tilt angle is about 0.01 to about 89 degrees. In some embodiments, the tilt angle is about 0.05 to about 15 degrees. In some embodiments, determining is performed using an image and without using additional images. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 400 nanometers (nm). In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 100 nanometers (nm). In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 50 nanometers (nm). In some embodiments, the method further includes calibrating the pivot point of the optical system. In some embodiments, calibrating the pivot point includes untilting the substrate, detector, or autofocus sensor.

[0007] This disclosure provides a method for autofocusing an optical system, comprising: tilting a sample stage of the optical system by a certain tilt angle, wherein a sample is fixed on the sample stage; obtaining an image of the sample on the tilted sample stage by an image sensor of the optical system; determining a z-shift by a processor based on the tilt angle and the xy-plane shift from the center of the image, wherein the xy-plane shift is determined based on the focused region of the image; and moving the sample stage by the determined z-shift relative to the focal plane of the objective lens of the optical system, thereby focusing on the sample.

[0008] This disclosure provides a method for autofocusing an optical system, comprising: tilting an image sensor of the optical system by a certain inclination angle; obtaining an image of a sample by the tilted image sensor of the optical system, wherein the sample is fixed on a sample stage; determining a z-shift by a processor based on the inclination angle and the xy-plane shift from the center of the image, wherein the xy-plane shift is determined based on the focused region of the image; and moving the sample stage by the determined z-shift relative to the focal plane of the objective lens of the optical system, thereby focusing on the sample.

[0009] This disclosure provides a method for autofocusing an optical system, comprising: tilting a sample stage of the optical system by a certain tilt angle such that a sample is fixed on the sample stage; obtaining an image of the sample on the tilted sample stage by an autofocus (AF) sensor of the optical system, which is different from the image sensor of the optical system; determining a z-shift by a processor based on the tilt angle and the xy-plane shift from the center of the image, such that the xy-plane shift is determined based on the focused region of the image; and moving the sample stage by the determined z-shift relative to the focal plane of the objective lens of the optical system, thereby focusing on the sample.

[0010] This disclosure provides a method for autofocusing an optical system, comprising: tilting an AF sensor of the optical system, which is different from the image sensor of the optical system, by a certain tilt angle; obtaining an image of a sample by the AF sensor of the optical system, wherein the sample is fixed on a sample stage; determining a z-shift by a processor based on the tilt angle and the xy-plane shift from the center of the image, wherein the xy-plane shift is determined based on the focused region of the image; and moving the sample stage by the determined z-shift relative to the focal plane of the objective lens of the optical system, thereby focusing the optical system on the sample. In some embodiments, the method further includes calibrating the pivot point of the optical system. In some embodiments, calibrating the pivot point of an optical system includes tilting the sample stage, image sensor, or AF sensor by an inclination angle or a second inclination angle; acquiring a calibration image of a sample fixed on the sample stage by the AF sensor or image sensor; determining the pivot point offset by a processor based on the region center of the focused area of ​​the calibration image and the image center of the calibration image; and untilting the sample stage, image sensor, or AF sensor by an inclination angle or a second inclination angle. In some embodiments, the method further includes untilting the tilted sample stage by an inclination angle. In some embodiments, the method further includes untilting the tilted image sensor by an inclination angle. In some embodiments, the method further includes untilting the tilted AF sensor by an inclination angle. In some embodiments, tilting the sample stage of an optical system by an inclination angle is a tilt around the x-axis or y-axis. In some embodiments, tilting the sample stage of an optical system by an inclination angle is a tilt in the xz-plane or yz-plane. In some embodiments, tilting the AF sensor or image sensor of an optical system by an angle of inclination is considered tilting around the x-axis or y-axis.In some embodiments, tilting the AF sensor or image sensor of the optical system by an angle of inclination is a tilt in the xz-plane or yz-plane. In some embodiments, the inclination angle is in the range of 0.01 to 89 degrees. In some embodiments, the inclination angle is in the range of 0.05 to 15 degrees. In some embodiments, the inclination angle is clockwise around the x-axis or y-axis. In some embodiments, the inclination angle is counterclockwise around the x-axis or y-axis. In some embodiments, the image of the sample obtained by the AF sensor or image sensor includes a single image. In some embodiments, the AF sensor is used only to acquire a signal for autofocusing the optical system. In some embodiments, the image sensor is used to autofocus the optical system and to take images using the optical system after autofocusing. In some embodiments, the optical system lacks an AF illumination source and is used only for autofocusing and not for imaging. In some embodiments, the method for autofocusing the optical system is completed in 100 to 990 milliseconds. In some embodiments, the method for autofocusing the optical system is completed in less than 600 milliseconds. In some embodiments, the image includes a field of view (FOV) that is the same size as the image sensor or AF sensor along the x or y axis. In some embodiments, the image includes a length or width in the range of 0.1 mm to 5 cm. In some embodiments, the image includes a length or width in the range of 0.5 mm to 9 mm. In some embodiments, the image includes a field of view (FOV) that is the same size as the image sensor or AF sensor along the x axis when the tilt angle is around the x axis, and along the y axis when the tilt angle is around the y axis. In some embodiments, the AF illumination source includes a laser. In some embodiments, the image includes a fluorescence signal from a sample.In some embodiments, the sample includes a flow cell comprising one or more surfaces and one or more substrates, at least one hydrophilic polymer coating layer, a plurality of oligonucleotide molecules attached to at least one hydrophilic polymer coating layer, and a plurality of clone-amplified sample nucleic acid molecules immobilized on the attached plurality of oligonucleotide molecules, wherein the plurality of immobilized clone-amplified sample nucleic acid molecules are located at a distance of less than λ / (2*NA), where λ is the central wavelength of the excitation energy source and NA is the numerical aperture of the optical system. In some embodiments, the sample includes a bead-shaped flow cell. In some embodiments, the bead-shaped flow cell includes a surface coated with chemically immobilized fluorescent beads on the surface. In some embodiments, the fluorescent beads are randomly distributed on the surface. In some embodiments, the fluorescent beads include one, two, three, four, five, or six different types of beads that emit different colors in response to laser excitation. In some embodiments, the fluorescent beads emit fluorescence of one or more wavelengths in response to laser excitation. In some embodiments, the sample includes a test target. In some embodiments, the test target includes a coating of a predetermined geometric shape or pattern that is repeated spatially. In some embodiments, the predetermined geometric pattern or shape is repeated in one or two dimensions. In some embodiments, the test target lacks a flow cell and liquid. In some embodiments, the test target includes one or more substrates having a predetermined refractive index. In some embodiments, the test target includes a top substrate having a predetermined refractive index. In some embodiments, the test target includes a bottom substrate. In some embodiments, at least a portion of the first or second substrate includes a coating having a predetermined geometric pattern or shape. In some embodiments, the thickness of the first substrate is configured to simulate the presence of a first virtual flow cell.In some embodiments, the thickness of the top substrate is configured to allow imaging of the bottom surface of the first channel of a virtual first flow cell. In some embodiments, a coating of a predetermined geometric shape or pattern includes optically opaque and transparent portions. In some embodiments, the optical system includes one, two, three, four, five, or six detection channels. In some embodiments, the optical system is configured to acquire a flow cell image having an FOV greater than 1.0 mm² after autofocusing of the optical system. In some embodiments, the optical system includes an objective lens, an image sensor, and a numerical aperture (NA) less than 0.6, and a processor is configured to process the flow cell image to correct optical aberrations and produce substantially identical optical resolution within the flow cell image. In some embodiments, the optical system further comprises one or more illumination sources, one or more of which lack an AF laser configured solely for autofocusing the optical system. In some embodiments, the method for autofocusing the optical system is configured to focus the optical system for imaging sample nucleic acid molecules immobilized on the flow cell in a first flow cycle and a second flow cycle in a sequencing run. In some embodiments, a method for autofocusing an optical system is configured to focus an optical system for imaging sample nucleic acid molecules immobilized on a first surface during a first flow cycle in a sequencing run, and to refocus an optical system for imaging sample nucleic acid molecules immobilized on the first or second surface during a second flow cycle in a sequencing run. In some embodiments, a method for autofocusing an optical system is configured to focus an optical system for imaging sample nucleic acid molecules immobilized on a first surface during a first flow cycle in a sequencing run, and to refocus an optical system for imaging sample nucleic acid molecules immobilized on a second surface during a first or second flow cycle in a sequencing run.In some embodiments, the method for autofocusing an optical system is configured to focus at least along the z-axis. In some embodiments, tilting the sample stage of the optical system by an inclination angle includes moving the sample stage in the xy-plane and tilting the sample stage by an inclination angle. In some embodiments, moving the sample stage in the xy-plane includes moving the sample stage to a predetermined spatial location. In some embodiments, untilting the inclined sample stage by an inclination angle includes moving the sample stage relative to the focal plane of the objective lens by a determined z-shift and simultaneously untilting the inclined sample stage by an inclination angle. In some embodiments, untilting an inclined image sensor by an inclination angle includes moving the sample stage by a determined z-shift and simultaneously untilting the inclined image sensor by an inclination angle. In some embodiments, untilting an inclined AF sensor by an inclination angle includes moving the sample stage by a determined z-shift and simultaneously untilting the inclined AF sensor by an inclination angle. In some embodiments, the error in the autofocus of the optical system is within the range of -400 nm to +400 nm. In some embodiments, the autofocus error of the optical system is within the range of -100 nm to +100 nm. In some embodiments, the autofocus error of the optical system is within the range of -50 nm to +50 nm. In some embodiments, the sample stage is an electrically operated stage that automatically tilts by a predetermined angle provided by the user. In some embodiments, an image sensor or AF sensor is fixed on an electrically operated stage that automatically tilts by a predetermined angle provided by the user. In some embodiments, the objective lens is fixed on a z-stage that is movable along the z-axis. In some embodiments, moving the sample stage by a determined z-shift relative to the focal plane of the objective lens of the optical system includes moving the objective lens, thereby moving the focal plane of the objective lens by a determined z-shift.In some embodiments, tilting the sample stage of an optical system by an inclination angle includes a motor coupled to the sample stage accepting the inclination angle and the motor tilting the sample stage by the inclination angle.

[0011] This disclosure provides a method for autofocusing an optical system, comprising: using the optical system to acquire one or more flow cell images of a first tile or subtile of a sample in a flow cycle of sequencing execution; moving a sample stage to position a second tile or subtile next to the first tile or subtile of the sample relative to the optical system; repeating the method for autofocusing the optical system; and using the optical system to acquire one or more flow cell images of a second tile or subtile of the sample in a flow cycle of sequencing execution.

[0012] Embedding by reference All publications, patents, and patent applications referenced herein are incorporated herein by whole to the same extent as each individual publication, patent, or patent application is specifically and individually indicated to be incorporated by whole. In the event of any conflict between terms used herein and terms used in incorporated references, the terms defined herein shall prevail.

[0013] Novel features of the concept of the present invention are described in detail in the appended claims. A better understanding of the features and advantages of this disclosure can be obtained by referring to the following detailed description, which describes exemplary embodiments in which the principles of this disclosure are used, and to the appended drawings. [Brief explanation of the drawing]

[0014] [Figure 1] Block diagrams illustrating next-generation sequencing (NGS) systems utilizing the optical systems disclosed herein for imaging sequencing reactions and sequencing analysis, according to several embodiments, are illustrated. [Figure 2A] An example of a non-limiting optical system is illustrated (top isometric view) that includes a dichroic beam splitter for receiving and redirecting an excitation light beam through a sample, and the resulting fluorescence emission reflected to four detection channels configured to detect the fluorescence emission at four different wavelengths or wavelength bands. [Figure 2B] An example of a non-limiting optical system is illustrated (bottom isometric view) that includes a dichroic beam splitter for receiving and redirecting an excitation light beam through a sample, and the resulting fluorescence emission, which is reflected to four detection channels configured to detect the fluorescence emission at four different wavelengths or wavelength bands. [Figure 3A] An optical path in the optical system shown in Figures 2A and 2B is illustrated (top view) (see top view), which includes a dichroic beam splitter for receiving and redirecting the resulting fluorescence emission by reflecting it through four detection channels for detecting the fluorescence emission at four different wavelengths or wavelength bands. [Figure 3B] The optical paths in the optical system shown in Figures 2A and 2B are illustrated (side view) (side view) in which an excitation light beam is transmitted through the sample, and the resulting fluorescence emission is received and redirected by a dichroic beam splitter that reflects the emission to four detection channels for detecting the fluorescence emission at four different wavelengths or wavelength bands. [Figure 4] Block diagrams illustrating computer systems for autofocusing optical systems, according to several embodiments, are provided. [Figure 5] A flowchart shows an example of an image-based autofocus method for an optical system according to several embodiments. [Figure 6A] A schematic diagram is shown illustrating how the sample stage is tilted relative to the image sensor and how the z-shift for autofocus of the optical system is determined according to an embodiment of this specification. [Figure 6B]An exemplary non-limiting image used to determine the x-y plane shift for autofocus of an optical system, according to an embodiment of this specification, is shown. [Figure 7A] Autofocus results using the methods and systems of this specification are shown by tilting a sample stage at different tilt angles compared to a reference z-shift, according to some embodiments. [Figure 7B] Autofocus results using the methods and systems of this specification are shown by tilting a sample stage at different tilt angles compared to a reference z-shift, according to some embodiments. [Figure 8] Autofocus results using the methods and systems of this specification are shown by tilting an image sensor compared to a reference z-shift, according to some embodiments. [Figure 9] A calibration image used to determine a pivot point offset prior to autofocus of an optical system using the methods and systems of this specification is shown, according to some embodiments. [Figure 10] A schematic view of a sample immobilized on a sample stage along the optical axis of an optical system, and their positions relative to an objective lens, is shown, according to some embodiments. [Figure 11] A schematic view of an example of an embodiment of a low-binding solid support of the present disclosure is shown, the support comprising a glass substrate and alternating layers of a hydrophilic coating covalently or non-covalently adhered to the glass, and further comprising a chemically reactive functional group that functions as an attachment site for oligonucleotide primers. [Figure 12] Schematic diagrams of various exemplary configurations of multivalent molecules. Left (Class I): Schematic diagram of a multivalent molecule having a "starburst" or "helical staircase" configuration. Center (Class II): Schematic diagram of a multivalent molecule having a dendrimer configuration. Right (Class III): Schematic diagram of multiple multivalent molecules formed by reacting streptavidin with 4-arm or 8-arm type PEG-NHS having biotin and dNTP. Nucleotide units are represented by "N", biotin is represented by "B", and streptavidin is represented by "SA". [Figure 13] Schematic diagram of an example of a multivalent molecule including a common core attached to a plurality of nucleotide arms. [Figure 14] Schematic diagram of an example of a multivalent molecule including a dendrimer core attached to a plurality of nucleotide arms. [Figure 15] Schematic diagram of an example of an exemplary multivalent molecule including a core attached to a plurality of nucleotide arms, where the nucleotide arms include biotin, a spacer, a linker, and nucleotide units. [Figure 16] Schematic diagram of an example of a nucleotide arm including a core attachment portion, a spacer, a linker, and nucleotide units. [[ID=1十二条]] [Figure 17] Chemical structure of an example of a spacer (upper), and chemical structures of various exemplary linkers including an 11-atom linker, a 16-atom linker, a 23-atom linker, and an N3 linker (lower). [Figure 18] Chemical structures of various examples of linkers including Linkers 1-9 are shown. [Figure 19] Chemical structures of various examples of linkers linked / attached to nucleotide units are shown. [Figure 20] Chemical structures of various examples of linkers linked / attached to nucleotide units are shown. [Figure 21] Chemical structures of various examples of linkers linked / attached to nucleotide units are shown. [Figure 22] Chemical structures of various examples of linkers linked / attached to nucleotide units are shown. [Figure 23] Chemical structure of an example of a biotinylated nucleotide arm is shown. In this example, the nucleotide unit is connected to the linker via a propargylamine bond at the 5-position of the pyrimidine base or the 7-position of the purine base. [Figure 24] An example of one embodiment of a test target disclosed herein is shown. [Figure 25]A schematic diagram of an example of a flow cell having a first surface coated with fluorescent beads (top) and a second surface coated with fluorescent beads (bottom) is shown. The coating can be applied directly onto the solid support of the flow cell. Flow cells with the coating(s) can be positioned on an array determination system for autofocusing an optical system by obtaining and analyzing images of the fluorescent beads. [Modes for carrying out the invention]

[0015] Accurate and reliable autofocus is required for multi-channel fluorescence imaging systems to ensure the quality of fluorescence images and the accuracy of sequencing analysis based thereon. Disclosed herein are systems and methods that can provide one or more of the following advantages: The systems and methods herein advantageously eliminate the need for dedicated AF hardware such as AF illumination sources, AF sensors, and / or AF tube lenses, resulting in reduced machine costs and complexity of the imaging system. Compared to image-based AF methods that use multiple images and / or machine learning algorithms, the systems and methods herein require only a single image, which reduces the time consumption and computational complexity in achieving autofocus. Furthermore, the systems and methods herein avoid acquiring multiple images after illumination at multiple z locations, thus reducing the level of photobleaching in existing autofocus methods that use dedicated AF hardware. More importantly, the systems and methods herein can achieve an error range of less than 100 nm in AF, which is equivalent to or better than existing AF methods. The tilting and untilting of the sample stage or sensor used in the methods disclosed herein can be performed simultaneously with other preparatory operations for imaging, such as moving the xy stage or objective lens relative to each other to position the desired area of ​​the flow cell for imaging, thereby saving the total time required to achieve autofocus and imaging. The total time for autofocus using the systems and methods herein can be completed in less than 500 milliseconds, and can be repeatedly used in each flow cycle in various sequencing applications.

[0016] Although the methods and systems described herein are disclosed in the context of multichannel fluorescence imaging systems for DNA sequencing applications, they may be used for autofocusing various optical systems in different applications requiring z-axis autofocus to render focused images.

[0017] Sequence determination system The optical systems disclosed herein can be used in a variety of applications that utilize focused images including optical signals, for example, in next-generation sequencing (NGS) sequencing applications or as part of an NGS sequencing system.

[0018] In some embodiments, the optical systems disclosed herein may include some or all of the optical elements of a multichannel fluorescence imaging module of an NGS sequencing system.

[0019] Figure 1 illustrates a block diagram of a computer-implemented system 100 configured to perform DNA sequencing and sequencing analysis according to one or more embodiments disclosed herein. System 100 may have a sequencing system 110 including a flow cell 112 or a test target simulating the presence of a flow cell, a sequencer 114, an optical system 116, data storage 122, and a user interface 124. The sequencing system 110 may be connected to a cloud 130. The sequencing system 110 may include one or more of a dedicated processor 118, a field-programmable gate array (FPGA) 120, and a computer system 126.

[0020] In some embodiments, a flow cell or a test target simulating the presence of a flow cell may be used for autofocusing the sequencing system. In some embodiments, the image that can be used for autofocusing the sequencing system may be generated by collecting the optical signals emitted from the flow cell or the test target simulating the presence of a flow cell.

[0021] In some embodiments, the flow cell may have a conventional 2D DNA sample immobilized thereon. In some embodiments, the flow cell may have a volumetric 3D sample immobilized thereon. The 3D sample may include cells and / or tissues of insights.

[0022] In some embodiments, the samples described herein may contain nucleotide acids that are unbalanced or balanced in one or more flow cycles.

[0023] In some embodiments, the flow cell 112 is configured to capture DNA fragments and form DNA sequences for base calling on the flow cell. The flow cell or test target 112 as herein may include a support as disclosed herein. The support may be a solid support. The support may include a surface coating thereon as disclosed herein. The surface coating may be a polymer coating as disclosed herein. The flow cell 112 may include a plurality of tiles or imaging regions thereon, each tile may be separated into a grid of subtiles. Each subtile may include a plurality of clusters or polony thereon. In some embodiments, the flow cell may comprise two or more substrates. The flow cell may comprise inner surfaces separated by fluid channels through which the analyte or reagent can flow. In some embodiments, the flow cell may comprise at least two, three, four, five, six, or more inner surfaces separated by corresponding fluid channels through which the analyte or reagent can flow. In such embodiments, autofocus and imaging may occur on each individual inner surface for various sequencing applications. Having multiple inner surfaces with sequencing reactions that can be imaged can favorably increase sequencing throughput compared to using a conventional flow cell with only one or two inner surfaces.

[0024] In some embodiments, the flow cell may comprise one or more surfaces and one or more substrates. The flow cell may comprise at least one hydrophilic polymer coating layer and a plurality of oligonucleotide molecules attached to the at least one hydrophilic polymer coating layer. In some embodiments, the flow cell may comprise at least one distinct region of one or more surfaces containing a plurality of clonely amplified sample nucleic acid molecules immobilized on the plurality of attached oligonucleotide molecules. When imaged, the sample nucleic acid molecules appear as bright spots or "polony" of signal.

[0025] In some embodiments, the flow cell may be a bead-shaped flow cell containing patterned or randomly distributed fluorescent or luminescent beads. In some embodiments, the flow cell includes a bead-shaped flow cell having randomly distributed microbeads having fluorescent labels to simulate fluorescence emission from a DNA sample when illuminated by an illumination source disclosed herein. In some embodiments, the fluorescent beads may be commercially available microbeads. In some embodiments, the microbeads are customized. In some embodiments, the bead-shaped flow cell includes a surface coated with fluorescent beads chemically immobilized on the surface. The fluorescent beads may include one, two, three, four, five, or six different types of beads that emit light of different colors and / or different frequencies in response to optical excitation, e.g., laser light. The fluorescent beads may emit fluorescent light of one or more wavelengths in response to laser excitation.

[0026] In some embodiments, the flow cell devices disclosed herein may include the support disclosed herein. The support may be solid. At least a portion of the support may be transparent. The support may include one or more substrates. At least a portion of one or more substrates may be transparent. Figure 25 shows an exemplary embodiment of the flow cell device 900. The flow cell device 900 includes a support 901 and other flow cell compounds such as a coating. The support may include a top substrate 910 and a bottom substrate 910. Each substrate 910 may have a predetermined thickness, and different substrates may have different thicknesses. The substrates may define one or more channels 920 of the device 900. The channels may allow the flow of fluid, such as liquid or air, through them. The flow cell device may include one or more inlets 920 and one or more outlets 930 within one or more substrates 910. Figures 9 and 11 show an exemplary device 900 having two substrates forming two channels, each channel having an inlet and an outlet. However, the number of substrates, channels, inlets, and outlets can differ in other embodiments. In some embodiments, the number of substrates, channels, inlets, and outlets can be any integer greater than 0. Figure 25 shows an exemplary flow cell 900 having two planar substrates with no curvature on the surface(s) of the substrates. However, the substrates do not need to be planar.

[0027] In some embodiments, the support and one or more substrates may include glass or plastic. In some embodiments, one or more substrates may be all glass or all plastic.

[0028] In some embodiments, one or more channels 920 can extend from the inlet 930 to the outlet 940 so that a fluid can flow from the inlet 930 through one or more channels 920 to the outlet 940. For example, a sequencing reagent can be introduced into the flow cell device through the inlet, flow through the channels, and then exit through the outlet. The channel(s) 920 may include an inner top surface 921 and an inner bottom surface 922. One or more of these surfaces may be coated with fluorescent beads.

[0029] Fluorescent beads can be chemically immobilized on a surface. Fluorescent beads can be covalently immobilized on a surface. Fluorescent beads can be immobilized or fixedly attached to surfaces 921, 922 by forming coatings 950, 951 on them, so that the fluorescent beads are fixed to or remain fixed to surfaces 921, 922. Coatings 950, 951 can be applied directly to and in contact with inner surfaces 921, 922. Alternatively, coatings 950, 951 can be applied indirectly to inner surfaces 921, 922, or do not come into direct contact with inner surfaces 921, 922. In some embodiments, coatings 950, 951 can be applied together with several compounds between surfaces 921, 922 and coatings 950, 951. For example, coatings 950 and 951 can be applied directly to surfaces 921 and 922, or applied on top of another coating that is in contact with surfaces 921 and 922. In some embodiments, the surfaces are passivated with another coating (not shown). The other coating can immobilize surface capture primers, nucleic acid template molecules, or both, to capture polynucleotides on surfaces 921 and 922. In some embodiments, surfaces 921 and 922 contain polynucleotides to be captured thereon.

[0030] In some embodiments, the coatings 951, 952 for attaching fluorescent beads can be mixed with one or more other coatings so that the mixed coating can be applied directly to and in contact with the inner surfaces 921, 922. The mixed coating can immobilize the fluorescent beads on the surface. Furthermore, the mixed coating can also immobilize surface capture primers, nucleic acid template molecules, or both, to capture polynucleotides on the surfaces 921, 922. In some embodiments, the immobilized coating can capture polynucleotides on the surfaces 921, 922, and administration of sequencing reagents can facilitate the sequencing of the polynucleotides as disclosed herein using various sequencing methods, such as avidite-mediated sequencing.

[0031] In some embodiments, the flow cell device 900 can be used on a sequencing system 1410 for DNA sequencing. The flow cell device 900 may receive various sequencing reagents before the sequencing cycle via an inlet 930, allowing the reagents to flow through one or more channels 920 and exit via an outlet 940. In some embodiments, fluorescent beads remain immobilized on surfaces 921, 922 during or after the administration of sequencing reagents to the flow cell device 900.

[0032] In some embodiments, a flow cell or bead-shaped flow cell may contain a sample immobilized thereon, such as nucleic acid molecules tethered onto the substrate of the flow cell.

[0033] In some embodiments, the test target includes a substrate having a gap or another substrate between it in order to simulate a fluid channel with a liquid.

[0034] In some embodiments, the test target includes a coating of a predetermined geometric shape or pattern. In some embodiments, the predetermined geometric pattern or shape is spatially repeated in one or two dimensions. For example, the test target may include a grid of intersecting lines. As another example, the test target may include microdots separated at the same distance in 2D. Figures 6B and 9 show a repeating geometric pattern of an exemplary test target. In some embodiments, the test target lacks a flow cell and liquid. In some embodiments, the test target includes one or more substrates having a predetermined refractive index. In some embodiments, the test target includes a top substrate having a predetermined refractive index [n-top substrate(1)]. In some embodiments, the test target includes a bottom substrate. At least a portion of the first or second substrate may include a coating of a predetermined geometric pattern or shape. In some embodiments, the thickness of the first substrate is configured to simulate the presence of a first virtual flow cell, the first virtual flow cell comprising a first channel having a top and bottom surface, the first channel comprising a specified first fluid, the first channel having a first specified thickness [T-channel(1)], and the first specified fluid having a refractive index [n-fluid(1)]. In some embodiments, the thickness of the top substrate is configured to allow imaging of the bottom surface of the first channel of the virtual first flow cell. In some embodiments, the coating of a predetermined geometric shape or pattern comprises optically opaque and transparent portions. In some embodiments, the height or thickness of the top substrate [T-top substrate(1)] depends on the refractive index of the top substrate [n-top substrate(1)], the first specified height of the first channel [T-channel(1)], and the refractive index of the first specified fluid [n-fluid(1)]. In some embodiments, the height or thickness of the top substrate [T-top substrate(1)] is (T-top substrate(1))=C*[((T-channel(1))*[((n-fluid(1)) / (n-top substrate(1))]] It can be calculated as follows, where C is a predetermined constant.

[0035] Figure 24 is a schematic diagram of an exemplary embodiment of a test target as described herein. The left schematic diagram shows an exemplary solid-state optical test target having a first substrate (top) and a second substrate (bottom), with an opaque layer between the first and second substrates. The opaque layer can be coated on the bottom surface of the first substrate or the top surface of the second substrate. The opaque layer forms a micropattern. The first substrate is transparent, allowing light transmission from its bottom surface and viewing of the micropattern. The solid-state optical test target lacks a flow cell and liquid. The thickness of the first substrate is adjusted to simulate the presence of a virtual flow cell containing a fluid / liquid, which may be located between the first and second substrates. For example, the first substrate is thicker and has an add-on thickness. The right schematic diagram shows a virtual flow cell including a channel having a thickness [T-channel], the channel containing a fluid / liquid having a refractive index [n-fluid]. The solid-state optical test target shown in Figure 2 can be positioned on an optical imaging system and used to evaluate the performance of the optical imaging system by obtaining image information about the bottom surface of a virtual flow cell channel.

[0036] The sequencer 114 may be configured to flow a nucleotide mixture onto a flow cell 112, cleave blockers from the nucleotides during the flowing operation, and perform other operations to form a DNA sequence on the flow cell 112. The nucleotides may have attached fluorescent elements that emit light or energy at wavelengths indicating the type of nucleotide. Each type of fluorescent element may correspond to a specific nucleotide base (e.g., A, G, C, T). The fluorescent elements may emit light at visible wavelengths. In some embodiments, the sequencer 114 and flow cell 112 may be configured to perform various sequencing methods, such as avidity sequencing. For example, each nucleotide base may be assigned a color. Different types of nucleotides may have different colors. For example, adenine (A) may be red, cytosine (C) may be blue, guanine (G) may be green, and thymine (T) may be yellow. The color or wavelength of the fluorescent element of each nucleotide may be selected based on the wavelength of light emitted by the fluorescent element so that the nucleotides are distinguishable from one another.

[0037] The test target may be used to simulate the presence of a virtual flow cell. It may contain a fluorescence signal similar to that of a flow cell, originating from a region of equivalent wavelength and size to a polony or cluster on the flow cell, and / or having an intensity equivalent to the signal from an actual sample immobilized on the flow cell.

[0038] The optical system 116 may be focused using the autofocus method described herein. The optical system 116 may be configured to capture an image of the flow cell or test target after autofocusing. In some embodiments, the optical system 116 or the image sensor of the optical system may include a camera configured to capture a digital image, such as an active pixel sensor (CMOS) or a CCD camera. The image sensor may be configured to capture an image at the wavelength of a nucleotide-bound fluorescent element. The image may be referred to as a flow cell image. The image may then be used for base calling.

[0039] In some embodiments, an image of a flow cell or test target may be captured in one or more color channels, with each image in a channel captured at a wavelength or wavelength spectrum that matches or contains one type of the majority of the fluorescent elements. In some other embodiments, an image may be captured as an image that captures all wavelengths of the fluorescent elements.

[0040] The resolution of the optical system 116 controls the level of detail in the flow cell image, including pixel size. In existing systems, this resolution is crucial because it controls the accuracy with which the spot search algorithm identifies Polony centers. One way to improve the accuracy of spot search is to improve the resolution of the optical system 116 (for example, by incorporating a higher resolution camera) or to improve the processing performed on the image captured by the optical system 116. This can involve detecting Polony centers in pixels other than those detected by the spot search algorithm. These processing-based methods may allow for improved Polony center detection accuracy without increasing the resolution of the optical system 116. The resolution of the optical system may be lower than that of existing systems with comparable performance, which may reduce the cost of the sequencing system 110. In some embodiments, the resolution of the optical system may be the same as that of existing systems, but superior performance may be achieved compared to those existing systems due to image processing.

[0041] The image quality of the flow cell image controls the base calling quality. One way to improve the accuracy of base calling is to improve the resolution of the optical system 116 or to improve the processing performed on the image captured by the optical system 116 to obtain better image quality. The methods described herein enable autofocus (AF) that can be conveniently and efficiently performed whenever needed, for example, before or during sequencing. In some embodiments, the methods described herein may be advantageously performed before imaging the flow cell, and such AF may be repeated as needed during sequencing.

[0042] The optical system 116 may be configured, for example, to perform autofocus before imaging in each flow cycle of the array determination execution. The operations or actions disclosed herein may be performed by a dedicated processor 118, FPGA(multiple) 120, computing system 126, or a combination thereof. One or more operations or actions in method 500 disclosed herein may be performed by a dedicated processor 118, FPGA(multiple) 120, computing system 126, or a combination thereof. In some embodiments, which operations or actions should be performed by a dedicated processor 118, FPGA(multiple) 120, computing system 126, or a combination thereof may be determined based on one or more of the computation time for a particular operation(multiple), the complexity of the computation in a particular operation(multiple), the need for data transmission between hardware devices, or a combination thereof.

[0043] The computing system 126 may include one or more general-purpose processor computers or hardware processors that provide interfaces for running various programs within an operating system such as Windows® or Linux®. Such operating systems typically offer users greater flexibility.

[0044] In some embodiments, the dedicated processor 118 may be configured to perform the operations described herein. These may be custom processors that have specific hardware or instructions for performing those operations, rather than being general-purpose processors. The dedicated processor directly runs specific software without an operating system. The absence of an operating system reduces overhead at the expense of the flexibility the processor can perform. The dedicated processor may utilize a custom programming language, which may be designed to operate more efficiently than software running on a general-purpose computer. This can increase the speed at which operations are performed, potentially enabling real-time processing.

[0045] In some embodiments, FPGAs (or multiple FPGAs) 120 may be configured to perform the operations disclosed herein. The FPGA is programmed as hardware to perform only a specific task. Software operations can be translated into hardware components using a special programming language. Once programmed, the hardware directly processes the provided digital data without executing software. Instead, the FPGA uses logic gates and registers to process the digital data. Because there is no overhead required by the operating system, FPGAs generally process data faster than general-purpose computers. As with dedicated processors, this comes at the expense of flexibility. Also, the absence of software overhead can allow FPGAs to operate faster than dedicated processors, but this depends on the exact processing being performed, as well as the specific FPGA and dedicated processor.

[0046] In some embodiments, the data storage 122 is used to store information used in the optical alignment method. This information may include the image itself or information derived from the image captured by the optical system 116 (e.g., pixel intensity, color, etc.).

[0047] The user interface 124 can be used by the user to operate the sequencing system or to access data stored in the data storage 122 or the computer system 126.

[0048] The computer system 126 may control the general operation of the sequencing system and may be coupled to the user interface 124. It may also perform operations disclosed herein for optical alignment. The computer system 126 may store information related to the operation of the sequencing system 110, such as configuration information, instructions for operating the sequencing system 110, or user information. The computer system 126 may be configured to pass information between the sequencing system 110 and the cloud 130.

[0049] As discussed above, the sequencing system 110 may have a dedicated processor 118, an FPGA(s) 120, or a computer system 126. The sequencing system may use one, two, or all of these elements to accomplish the required processing described above. In some embodiments, when these elements are present together, the processing tasks are divided among them.

[0050] Cloud 130 may be a network, remote storage, or some other remote computing system separate from the sequencing system 110. Connecting to Cloud 130 may enable access to data stored outside the sequencing system 110 or enable software updates within the sequencing system 110.

[0051] Optical systems In some embodiments, the AF methods and systems described herein may be used for autofocusing various optical systems. These various optical systems may be used in different applications requiring z-axis autofocus to render a focused image. While some embodiments may, but are not limited to, the AF methods and systems described herein for autofocusing various optical systems, they are not limited to those described herein.

[0052] In some embodiments, AF methods and systems, the details of which are disclosed in PCT Patent Application No. PCT / US2024 / 012802 and which are incorporated herein by reference in their entirety, may be used for autofocusing optical systems or optical assemblies.

[0053] The sequencing systems disclosed herein (e.g., 100 in Figure 1) may include an optical system 116. In some embodiments, the optical system 116 is a multi-channel imaging module. In some embodiments, the multi-channel imaging module may comprise one or more illumination sources, an objective lens shared by a plurality of detection channels, a sample immobilized on a flow cell or test target, a sample stage configured to hold the test target or flow cell thereon, a numerical aperture within a predetermined range, a processor configured to determine the z-shift for autofocus, or a combination thereof. Each detection channel may include a corresponding tube lens and a corresponding image sensor. The sample stage and / or image sensor may be motorized or mounted on a motorized stage so as to be tiltable by a certain tilt angle provided by the user.

[0054] Figures 2A and 2B illustrate non-limiting examples of the optical system 116 disclosed herein. The optical system 116 may include an objective lens 210, one or more illumination sources 215, and one or more detection channels 220.

[0055] The optical system 116 may also include one or more dichroic filters 230, 235, 240, which may include dichroic reflectors or beam splitters.

[0056] As shown in Figures 2A and 2B, the optical system 116 may include hardware used solely for autofocusing and not for imaging purposes. Such hardware may include, but is not limited to, one or more AF illumination sources, an AF sensor 202, an AF tube lens, and one or more dichroic filters or beam splitters. One or more AF illumination sources may include an AF laser, for example, an AF laser that projects a spot whose size is monitored to determine when the optical system is focused. Figures 2A and 2B also show a dichroic filter 235, which may include a dichroic beam splitter or beam combiner, for example, used to direct the autofocus laser through the objective lens onto a sample support structure.

[0057] In some embodiments, the AF sensor may be tiltable by the tilt angles disclosed herein. The AF sensor may be connected to a motor or a hexagon so that it can automatically tilt in response to commands from a user or computer system.

[0058] In some embodiments, the optical system 116 may include hardware configured for both autofocus and imaging purposes. In some embodiments, the optical system 116 may not include any hardware used solely for autofocus. In other words, the hardware within the optical system 116 can be used for both autofocus and imaging purposes, or solely for imaging purposes. Such hardware dedicated to autofocus includes one or more of the following: an AF illumination source, an AF sensor 202, an AF tube lens, and a dichroic filter or beam splitter. In some embodiments, the optical system 116 lacks an AF illumination source and an AF sensor. In some embodiments, an optical system lacking dedicated hardware for AF purposes may appear identical to that in Figures 2A-2B, except that the dedicated AF laser and AF sensor 202 are removed. In some embodiments, the dichroic filter 235 may also be removed, as it works in directing illumination to the AF sensor.

[0059] Some or all components of the optical system 116 may be coupled to the base plate 205, either fixed or movable. The objective lens 210 may be fixedly coupled to a z-stage that is movable relative to the base plate 205. The z-stage may move along the optical axis 1090 or the z-axis of the optical system. The z-stage may be an electric stage, and its movement may be automatic after receiving a command or input from either a user or a computer system, as disclosed herein.

[0060] The optical axis of the optical system is shown in Figure 10. As disclosed herein, the optical axis is used here interchangeably with the z-axis. The optical axis may be a straight line passing through the geometric center of the objective lens and the geometric center of the field of view imaged in the sample. In some embodiments, the optical axis may be a straight line passing through the geometric center of each image sensor in the optical system. In some embodiments, the center of the image acquired using the optical system is aligned with the optical axis.

[0061] In some embodiments, the optical system 116 may include a sample stage for holding a test target or sample support, such as a flow cell, on which the sample is fixed. The sample stage may be positioned next to the objective lens along the optical axis 1190 of the optical system. In some embodiments, the sample stage may be motorized or mounted on a motorized stage so as to be tiltable by a certain angle. In some embodiments, the sample stage may be movable in three dimensions (3D) (translatable and / or tiltable). In some embodiments, the sample stage may be movable in 3D relative to the objective lens. Figure 10 shows an exemplary sample stage 1080 that is motorized and on which a flow cell is fixed. The flow cell may include multiple tiles or subtiles. The sample stage may be moved such that the geometric center 1099 of a particular tile or subtile is on the optical axis 1090 when the corresponding tile or subtile is being imaged. The sample stage may move in the xy plane 1081, for example, in the image plane.

[0062] As disclosed herein, the tilt angle for tilting any optical element of the optical system 116, such as a sample stage, image sensor, etc., can be around any axis in 3D. In some embodiments, the tilt angle is around the x-axis or y-axis. In some embodiments, the tilt angle lies in the xz-plane or yz-plane. In some embodiments, the tilt angle may be determined based on the sample size, the size of the image sensor, and / or a combination thereof. In some embodiments, the tilt angle is large enough so that the entire focused region is within the FOV of the image 600. In some embodiments, the tilt angle is small enough so that the focused region, in its minimum dimensions, includes at least a certain number of pixels along the x-axis, as shown in Figure 6B, for example.

[0063] In some embodiments, the tilt angle is in the range of 0.01 degrees to 89.9 degrees. In some embodiments, the tilt angle is in the range of 0.05 degrees to 15 degrees. In some embodiments, the tilt angle is in the range of 0.05 degrees to 5 degrees. In some embodiments, the tilt angle is clockwise around the x-axis or y-axis. In some embodiments, the tilt angle is counterclockwise around the x-axis or y-axis. In some embodiments, the tilt angle is clockwise in the zx or yz plane. In some embodiments, the tilt angle is counterclockwise in the zx or yz plane.

[0064] The optical system may comprise one or more illumination sources 215. In some embodiments, the illumination sources 215 lack any AF illumination sources used solely for autofocus purposes. The AF illumination sources may include one or more AF lasers configured solely for autofocus purposes. In some embodiments, the illumination sources 215 as described herein are used for both autofocus and post-autofocus imaging. In some embodiments, the illumination sources 215 include lasers.

[0065] The illumination source 215 may include any suitable light source configured to produce light of a predetermined excitation wavelength(s). The light source may be a broadband source emitting light within one or more excitation wavelength ranges (or bands). The light source may be a narrowband source emitting light within one or more narrower wavelength ranges. In some embodiments, the light source may produce a single isolated wavelength(s) or multiple isolated wavelengths(s) corresponding to a desired excitation wavelength. In some embodiments, the lines may have several very narrow bandwidths. Exemplary light sources that may be suitable for use in the illumination source 215 include, but are not limited to, incandescent filaments, xenon arc lamps, mercury vapor lamps, light-emitting diodes, laser diodes or solid-state lasers, or other types of light sources. In some designs, as will be discussed below, the light source may include a polarization source, such as a linear polarization source. In some embodiments, the orientation of the light source is such that s-polarization occurs on one or more surfaces of one or more optical components, such as the dichroic reflectors of one or more dichroic filters.

[0066] The illumination source 215 may further include one or more additional optical components, such as lenses, filters, optical fibers, or any other suitable transmissive or reflective optical systems, as appropriate, to output an excitation light beam having suitable characteristics toward the dichroic filter 230. For example, a beam shaping optical system may be included, for example, to receive light from an optical emitter in the light source, generate a beam, and / or provide the desired beam characteristics. Such an optical system may include, for example, a collimating lens configured to reduce the divergence of light and / or increase collimation and / or collimate the light.

[0067] In some embodiments, multiple light sources are included within the optical system 116. In some such embodiments, different light sources may produce light having different spectral characteristics, for example, light that excites different fluorescent dyes. In some embodiments, the light produced by different light sources may be directed to coincide and form a combined excitation light beam. This combined excitation light beam may consist of excitation light beams from each of the light sources. The combined excitation light beam has more optical power than the individual beams that overlap to form the combined beam. For example, in an embodiment including two light sources that produce two excitation light beams, the combined excitation light beam formed from the two individual excitation light beams may have an optical power that is the sum of the optical powers of the individual beams. Similarly, in some embodiments, three, four, five, or more light sources may be included, and each of these light sources may output an excitation light beam that together forms a combined beam having an optical power that is the sum of the optical powers of the individual beams.

[0068] In some embodiments, the light source 215 outputs a sufficient amount of light to produce a sufficiently strong fluorescence emission. A stronger fluorescence emission can increase the signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) of the image acquired by the fluorescence imaging module. In some embodiments, the output of the light source and / or the excitation light beam derived therefrom (including a composite excitation light beam) may range in power from about 0.5 watts to about 5.0 watts or more.

[0069] Referring again to Figures 2A and 2B, the dichroic filter 230 is positioned relative to a light source and can receive light from it. The dichroic filter may include a dichroic mirror, dichroic reflector, dichroic beam splitter, or dichroic beam combiner, configured to transmit light in a first spectral region (or wavelength range) and reflect light having a second spectral region (or wavelength range). The first spectral region may include one or more spectral bands, for example, one or more spectral bands within the ultraviolet and blue wavelength ranges. Similarly, the second spectral region may include one or more spectral bands, for example, one or more spectral bands extending from green to red and infrared wavelengths. Other spectral regions or wavelength ranges are also possible.

[0070] In some embodiments, the dichroic filter 230 may be configured to transmit light from a light source to a sample support structure, such as a microscope slide, capillary, flow cell, test target, microfluidic chip, or another substrate or support structure. The sample support structure supports and positions the sample, for example, a composition comprising a fluorescently labeled nucleic acid molecule or its complement, relative to the optical system 116. In some embodiments, for example, during optical alignment as described herein, the sample may be a test target having a geometric shape and / or pattern that simulates the presence of the fluorescently labeled nucleic acid. Thus, the first optical path extends from the light source to the sample via the dichroic filter 230. In various embodiments, the sample support structure includes at least one surface on which the sample is placed or to which the sample is bound. In some embodiments, the sample may be placed in or bound to different localized regions or sites on at least one surface of the sample support structure.

[0071] In some embodiments, the support structure may include two surfaces located at different distances (e.g., different positions or depths along the optical axis of the objective lens 210) from the objective lens 210 in which the sample is placed. As discussed below, for example, the flow cell may include a fluid channel at least partially formed by first and second (e.g., upper and lower) inner surfaces, and the sample may be placed on the first inner surface, the second inner surface, or a localized area on both inner surfaces. The first and second surfaces may be separated by regions corresponding to the fluid channel through which the solution flows, and are therefore at different distances or depths from the objective lens 210 of the optical system 116.

[0072] In some embodiments, the optical system 116 includes at least one objective lens 210. In some embodiments, the optical system 116 includes a single objective lens 210. The objective lens 210 may be shared by some or all of the detection channels. The objective lens may be fixedly or movably mounted to the base plate 205. In some embodiments, the objective lens 210 is fixedly mounted to the base plate 205. Movement of the base plate 205 moves the objective lens accordingly, for example, to focus a sample on the focal plane of the objective lens. In some embodiments, the objective lens 210 is movably mounted to the base plate 205. Movement of the objective lens relative to the sample stage can be made by moving the objective lens 210 itself.

[0073] The objective lens 210 may be included in a first optical path between the dichroic filter 230 and the sample or test target. This objective lens may be configured, for example, to have a focal length and working distance, and / or to focus light from a light source(s) onto the sample, for example, the surface of a microscope slide, capillary, flow cell, microfluidic tip, or other substrate or support structure. Similarly, the objective lens 210 may be configured to have a suitable focal length and working distance, and / or to collect light reflected, scattered, or emitted from the sample (e.g., fluorescence emission), and to form an image of the sample (e.g., a fluorescence image).

[0074] In some embodiments, the objective lens 210 may include a microscope objective lens, such as a commercially available objective lens. In some embodiments, the objective lens 210 may include a custom objective lens. Examples of custom objective lenses and / or combinations of custom objective lenses with tube lenses are described below and in U.S. Patent No. 11,060,138, which is incorporated herein by reference in whole. The objective lens 210 may be designed to reduce or minimize optical aberrations at two locations, such as two planes corresponding to two surfaces of a flow cell or other sample support structure. The objective lens 210 may be designed to reduce optical aberrations at a selected location or plane, for example, the first and second surfaces of a double-surface flow cell, compared to other locations or planes in the optical path. For example, the objective lens 210 may be designed to reduce optical aberrations at two depths or planes located at different distances from the objective lens compared to optical aberrations associated with other depths or planes at other distances from the objective lens. For example, in some embodiments, optical aberrations may be less for imaging the first and second surfaces of the flow cell than those exhibited elsewhere in the region extending 1 to 10 mm from the front of the objective lens. Furthermore, the custom objective lens 210 may, in some embodiments, be configured to compensate for optical aberrations induced by the transmission of fluorescence emission light through one or more portions of the sample support structure, such as a layer containing one or more of the flow cell surfaces on which the sample is placed, or a layer containing a solution filling the fluid channels of the flow cell. These layers may include, for example, glass, quartz, plastic, or another transparent material with a refractive index, and may result in optical aberrations.

[0075] In some embodiments, the objective lens 210 may have a numerical aperture (NA) of 0.6 or greater. Such a numerical aperture may provide a reduction in depth of field and / or depth of focus, improved background discrimination, and increased imaging resolution. In some embodiments, the objective lens 210 may have a numerical aperture (NA) of 0.6 or less. Such a numerical aperture may provide an increase in depth of field and / or depth of focus. Such an increase in depth of field and / or depth of focus may increase the ability to image planes separated by a distance such that the first and second surfaces of a bi-surface flow cell are separated.

[0076] In some embodiments, the flow cell according to this specification may include one or more surfaces and one or more substrates, at least one separate region of one or more surfaces comprising at least one hydrophilic polymer coating layer, a plurality of oligonucleotide molecules attached to at least one hydrophilic polymer coating layer, and a plurality of clone-amplified sample nucleic acid molecules immobilized on the plurality of attached oligonucleotide molecules, wherein the plurality of immobilized clone-amplified sample nucleic acid molecules are located at a distance of less than λ / (2*NA), where λ is the central wavelength of the excitation energy source and NA is the numerical aperture of the imaging system.

[0077] In some embodiments, the objective lens 210 and / or optical system 116 may be configured to provide a depth of field and / or depth of focus large enough to image both the first and second inner surfaces of the flow cell, or both the bottom surface of the first substrate and the top surface of the bottom substrate of the test target. The depth of focus may be enabled by continuously refocusing the imaging module while imaging the first and second surfaces, or by simultaneously ensuring a sufficiently large depth of field and / or depth of focus with equivalent optical resolution. In some embodiments, the depth of field and / or depth of focus may be at least as large as, or even larger than, the distance separating the first and second surfaces of the flow cell to be imaged, such as the first and second inner surfaces of the flow cell. In some embodiments, the first and second surfaces, for example, the first and second inner surfaces of a double-surface flow cell or test target, may be separated by a distance in the range of, for example, about 10 μm to about 700 μm or more. In some embodiments, the depth of field and / or depth of focus may therefore be in the range of about 10 μm to about 700 μm or more.

[0078] In some designs, the adaptive optics system (e.g., “optical compensator” or “compensator”) may be moved in and out of the optical path within the imaging module, for example, the optical path through which light collected by the objective lens 210 is delivered to the image sensor, enabling the imaging module to image the first and second surfaces of the dual-surface flow cell. The optical system 116 may be configured to image the first surface when the adaptive optics system is included in the optical path between the objective lens and an image sensor or photodetector array configured to capture an image of the first surface. In such a design, the imaging module may be configured to image the second surface when the adaptive optics system is removed from or not included in the optical path between the objective lens 210 and an image sensor or photodetector array configured to capture an image of the second surface. The need for an optical compensator may be more pronounced when using an objective lens 210 with a high numerical aperture (NA) value, for example, for an aperture value of at least 0.6, at least 0.65, at least 0.7, at least 0.75, at least 0.8, at least 0.85, at least 0.9, at least 0.95, at least 1.0, or higher. In some embodiments, the optical adaptive optics system (e.g., an optical compensator or compensator) includes refractive optical elements such as lenses, plates of optically transparent materials such as glass, or, in the case of a polarized beam, a quadrant plate or half-wave plate. Other configurations may be employed to allow the first and second surfaces to be imaged at different times. For example, one or more lenses or optical elements may be configured to translate in and out of the optical path between the objective lens 210 and the image sensor, or along the optical path.

[0079] In some embodiments, the optical systems described herein enable imaging of the first and second surfaces without moving an adaptive optics system, such as a compensator, in, out of, or along the optical path of the optical system herein. In some embodiments, the objective lens 210 is configured to provide a sufficiently large depth of field and / or depth of field to enable imaging of the first and second surfaces with equivalent optical resolution without such adaptive optics moving in and out of the optical path within the imaging module, such as the optical path between the objective lens and the image sensor or photodetector array. Similarly, in some embodiments, the objective lens 210 is configured to provide a sufficiently large depth of field and / or depth of field to enable imaging of the first and second surfaces with equivalent optical resolution without moving an optical system, such as one or more lenses or other optical components translated along the optical path within the imaging module, such as the optical path between the objective lens and the image sensor or photodetector array. Examples of such objective lenses are described in more detail below.

[0080] In some embodiments, the objective lens (or microscope objective lens) 210 may be configured to have a reduced magnification. For example, the objective lens 210 may be configured such that the fluorescence imaging module has a magnification of less than 2x to less than 10x (as will be discussed in more detail below). Such a reduced magnification may modify design constraints so that other design parameters can be achieved. For example, the objective lens 210 may also be configured such that the fluorescence imaging module has a large field of view (FOV) in the range of about 1.0 mm to about 5.0 mm (e.g., in diameter, width, length, or longest dimension), as will be discussed in more detail below.

[0081] In some embodiments, the objective lens 210 may be configured to provide a field of view to the fluorescence imaging module such that the field of view (FOV) has diffraction-limited performance for aberrations over at least 60%, 70%, 80%, 90%, or 95% of the field of view, for example, less than 0.10, 0.12, or 0.15 wavelengths.

[0082] In some embodiments, the objective lens 210 may be configured to provide a field of view to the fluorescence imaging module such that the field of view (FOV) has diffraction-limiting performance, for example, a Strehl ratio greater than 0.6, 0.7, or 0.8 over at least 60%, 70%, 80%, 90%, or 95% of the field of view.

[0083] Referring again to Figures 2A and 2B, the dichroic beam splitter or beam combiner 230 is positioned in a first optical path between the light source and the sample to irradiate the sample with one or more excitation beams. This dichroic beam splitter or combiner may also be in one or more second optical paths to different optical channels used to detect fluorescence emission from the sample. Thus, the dichroic filter 230 couples the first optical path of the excitation beam emitted by the illumination source 215 and the second optical path of the emitted light emitted by the sample into various optical channels, to which the light is directed to their respective image sensors or photodetector arrays to capture an image of the sample.

[0084] In various embodiments, the dichroic filter 230, for example, a dichroic reflector or a beam splitter or beam combiner, has a passband selected to transmit light from the illumination source 215 only within a specific wavelength band or a plurality of wavelength bands that include a desired excitation wavelength(s). For example, the dichroic beam splitter 230 includes a reflective surface, for example, a dichroic reflector having a spectral transmittance response configured to transmit light having at least some of the wavelengths output by a light source that forms part of the excitation beam. The spectral transmittance response may be configured not to transmit (e.g., reflect instead) light of one or more other wavelengths, for example, one or more other fluorescence emission wavelengths. In some embodiments, the spectral transmittance response may also be configured not to transmit (e.g., reflect instead) light of one or more other wavelengths output by a light source.

[0085] Therefore, the dichroic filter 230 can be used to select which wavelengths of light emitted by the light source reach the sample. Conversely, the dichroic reflector in the dichroic beam splitter 230 has a spectral reflectance response that reflects light having one or more wavelengths corresponding to desired fluorescence emission from the sample, and optionally reflects light having one or more wavelengths emitted from a light source that is not intended to reach the sample. Thus, in some embodiments, the dichroic reflector has a spectral transmittance that includes one or more passbands that transmit light incident on the sample, and one or more stopbands that reflect light outside the passbands, e.g., one or more emission wavelengths and optionally one or more wavelengths emitted by a light source that are not intended to reach the sample. Similarly, in some embodiments, the dichroic reflector has a spectral reflectance that includes one or more spectral regions configured to reflect one or more emission wavelengths and optionally one or more wavelengths emitted by a light source that are not intended to reach the sample, and one or more regions that transmit light outside these reflective regions. The dichroic reflector included in the dichroic filter 230 may include a reflective filter such as an interference filter (e.g., a quadruple stack) configured to provide a suitable spectral transmission and reflection distribution.

[0086] The optical system 116 shown in Figures 2A and 2B is configured such that the excitation beam is transmitted to the objective lens 210 by the dichroic filter 230, although in some designs the illumination source 215 may be positioned relative to the dichroic filter 230 and / or the dichroic filter 230 is configured (e.g., oriented) such that the excitation beam is reflected to the objective lens 210 by the dichroic filter 230. Similarly, in some such designs, the dichroic filter 230 is configured to transmit fluorescence emission from the sample and, optionally, light of one or more wavelengths emitted from a light source not intended to reach the sample. Designs in which fluorescence emission is transmitted instead of reflected may potentially reduce wavefront errors in the detected emission and / or may have other advantages. In any case, in various embodiments, the dichroic reflector 230 is positioned in a second optical path to receive fluorescence emission from the sample, at least some of which follow the detection channel 220.

[0087] Figures 3A and 3B illustrate the optical paths in the optical systems of Figures 2A and 2B. In the examples shown in Figures 2A and 3A, the detection channel 220 is positioned to receive fluorescence emission from a sample that is transmitted by the objective lens 210 and reflected by the dichroic filter 230. In some embodiments, the detection channel 220 may be positioned to receive a portion of the transmitted emission light rather than the portion reflected by the dichroic filter 230. In any case, the detection channel 220 may include an optical system or optical element for receiving or reflecting at least a portion of the emitted light.

[0088] In some embodiments, the detection channel 220 may include one or more lenses, such as a tube lens 221, and one or more image sensors or detectors 224, such as a photodetector array (e.g., a CCD or CMOS sensor array), for imaging or otherwise generating a signal based on the received light. The tube lens may include one or more lens elements configured to form an image of a sample on the sensor or photodetector array, for example, to capture its image. Further consideration of detection channels is contained in U.S. Patent No. 11,060,138, which is incorporated herein by reference in its entirety. In some embodiments, improved optical resolution can be achieved using an image sensor having relatively high sensitivity, small pixels, and a high number of pixels, in conjunction with a preferred sampling scheme, which may include oversampling or undersampling. In some embodiments, the detection channel 220 may include an emission filter 223 that can be positioned between the image sensor 224 and the tube lens 221. The emission filter 223 may be optional. The emission filter may be a bandpass filter that functions to remove certain wavelengths before the signal is captured by the image sensor. In some embodiments, the detection channel 220 may include one or more corresponding dichroic filters, which may correspond to a single detection channel or be shared by two or more detection channels. The dichroic filters 230, 235, 240 may include one or more dichroic mirrors, dichroic reflectors, dichroic beam splitters, or dichroic beam combiners. In some embodiments, the dichroic filters 230, 235, 240 may be configured to transmit light in a first spectral region (or wavelength range) and reflect light having a second spectral region (or wavelength range). The first spectral region may include one or more spectral bands, for example, one or more spectral bands within the ultraviolet and blue wavelength ranges. The second spectral region may include one or more spectral bands, for example, one or more spectral bands extending from green to red and infrared wavelengths.In other embodiments, the first spectral region may include one or more spectral bands, for example, one or more spectral bands extending from green to red and infrared wavelengths. The second spectral region may include one or more spectral bands, for example, one or more spectral bands within the ultraviolet and blue wavelength ranges. Other spectral regions or wavelength ranges are also possible.

[0089] The systems and methods described herein may be used to optically autofocus one or more detection channels so that the focal plane of the objective lens is substantially aligned with the sample being imaged and the sample can be focused in the acquired flow cell image. In embodiments in which each detection channel may include its corresponding objective lens (not shown) and tube lens, the focal plane may be that of the corresponding objective lens within the detection channel.

[0090] Figures 3A and 3B are ray tracing diagrams illustrating the optical paths of the optical system 116 in Figures 2A and 2B. Figure 3A corresponds to a top view of the optical system. Figure 3B corresponds to a side view of the optical system. The optical system 116 illustrated in these figures includes four detection channels 220. However, it will be understood that the optical system may be equally implemented in systems including more than or less than four detection channels 220. For example, the multi-channel systems disclosed herein may be implemented with as few as one detection channel 220, or up to two, three, four, five, six, seven, eight, or more than eight detection channels 220, without departing from the scope of this disclosure.

[0091] Non-limiting examples of the optical system 116 illustrated in Figures 3A and 3B include four detection channels 220, a dichroic filter 230 that reflects the emitted beam 250, a second dichroic filter (e.g., a dichroic beam splitter) 235 that splits the beam 250 into a transmitted portion and a reflective portion, and two channel-specific dichroic filters (e.g., dichroic beam splitters) 240 that further split the transmitted and reflective portions of the beam 250 between the individual detection channels 220. The dichroic reflectors in the dichroic beam splitters 235 and 240 for splitting the beam 250 between the detection channels are shown to be positioned at 45 degrees with respect to the central beam axis of the beam 250 or the optical axis of the imaging module. However, angles less than 45 degrees may be used, as will be discussed below, and may offer advantages such as a sharper transition from the passband to the stopband.

[0092] Each of the different detection channels 220 may include an image sensor 224, such as a photodetector array (e.g., a CCD or CMOS detector array). The different detection channels 220 may further include an optical system 226, such as a lens (e.g., one or more tube lenses, each containing one or more lens elements), positioned to focus a portion of the emitted light entering the detection channel 220 onto a focal plane coinciding with the plane of the photodetector array 224. The optical system 226 (e.g., tube lenses) combined with the objective lens 210 is configured to capture an image of the sample, such as an image of the surface on a flow cell or other sample support structure after the sample has bonded to its surface, by forming an image of the sample on the image sensor 224, such as a photodetector array. Thus, such an image of the sample or test target may include multiple fluorescence emission spots or regions over a spatial range of the sample support structure where the sample emits fluorescence. The objective lens 210, together with the optical system 226 (e.g., tube lenses), may provide a field of view (FOV) encompassing a portion or the entire sample. Similarly, the photodetector array 224 of different detection channels 220 may be configured to capture an image of the entire field of view (FOV) provided by the objective lens and the tube lens, or a portion thereof. In some embodiments, the photodetector array 224 of some or all detection channels 220 may detect emitted light emitted by a sample placed on or on the surface of a sample support structure, e.g., a flow cell, and record electronic data representing the image thereof. In some embodiments, the photodetector array 224 of some or all detection channels 220 may detect characteristics of emitted light emitted by a sample without capturing and / or storing an image of the sample placed on the flow cell surface and / or an image of the entire field of view (FOV) provided by the objective lens and optical system 226 and / or 222 (e.g., elements of the tube lens). In some embodiments, the FOV of the disclosed imaging module (e.g., provided by the combination of the objective lens 210 and optical system 226 and / or 222) may range from about 1 mm to 5 mm (e.g., in diameter, width, length, or longest dimension), as considered below, for example.The field of view (FOV) can be selected, for example, to provide a balance between the magnification and resolution of the imaging module, and / or based on one or more characteristics of the image sensor and / or objective lens. For example, a relatively small FOV may be provided in conjunction with a smaller, faster image sensor to achieve high throughput.

[0093] In some embodiments, one or more image sensors in an optical system may be used for both imaging and autofocus. One or more image sensors may be used to acquire one or more images for determining the z-shift for autofocus. In some embodiments, the image obtained by the image sensor for AF purposes includes a single image. A single image may include a field of view (FOV) that is identical to the size of the image sensor or AF sensor along the x-axis or y-axis. Figure 6B shows an exemplary single image 600 having a size along the x-axis that is identical to the size of the image sensor along the x-axis. In some embodiments, an image(s) may include a length (along the x-axis) or width (along the y-axis) in the range of 0.1 mm to 5 cm. In some embodiments, an image(s) may include a length (along the x-axis) or width (along the y-axis) in the range of 0.5 mm to 9 mm. In some embodiments, an image(s) may include a length (along the x-axis) or width (along the y-axis) in the range of 0.8 mm to 4 mm. In some embodiments, an image(s) may include a FOV that is identical to the size of the image sensor along the x-axis when the tilt angle is around the x-axis. In some embodiments, the image includes an FOV that is identical to the size of the image sensor along the y-axis when the tilt angle is around the y-axis.

[0094] Figure 6A shows the sample stage and its tilt angle relative to the focal plane of the objective lens, or otherwise, to the focal plane of the optical system. In this embodiment, the tilt angle is along the x-axis. In some embodiments, the tilt angle is tilted in the xz plane around the y-axis. In some embodiments, an image of the sample or test target is acquired while the sample stage remains tilted. In some embodiments, the image includes a fluorescence signal or other optical signal emitted from the sample or test target disclosed herein. In this particular embodiment, the size of the image along x is the same as the size of the image sensor along the x-axis. In this embodiment, the size of the image along y is also the same as the size of the image sensor along the y-axis. In other embodiments, the size of the images along the y-axis and / or x-axis may be reduced to save image processing time and storage space.

[0095] Tilting is shown in Figure 6A as tilting the sample stage, but any other tilting scheme can be used to achieve the same effect of having a predetermined tilt angle from the image sensor relative to the sample stage. For example, in some embodiments, the image sensor(s) are connected to a motor, e.g., a hexagon, and as a result, the image sensor(s) can be tilted by an angle automatically controlled by the motor, while the sample may remain stationary. In some embodiments, to achieve a tilt effect in the image, one of the image sensor(s) and the sample stage(s) may remain stationary, while the other(s) can be tilted. In some embodiments, to achieve a tilt effect in the image, both the image sensor(s) and the sample stage(s) can be tilted, but each has a smaller angle to achieve a tilt effect equal to the sum of the sums of two smaller angles.

[0096] In some embodiments, tilting and then untilting the image sensor(s) may be undesirable because such movement may affect the optical alignment and other features of the optical system. In some embodiments, the image sensor(s)

[0097] Referring again to Figures 3A and 3B, in some embodiments, the optical system 226 (e.g., a tube lens 221) within the detection channel may be configured to reduce optical aberrations in the image acquired using the optical system 226 in combination with the objective lens 210. In some embodiments, the imaging module 200 may include multiple detection channels for imaging at different emission wavelengths, and the optical systems 226 (e.g., tube lenses) for different detection channels may have different designs to reduce aberrations for each emission wavelength to which that particular channel is configured to image. In some embodiments, the optical system 226 (e.g., a tube lens) may be configured to reduce aberrations when imaging a particular surface (e.g., a plane, an object plane, etc.) on a sample support structure including a fluorescent sample portion placed thereon, compared to other locations (e.g., other planes in object space). In some embodiments, the optical system 226 (e.g., a tube lens) may be configured to reduce aberrations when imaging first and second surfaces (e.g., first and second planes, first and second object planes, etc.) on a double-surface sample support structure (e.g., a double-surface flow cell or test target) having a fluorescent sample portion placed thereon, compared to other locations (e.g., other planes in object space). For example, the optical system 226 in the detection channel (e.g., a tube lens) may be designed to reduce aberrations at two depths or planes located at different distances from the objective lens compared to aberrations associated with other depths or planes at other distances from the objective lens. For example, optical aberrations may be less for imaging the first and second surfaces than at other locations in the region about 1 to about 10 mm from the objective lens. Furthermore, the custom optical system 226 within the detection channel (e.g., a tube lens) may, in some embodiments, be configured to compensate for aberrations induced by the transmission of emitted light through one or more portions of the sample support structure, such as a layer containing one of the surfaces on which the sample is placed, and optionally a solution adjacent to and in contact with the surface on which the sample is placed. The layer containing one of the surfaces on which the sample is placed may include, for example, glass, quartz, plastic, or another transparent material having a refractive index and introducing optical aberrations.The custom optical system 226 within the detection channel (e.g., a tube lens) may be configured, for example in some embodiments, to compensate for optical aberrations induced by the sample support structure, e.g., a coverslip or flow cell wall, or other sample support structure components, and optionally by a solution adjacent to and in contact with the surface on which the sample is placed.

[0098] In some embodiments, the optical system 226 (e.g., a tube lens) within the detection channel 220 is configured to have a reduced magnification. The optical system 226 (e.g., a tube lens) within the detection channel may be configured such that the fluorescence imaging module has a magnification of, for example, less than 10x, as will be further discussed below. Such a reduced magnification allows for modification of design constraints so that other design parameters can be achieved. For example, the optical system 226 (e.g., a tube lens) may also be configured such that the fluorescence imaging module has a large field of view (FOV) of, for example, at least 1.0 mm (e.g., in diameter, width, length, or longest dimension), as will be further discussed below.

[0099] In some embodiments, the optical system 226 (e.g., a tube lens) may be configured to provide the above-described field of view to the fluorescence imaging module such that the FOV has an aberration of less than 0.15 over at least 60%, 70%, 80%, 90%, or 95% of the field of view, as will be further discussed below.

[0100] Referring again to Figures 3A and 3B, in various embodiments, the sample immobilized on a flow cell or test target is located at or near the focal position 212 of the objective lens 210. In embodiments where the optical system does not have an objective lens, the focal position 212 can be that of the entire optical system. Details of the optical system without an objective lens are disclosed in PCT application PCT / US2024 / 012802, which is incorporated herein by reference in its entirety. As described with reference to Figures 2A and 2B, a light source, such as a laser light source, provides an excitation beam to the sample to induce fluorescence. At least a portion of the fluorescence emission is collected as emitted light by the objective lens 210. The objective lens 210 can transmit emitted light toward the dichroic filter 230, which can reflect some or all of the emitted light toward a different detection channel as a beam 250 incident on a second dichroic filter 235, each of which includes an optical system 226 that forms an image of the sample (e.g., multiple fluorescent sample areas on the surface of a sample support structure) on a corresponding image sensor 224 within the detection channel, for example, a photodetector array.

[0101] As discussed above, in some embodiments, the sample support structure includes a flow cell or test target having two surfaces (e.g., two inner surfaces, a first surface and a second surface) containing sample sites that emit fluorescence. These two surfaces may be separated from each other by distance in the longitudinal (Z) direction along the central axis of the excitation beam and / or the optical axis of the objective lens. This separation may correspond, for example, to a flow channel in the flow cell. The analyte or reagent may be flowed through the flow channel and brought into contact with the first and second inner surfaces of the flow cell, thereby bringing it into contact with the binding composition such that fluorescence emission is emitted from multiple sites on the first and second inner surfaces. The imaging optical system (e.g., objective lens 210) is positioned at a suitable distance from the sample (e.g., a distance corresponding to the working distance) and can form a focused image of the sample on one or more image sensors or detector arrays 224. In various designs, the objective lens 210 (and possibly in combination with the optical system 226) may have a depth of field and / or depth of focus that is at least equivalent in size to the longitudinal separation between the first and second surfaces. Thus, the objective lens 210 and the optical system 226 (for each detection channel) can simultaneously form images of both the first and second flow cell surfaces on the photodetector array 224, and these images of the first and second surfaces are both in focus and have equivalent optical resolution (or can be focused with only slight refocusing of the object to obtain images of the first and second surfaces having equivalent optical resolution). In various embodiments, the adaptive optics do not need to move in and out of the optical path of the imaging module (e.g., in and out of the first and / or second optical path) to form focused images of the first and second surfaces having equivalent optical resolution.Similarly, in various embodiments, when one or more optical elements (e.g., lens elements) within an imaging module (e.g., objective lens 210 or optical system 226) are used to form a focused image of a second surface, they do not need to be moved longitudinally, for example, along the first and / or second optical paths to form a focused image of the first surface compared to the location of the one or more optical elements. In some embodiments, the imaging module includes an autofocus system configured to rapidly and continuously refocus the imaging module on the first and / or second surface so that the image has equivalent optical resolution. In some embodiments, the objective lens 210 and / or optical system 226 are configured so that both the first and second flow cell surfaces are focused simultaneously with equivalent optical resolution without moving the optical compensator in and out of the first and / or second optical paths, and without moving one or more lens elements (e.g., objective lens 210 and / or optical system 226 (e.g., tube lenses)) longitudinally along the first and / or second optical paths. In some embodiments, images of the first and / or second surfaces acquired sequentially (e.g., with refocusing between surfaces) or simultaneously (e.g., without refocusing between surfaces) using the novel objective and / or tube lens designs disclosed herein may be further processed using image processing algorithms suitable for enhancing the effective optical resolution of the images so that the images of the first and second surfaces have equivalent optical resolution. In various embodiments, the sample plane is sufficiently focused to resolve sample portions on the first and / or second flow cell surfaces, and the sample portions are closely spaced in the lateral direction (e.g., X and Y directions).

[0102] As discussed herein, dichroic filters may include interference filters that selectively transmit and reflect light of different wavelengths based on the principle of thin-film interference, using layers of optical coatings having different refractive indices and specific thicknesses. Therefore, the spectral response (e.g., transmission and / or reflection spectra) of dichroic filters implemented within a multi-channel fluorescence imaging module may depend at least partially on the angle of incidence or range of angles of incidence at which the excitation and / or emission beam light enters the dichroic filter. Such effects may be particularly important with respect to dichroic filters in the detection optical path (e.g., dichroic filters 235 and 240 in Figures 3A and 3B).

[0103] System and method for autofocus In one embodiment, the Disclosure provides a method for focusing an optical system, the method comprising: (a) receiving an image of a substrate of the optical system, wherein a portion but less than all of the image is in focus, and the portion of the focused image is offset from the center of the image; (b) using at least the portion of the focused image and the distance from the center of the image to determine the amount of misfocus in the image; and (c) adjusting the parameters of the optical system to adjust for the misfocus. In some embodiments, the image may be an image of a flow cell. In some embodiments, the image may be acquired using an image sensor, and light collected by the objective lens 210 may be delivered to the image sensor. In some cases, the flow cell 112 may be configured to capture DNA fragments and form a DNA sequence for base calling. In some cases, the misfocus may be a z-shift as described elsewhere in this Spec. The misfocus may be the distance from the imaging plane to the focal plane of the optical system.

[0104] In some cases, adjusting the parameters of an optical system to correct for focus misalignment may involve moving the sample stage relative to the focal plane of the optical system's objective lens by a determined amount of focus misalignment, thereby autofocusing the optical system. In some embodiments, the adjustment may be automatic. For example, the sample stage may be motorized, or otherwise connected to a motor, so as disclosed herein, to receive and respond to commands provided by a user or computer system, the movement of the sample stage may be performed automatically.

[0105] In some embodiments, the image may be received from an autofocus element. Such an autofocus element may include, but is not limited to, an autofocus illumination source, an autofocus sensor 202, an autofocus tube lens, and one or more dichroic filters or beam splitters.

[0106] In some embodiments, determining the amount of focus shift in an image using the method disclosed herein can be done in a maximum of 600 ms. In some embodiments, determining the amount of focus shift can be done in a maximum of 500 ms. In some embodiments, determining the amount of focus shift can be done in a maximum of 400 ms. In some embodiments, determining the amount of focus shift can be done in a maximum of 300 ms. In some embodiments, determining the amount of focus shift can be done in a maximum of 200 ms. In some embodiments, determining the amount of focus shift can be done in a maximum of 100 ms.

[0107] In some embodiments, the method further includes imaging a substrate, which includes using a light source and a detector to generate an image. Any suitable light source configured to produce light of a predetermined excitation wavelength(s) may be used. The substrate may be one of those described elsewhere in this specification (e.g., a flow cell, a glass substrate, etc.).

[0108] In some embodiments, determining the amount of focus shift can be performed using only a single image, rather than multiple images. Using only a single image reduces time consumption and computational complexity compared to existing autofocus methods that rely on at least two images and / or machine learning algorithms.

[0109] In some embodiments, the image may include a length or width in the range of about 0.1 millimeters to about 5 centimeters. In some embodiments, the image may include a length or width in the range of about 0.5 millimeters to about 9 millimeters.

[0110] In some embodiments, the error in the amount of focus shift from the true amount of focus shift may be at most about 400 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift may be at most about 350 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift may be at most about 300 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift may be at most about 250 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift may be at most about 200 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift may be at most about 150 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift may be at most about 100 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift may be at most about 50 nanometers.

[0111] In some embodiments, the center of the focused region may be determined using an image processing algorithm. In some embodiments, the image processing algorithm may include determining the center of the focused region by separating the image into a predetermined number of regions and using the sum or average intensity of each region to identify the location of the focused region. In some embodiments, since the focused region of the image may have a higher intensity than the unfocused, dark region, the sum or average image intensity of each region can be used to identify the approximate location of the focused region. In some embodiments, image intensity (e.g., intensity projection) and / or spatial frequency (e.g., Fourier transform of intensity) may be used to locate the center of the focused region 606a. In some embodiments, information about geometric patterns in the image may be used to determine which image processing algorithm(s) are used to find the center 606a.

[0112] In one embodiment, the Disclosure provides a method for focusing an optical system, the method comprising: (a) using a detector to image a substrate tilted at a certain tilt angle such that the image of the substrate includes a focused portion and an out-of-focus portion; (b) using a processor to determine the focus shift of the optical system based at least in part on the tilt angle and the distance of the focused portion from the center of the image; (c) adjusting the substrate to eliminate the tilt angle; and (d) adjusting the substrate by the focus shift so as to focus the optical system.

[0113] In some embodiments, determining the focus shift of an optical system further includes defining a vector to the center of the image of the focused portion. In some cases, the vector may be an xy-plane shift as defined elsewhere herein.

[0114] A method for focusing an optical system may further include a motor coupled to a substrate, the motor being configured to impart an inclination angle. In some cases, the sample stage may be motorized, or otherwise connected to a motor, so that the movement of the sample stage is automatic in response to receiving any of the commands provided by the user or by a computer system, as disclosed herein.

[0115] In some embodiments, the image may be received from an autofocus element. Such an autofocus element may include, but is not limited to, an autofocus illumination source, an autofocus sensor 202, an autofocus tube lens, and one or more dichroic filters or beam splitters. In some embodiments, the optical system may include an image sensor 224, such as a photodetector array (e.g., a CCD or CMOS detector array).

[0116] In some embodiments, the method may further include tilting the substrate to an inclination angle. In some cases, the method may include tilting the sample stage of an optical system by an inclination angle, with the sample fixed on the sample stage. The tilting of the sample stage may be relative to the focal plane of the objective lens. Alternatively, when the optical system lacks an objective lens, the tilting may be relative to the focal plane of the optical system. In some alternative embodiments, the operation may include tilting an image sensor or a dedicated autofocus sensor by an inclination angle instead of the sample stage to achieve an equivalent effect on the acquired image. Such tilting is relative to the focal plane of the objective lens or the focal plane of the optical system. However, tilting the sample stage may be preferable because tilting the image sensor in each autofocus process and then untilting it back for imaging after autofocus is complete can result in inconsistency or errors in the optical alignment of the image sensor relative to other optical elements of the optical system, such as the corresponding tube lens. Tilting the autofocus sensor has the advantage that it does not need to be untilted back. Tilting the autofocus sensor has the advantage of being dedicated solely to autofocus use, meaning the autofocus sensor can remain tilted. However, tilting the autofocus sensor can add further cost and complexity to the optical system compared to optical systems without an autofocus sensor.

[0117] In some embodiments, the method may include an operation to un-tilt the substrate. The method may include untilting a tilted sample stage, tilted image sensor, or tilted autofocus sensor, which is tilted in operation 510, by the tilt angle (in the opposite direction), and returning it to its spatial position before the tilt operation 510.

[0118] In some embodiments, tilting the substrate may involve tilting a plane perpendicular to the optical axis of the optical system. In some embodiments, a vector as defined herein may be the distance from the image center corresponding to the intersection of the optical axis and the image plane (e.g., the xy-plane) to the center of the focused region. The center of the focused region may lie on a straight line in the xy-plane. The center of the focused region may lie on a straight line perpendicular to the tilt axis of the tilt angle.

[0119] In some embodiments, the tilt angle may range from about 0.01 to about 89 degrees. In some embodiments, the tilt angle may range from about 0.05 to about 15 degrees. In some embodiments, the tilt angle may range from about 0.05 to about 8 degrees.

[0120] In some embodiments, the angular resolution of the tilt angle may be about 0.001 degrees to about 0.2 degrees. In some embodiments, the angular resolution of the tilt angle may be about 0.01 degrees to about 0.1 degrees. In some embodiments, the angular resolution of the tilt angle may be about 0.01 degrees to 0.08 degrees.

[0121] In some embodiments, determining the focus shift in this method can be performed using only a single image, rather than multiple images. Using only a single image reduces time consumption and computational complexity compared to existing autofocus methods that rely on at least two images and / or machine learning algorithms.

[0122] In some embodiments, the substrate may include a flow cell, the flow cell comprising one or more surfaces, at least one hydrophilic polymer coating layer, a plurality of oligonucleotide molecules attached to the at least one hydrophilic polymer coating layer, and a plurality of clone-amplified nucleic acid molecules immobilized on the attached plurality of oligonucleotide molecules, the plurality of immobilized clone-amplified sample nucleic acid molecules being located at a distance of less than λ / (2*NA), where λ is the central wavelength of the excitation energy source and NA is the numerical aperture of the optical system.

[0123] In some embodiments, the low nonspecific bonding coating may include a hydrophilic polymer that is nonspecifically adsorbed to or covalently grafted onto the support. Passivation may be performed using poly(ethylene glycol) (PEG, also known as polyethylene oxide (PEO) or polyoxyethylene), or other hydrophilic polymers having different molecular weights and end groups bonded to the support, for example, using silane chemistry. The distal end groups from the surface may include, but are not limited to, biotin, methoxyether, carboxylate, amine, NHS ester, maleimide, and bis-silane. In some embodiments, two or more layers of hydrophilic polymers, such as linear polymers, branched polymers, or highly branched polymers, may be deposited on the surface.

[0124] In some embodiments, the substrate includes a bead-shaped flow cell. In some embodiments, the bead-shaped flow cell includes a surface containing fluorescent beads chemically immobilized on the substrate. In some embodiments, the fluorescent beads are randomly distributed on the surface. In some embodiments, the fluorescent beads are patterned on the surface. In some embodiments, the fluorescent beads include at least about four different types of beads configured to emit different colors in response to excitation from a laser. In some embodiments, the fluorescent beads can be commercially available microbeads. In some embodiments, the microbeads are customized. In some embodiments, the bead-shaped flow cell includes a surface coated with fluorescent beads chemically immobilized on the surface. The fluorescent beads may include one, two, three, four, five, or six different types of beads that emit light of different colors and / or different frequencies in response to optical excitation, e.g., laser light. The fluorescent beads may emit fluorescent light of one or more wavelengths in response to laser excitation.

[0125] In some embodiments, the error between the distance from the focal plane and the true distance from the focal plane may be at most about 400 nanometers. In some embodiments, the error between the distance from the focal plane and the true distance from the focal plane may be at most about 350 nanometers. In some embodiments, the error between the distance from the focal plane and the true distance from the focal plane may be at most about 300 nanometers. In some embodiments, the error between the distance from the focal plane and the true distance from the focal plane may be at most about 250 nanometers. In some embodiments, the error between the distance from the focal plane and the true distance from the focal plane may be at most about 200 nanometers. In some embodiments, the error between the distance from the focal plane and the true distance from the focal plane may be at most about 150 nanometers. In some embodiments, the error between the distance from the focal plane and the true distance from the focal plane may be at most about 100 nanometers. In some embodiments, the error between the distance from the focal plane and the true distance from the focal plane may be at most about 50 nanometers.

[0126] In some embodiments, the substrate is adjusted by a misfocus, thereby focusing the optical system, which can then be used to image nucleic acid molecules immobilized on the substrate in a first flow cycle. In some embodiments, the actions of imaging a substrate tilted at an inclination angle, determining the misfocus, adjusting the substrate to eliminate the inclination angle, and adjusting the substrate by a misfocus to focus the optical system can be repeated during a second flow cycle.

[0127] In one embodiment, the Disclosure provides a method for focusing an optical system, the method comprising: (a) imaging a substrate using a detector tilted at a certain tilt angle such that the image of the substrate includes a focused portion and an out-of-focus portion; (b) using a processor to determine the focus shift of the optical system based at least partially on the tilt angle and the distance from the center of the image of the focused portion; and (c) adjusting the substrate by the focus shift so as to focus the optical system.

[0128] In some embodiments, the method further includes adjusting the substrate by the amount of misfocus, thereby bringing the substrate into focus. In some embodiments, the method further includes tilting the detector by the tilt angle. In some cases, the method of tilting the detector may include tilting an image sensor or a dedicated autofocus sensor by the tilt angle instead of a sample stage. In some embodiments, the method further includes untilting the detector following the adjustment of the substrate by the amount of misfocus. In some embodiments, tilting means tilting a plane perpendicular to the optical axis of the optical system.

[0129] In some embodiments, the tilt angle may range from about 0.01 to about 89 degrees. In some embodiments, the tilt angle may range from about 0.05 to about 15 degrees. In some embodiments, the tilt angle may range from about 0.05 to about 8 degrees.

[0130] In some embodiments, determining the focus shift in this method can be performed using only a single image, rather than multiple images. Using only a single image reduces time consumption and computational complexity compared to existing autofocus methods that rely on at least two images and / or machine learning algorithms.

[0131] In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 400 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 350 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 300 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 250 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 200 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 150 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 100 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 50 nanometers.

[0132] In some embodiments, the method further includes calibrating the swivel point of the optical system. In some embodiments, calibrating the swivel point includes de-tilting the substrate, detector, or autofocus sensor. In some cases, calibrating the swivel point may include determining a swivel point offset based on the region center of the focused area of ​​the calibration image and the image center of the calibration image. The swivel point offset may be from the optical axis 1099. Referring to Figure 9, the swivel point offset is the distance between the center of image 1099 corresponding to the intersection of the optical axis with the xy plane or image plane and the region center 1091 of the focused area. If there is no swivel point offset, the center of image 1099 may overlap with the center of the focused area 1091. If there is a swivel point offset, after tilting, the center of the focused area may shift away from the center of the image. The region center can be determined using various image processing algorithms that can be used in operation 530. After the pivot point offset is determined, the calibration operation may include untilting the sample stage, image sensor, or autofocus sensor back to its position before the calibration operation began.

[0133] In one embodiment, the Disclosure provides an optical system comprising: a substrate; an autofocus module configured to capture an image of the substrate, including a focused portion and an out-of-focus portion, wherein the substrate or the autofocus module is tilted at a certain angle; and a processor configured to determine the focus shift of the substrate to the focal plane of the optical system, using at least the distance from the focused portion to the center of the image and the angle of inclination.

[0134] In some embodiments, the processor may include one or more processing units, integrated circuits, or combinations thereof. For example, the processing units may include a central processing unit (CPU) and / or a graphics processing unit (GPU). The integrated circuits may include chips such as field-programmable gate arrays (FPGAs).

[0135] In some embodiments, the substrate may be tilted at a certain angle. In some embodiments, the processor may use the tilt angle of the substrate when determining the focus shift. In some embodiments, the autofocus module may be tilted at a certain angle. In some embodiments, the processor may use the tilt angle of the autofocus module when determining the focus shift.

[0136] In some embodiments, the autofocus module includes an illumination source and a detector. In some embodiments, the illumination source is configured to illuminate at least a portion of the substrate, and the detector is configured to image at least a portion of the portion of the substrate.

[0137] In some embodiments, the tilt angle may range from about 0.01 to about 89 degrees. In some embodiments, the tilt angle may range from about 0.05 to about 15 degrees. In some embodiments, the tilt angle may range from about 0.05 to about 8 degrees.

[0138] In some embodiments, determining the focus shift in this system can be performed using only a single image, rather than multiple images. Using only a single image reduces time consumption and computational complexity compared to existing autofocus methods that rely on at least two images and / or machine learning algorithms.

[0139] In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 400 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 350 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 300 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 250 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 200 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 150 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 100 nanometers. In some embodiments, the error in the amount of focus shift from the true amount of focus shift is at most about 50 nanometers.

[0140] In some embodiments, the autofocus module may comprise one or more of the following: an autofocus illumination source, an autofocus sensor, an autofocus tube lens, a dichroic filter, or a beam splitter.

[0141] In some embodiments, the optical system may comprise one or more image sensors. In some embodiments, one or more image sensors may be used for both imaging the substrate and focusing the optical system. In some embodiments, the image is acquired by an autofocus module, which is configured solely for autofocusing and not for imaging the substrate after autofocusing is complete.

[0142] In some embodiments, the methods disclosed herein enable accurate and reliable autofocus of the optical system 116 prior to imaging, for example, imaging of the sequencing reaction of a sample immobilized on a flow cell. Refocusing of the optical system can be performed at any time as needed. For example, refocusing of the optical system may occur in different flow cycles prior to imaging different samples, different surfaces of the same flow cell, different tiles or subtiles of the flow cell, and / or the same spatial region of the sample.

[0143] In some embodiments, the method can be used to focus an optical system before imaging a sample nucleic acid molecule immobilized on a flow cell in a first flow cycle, and then to refocus before imaging the sample molecule again in a second flow cycle of a sequencing run. In some embodiments, the method can be used to focus an optical system before imaging a sample nucleic acid molecule immobilized on a first surface in a first flow cycle of a sequencing run, and to focus an optical system before imaging a sample nucleic acid molecule immobilized on the first or second surface in a second flow cycle of a sequencing run. In some embodiments, the method can be used to focus an optical system before imaging a sample nucleic acid molecule immobilized on a first surface in a first flow cycle of a sequencing run, and to refocus an optical system for imaging a sample nucleic acid molecule immobilized on a second surface in a first or second flow cycle of a sequencing run.

[0144] In some embodiments, the method can be used to focus an optical system for imaging a sample at various signal-to-noise ratios (SNRs) or contrast-to-noise ratios (CNRs). For example, the method can be used to focus an optical system that uses (or images a sample of) a sample at a conventional CNR that can be achieved using conventional supports and hybridization, amplification, and / or NGS sequencing protocols. For example, the method can be used to focus an optical system for imaging a sample at a CNR higher than the conventional CNR that can be achieved using conventional supports and hybridization, amplification, and / or NGS sequencing protocols.

[0145] In some embodiments, the method can be used to focus an optical system for imaging low nucleotide diversity sequencing data or unbalanced nucleotide diversity sequencing data. In some embodiments, the method can be used to focus an optical system using a sample of unbalanced nucleotide diversity sequencing data. Nucleotide diversity of a population of immobilized nucleotide acid molecules can refer to the relative proportions of nucleotides A, G, C, and T present in each sequencing cycle. Balanced diversity data can generally have approximately equal proportions of all four nucleotides represented in each cycle of sequencing run. Unbalanced diversity data can generally have a high proportion of one particular nucleotide and a low proportion of other nucleotides, for example, A, G, C, and T may be 5%, 30%, 25%, and 40% of the total nucleotides in one or more cycles.

[0146] In some embodiments, the method can be used to focus an optical system for imaging a sample containing amplified nucleotide acid molecules in a template module, for example, via rolling circle amplification, using various methods. In some embodiments, the method can be used to focus an optical system for imaging a sample at various signal densities. In some embodiments, the density of template nucleotide molecules immobilized on the support is 1 mm 2 10 hits 2 ~10 15 That is the case.

[0147] In some embodiments, the method can be used to focus an optical system using a sample containing amplified nucleotide acid molecules in a template module, for example, via rolling circle amplification, using various methods. In some embodiments, the method can be used to focus an optical system using a sample at various signal densities. In some embodiments, the density of template nucleotide molecules immobilized on the support is 1 mm 2 10 hits 2 ~10 15 That is the case.

[0148] Figure 5A shows a flowchart of a method for performing autofocus using a single image acquired from an inclined sample, according to several embodiments. Method 500 may include some or all of the operations disclosed herein. The operations may be performed in the order described herein, but are not limited to that order.

[0149] Some or all of the operations of Method 500 may be performed by one or more processors disclosed herein. In some embodiments, the processor may include one or more processing units, integrated circuits, or combinations thereof. For example, a processing unit may include a central processing unit (CPU) and / or a graphics processing unit (GPU). An integrated circuit may include a chip such as a field-programmable gate array (FPGA).

[0150] In some embodiments, some or all of the operations in Method 500 may be performed by an FPGA(or more). In embodiments, when some operations are performed by an FPGA, the data after the operations performed by the FPGA may be communicated by the FPGA to the CPU so that the CPU can use such data to perform subsequent operations(or more) in Method 500. In some embodiments, all of the operations in Method 500 may be performed by a CPU(or more). Alternatively, the operations performed by a CPU(or more) may be performed by a dedicated processor or another processor such as a GPU(or more).

[0151] In some embodiments, method 500 includes an operation 510 to tilt the sample stage of an optical system by a certain angle, on which the sample is immobilized. The tilting of the sample stage may be relative to the focal plane of an objective lens when the optical system lacks one, or otherwise relative to the focal plane of the optical system. In some embodiments, the sample may be immobilized on a flow cell and immobilized on the sample stage. In some embodiments, the sample may be a test target simulating the presence of a flow cell on which the sample is immobilized. As disclosed herein, the sample may also be a bead-shaped flow cell on which the sample(s) are immobilized.

[0152] In some alternative embodiments, operation 510 may include tilting an image sensor or a dedicated AF sensor by an angle of inclination instead of the sample stage to achieve an equivalent effect on the image acquired in operation 520. Such inclination is with respect to the focal plane of the objective lens or the focal plane of the optical system. However, tilting the image sensor each time the autofocus process is performed and then untilting it back for imaging after the autofocus is complete may introduce inconsistencies or errors in the optical alignment of other optical elements of the optical system, such as the optical alignment of the image sensor of the corresponding tube lens, so tilting the sample stage may be preferable in some cases. Tilting the AF sensor has the advantage that it does not need to be untilted and back, and can remain tilted because it is dedicated to AF use only. However, it may add further cost and complexity to the optical system than one without an AF sensor.

[0153] The sample stage may be motorized or otherwise connected to a motor so that tilting of the sample stage can occur automatically with a predetermined angular resolution. In some embodiments, tilting may occur after receiving a command from a user or computer system, as disclosed herein. In some embodiments, tilting the sample stage of an optical system by an angle of inclination is around the x-axis or y-axis. In some embodiments, tilting the sample stage of an optical system by an angle of inclination lies in the xz-plane or yz-plane. In some embodiments, tilting the AF sensor or image sensor of an optical system by an angle of inclination is around the x-axis or y-axis. In some embodiments, tilting the AF sensor or image sensor of an optical system by an angle of inclination lies in the xz-plane or yz-plane. The title angle may be in the range of 0.01 to 89 degrees. The inclination angle may be in the range of 0.05 to 15 degrees. The inclination angle may be in the range of 0.05 to 8 degrees. In some embodiments, the title angle is clockwise around the x-axis or y-axis. In some embodiments, the title angle is counterclockwise around the x-axis or y-axis. In some embodiments, the angular resolution of the tilt angle is in the range of 0.001 degrees to 0.2 degrees. In some embodiments, the angular resolution of the tilt angle is in the range of 0.01 degrees to 0.1 degrees. In some embodiments, the angular resolution of the tilt angle is in the range of 0.01 degrees to 0.08 degrees.

[0154] In some embodiments, operation 510 includes an operation in which a motor coupled to the sample stage receives a tilt angle. The tilt angle can be included in the command received by the motor. Such a command can be provided by the user, for example, by inputting the tilt angle at an input device of the optical system, or by being automatically input by the computer system of the sequencing system 100.

[0155] In some embodiments, operation 510 includes an operation in which a motor automatically tilts the sample stage by an inclination angle. Figure 6A shows a schematic diagram of the tilting of the sample stage.

[0156] In embodiments of sequencing nucleic acids using the sequencing system 100 of this specification, the operation 510 of tilting the sample stage of the optical system by a certain inclination angle may be performed simultaneously with moving the sample stage in the xy plane. In such embodiments, moving the sample stage in the xy plane includes moving the sample stage relative to the objective lens from the current tile / subtile to the next tile or subtile in the flow cell to position the next tile or subtile in a predetermined spatial location, for example, together with the imaging area of ​​the objective lens. For example, after the first tile has been imaged, the sample stage moves in the xy plane to position a second tile for imaging. While moving in the xy plane, the sample stage may also be tilted by an inclination angle such that tilting the sample stage adds a minimum additional time (if any) to the existing sequencing time.

[0157] In some embodiments, method 500 includes an operation 520 to obtain an image of a sample on an inclined sample stage using an image sensor of an optical system.

[0158] In some embodiments, the method may further include an operation in which a sequencing system cycles the sequencing reaction prior to operation 520. In some embodiments, cycling the sequencing reaction by the sequencing system involves contacting a nucleotide acid molecule immobilized on a support structure, e.g., a flow cell, with a mixture of multiple sequencing primers, multiple polymerases, and different types of avidites. Each avidite in the mixture comprises a core to which multiple nucleotide arms are attached, and each arm of the individual avidite may contain the same type of nucleotide base. In some embodiments, cycling the sequencing reaction by the sequencing system includes capturing an optical color signal emitted from the nucleotide reagent bound to the nucleotide acid molecule by an image sensor.

[0159] In an alternative embodiment, operation 520 may be performed by an AF sensor instead of an image sensor. In an embodiment in which the sample stage is tilted in operation 510, then an untilted image sensor or an untilted AF sensor can be used to obtain an image in operation 520. In an embodiment in which the image sensor or AF sensor is tilted in operation 510, a tilted image sensor or a tilted AF sensor can each be used to obtain an image in operation 520.

[0160] As shown in the lower right of Figure 6A, a partially "out-of-focus" image 600 of the sample on a tilted sample stage is shown in Figure 6B. The image center 607 corresponds to the center O in the optical axis and the xy-plane. Tilting the sample stage darkens a portion of the image because the sample corresponding to the dark areas is out of focus. Only a small area 606 near the edge of the image remains in focus. The distance from the center 606a of the focused area 606 to the image center 607 can be the xy-plane shift. When the tilt is around the y-axis, the xy-plane shift corresponds to the x-shift in Figure 6A. The size of the focused area may depend on the tilt angle of the optical system, depth of field, image resolution, and / or other parameters.

[0161] In some embodiments, image 600 includes only a single image. In some embodiments, the image sensor is used to autofocus the optical system and to image the sample(s) using the optical system. The image sensor may be one of the image sensors in the detection channels of a multi-channel fluorescence imaging module.

[0162] In some embodiments, image 600 includes sizes along the x and / or y axes, which are identical to the size along the image sensor or the corresponding axis of the AF sensor (if acquired by the AF sensor). When the tilt angle is around the y axis, the image size along the y axis is the same as the image sensor size along the y axis, while the size along the x axis can be different from the image sensor size along the y axis, for example, it can be smaller. For example, the size of image 600 along the x axis is the same as the image sensor size along the x axis. In some embodiments, an image having a smaller width (along the y axis) than image 600 can function equivalently as image 600 in autofocus, but can save some advantage in computation time for processing smaller imaging and / or storage space when storing the image.

[0163] In some embodiments, the image includes a length or width within the range of 0.1 mm to 5 cm. In some embodiments, the image includes a length (along the x-axis) or width (along the y-axis) within the range of 0.1 mm to 30 mm. In some embodiments, the image includes a length (along the x-axis) or width (along the y-axis) within the range of 0.5 mm to 10 mm. In some embodiments, the image includes a length (along the x-axis) or width (along the y-axis) within the range of 0.5 mm to 5 mm.

[0164] The image may contain a varying number of pixels along the x or y axis. For example, image 600 may contain a matrix size of approximately 5400 × 3600. In some embodiments, the image may contain 60 to 60,000 pixels along the x and / or y axis. In some embodiments, the image may contain 600 to 8,000 pixels along the x and / or y axis. In some embodiments, the matrix size may be optimized to achieve accurate determination of the center of the focused region 606a without increasing unnecessary imaging and / or image processing time.

[0165] In some embodiments, the image 600 in operation 520 may be acquired by an AF sensor that is dedicated solely to the purpose of autofocus, but is not used for imaging after autofocus is complete.

[0166] In some embodiments, method 500 includes an operation 530 in which a processor determines the z-shift. The z-shift can be determined based on: (1) the tilt angle, and (2) the xy-plane shift from the center of the image. The xy-plane shift is determined based on the focused region of the image.

[0167] Referring back to Figure 6A, in this particular embodiment, the sample stage is tilted counterclockwise along the x-axis by an angle of 609 in the xz-plane defined by the x and z axes. When the sample stage is in the focal plane of the objective lens, for example, when it is focused, tilting it around the center O, for example, the intersection of the optical axis or z-axis with the x-axis, the focused region remains at the center O (bottom left of Figure 6A). When the sample stage is not in the focal plane of the objective lens, for example, when it is not focused, tilting it around the center O results in an xy-plane shift, which is a shift along the x-axis of the focused region away from the center O (bottom right of Figure 6A). The z-shift 608 is (z-shift) = (xy-plane shift) * tan(angle of inclination) It can be determined as follows, where z-shift is the spatial shift along the z-axis, tan() is the tangent function, the inclination angle is the angle of inclination from the original position around the axis in the xy-plane, and xy-plane shift is the spatial shift from the center of the focused region of the image to the center of the entire image.

[0168] In some embodiments, the xy-plane shift can be any shift within the xy-plane. In some embodiments, the xy-plane shift can be any shift along the x-axis or the y-axis.

[0169] In some embodiments, the xy-plane shift is the distance from the image center corresponding to the intersection of the optical axis and the image plane (e.g., the xy-plane) to the center of the focused region. The center of the focused region can lie on a straight line in the xy-plane. The center of the focused region can lie on a straight line perpendicular to the tilt axis of the tilt angle. For example, as shown in Figure 6B, the center 606a of the focused region 606 lies on the x-axis in the xy-plane. As shown in Figure 6A, the tilt angle is also around the x-axis, and the center 606a lies on the x-axis perpendicular to the y-axis, which is the tilt axis of the tilt angle.

[0170] The center 606a of the focused region can be determined using various image processing algorithms. For example, an image can be separated into a predetermined number of regions, e.g., 20 to 40 regions, and since the focused region contains higher intensity than the out-of-focus, darker regions, the approximate location of the focused region can be identified using the sum or average image intensity of each region. Subsequently, the center 606a can be located using the approximate image intensity (e.g., intensity projection) and / or spatial frequency (Fourier transform of intensity) information of the focused region. In some embodiments, information about geometric patterns in the image may be a factor in determining the image processing algorithm(s) for finding the center 606a.

[0171] In some embodiments, tilting along the x-axis or y-axis may be simpler or more convenient to implement than tilting in other directions within the xy-plane. As a result of such tilting along the x-axis or y-axis, determining the xy-plane shift along the x-axis or y-axis may be more computationally convenient and efficient.

[0172] In some embodiments, method 500 may include an operation 540 in which the sample stage is moved by a determined z-shift relative to the focal plane of the objective lens of the optical system, thereby autofocusing the optical system. After determining the z-shift in operation 530, the sample stage can be moved relative to the focal plane of the objective lens to focus on the sample. This relative movement may be achieved by keeping the sample stage in the same position relative to the base plate (205 in Figures 2A-2B) and moving the objective lens relative to the base plate, thereby moving the focal plane closer and substantially overlapping it with the sample stage (e.g., within ±200 nm or ±100 nm). Alternatively, the sample stage may be moved relative to the base plate by the z-shift, while the objective lens and its focal plane remain in the same spatial location relative to the base plate.

[0173] As disclosed herein, the sample stage may be motorized, or otherwise connected to a motor, so that its movement can be automated in response to receiving any of the commands provided by the user or a computer system, as disclosed herein. Similarly, the objective lens may be coupled to a motorized stage, such as a z-stage, so that its movement can be controlled in a similar manner and it can move automatically in response to commands from the user or a computer system.

[0174] In some embodiments, method 500 includes de-tilting a tilted sample stage, tilted image sensor, or tilted AF sensor that is tilted in operation 510 by the tilt angle (in the opposite direction) and returning it to its spatial position before the tilt operation 510.

[0175] In embodiments of sequencing nucleic acids using the sequencing system 100 described herein, the operation of untilting a tilted sample stage, a tilted AF sensor, or a tilted image sensor and returning it to its position before the tilt operation 510 may be performed at least partially simultaneously with the operation 540, which moves the sample stage by a determined z-shift relative to the focal plane of the objective lens. Untilting and moving the focused sample stage by operation 540 may be performed simultaneously to reduce the time required to focus on the sample, and therefore the total time for sequencing. In some embodiments, the AF sensor may remain tilted and does not need to be untilted and returned.

[0176] In some embodiments, method 500 as described herein can be used for autofocus along the z-axis. In some embodiments, the z-shift of the objective lens relative to the sample is determined to position the sample at the focal plane of the objective lens. In some embodiments, the error in the autofocus of the optical system is in the range of -400 nm to +400 nm. In some embodiments, the error in the autofocus of the optical system is in the range of -200 nm to +200 nm. In some embodiments, the error in the autofocus of the optical system is in the range of -100 nm to +100 nm. In some embodiments, the error in the autofocus of the optical system is in the range of -50 nm to +50 nm.

[0177] Figures 7A-7B and 8 show the z-shifts determined using the systems and methods described herein, compared to the actual z-shifts generated by directly moving the objective lens out of focus relative to the sample stage by a predetermined z-shift. Figure 7A shows the difference between the estimated z-shift and the actual z-shift by tilting the sample stage while keeping the image sensor fixed to the base plate using the methods described herein. The difference is less than ±100 nm, or even less than ±50 nm, at all different z locations. The tilt angle is 0.2 degrees in Figure 7A and 0.8 degrees in Figure 7B. Figure 8 shows the difference between the estimated z-shift and the actual z-shift by tilting the image sensor using the methods described herein. The tilt angle in Figure 8 is 3 degrees. The estimated z-shifts are isolated points in Figures 7A-7B and 8. Various types of fittings can be used to fit the isolated points. For example, first-order and / or second-order polynomial fittings may be used. The differences between isolated estimated points and other points between them are shown in Figures 7A-7B and the lower panel of Figure 8. The differences between isolated points are estimated using fitting lines. As mentioned above, fitting lines can be generated using various fitting methods, and the differences may be obtained as the best fitting result. Alternatively, the fitting may be limited to a specific algorithm, e.g., polynomial fitting up to order 3, in determining the difference between the estimated z-shift and the actual z-shift.

[0178] In some embodiments, autofocus using the method 500 disclosed herein for an optical system can be completed within 50 to 1200 milliseconds. In some embodiments, autofocus using the method disclosed herein for an optical system can be completed within 50 to 990 milliseconds. In some embodiments, autofocus using the method disclosed herein for an optical system can be completed in less than 400, 500, or 600 milliseconds.

[0179] Turn point calibration In some embodiments, method 500 as described herein includes an operation to calibrate the swivel point of the optical system. Such an operation can be performed before any of the autofocus operations 510–540. The swivel point calibration operation can be used to determine whether the swivel point is aligned with the optical axis of the optical system. The calibrated swivel point is the apex of the tilt angle during autofocus (e.g., center O in Figure 6A). The swivel point calibration operation can be performed as needed. For example, it may be performed only once before the sequence determination run begins and does not need to be repeated for different flow cycles. As another example, it may be performed during the sequence determination run in a particular flow cycle(s).

[0180] In some embodiments, the operation to calibrate the pivot point of the optical system includes tilting the sample stage, image sensor, or AF sensor. In some embodiments, the sample stage, image sensor, or AF sensor is focused along z prior to the calibration operation. The tilt angle for calibration may be the same as the tilt angle used in the autofocus operation 510. Alternatively, the tilt angle for calibration may be a second tilt angle different from the tilt angle in operation 510. In some embodiments, the operation to calibrate the pivot point of the optical system includes acquiring a calibration image of a sample fixed on the sample stage.

[0181] Figure 9 shows an example of a calibration image of a test target as a sample fixed on a sample stage. The calibration image can be acquired by either an image sensor or a dedicated AF sensor. Calibrating the swivel point may include an operation to determine the swivel point offset based on the region center of the focused area of ​​the calibration image and the image center of the calibration image. The swivel point offset may be from the optical axis 1099. Referring to Figure 9, the swivel point offset is the distance between the center of image 1099, which corresponds to the intersection of the optical axis with the xy plane or image plane, and the region center 1091 of the focused area. If there is no swivel point offset, the center of image 1099 may overlap with the center of the focused area 1091. If there is a swivel point offset, after tilting, the center of the focused area may shift away from the center of the image. The region center can be determined using various image processing algorithms that can be used in operation 530. After the swivel point offset is determined, the calibration operation may include untilting the sample stage, image sensor, or AF sensor back to its position before the calibration operation began.

[0182] In some embodiments, the determined pivot point offset may be taken into consideration in operation 530 to determine the xy-plane shift. In some embodiments, operation 530 may include the operation of subtracting the determined pivot point offset from the xy-plane shift to obtain the xy-plane shift, such that the z-shift can be calculated as follows: (z-shift) = [(xy-plane shift) - (turn point offset)] * tan(angle of inclination)

[0183] Computer system Figure 4 illustrates block diagrams of computer systems for autofocus according to several embodiments. Various aspects of the methods described herein, for example, method 500, as well as combinations and subcombinations thereof, may be carried out using one or more computer systems, such as computer system 400 shown in Figure 4.

[0184] The computer system 126 in Figure 1 may include one or more computer systems 400. Each computer system 400 may include one or more hardware processors 404. The hardware processors 404 may include a central processing unit (CPU), a graphics processing unit (GPU), or a combination thereof. The processors 404 may be connected to a bus or communication infrastructure 406.

[0185] The computer system 400 may also include user input / output devices 403, such as monitors, keyboards, and pointing devices, which can communicate with a communication infrastructure 406 via user input / output interfaces 402. The user input / output devices 403 may be coupled to the user interface 124 in Figure 1.

[0186] One or more of the processors 404 may be graphics processing units (GPUs). In one embodiment, a GPU may be a processor that is a specialized electronic circuit designed to handle mathematically intensive applications. A GPU may have a parallel structure that is efficient for parallel processing of large data blocks, such as mathematically intensive data common to computer graphics applications, images, videos, vector processing, array processing, etc., as well as encryption (including brute-force cracking), generation of cryptographic hashes or hash arrays, solving partial hash reversal problems, and / or generation of results for other proof-of-work calculations for some blockchain-based applications. Due to the general-purpose computing capabilities on graphics processing units (GPGPUs), GPUs may be particularly useful in at least the image recognition and machine learning embodiments described herein.

[0187] Furthermore, one or more of the processors 404 may include a hardware-accelerated cryptographic coprocessor, or an implementation of a coprocessor or other logic to accelerate cryptographic computations or other specialized mathematical functions. Such an accelerated processor may further include an instruction set(s) to accelerate using the coprocessor and / or other logic to facilitate such acceleration.

[0188] The computer system 400 may also include main memory or primary memory 408, and a data storage device such as random access memory (RAM). The main memory 408 may include one or more levels of cache. The main memory 408 may store control logic (i.e., computer software) and / or data within it.

[0189] The computer system 400 may also include one or more secondary data storage devices or secondary memory 410. The secondary memory 410 may include, for example, a main storage drive 412 and / or a removable storage device or drive 414. The main storage drive 412 may be, for example, a hard disk drive or a solid-state drive. The removable storage drive 414 may be a floppy disk drive, a magnetic tape drive, a compact disk drive, an optical storage device, a tape backup device, and / or any other storage device / drive.

[0190] The removable storage drive 414 can communicate with the removable storage unit 418.

[0191] The removable storage unit 418 may include a computer-accessible or readable storage device that stores computer software and / or data. The software may include control logic. The software may include instructions that can be executed by the hardware processor 404. The removable storage unit 418 may be a floppy disk, magnetic tape, compact disk, DVD, optical storage disk, and / or any other computer data storage device. The removable storage drive 414 may read from and / or write to the removable storage unit 418.

[0192] The secondary memory 410 may include other methods, devices, components, means, or other techniques for enabling the computer system 400 to access computer programs and / or other instructions and / or data. Such methods, devices, components, means, or other techniques may include, for example, a removable storage unit 422 and an interface 420. Examples of removable storage units 422 and interfaces 420 include program cartridges and cartridge interfaces (such as those found in video game devices), removable memory chips (such as EPROMs or PROMs) and associated sockets, memory sticks and USB ports, memory cards and associated memory card slots, and / or any other removable storage units and associated interfaces.

[0193] The computer system 400 may further include a communication or network interface 424. The communication interface 424 may enable the computer system 400 to communicate and interact with any combination of external devices, external networks, external entities, etc. (referenced individually and collectively by reference number 428). For example, the communication interface 424 may enable the computer system 400 to communicate with an external or remote device 428 via a communication path 426, which may be wired and / or wireless (or a combination thereof) and may include any combination of LAN, WAN, internet, etc. Control logic and / or data may be transmitted to and from the computer system 400 via the communication path 426. In some embodiments, the communication path 426 is a connection to the cloud 130, as shown in Figure 1. External devices, etc., referenced by reference number 428 may be devices, networks, entities, etc., within the cloud 130.

[0194] The computer system 400 may also be, to name some non-limiting examples or any combination thereof, a personal digital assistant (PDA), a desktop workstation, a laptop or notebook computer, a netbook, a tablet, a smartphone, a smartwatch, or any other wearable, appliance, part of the Internet of Things (IoT), and / or an embedded system.

[0195] It should be understood that the frameworks described herein may be implemented as methods, processes, apparatus, systems, or products, such as non-temporary computer-readable media or devices.

[0196] Computer system 400 may be a client or server that accesses or hosts any application and / or data through any delivery paradigm, including but not limited to remote or distributed cloud computing solutions, local or on-premises software (e.g., “on-premises” cloud-based solutions), “as a service” models (e.g., Content as a Service (CaaS), Digital Content as a Service (DCaaS), Software as a Service (SaaS), Managed Software as a Service (MSaaS), Platform as a Service (PaaS), Desktop as a Service (DaaS), Framework as a Service (FaaS), Backend as a Service (BaaS), Mobile Backend as a Service (MBaaS), Infrastructure as a Service (IaaS), Database as a Service (DBaaS), etc.), and / or hybrid models that include any combination of the above examples or other service or delivery paradigms.

[0197] Any applicable data structure, file format, and schema may be derived from standards including, but not limited to, JavaScript® Object Notation (JSON), Extensible Markup Language (XML), another Markup Language (YAML), Extensible Hypertext Markup Language (XHTML), Wireless Markup Language (WML), MessagePack, XML User Interface Language (XUL), or other functionally similar representations, either alone or in combination. Alternatively, one may use their own data structure, format, or schema, exclusively or in combination with known or open standards.

[0198] Any related data, files, and / or databases may be stored, retrieved, accessed, and / or transmitted in human-readable formats such as numerical, text, graphic, or multimedia formats, further including various types of markup languages, among other possible formats. Alternatively, or in combination with the above formats, data, files, and / or databases may be stored, retrieved, accessed, and / or transmitted in binary, encoded, compressed, and / or encrypted formats, or any other machine-readable format.

[0199] Interfaces or interconnections between various systems and layers may use any number of mechanisms, such as any number of protocols, programmatic frameworks, floor plans, or application programming interfaces (APIs), including, but not limited to, the Document Object Model (DOM), Discovery Services (DS), NSUserDefaults, Web Services Description Language (WSDL), Message Exchange Pattern (MEP), Web Distributed Data Exchange (WDDX), Web Hypertext Application Technologies Working Group (WHATWG), HTML5 Web Messaging, Representation State Transfer (REST or RESTful Web Services), Extensible User Interface Protocol (XUP), Simple Object Access Protocol (SOAP), XML Schema Definition (XSD), XML Remote Procedure Call (XML-RPC), or any other mechanism capable of achieving similar functionality and results.

[0200] Such interfaces or interconnections may also utilize uniform resource identifiers (URIs), which may further include uniform resource locators (URLs) or uniform resource names (URNs). Other forms of uniform and / or unique identifiers, locators, or names may be used exclusively or in combination with forms such as those described above.

[0201] Any of the protocols or APIs described above may interface with, implement, compile, or interpret in any programming language, procedural language, functional language, or object-oriented language. Non-exclusive examples include virtually any other language by any kind of framework, runtime environment, virtual machine, interpreter, stack, engine, or similar mechanism in C, C++, C#, Objective-C, Java®, Scala, Clojure, Elixir, Swift, Go, Perl, PHP, Python®, Ruby, JavaScript®, WebAssembly, or any other library or schema (including, but not limited to, Node.js, V8, Knockout, jQuery, Dojo, Dijit, OpenUI5, AngularJS, ExpressJS, Backbone.js, Ember.js, DHTMLX, Vue, React, Electron, etc.).

[0202] In some embodiments, a tangible non-temporary device or product including a tangible non-temporary computer-usable or readable medium storing control logic (software) may be referred to herein as a computer program product or program storage device. This includes, but is not limited to, a tangible product embodying a computer system 400, main memory 408, secondary memory 410, and removable storage units 418 and 422, as well as any combination thereof. When such control logic is executed by one or more data processing devices (such as computer system 400), such data processing devices may be made to operate as described herein.

[0203] Based on the teachings contained herein, methods for creating and using embodiments of this disclosure using data processing devices, computer systems, and / or computer architectures other than those shown in Figure 4 will be apparent to those skilled in the art. In particular, embodiments may operate with software, hardware, and / or operating system implementations other than those described herein.

[0204] Support and low nonspecific coating In some embodiments, NGS sequencing compositions and methods, such as pairwise sequencing, utilize a support on which multiple oligonucleotide surface primers are immobilized. In some embodiments, the support is passivated with a low nonspecific binding coating. The surface coatings described herein exhibit very low nonspecific binding to reagents typically used for nucleic acid capture, amplification, and sequencing workflows, such as dyes, nucleotides, enzymes, and nucleic acid primers. Compared to conventional surface coatings, the surface coatings exhibit lower background fluorescence signals or higher contrast-to-noise (CNR) ratios.

[0205] Low nonspecific binding coatings comprise one or more layers (Figure 11). In some embodiments, multiple surface primers are immobilized on the low nonspecific binding coating. In some embodiments, at least one surface primer is embedded within the low nonspecific binding coating. Low nonspecific binding coatings enable improved nucleic acid hybridization and amplification performance. Generally, a support comprises a substrate (or support structure) and one or more layers of low binding and chemical modification, covalently or acovalently attached, such as silane layers, polymer films, and one or more covalently or acovalently attached surface primers that can be used to tether single-stranded nucleic acid library molecules to the support. In some embodiments, the formulation of the coating, e.g., the chemical composition of one or more layers, the coupling chemistry used to crosslink one or more layers to and / or to the support, and the total number of layers, can be varied so that nonspecific binding of proteins, nucleic acid molecules, and other hybridization and amplification reaction components to the coating is minimized or reduced compared to an equivalent monolayer. The coating formulations described herein may be varied so that nonspecific hybridization on the coating is minimized or reduced compared to an equivalent monolayer. The coating formulations may be varied so that nonspecific amplification on the coating is minimized or reduced compared to an equivalent monolayer. The coating formulations may be varied so that the specific amplification rate and / or yield on the coating is maximized. Amplification levels suitable for detection are achieved in 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30 or fewer, or more than 30 amplification cycles, in some cases disclosed herein.

[0206] A support structure comprising one or more chemically modified layers, such as a layer of low nonspecific binding polymers, may be independent or integrated within another structure or assembly. For example, in some embodiments, the support structure may comprise one or more surfaces within an integrated or assembled microfluidic flow cell. The support structure may comprise one or more surfaces within a microplate format, such as the bottom surfaces of wells in a microplate. In some embodiments, the support structure comprises the inner surface of a capillary (e.g., the lumen surface). In some embodiments, the support structure comprises the inner surface of a capillary etched within a planar chip (e.g., the lumen surface).

[0207] The bonding chemistry used to graft the first chemically modified layer onto the surface of the support generally depends on both the material from which the surface is manufactured and the chemical properties of the layer. In some embodiments, the first layer may adhere covalently to the surface. In some embodiments, the first layer may adhere to the support non-covalently, e.g., by adsorption, via non-covalent interactions between the support and the molecular components of the first layer, e.g., electrostatic interactions, hydrogen bonds, or van der Waals interactions. In any case, the support may be treated before the adhesion or deposition of the first layer. Any of the various surface preparation techniques known to those skilled in the art may be used to clean or treat the surface. For example, a glass or silicon surface may be acid-washed using a piranha solution (a mixture of sulfuric acid (H2SO4) and hydrogen peroxide (H2O2)), a base treatment in KOH and NaOH, and / or cleaned using an oxygen plasma treatment method.

[0208] Silane chemistry has developed non-limiting methods for covalently modifying silanol groups on glass or silicon surfaces to attach more reactive functional groups (e.g., amine or carboxyl groups), which can then be used in coupling linker molecules (e.g., linear hydrocarbon molecules of various lengths, e.g., C6, C12, C18 hydrocarbons, or linear polyethylene glycol (PEG) molecules) or layer molecules (e.g., branched PEG molecules or other polymers) to the surface. Examples of suitable silanes that can be used in the preparation of any of the disclosed low-bonding coatings include, but are not limited to, (3-aminopropyl)trimethoxysilane (APTMS), (3-aminopropyl)triethoxysilane (APTES), any of the various PEG silanes (e.g., those with molecular weights such as 1K, 2K, 5K, 10K, 20K, etc.), amino-PEG silanes (e.g., those containing free amino functional groups), maleimide-PEG silanes, and biotin-PEG silanes.

[0209] Any of the various molecules known to those skilled in the art, including but not limited to amino acids, peptides, nucleotides, oligonucleotides, other monomers, or polymers, or combinations thereof, may be used in the preparation of one or more chemically modified layers on a support, and the selection of components used may vary to modify one or more properties of the layer, such as the surface density of functional groups and / or tethered oligonucleotide primers, the hydrophilicity / hydrophobicity of the layer, or the three-dimensional properties of the layer (e.g., "thickness"). Examples of polymers that may be used to prepare one or more layers of low nonspecific binding material in any of the disclosed coatings include, but are not limited to, polyethylene glycol (PEG) of various molecular weights and branched structures, streptavidin, polyacrylamide, polyester, dextran, poly-lysine, and poly-lysine copolymers, or any combination thereof. Examples of conjugation chemistry that can be used to graft one or more layers of a material (e.g., polymer layers) onto a surface and / or to crosslink the layers with each other include, but are not limited to, biotin-streptavidin interactions (or their variants), his-tag-Ni / NTA conjugation chemistry, methoxyether conjugation chemistry, carboxylate conjugation chemistry, amine conjugation chemistry, NHS esters, maleimides, thiols, epoxys, azides, hydrazides, alkynes, isocyanates, and silanes.

[0210] Low nonspecific bonding surface coatings can be applied uniformly across the entire support. Alternatively, the surface coating can be patterned such that the chemically modified layer is limited to one or more distinct regions of the support. For example, the coating can be patterned using photolithography techniques to create an aligned array or random pattern of chemically modified regions on the support. Alternatively or in combination, the coating can be patterned using, for example, contact printing and / or inkjet printing techniques. In some embodiments, an aligned array or random pattern of chemically modified regions may include at least one, five, ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety, one hundred, two hundred, three hundred, four hundred, five hundred, six hundred, seven hundred, eighty, ninety, one hundred, two hundred, three hundred, four hundred, five hundred, six hundred, seven hundred, eighty, ninety, one hundred, two hundred, three hundred, four hundred, five hundred, six hundred, seven hundred, eighty, ninety, or ten thousand or more individual regions.

[0211] In some embodiments, low nonspecific binding coatings include hydrophilic polymers that are nonspecifically adsorbed to or covalently grafted onto a support. Passivation can be performed using poly(ethylene glycol) (PEG, also known as polyethylene oxide (PEO) or polyoxyethylene), or other hydrophilic polymers having different molecular weights and end groups bonded to the support, for example, using silane chemistry. End groups distal to the surface may include, but are not limited to, biotin, methoxyether, carboxylate, amine, NHS ester, maleimide, and bis-silane. In some embodiments, two or more layers of hydrophilic polymers, e.g., linear polymers, branched polymers, or highly branched polymers, may be deposited on the surface. In some embodiments, two or more layers may be covalently coupled to each other or internally crosslinked to improve the stability of the resulting coating. In some embodiments, surface primers having different nucleotide sequences and / or base modifications (or other biomolecules, e.g., enzymes or antibodies) may be tethered to the resulting layer at varying surface densities. In some embodiments, for example, both the surface functional group density and the surface primer concentration can be varied to achieve a desired surface primer density range. Furthermore, the surface primer density can be controlled by diluting the surface primer with other molecules possessing the same functional groups. For example, to reduce the final primer density, an amine-labeled surface primer can be diluted with amine-labeled polyethylene glycol in reaction with an NHS ester coated surface. Alternatively, surface primers having linkers of different lengths between the hybridization region and the surface-attached functional groups can be applied to control the surface density. Suitable linker examples include poly-T and poly-A chains at the 5' end of the primer (e.g., 0 to 20 bases), PEG linkers (e.g., 3 to 20 monomer units), and carbon chains (e.g., C6, C12, C18, etc.).To measure primer density, fluorescently labeled primers may be tethered to a surface, and then fluorescent leads may be compared to those for a dye solution of known concentration.

[0212] In some embodiments, the low nonspecific bonding coating comprises a functionalized polymer coating layer covalently bonded to at least a portion of a support via chemical groups on the support, a primer grafted onto the functionalized polymer coating, and a water-soluble protective coating on the primer and the functionalized polymer coating. In some embodiments, the functionalized polymer coating comprises poly(N-(5-azidoacetamidylpentyl)acrylamide-co-acrylamide (PAZAM).

[0213] Supports containing multilayer coatings of PEG and other hydrophilic polymers have been developed to adjust primer surface density and add additional dimensionality to hydrophilic or amphoteric coatings. By using hydrophilic and amphoteric surface layering techniques, including but not limited to the polymer / copolymer materials described below, it is possible to significantly increase the primer load density on the support. Conventional PEG coating techniques use monolayer primer deposition, which has generally been reported for single-molecule applications but does not yield high copy numbers for nucleic acid amplification applications. “Lamination,” as described herein, can be achieved with any compatible polymer or monomer subunit, allowing for the sequential construction of surfaces containing two or more highly crosslinked layers using conventional crosslinking techniques. Examples of suitable polymers include, but are not limited to, streptavidin, polyacrylamide, polyester, dextran, polylysine, and copolymers of polylysine and PEG. In some embodiments, different layers may adhere to each other via any of a variety of conjugation reactions, including, but not limited to, biotin-streptavidin bonding, azide-alkyne click reactions, amine-NHS ester reactions, thiol-maleimide reactions, and ionic interactions between positively charged and negatively charged polymers. In some embodiments, high-primer-density materials may be constructed in solution and then layered onto a surface in multiple operations.

[0214] Examples of materials from which support structures can be manufactured include, but are not limited to, glass, fused silica, silicon, polymers (e.g., polystyrene (PS), macroporous polystyrene (MPPS), polymethyl methacrylate (PMMA), polycarbonate (PC), polypropylene (PP), polyethylene (PE), high-density polyethylene (HDPE), cyclic olefin polymer (COP), cyclic olefin copolymer (COC), polyethylene terephthalate (PET)), or any combination thereof. Various compositions of both glass and plastic support structures are intended.

[0215] The support structure may be of any of the various geometric shapes and dimensions known to those skilled in the art, and may comprise any of the various materials known to those skilled in the art. For example, the support structure may be locally planar (e.g., including a microscope slide or the surface of a microscope slide). Generally, the support structure may be cylindrical (e.g., including a capillary or the inner surface of a capillary), spherical (e.g., including the outer surface of a non-porous bead), or irregular (e.g., including the outer surface of a non-porous bead or particle of an irregular shape). In some embodiments, the surface of the support structure used for nucleic acid hybridization and amplification may be a solid non-porous surface. In some embodiments, the surface of the support structure used for nucleic acid hybridization and amplification may be porous, so that the coating described herein penetrates the porous surface and the nucleic acid hybridization and amplification reactions performed thereon may occur within the pores.

[0216] A support structure comprising one or more chemically modified layers, such as layers of low nonspecific binding polymers, may be independent or integrated within another structure or assembly. For example, the support structure may comprise one or more surfaces within an integrated or assembled microfluidic flow cell. The support structure may comprise one or more surfaces within a microplate format, such as the bottom surfaces of wells in a microplate. In some embodiments, the support structure comprises the inner surface of a capillary (e.g., the lumen surface). In some embodiments, the support structure comprises the inner surface of a capillary etched within a planar chip (e.g., the lumen surface).

[0217] As described above, the low nonspecific binding supports of this disclosure exhibit reduced nonspecific binding of proteins, nucleic acids, and other components of hybridization and / or amplification formulations used for solid-phase nucleic acid amplification. The degree of nonspecific binding exhibited by a given support surface can be evaluated either qualitatively or quantitatively. Exposing the surface to, for example, a fluorescent dye (e.g., cyanine, e.g., Cy3 or Cy5, fluorescein, coumarin, rhodamine, or other dyes disclosed herein), a fluorescently labeled nucleotide, a fluorescently labeled oligonucleotide, and / or a fluorescently labeled protein (e.g., polymerase) under a set of standardized conditions, followed by a specific rinsing protocol and fluorescence imaging, can be used as a qualitative tool for comparing nonspecific binding on supports containing different surface formulations. In some embodiments, exposing a surface to, for example, a fluorescent dye, fluorescently labeled nucleotide, fluorescently labeled oligonucleotide, and / or fluorescently labeled protein (e.g., polymerase) under a set of standardized conditions, followed by a specific rinsing protocol and fluorescence imaging, can be used as a quantitative tool for comparing nonspecific binding on supports containing different surface formulations, provided that the fluorescence imaging is performed under conditions where the fluorescence signal is linearly related (or related in a predictable manner) to the number of fluorophores on the support (e.g., under conditions where fluorophore signal saturation and / or self-quenching is not a concern), and care is taken to ensure that suitable calibration criteria are used. In some embodiments, other techniques known to those skilled in the art, e.g., radioisotope labeling and counting methods, can be used for quantitative assessment of the degree to which nonspecific binding is exhibited by different support surface formulations of this disclosure.

[0218] Some surfaces disclosed herein exhibit a ratio of specific fluorescence to nonspecific fluorescence of fluorophores such as Cy3, at least 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 30, 35, 40, 50, 75, 100, or greater than 100, or any intermediate value encompassed by the range described herein.

[0219] The degree of nonspecific binding exhibited by the disclosed low-binding supports can be evaluated under a set of standardized incubation and rinsing conditions using a standardized protocol for contacting the surface with labeled proteins (e.g., bovine serum albumin (BSA), streptavidin, DNA polymerase, reverse transcriptase, helicase, single-strand binding protein (SSB), etc., or any combination thereof), labeled nucleotides, labeled oligonucleotides, etc., followed by detection of the amount of label remaining on the surface and comparison of the resulting signal with an appropriate calibration standard. In some embodiments, the label may include a fluorescent label. In some embodiments, the label may include a radioisotope. In some embodiments, the label may include any other detectable label known to those skilled in the art. Thus, in some embodiments, the degree of nonspecific binding exhibited by a given support surface formulation can be evaluated in terms of the number of nonspecifically bound protein molecules (or nucleic acid molecules, or other molecules) per unit area. In some embodiments, the low-binding supports of the Disclosure may exhibit nonspecific protein binding (or nonspecific binding of other specific molecules (e.g., cyanines, e.g., Cy3 or Cy5, fluorescein, coumarin, rhodamine, or other dyes disclosed herein)) of less than 0.001 molecules per μm², less than 0.01 molecules per μm², less than 0.1 molecules per μm², less than 0.25 molecules per μm², less than 0.5 molecules per μm², less than 1 molecule per μm², less than 10 molecules per μm², less than 100 molecules per μm², or less than 1,000 molecules per μm²). Those skilled in the art will recognize that a given support surface of the Disclosure may exhibit nonspecific binding of any value within this range, for example, less than 86 molecules per μm². For example, some of the modified surfaces disclosed herein exhibit nonspecific protein binding of less than 0.5 molecules / μm² after contact with a 1 μM solution of Cy3-labeled streptavidin (GE Amersham) in phosphate-buffered saline (PBS) buffer for 15 minutes, followed by three rinses with deionized water.Several modified surfaces disclosed herein exhibit nonspecific binding of Cy3 dye molecules at a rate of less than 0.25 molecules per 1 μm². In independent nonspecific binding assays, 1 μM labeled Cy3 SA (ThermoFisher), 1 μM Cy5 SA dye (ThermoFisher), 10 μM aminoallyl-dUTP-ATTO-647N (Jena Biosciences), 10 μM aminoallyl-dUTP-ATTO-Rhol 1 (Jena Biosciences), 10 μM aminoallyl-dUTP-ATTO-Rhol 1 (Jena Biosciences), 10 μM 7-propargylamino-7-deaza-dGTP-Cy5 (Jena Biosciences), and 10 μM 7-propargylamino-7-deaza-dGTP-Cy3 (Jena Biosciences) were found to be nonspecific. The Biosciences (Biosciences) was incubated on a low-binding coated support at 37°C for 15 minutes in a 384-well plate format. Each well was rinsed 2-3 times with 50 μl of deionized RNase / DNase-free water and 2-3 times with 25 mM ACES buffer at pH 7.4. The 384-well plates were imaged in a GE Typhoon instrument using Cy3, AF555, or Cy5 filter sets as specified by the manufacturer (according to the dye tests performed), with a PMT gain setting of 800 and a resolution of 50-100 μm. For higher resolution imaging, images were taken using a total internal reflection fluorescence (TIRF) objective lens (100×, 1.5NA, Olympus), a CCD camera (e.g., Olympus EM-CCD monochrome camera, Olympus XM-10 monochrome camera, or Olympus DP80 color and monochrome camera), and an illumination source (e.g., Olympus 100W). The images were collected using an Olympus IX83 microscope (e.g., an inverted fluorescence microscope) with an excitation wavelength of 532 nm or 635 nm (Hg lamp, Olympus 75W Xe lamp, or Olympus U-HGLGPS fluorescence light source) (Olympus Corp., Center Valley, Pa.).The dichroic mirrors were purchased from Semrock (IDEX Health & Science, LLC, Rochester, NY) and were, for example, 405, 488, 532, or 633 nm dichroic reflectors / beam splitters, and the bandpass filters were selected as 532LP or 645LP to match the appropriate excitation wavelength. Some of the modified surfaces disclosed herein exhibit nonspecific binding of less than 0.25 dye molecules per 1 μm². In some embodiments, the coated support was immersed in a buffer (e.g., 25 mM ACES, pH 7.4) while the image was acquired.

[0220] In some embodiments, the surfaces disclosed herein exhibit a ratio of specific fluorescence to nonspecific fluorescence signals for fluorophores such as Cy3, at least 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 30, 35, 40, 50, 75, 100, or greater than 100, or any intermediate value encompassed by the range described herein.

[0221] Low background surfaces consistent with the disclosures herein may exhibit specific dye attachment (e.g., Cy3 attachment) to nonspecific dye adsorption (e.g., Cy3 dye adsorption) ratios of at least 4:1, 5:1, 6:1, 7:1, 8:1, 9:1, 10:1, 15:1, 20:1, 30:1, 40:1, and 50:1, or more than 50 attached specific dye molecules per nonspecifically adsorbed molecule. Similarly, low background surfaces consistent with the disclosures herein, with fluorophores, e.g., Cy3, attached when subjected to excitation energy, may exhibit specific fluorescence signal to nonspecific adsorbed dye fluorescence signal ratios of at least 4:1, 5:1, 6:1, 7:1, 8:1, 9:1, 10:1, 15:1, 20:1, 30:1, 40:1, 50:1, or greater than 50:1 (e.g., resulting from Cy3-labeled oligonucleotides attached to the surface).

[0222] In some embodiments, the degree of hydrophilicity (or "wettability" with aqueous solutions) of the disclosed support surface may be evaluated, for example, by measuring the water contact angle, in which a small water droplet is placed on the surface and its contact angle with the surface is measured, for example, using an optical tensiometer. In some embodiments, a static contact angle may be determined. In some embodiments, an advancing or receding contact angle may be determined. In some embodiments, the water contact angle for the surface-treated hydrophilic low-bonding support disclosed herein may be in the range of about 0 to about 30 degrees. In some embodiments, the water contact angle for the surface-treated hydrophilic low-bonding support disclosed herein may be 50 degrees, 40 degrees, 30 degrees, 25 degrees, 20 degrees, 18 degrees, 16 degrees, 14 degrees, 12 degrees, 10 degrees, 8 degrees, 6 degrees, 4 degrees, 2 degrees, or 1 degree or less. In many cases, the contact angle is 40 degrees or less. It will be recognized by those skilled in the art that a given hydrophilic low-bonding support surface of this disclosure may exhibit a water contact angle having a value within this range.

[0223] In some embodiments, the hydrophilic surfaces disclosed herein often facilitate reduced washing times in bioassays due to reduced nonspecific binding of biomolecules to low-binding surfaces. In some embodiments, a suitable washing operation can be performed within 60, 50, 40, 30, 20, 15, or 10 seconds, or within less than 10 seconds. For example, a suitable washing operation can be performed within 30 seconds.

[0224] Some of the low-binding surfaces of this disclosure exhibit significant improvements in stability or durability against prolonged exposure to solvents and high temperatures, or against repeated cycles of solvent exposure or temperature changes. For example, the stability of the disclosed surfaces can be tested by fluorescently labeling functional groups on the surface or tethered biomolecules (e.g., oligonucleotide primers) on the surface and monitoring the fluorescence signal before, during, and after prolonged exposure to solvents and high temperatures, or to repeated cycles of solvent exposure or temperature changes. In some embodiments, the degree of change in fluorescence used to assess surface quality may be less than 1%, 2%, 3%, 4%, 5%, 10%, 15%, 20%, or 25% (or any combination of these percentages when measured over these periods) over periods of 1 minute, 2 minutes, 3 minutes, 4 minutes, 5 minutes, 10 minutes, 20 minutes, 30 minutes, 40 minutes, 50 minutes, 60 minutes, 2 hours, 3 hours, 4 hours, 5 hours, 6 hours, 7 hours, 8 hours, 9 hours, 10 hours, 15 hours, 20 hours, 25 hours, 30 hours, 35 hours, 40 hours, 45 hours, 50 hours, or 100 hours of exposure to the solvent and / or high temperature (or any combination of these percentages when measured over these periods). In some embodiments, the degree of change in fluorescence used to assess surface quality may be less than 1%, 2%, 3%, 4%, 5%, 10%, 15%, 20%, or 25% (or any combination of these percentages when measured over this range of cycles) over repeated exposure to solvent changes and / or temperature changes over 5, 10, 20, 30, 400, 500, 600, 700, 800, 900, or 1,000 cycles.

[0225] In some embodiments, the surfaces disclosed herein may exhibit a high ratio of specific signals to nonspecific signals or other backgrounds. For example, when used for nucleic acid amplification, some surfaces may exhibit amplification signals at least 4, 5, 6, 7, 8, 9, 10, 15, 20, 30, 40, 50, 75, 100, or more than 100 times greater than the signals of adjacent non-aggregated regions of the surface. Similarly, some surfaces may exhibit amplification signals at least 4, 5, 6, 7, 8, 9, 10, 15, 20, 30, 40, 50, 75, 100, or more than 100 times greater than the signals of adjacent amplified nucleic acid aggregated regions of the surface.

[0226] In some embodiments, the disclosed low-background surface fluorescence images, when used in nucleic acid hybridization or amplification applications to produce polony of hybridized or clone-amplified nucleic acid molecules (e.g., directly or indirectly labeled with fluorophores), exhibit contrast-to-noise ratios (CNRs) of at least 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 20, 210, 220, 230, 240, 250, or greater than 250.

[0227] One or more types of primers may adhere to or tether to the support surface. In some embodiments, one or more types of adapters or primers may include spacer sequences, adapter sequences for hybridization to adapter-ligated target library nucleic acid sequences, forward amplification primers, reverse amplification primers, sequencing primers, and / or molecular barcode sequences, or any combination thereof. In some embodiments, one primer sequence or adapter sequence may tether to at least one layer of the surface. In some embodiments, at least two, three, four, five, six, seven, eight, nine, ten, or more than ten different primer or adapter sequences may tether to at least one layer of the surface.

[0228] In some embodiments, the tethered adapter and / or primer sequence may be in the range of about 10 to about 100 nucleotides in length. In some embodiments, the tethered adapter and / or primer sequence may be at least 10, at least 20, at least 30, at least 40, at least 50, at least 60, at least 70, at least 80, at least 90, or at least 100 nucleotides in length. In some embodiments, the tethered adapter and / or primer sequence may be up to 100, up to 90, up to 80, up to 70, up to 60, up to 50, up to 40, up to 30, up to 20, or up to 10 nucleotides in length. Any of the lower and upper limits described in this paragraph may be combined to form a range included in the disclosure; for example, in some embodiments, the length of the tethered adapter and / or primer sequence may be in the range of about 20 to about 80 nucleotides. It will be recognized by those skilled in the art that the length of the tethered adapter and / or primer sequence may have any value within this range, for example, about 24 nucleotides.

[0229] In some embodiments, the surface density of the primer (e.g., capture primer) on the surface of the low-binding support of the Disclosure may range from about 100 primer molecules per μm² to about 100,000 primer molecules per μm². In some embodiments, the surface density of the primer on the surface of the low-binding support of the Disclosure may range from about 1,000 primer molecules per μm² to about 1,000,000 primer molecules per μm². In some embodiments, the surface density of the primer may be at least 1,000, at least 10,000, at least 100,000, or at least 1,000,000 molecules per μm². In some embodiments, the surface density of the primer may be up to 1,000,000, up to 100,000, up to 10,000, or up to 1,000 molecules per μm². Any combination of the lower and upper limits described in this paragraph may form the range included in this disclosure, for example, in some embodiments the surface density of the primer may range from about 10,000 molecules per μm² to about 100,000 molecules per μm². It will be recognized by those skilled in the art that the surface density of the primer molecules may have any value within this range, for example, about 455,000 molecules per μm². In some embodiments the surface density of the target library nucleic acid sequence initially hybridized to the adapter sequence or primer sequence on the support surface may be less than or equal to that shown for the surface density of the tethered primer. In some embodiments the surface density of the clonely amplified target library nucleic acid sequence hybridized to the adapter sequence or primer sequence on the support surface may encompass the same range as shown for the surface density of the tethered primer.

[0230] The local densities listed above do not exclude the possibility of density variations across the surface, such that the surface may include regions having, for example, an oligo density of 500,000 / μm2, as well as at least a second region having a substantially different local density.

[0231] Contrast-to-noise ratio (CNR) In some embodiments, the performance of nucleic acid hybridization and / or amplification reactions using the disclosed reaction formulations and low-binding supports can be evaluated using fluorescence imaging techniques, and the contrast-to-noise ratio (CNR) of the image provides an important metric in evaluating amplification specificity and nonspecific binding on the support. CNR is generally defined as CNR = (signal - background) / noise. The background term is generally considered to be the signal measured over the interstitial region surrounding a specific feature (diffraction-limited spot, DLS) in a particular region of interest (ROI). While the signal-to-noise ratio (SNR) is often considered a benchmark for overall signal quality, it can be shown that an improved CNR can offer a significant advantage over SNR as a benchmark for signal quality in applications requiring rapid image capture (e.g., sequencing applications where cycle time must be minimized). Even a moderate improvement in CNR can significantly reduce the imaging time required to achieve accurate identification (and therefore, accurate base calling in the case of sequencing applications) with a high CNR. Improved CNR in imaging data for imaging integration time provides a method for more accurately detecting features such as cloned amplified nucleic acid colonies on the support surface.

[0232] In most ensemble-based sequencing methods, the background term is typically measured as a signal associated with “interstitial” regions. In addition to “interstitial” background (Binter), “intrastitial” background (Bintra) is present within the region occupied by amplified DNA colonies. The combination of these two background signals determines the achievable CNR, which then directly impacts optical instrument requirements, architecture costs, reagent costs, run time, cost / genome, and ultimately, the accuracy and data quality for circular array-based sequencing applications. Binter background signals arise from various sources, some examples of which include autofluorescence from consumable flow cells, nonspecific adsorption of detection molecules resulting in spurious fluorescence signals that can obscure signals from ROIs, and the presence of nonspecific DNA amplification products (e.g., those arising from primer dimers). In many next-generation sequencing (NGS) applications, this background signal in the current field of view (FOV) is averaged and subtracted over time. The signals emanating from individual DNA colonies (e.g., (signal)-B (interstitial) in the FOV) provide distinguishable features that can be classified. In some embodiments, intrastitial background (B (intrastitial)) can contribute to confounding fluorescence signals present in the same ROI, which are not specific to the target of interest, thus making averaging and subtraction much more difficult.

[0233] Nucleic acid amplification on the low-binding coated supports described herein may reduce the interstitial (B) background signal by reducing nonspecific binding, resulting in improvements in specific nucleic acid amplification and a reduction in nonspecific amplification that can affect background signals arising from both interstitial and intrastitial regions. In some embodiments, the disclosed low-binding coated supports, used optionally in combination with the disclosed hybridization and / or amplification reaction formulations, may provide improvements in CNR by 2, 5, 10, 100, 250, 500, or 1000 times compared to those achieved using conventional supports and hybridization, amplification, and / or sequencing protocols. Although described herein in the context of using fluorescence imaging as a readout or detection mode, the same principles apply to the use of the disclosed low-binding coated supports and nucleic acid hybridization and amplification formulations for other detection modes, including both optical and non-optical detection modes.

[0234] Method for sequencing This disclosure provides a method for autofocusing an optical system that can be used to sequence immobilized or unimmobilized template nucleotide acid molecules. In some embodiments, the immobilized template molecule comprises a plurality of nucleic acid template molecules having one copy of the target sequence of interest. In some embodiments, the nucleic acid template molecule having one copy of the target sequence of interest can be generated by performing bridge amplification using a linear library molecule. In some embodiments, the immobilized template molecule comprises a plurality of nucleic acid template molecules (e.g., concatemers) each having two or more tandem copies of the target sequence of interest. In some embodiments, the nucleic acid template molecule comprising concatemer molecules can be generated by performing rolling circle amplification of a cyclic linear library molecule. In some embodiments, the unimmobilized template molecule comprises a cyclic molecule. In some embodiments, the method for sequencing uses a soluble (e.g., unimmobilized) sequencing polymerase or a sequencing polymerase immobilized on a support.

[0235] In some embodiments, the sequencing reaction uses detectably labeled nucleotide analogs. In some embodiments, the sequencing reaction uses a two-step sequencing reaction comprising conjugation to a detectably labeled polyvalent molecule and incorporation of a nucleotide analog. In some embodiments, the sequencing reaction uses unlabeled nucleotide analogs. In some embodiments, the sequencing reaction uses phosphate-chain labeled nucleotides.

[0236] polyvalent molecules This disclosure provides a method for autofocusing an optical system that can be used for sequencing template nucleic acid molecules. In some embodiments, a sample immobilized on a support or otherwise positioned may contain at least one polyvalent molecule. In some embodiments, a sample used to autofocus the optical system may contain at least one polyvalent molecule. In some embodiments, a sequencing method utilizing an optical system for imaging may use at least one polyvalent molecule. In some embodiments, a sequencing method utilizing an optical system for imaging may include autofocusing the optical system before imaging one or more surfaces in the flow cycle of the sequencing run.

[0237] In some embodiments, the polyvalent molecule comprises a plurality of nucleotide arms, which are attached to a core and have one of the following configurations: starburst, helter skelter, or bottlebrush configuration (e.g., Figure 12). The polyvalent molecule comprises (1) a core and (2) a plurality of nucleotide arms, which comprises (i) a core attachment portion, (ii) a spacer containing a PEG portion, (iii) a linker, and (iv) a nucleotide unit, where the core is attached to the plurality of nucleotide arms, the spacer is attached to the linker, and the linker is attached to the nucleotide unit. In some embodiments, the nucleotide unit comprises a base, a sugar, and at least one phosphate group, and the linker is attached to the nucleotide unit via the base. In some embodiments, the linker comprises an aliphatic chain or an oligoethylene glycol chain, and both linker chains have 2 to 6 subunits. In some embodiments, the linker also comprises an aromatic portion. An example of a nucleotide arm is shown in Figure 16. Examples of polyvalent molecules are shown in Figures 12 to 15. An example of a spacer is shown in Figure 17 (top), and examples of linkers are shown in Figure 17 (bottom) and Figure 18. Examples of nucleotides attached to a linker are shown in Figures 19 to 22. An example of a biotinylated nucleotide arm is shown in Figure 23.

[0238] In some embodiments, the polyvalent molecule comprises a core attached to a plurality of nucleotide arms, the plurality of nucleotide arms having the same type of nucleotide unit selected from the group consisting of dATP, dGTP, dCTP, dTTP, and dUTP.

[0239] In some embodiments, a polyvalent molecule comprises a core attached to a plurality of nucleotide arms, each arm comprising a nucleotide unit. A nucleotide unit comprises an aromatic base, a five-carbon sugar (e.g., ribose or deoxyribose), and one or more phosphate groups (e.g., about 1 to 10 phosphate groups). A plurality of polyvalent molecules may include one type of polyvalent molecule having one type of nucleotide unit selected from the group consisting of dATP, dGTP, dCTP, dTTP, and dUTP. A plurality of polyvalent molecules may also be included in a mixture of any combination of two or more types of polyvalent molecules, where each individual polyvalent molecule in the mixture comprises a nucleotide unit selected from the group consisting of dATP, dGTP, dCTP, dTTP, and / or dUTP.

[0240] In some embodiments, the nucleotide unit comprises a chain of one, two, or three phosphorus atoms, which is typically attached to the 5' carbon of the sugar moiety via an ester bond or a phosphoramide bond. In some embodiments, at least one nucleotide unit is a nucleotide analog having a phosphorus chain, in which the phosphorus atoms are bonded together with intervening O, S, NH, methylene, or ethylene. In some embodiments, the phosphorus atoms in the chain comprise a substituted side chain group comprising O, S, or BH3. In some embodiments, the chain comprises a phosphate group substituted with analogs comprising phosphoramidate, phosphorothioate, phosphordithioate, and O-methylphosphoramidite groups.

[0241] In some embodiments, the polyvalent molecule comprises a core attached to multiple nucleotide arms, each nucleotide arm comprising a nucleotide unit, the nucleotide unit being a nucleotide analog having a chain termination portion (e.g., a blocking portion) at the 2', 3', or both 2' and 3' sugar positions. In some embodiments, the nucleotide unit contains the chain termination portion (e.g., a blocking portion) at the 2', 3', or both 2' and 3' sugar positions. In some embodiments, the chain termination portion can inhibit polymerase-catalyzed incorporation of subsequent nucleotide units or free nucleotides in the nascent chain during primer extension reactions. In some embodiments, the chain termination portion is attached to the 3' sugar position, where the sugar comprises a ribose or deoxyribose sugar portion. In some embodiments, the chain termination portion is removable / cleavable from the 3' sugar position to produce a nucleotide having a 3'OH sugar group that can be extended by a subsequent nucleotide in a polymerase-catalyzed nucleotide incorporation reaction. In some embodiments, the chain termination group comprises an alkyl group, alkenyl group, alkynyl group, allyl group, aryl group, benzyl group, azide group, amine group, amide group, keto group, isocyanate group, phosphate group, thio group, disulfide group, carbonate group, urea group, or silyl group. In some embodiments, the chain termination group can be cleaved / removed from the nucleotide unit, for example, by reacting the chain termination group with a chemical agent, pH change, light, or heat. In some embodiments, the alkyl, alkenyl, alkynyl, and allyl chain termination groups can be cleaved using tetrakis(triphenylphosphine)palladium(0)(Pd(PPh3)4) having piperidine, or 2,3-dichloro-5,6-dicyano-1,4-benzo-quinone (DDQ). In some embodiments, the aryl and benzyl chain termination groups can be cleaved using H2Pd / C. In some embodiments, the chain termination portion, which is an amine, amide, keto, isocyanate, phosphate, thio, or disulfide, can be cleaved using a phosphine or a thiol group containing beta-mercaptoethanol or dithiotitol (DTT).In some embodiments, the chain-ending carbonate can be cleaved using potassium carbonate (K2CO3) in MeOH, triethylamine in pyridine, or Zn in acetic acid (AcOH). In some embodiments, the chain-ending urea and silyl can be cleaved using tetrabutylammonium fluoride, pyridine-HF, ammonium fluoride, or triethylamine trihydrofluoride.

[0242] In some embodiments, the nucleotide unit contains a chain termination moiety (e.g., a blocking moiety) at the 2', 3', or both 2' and 3' positions. In some embodiments, the chain termination moiety contains an azide, azido, or azidomethyl group. In some embodiments, the chain termination moiety contains a 3'-O-azide or 3'-O-azidomethyl group. In some embodiments, the azide, azido, and azidomethyl groups that constitute the chain termination moiety are cleavable / removable using a phosphine compound. In some embodiments, the phosphine compound contains a derivatized trialkylphosphine moiety or a derivatized triarylphosphine moiety. In some embodiments, the phosphine compound contains tris(2-carboxyethyl)phosphine (TCEP), bis-sulfotriphenylphosphine (BS-TPP), or tris(hydroxypropyl)phosphine (THPP). In some embodiments, the cleavage agent contains 4-dimethylaminopyridine (4-DMAP).

[0243] In some embodiments, a nucleotide unit comprising a chain termination portion selected from the group consisting of 3'-deoxynucleotide, 2',3'-dideoxynucleotide, 3'-methyl, 3'-azide, 3'-azidomethyl, 3'-O-azidoalkyl, 3'-O-ethynyl, 3'-O-aminoalkyl, 3'-O-fluoroalkyl, 3'-fluoromethyl, 3'-difluoromethyl, 3'-trifluoromethyl, 3'-sulfonyl, 3'-malonyl, 3'-amino, 3'-O-amino, 3'-sulfhydral, 3'-aminomethyl, 3'-ethyl, 3'-butyl, 3'-tertbutyl, 3'-fluorenylmethyloxycarbonyl, 3'tert-butyloxycarbonyl, 3'-O-alkylhydroxylamino group, 3'-phosphorothioate, and 3'-O-benzyl, or derivatives thereof.

[0244] In some embodiments, the polyvalent molecule comprises a core attached to a plurality of nucleotide arms, the nucleotide arms comprising spacers, linkers, and nucleotide units, and the core, linkers, and / or nucleotide units are labeled with a detectable reporter moiety. In some embodiments, the detectable reporter moiety comprises a fluorophore. In some embodiments, a specific detectable reporter moiety (e.g., a fluorophore) bound to the polyvalent molecule can correspond to a base of a nucleotide unit (e.g., dATP, dGTP, dCTP, dTTP, or dUTP) to enable the detection and identification of nucleotide bases.

[0245] In some embodiments, at least one nucleotide arm of the polyvalent molecule has a nucleotide unit attached to a detectable reporter moiety. In some embodiments, the detectable reporter moiety is bound to a nucleotide base. In some embodiments, the detectable reporter moiety includes a fluorophore. In some embodiments, a specific detectable reporter moiety (e.g., a fluorophore) bound to the polyvalent molecule can correspond to a base of a nucleotide unit (e.g., dATP, dGTP, dCTP, dTTP, or dUTP) to enable the detection and identification of the nucleotide base.

[0246] In some embodiments, the core of the polyvalent molecule comprises an avidin-like or streptavidin-like moiety, and the core-attached moiety comprises biotin. In some embodiments, the core comprises a streptavidin-type or avidin-type moiety comprising an avidin protein, as well as any derivatives, analogs, and other non-natural forms of avidin that can bind to at least one biotin moiety. Other forms of the avidin moiety include natural and recombinant avidin and streptavidin, as well as derivatized molecules, such as unglycosylated avidin and cleaved streptavidin. For example, the avidin portion may include deglycosylated forms of avidin, bacterial streptavidin produced by Streptomyces (e.g., Streptomyces avidinii), and derivatized forms, such as N-acylavidins, e.g., N-acetyl, N-phthalyl, and N-succinylavidin, as well as commercially available products such as EXTRAVIDIN, CAPTAVIDIN, NEUTRAVIDIN, and NEUTRALITE AVIDIN.

[0247] In some embodiments, any of the methods for sequencing nucleic acid molecules described herein may include forming a binding complex, the binding complex comprising (i) a polymerase, a primer and a double-stranded nucleic acid template molecule, and a nucleotide, or the binding complex comprising (ii) a polymerase, a primer and a double-stranded nucleic acid template molecule, and a nucleotide unit of a polyvalent molecule. In some embodiments, the binding complex has a duration of about 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, or more than 1 second. The binding complex has a duration of approximately 0.1–0.25 seconds, or approximately 0.25–0.5 seconds, or approximately 0.5–0.75 seconds, or approximately 0.75–1 second, or approximately 1–2 seconds, or approximately 2–3 seconds, or approximately 3–4 seconds, or more than approximately 4–5 seconds, and / or the method is carried out or may be carried out at a temperature of 15°C or higher, 20°C or higher, 25°C or higher, 35°C or higher, 37°C or higher, 42°C or higher, 55°C or higher, 60°C or higher, or 72°C or higher, or 80°C or higher, or within the range defined by any of the foregoing. The binding complex (e.g., ternary complex) remains stable until it is subjected to conditions that cause dissociation of the interaction between the polymerase, template molecule, primer, and / or nucleotide units or any of the nucleotides. For example, dissociation conditions include contacting the binding complex with one of a washing agent, EDTA, and / or water, or any combination thereof. In some embodiments, the Disclosure provides a method wherein the binding complex is deposited on, attached to, or hybridized to a surface exhibiting a contrast-to-noise ratio greater than 20 in detection operation. In some embodiments, the Disclosure provides a method wherein the contact is performed under conditions that stabilize the binding complex when a nucleotide or nucleotide unit is complementary to the next base of the template nucleic acid, and destabilize the binding complex when a nucleotide or nucleotide unit is not complementary to the next base of the template nucleic acid.

[0248] Method for sequencing using phosphate-labeled nucleotides In some embodiments, the methods described herein can be used for autofocusing an optical system that can be used for sequencing using an immobilized sequencing polymerase that binds an unimmobilized template molecule. The disclosure provides a method for sequencing using an immobilized sequencing polymerase that binds an unimmobilized template molecule, wherein the sequencing reaction is carried out by a phosphate-labeled nucleotide. In some embodiments, the sequencing method comprises: operation (a): providing a support having a plurality of sequencing polymerases immobilized on the support. In some embodiments, the sequencing polymerase includes a processable DNA polymerase. In some embodiments, the sequencing polymerase includes a wild-type or mutant DNA polymerase, for example, Phi29 DNA polymerase. In some embodiments, the support comprises a plurality of separate compartments, the sequencing polymerases being immobilized at the bottom of the compartments. In some embodiments, the separate compartments include a silica bottom through which light can pass. In some embodiments, the separate compartments include a silica bottom composed of a nanophotonic constraint structure including holes in a metal cladding film (e.g., an aluminum cladding film). In some embodiments, the holes in the metal cladding have small openings, for example, about 70 nm. In some embodiments, the height of the nanophotonic confinement structure is about 100 nm. In some embodiments, the nanophotonic confinement structure includes a zero-mode waveguide (ZMW). In some embodiments, the nanophotonic confinement structure contains a liquid.

[0249] In some embodiments, the sequencing method further comprises (b) operation: contacting multiple immobilized sequencing polymerases with multiple single-stranded cyclic nucleic acid template molecules and multiple oligonucleotide sequencing primers under conditions suitable for each immobilized sequencing polymerase to bind to the single-stranded cyclic template molecule and for each sequencing primer to hybridize to each single-stranded cyclic template molecule, thereby generating multiple polymerase / template / primer complexes. In some embodiments, each sequencing primer hybridizes to a universal sequencing primer binding site on the single-stranded cyclic template molecule.

[0250] In some embodiments, the sequencing method comprises (c) contacting multiple polymerase / template / primer complexes with multiple phosphate-labeled nucleotides, each containing an aromatic base, a five-carbon sugar (e.g., ribose or deoxyribose), and a phosphate chain containing 3 to 20 phosphate groups, wherein the terminal phosphate groups are bound to a detectable reporter moiety (e.g., a fluorophore). The first, second, and third phosphate groups may be referred to as alpha, beta, and gamma phosphate groups. In some embodiments, the specific detectable reporter moiety attached to the terminal phosphate groups corresponds to a nucleotide base (e.g., dATP, dGTP, dCTP, dTTP, or dUTP) to enable the detection and identification of nucleobases. In some embodiments, multiple polymerase / template / primer complexes are contacted with multiple phosphate-labeled nucleotides under conditions suitable for polymerase-catalyzed nucleotide incorporation. In some embodiments, sequencing polymerases can bind complementary phosphate-labeled nucleotides, incorporating the complementary nucleotide opposite the nucleotide in the template molecule. In some embodiments, the polymerase-catalyzed nucleotide incorporation reaction involves cleavage between the alpha-phosphate and beta-phosphate groups, thereby releasing the polyphosphate chain bound to the fluorophore.

[0251] In some embodiments, the sequencing method further includes operation (d): detecting a fluorescent signal emitted by a phosphate-labeled nucleotide that is bound by a sequencing polymerase and incorporated into the terminals of a sequencing primer. In some embodiments, operation (d) further includes identifying a phosphate-labeled nucleotide that is bound by a sequencing polymerase and incorporated into the terminals of a sequencing primer.

[0252] In some embodiments, the sequencing method further comprises the action (d): repeating the action (c) to (d) at least once. In some embodiments, the sequencing method using phosphate-labeled nucleotides can be carried out in accordance with the methods described in U.S. Patent No. 7,170,050, No. 7,302,146, and / or No. 7,405,281.

[0253] The titles provided herein are not limitations on any particular aspect of this disclosure, and these aspects can be understood by referring to this entire specification.

[0254] Unless otherwise defined, all technical and scientific terms used herein have meanings that are generally understood by those skilled in the art. Generally, the terms relating to molecular biology, nucleic acid chemistry, protein chemistry, genetics, microbiology, gene transcellular cell production, and hybridization techniques described herein are well known and commonly used in the art. The techniques and procedures described herein are generally carried out in accordance with conventional methods well known in the art and are carried out as described in the various general and more specific references cited and discussed throughout this specification. See, for example, Sambrook et al., Molecular Cloning: A Laboratory Manual (Third ed., Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY2000). Also see Ausubel et al., Current Protocols in Molecular Biology, Greene Publishing Associates (1992). The nomenclature used in relation to the experimental procedures and techniques described herein, as well as the experimental procedures and techniques themselves, are well known and commonly used in the art.

[0255] Unless otherwise specified herein by context, singular terms include plural forms, and plural terms include singular forms. Unless explicitly and explicitly limited to a single reference, the use of the singular forms "a," "an," and "the," as well as the singular form of any of these words, includes plural references.

[0256] The use of alternative terms (e.g., "or") is understood to mean one or both of the alternative forms, or any combination thereof.

[0257] As used herein, the term “and / or” should be understood to mean a specific disclosure that each of a particular feature or component may or may not have the other. For example, when used herein in phrases such as “A and / or B,” the term “and / or” includes “A and B,” “A or B,” “A” (A only), and “B” (B only). Similarly, when used in phrases such as “A, B, and / or C,” the term “and / or” includes each of the following embodiments: “A, B, and C”; “A, B, or C”; “A or C”; “A or B”; “B or C”; “A and B”; “B and C”; “A and C”; “A” (A only); “B” (B only); and “C” (C only).

[0258] As used herein and in the appended claims, the terms “comprising,” “including,” “having,” and “containing,” and their grammatical variations as used herein, are intended to be non-limiting so as not to exclude any other items that one or more items in a list may replace or add to the listed items. Wherever an aspect is described herein in the term “comprising,” it is understood that other similar aspects described in the terms “consisting of” and / or “essentially consisting of” are also provided.

[0259] As used herein, the terms “about,” “approximately,” and “substantially” refer to a value or composition that falls within an acceptable error range for a particular value or composition, as determined by those skilled in the art, the acceptable error range depending in part to how the value or composition is measured or determined, i.e., the limitations of the measuring system. For example, “about,” “approximately,” or “substantially” may mean within one or more standard deviations per practice in the art. Alternatively, “about,” or “approximately,” depending on the limitations of the measuring system, may mean a range of up to 10% (i.e., ±10%) or more. For example, about 5 mg may include any number between 4.5 mg and 5.5 mg. Furthermore, particularly with respect to biological systems or processes, the term may mean a value of up to one order of magnitude or up to five times the value. When a particular value or composition is provided in this disclosure, unless otherwise stated, the meaning of “about,” “approximately,” and “substantially” should be understood to mean that it falls within an acceptable error range for that particular value or composition. Also, where a range and / or subrange of a value is provided, the range and / or subrange may include the endpoint of the range and / or subrange.

[0260] As used herein, the term "polony" refers to the ability to clonally amplify a nucleic acid library molecule in solution or on a support to produce an amplicon that can function as a template molecule for sequencing. In some embodiments, a linear library molecule can be cyclized to produce a cyclized library molecule, and the cyclized library molecule can be clonally amplified in solution or on a support to produce a concatemer. In some embodiments, the concatemer can function as a nucleic acid template molecule that can be sequenced. The concatemer is sometimes referred to as a pollony. In some embodiments, the pollony contains a chain of nucleotides.

[0261] References in this specification to “one embodiment,” “one embodiment,” “exemplary embodiment,” “several embodiments,” or similar phrases indicate that the embodiments described may include certain features, structures, or characteristics, but not all embodiments may necessarily include those features, structures, or characteristics. Furthermore, such phrases do not necessarily refer to the same embodiment. Also, where certain features, structures, or characteristics are described in relation to an embodiment, incorporating such features, structures, or characteristics into other embodiments, whether or not they are expressly mentioned or described herein, would be within the knowledge of those skilled in the art.

[0262] It should be understood that, for the purpose of interpreting the claims, the section describing embodiments for carrying out the invention is intended to be used, and not any other section. Other sections may describe one or more exemplary embodiments, as contemplated by the inventor(s), but these are not exhaustive and are therefore not intended to limit in any way the scope of this disclosure or the appended claims.

[0263] While this disclosure describes exemplary embodiments for exemplary fields and applications, it should be understood that this disclosure is not limited thereto. Other embodiments and modifications thereof are possible and are included within the scope and spirit of this disclosure. For example, without limiting the generality of this paragraph, embodiments are not limited to the software, hardware, firmware, and / or entities illustrated in the drawings and / or described herein. Furthermore, embodiments (whether expressly described herein or not) have significant utility for fields and applications beyond the embodiments described herein.

[0264] In this specification, embodiments are described using functional building blocks that illustrate the implementation of specific functions and their relationships. The boundaries of these functional building blocks are arbitrarily defined in this specification for the sake of clarity. Alternative boundaries may be defined, as long as the specified functions and relationships (or their equivalents) are adequately performed. Furthermore, alternative embodiments may perform functional blocks, steps, operations, methods, etc., using a different ordering than that described herein. [Examples]

[0265] These embodiments are provided for illustrative purposes only and do not limit the scope of the claims provided herein. Non-limiting examples of sequencing methods and systems that can be used in conjunction with this disclosure can be found in PCT applications PCT / US2023 / 081406 and PCT / US2020 / 034409, each of which is incorporated herein by reference in whole.

[0266] Example 1 - Expected example using an optical system The objective of this embodiment is to demonstrate nucleic acid sequencing using a focused optical system as described herein. Such optical systems and focusing methods offer further advantages and utility for nucleic acid sequencing applications due to reduced optical components, fewer moving parts, and higher throughput.

[0267] In this embodiment, a flow cell is inserted into an optical system. The flow cell can be tilted out of the focal plane of the optical system and the image of the flow cell captured by the image detector of the autofocus element of the optical system. The image is then processed using a computer processor operably coupled to the detector, and the amount of focus shift in the flow cell is determined using the distance from the center of the image of the focused portion of the image. The optical system then untilts the flow cell and moves it by the amount of focus shift to place the flow cell within the focal plane of the optical system.

[0268] The sample is delivered to the hydrophobic pad of the flow cell by a liquid processing system. The sample is drawn into the inner channel of the flow cell by a vacuum pump. The nucleic acid sequence present in the sample reacts with primers attached to the wall of the inner channel of the flow cell. The nucleic acid sequence of the sample is then amplified and washed. After amplification and washing, a solution containing (1) a DAPI-modified nucleotide conjugate complementary to the A nucleotide, (2) a FITC-modified nucleotide conjugate complementary to the G nucleotide, (3) a TRITC-modified nucleotide conjugate complementary to the C nucleotide, and (4) a fourth nucleotide conjugate modified by both DAPI and TRITC and complementary to the T nucleotide is introduced into flow cell 4521 and reacted with the primed nucleic acid sequence. The sample in flow cell 4521 is then irradiated with a 0.1-second UV-blue light pulse via the first LED light source 4522, thereby exciting the DAPI fluorophore. Synchronized with a UV-blue light pulse, the imaging sensor acquires a first image capturing the emission of light emitted by an arbitrary DAPI-modified nucleotide conjugate specifically bound to the sample. Since the UV-blue excitation light emitted by the first light source is negligible beyond 405 nm, only the light emitted by DAPI fluorescence emission is collected by the imaging sensor. This light is blocked by a triband bandpass filter (Edmund Scientific stock #87-236) with multiband center wavelengths of 432 nm, 517 nm, and 615 nm. The bandwidths of this filter are 36 at 432 nm, 23 at 517 nm, and 61 at 615 nm. Next, the sample is pulsed with green light for 0.1 seconds via a second LED light source 4523 capable of exciting FITC fluorophores. Synchronized with the green light pulse, a second image is acquired capturing the emission of light emitted by an FITC-modified nucleotide conjugate specifically bound to the sample. Next, the sample can be pulsed with red light for 0.1 seconds via a third LED light source 4524, thereby exciting the TRITC fluorophore.A third image is acquired that captures the light emitted by an arbitrary TRITC-modified nucleotide conjugate specifically bound to the sample, synchronized with a red light pulse. In this embodiment, an excitation filter is used for each LED light source to minimize crosstalk in the fluorescence channel or bleed-through of excitation light into the emission bandpass (notch) of the triband bandpass filter.

[0269] In this example, the base calling process is as follows. Analyze the first image of the cycle for regions of interest (ROIs) that exhibit strong fluorescence signals. The ROIs that exhibit strong fluorescence signals in the first image indicate nucleic acid amplicons that have either A or T at the open position before exposure to nucleotide conjugates. This is because the capture of the first image was synchronized with sample illumination by UV-blue light, thereby exciting DAPI. Since the nucleotide conjugate complementary to A was labeled with DAPI and the nucleotide conjugate complementary to T was labeled with both DAPI and TRITC, the ROIs in the first image that exhibit strong fluorescence indicate either A or T. Next, analyze the second image of the cycle for the strong fluorescence signal of the ROI. Since the nucleotide conjugate complementary to G was labeled with FITC and the capture of the second image was synchronized with a green pulse that enables excitation of FITC, the ROI in the second image that exhibits a strong fluorescence signal indicates G. Next, analyze the third image of the cycle for the strong fluorescence signal of the ROI. These ROIs indicate nucleic acid amplicons that have either C or T at the open position before exposure to nucleotide conjugates. This is to irradiate the sample with red light in synchronization with the capture of the third image, thereby exciting TRITC. The nucleotide conjugate complementary to C was labeled with TRITC and the nucleotide conjugate complementary to T was labeled with both DAPI and TRITC. ROIs that have strong fluorescence signals observed in both the first and third images indicate that there is a T nucleotide at the open position before exposure to nucleotide conjugates. Subsequently, the identification of ROIs containing T enables the identification of ROIs containing A and C. The sequencing and imaging cycles are repeated until the entire nucleic acid sequence is identified.

[0270] Anticipated Example 2 - Using a Super-Resolution Improvement Optical System The objective of this embodiment is to demonstrate nucleic acid sequencing using an ultra-high-resolution optical system as described herein. Such a system offers further advantages and utility for nucleic acid sequencing applications by providing ultra-high-resolution readout while reducing optical components, fewer moving parts, and higher throughput.

[0271] In this embodiment, a flow cell is inserted into an optical system. The flow cell can be tilted out of the focal plane of the optical system and the image of the flow cell captured by the image detector of the autofocus element of the optical system. The image is then processed using a computer processor operably coupled to the detector, and the amount of focus shift in the flow cell is determined using the distance from the center of the image of the focused portion of the image. The optical system then untilts the flow cell and moves it by the amount of focus shift to place the flow cell within the focal plane of the optical system.

[0272] The sample is delivered to a capillary flow cell. Sample regions containing nucleic acid sequences react with primers attached to the inner channel walls of the capillary flow cell. The nucleic acid sequences of the sample are then amplified and washed. After amplification and washing, a solution containing (1) a DAPI-modified nucleotide conjugate complementary to the A nucleotide, (2) a FITC-modified nucleotide conjugate complementary to the G nucleotide, (3) a TRITC-modified nucleotide conjugate complementary to the C nucleotide, and (4) a fourth nucleotide conjugate complementary to the T nucleotide, modified with both DAPI and TRITC, is introduced into the capillary flow cell and reacted with the primed nucleic acid sequences. The sample in the capillary flow cell is then irradiated with a 0.1-second UV-blue light pulse via a first LED light source, thereby exciting the DAPI fluorophores. Synchronized with the UV-blue light pulse, the imaging sensor acquires a first image capturing the light emission from any DAPI-modified nucleotide conjugate specifically bound to the sample. The UV-blue excitation light emitted by the first light source is negligible beyond 405 nm, so only the light emitted by DAPI fluorescence emission is collected by the imaging sensor. This light is blocked by a triband stop filter. Next, the sample is pulsed with green light for 0.1 seconds through a second LED light source capable of exciting FITC fluorophores. Synchronized with the green light pulse, a second image is acquired capturing the emission of light from FITC-modified nucleotide conjugates specifically bound to the sample. The sample can be pulsed with red light for 0.1 seconds through a third LED light source, thereby exciting TRITC fluorophores. Synchronized with the red light pulse, a third image is acquired capturing the light emitted from any TRITC-modified nucleotide conjugate specifically bound to the sample. In this embodiment, excitation filters are used for each LED light source to minimize fluorescence channel crosstalk, or bleed-through of excitation light that cannot be stopped by the notch, or band stopping of the triband stop filter.

[0273] To image the entire inner surface of the capillary flow cell 5201, wedge blocks can be included in each optical subsystem. When the top wedge piece is aligned with the bottom wedge piece, the optical subsystem acquires an image of the distal side of the inner surface of the capillary flow cell. When the top wedge piece is de-aligned, increasing the optical path length, the optical subsystem acquires an image of the anterior inner surface of the capillary flow cell.

[0274] The optical system in this embodiment is capable of super-resolution imaging, and at least one sample site includes clone-amplified sample nucleic acid molecules immobilized on multiple attached oligonucleotide molecules, the multiple immobilized clone-amplified sample nucleic acid molecules located at a distance of less than λ / (2*NA), where λ is the central wavelength of the excitation energy source and NA is the numerical aperture of the imaging system. Stochastic photoswitching chemistry is then simultaneously applied to the clone-amplified sample nucleic acid molecules so that the multiple clone-amplified sample nucleic acid molecules fluoresce in up to four different color on and off events by stochastic photoswitching, the on and off events are detected in real time in each color channel when on and off events occur for the multiple clone-amplified sample nucleic acid molecules, and the identification of the nucleotides of the clone-amplified sample nucleic acid molecules is determined.

[0275] In this embodiment, the base calling process is as follows: The first image of the cycle is analyzed for a region of interest (ROI) showing a strong fluorescence signal. The ROI showing a strong fluorescence signal in the first image indicates a nucleic acid amplicon having either A or T in the open position before exposure to the nucleotide conjugate for the following reasons: The capture of the first image is synchronized with sample illumination with UV-blue light, thereby exciting DAPI. Since the nucleotide conjugate complementary to A is labeled with DAPI and the nucleotide conjugate complementary to T is labeled with both DAPI and TRITC, the ROI in the first image showing a strong fluorescence indicates either A or T. Next, the second image of the cycle is analyzed for the strong fluorescence signal of the ROI. Since the nucleotide conjugate complementary to G is labeled with FITC and the capture of the second image is synchronized with a green pulse that allows excitation of FTIC, the ROI in the second image showing a strong fluorescence signal indicates G. Next, the third image of the cycle is analyzed for the strong fluorescence signal of the ROI. These ROIs indicate nucleic acid amplicons where either C or T is present in the open position before exposure to the nucleotide conjugate. This is because the sample is irradiated with red light in sync with the capture of the third image, thereby exciting TRITC. Nucleotide conjugates complementary to C are labeled with TRITC, and nucleotide conjugates complementary to T are labeled with both DAPI and TRITC. ROIs with a strong fluorescence signal observed in both the first and third images indicate the presence of the T nucleotide in the open position before exposure to the nucleotide conjugate. Subsequently, the identification of ROIs containing T allows for the identification of ROIs containing A and C. The sequencing and imaging cycle is repeated until the entire nucleic acid sequence is identified.

[0276] Numbered embodiments of this disclosure 1. A method for focusing an optical system, (a) Receiving an image of the substrate of the optical system, wherein a portion of the image but less than all of it is in focus, and the focused portion of the image is offset from the center of the image; (b) Using at least the portion of the focused image and the distance from the center of the image to determine the amount of focus shift in the image, (c) A method comprising adjusting the parameters of the optical system in order to correct the focus shift. 2. The method according to any of the prior embodiments, wherein the image is an image of a flow cell and the substrate is a flow cell. 3. The method according to any of the prior embodiments, wherein the adjustment in (c) is an automatic adjustment. 4. The method according to any of the prior embodiments, wherein the image is received from an autofocus element. 5. The method according to any of the prior embodiments, wherein the determination is made in a maximum of about 600 milliseconds (ms). 6. The method according to any of the prior embodiments, wherein the determination is made within a maximum of approximately 100 ms. The method of any of the prior embodiments, further comprising imaging a substrate using a light source and a detector to generate the image, prior to 7.(a). 8. The method of any of the prior embodiments, wherein the determination is performed using the image and without using additional images. 9. The method according to any of the prior embodiments, wherein the image includes a length or width within the range of about 0.1 millimeters (mm) to about 5 centimeters (cm). 10. The method according to any of the prior embodiments, wherein the image includes a length or width in the range of approximately 0.5 mm to approximately 9 mm. 11. The method according to any of the prior embodiments, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 400 nanometers (nm). 12. The method according to any of the prior embodiments, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 100 nanometers (nm). 13. The method according to any of the prior embodiments, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 50 nanometers (nm). 14. The method according to any of the prior embodiments, wherein the center of the focused region is determined using an image processing algorithm. 15. The method according to any of the prior embodiments, wherein the image processing algorithm comprises separating the image into a predetermined number of regions and determining the center of the focused region by using the sum or average intensity of each region to identify the location of the focused region. 16. The method according to any of the prior embodiments, wherein image intensity or spatial frequency information of the location in the focused region is used to locate the center of the focused region. 17. The method according to any of the prior embodiments, wherein information regarding a geometric pattern in the image determines the image processing algorithm. 18. A method for focusing an optical system, (a) Using a detector to image a substrate tilted at a certain angle, wherein the image of the substrate includes both in-focus and out-of-focus portions. (b) Using a processor to determine the focus shift of the optical system, at least partially based on the tilt angle and the distance of the focused portion from the center of the image, (c) Adjusting the substrate in order to eliminate the inclination angle, (d) A method comprising adjusting the substrate by the misfocus and thereby focusing the optical system. The method of any of the prior embodiments, further comprising using a vector from the center of the image of the focused portion of 19.(b) to determine the prior portion. 20. The method according to any of the prior embodiments, further comprising a motor coupled to the substrate configured to impart the inclination angle. 21. The method according to any of the prior embodiments, wherein the detector is part of an autofocus element. 22. The method according to any of the prior embodiments, wherein the optical system further comprises an additional detector configured to image the substrate. The method according to any of the prior embodiments, further comprising tilting the substrate to the inclination angle before 23.(a). The method according to any of the prior embodiments, further comprising releasing the tilt of the substrate following 24.(d). 25. The method according to any of the prior embodiments, wherein the tilting is the tilting of a plane perpendicular to the optical axis of the optical system. 26. The method according to any of the prior embodiments, wherein the inclination angle is approximately 0.01 to approximately 89 degrees. 27. The method according to any of the prior embodiments, wherein the inclination angle is approximately 0.05 to approximately 15 degrees. 28. The method according to any of the prior embodiments, wherein the angular resolution of the inclination angle is about 0.001 degrees to about 0.2 degrees. 29. The method according to any of the prior embodiments, wherein the angular resolution of the inclination angle is about 0.01 degrees to about 0.1 degrees. 30. The method according to any of the prior embodiments, wherein the angular resolution of the inclination angle is about 0.01 degrees to about 0.08 degrees. 31. The method of any of the prior embodiments, wherein the determination is performed using the image and without using additional images. 32. The base material is (a) One or more surfaces and (b) at least one hydrophilic polymer coating layer, (c) A plurality of oligonucleotide molecules attached to the at least one hydrophilic polymer coating layer, (d) The method of any of the prior embodiments, comprising a flow cell comprising at least one distinct region of one or more surfaces, which includes a plurality of clone-amplified nucleic acid molecules immobilized on the plurality of attached oligonucleotide molecules, wherein the plurality of immobilized clone-amplified sample nucleic acid molecules are located at a distance of less than λ / (2*NA), where λ is the central wavelength of the excitation energy source and NA is the numerical aperture of the optical system. 33. The method according to any of the preceding embodiments, wherein the substrate comprises a bead flow cell. 34. The method according to any of the preceding embodiments, wherein the bead flow cell comprises a surface comprising fluorescent beads chemically immobilized on the substrate. 35. The method according to any of the preceding embodiments, wherein the fluorescent beads are randomly distributed on the surface. 36. The method according to any of the preceding embodiments, wherein the fluorescent beads comprise at least about four types of beads configured to emit different colors in response to excitation from a laser. 37. The method according to any of the preceding embodiments, wherein the error between the distance from the focal plane and the true distance from the focal plane is at most about 400 nanometers (nm). 38. The method according to any of the preceding embodiments, wherein the error between the distance from the focal plane and the true distance from the focal plane is at most about 100 nanometers (nm). 39. The method according to any of the preceding embodiments, wherein the error between the distance from the focal plane and the true distance from the focal plane is at most about 50 nanometers (nm). 40. The method according to any of the preceding embodiments, wherein (d) occurs before the optical system images the nucleic acid molecules immobilized on the substrate in a first flow cycle. 41. The method according to any of the preceding embodiments, further comprising repeating (a)-(d) to refocus the optical system for a second flow cycle. 42. A method of focusing an optical system, comprising: (a) imaging a substrate using a detector tilted at an angle, wherein the image of the substrate comprises a focused portion and an unfocused portion; (b) using a processor to determine a focus shift of the optical system based at least in part on the tilt angle and the distance from the center of the image of the focused portion; and (c) adjusting the substrate based on the focus shift, thereby focusing the optical system. 43. The method according to any of the prior embodiments, further comprising adjusting the substrate by a focus shift, thereby bringing the substrate into focus. The method of any of the prior embodiments, further comprising tilting the detector to the tilt angle before 44.(a). The method according to any of the prior embodiments, further comprising releasing the tilt of the detector following 45.(c). 46. ​​The method according to any of the prior embodiments, wherein the tilting is the tilting of a plane perpendicular to the optical axis of the optical system. 47. The method according to any of the prior embodiments, wherein the inclination angle is approximately 0.01 to approximately 89 degrees. 48. The method according to any of the prior embodiments, wherein the inclination angle is approximately 0.05 to approximately 15 degrees. 49. The method of any of the prior embodiments, wherein the determination is performed using the image and without using additional images. 50. The method according to any of the prior embodiments, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 400 nanometers (nm). 51. The method according to any of the prior embodiments, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 100 nanometers (nm). 52. The method according to any of the prior embodiments, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 50 nanometers (nm). 53. The method according to any of the prior embodiments, further comprising calibrating the pivot point of the optical system. 54. The method according to any of the prior embodiments, wherein the calibration of the pivot point includes releasing the tilt of the substrate, the detector, or the autofocus sensor. 55. An optical system, (a) Substrate and (b) an autofocus module configured to capture an image of the substrate, including in-focus and out-of-focus portions, wherein the substrate or the autofocus module is tilted at a certain angle, (c) An optical system comprising a processor configured to determine the focus misalignment of the substrate to the focal plane of the optical system, using at least the distance from the focused portion to the center of the image and the tilt angle. 56. An optical system according to any of the prior embodiments, wherein the substrate is inclined at a certain angle. 57. An optical system according to any of the prior embodiments, wherein the processor uses the tilt angle when determining the focus shift. 58. The optical system according to any of the prior embodiments, wherein the autofocus module is tilted at a certain angle. 59. An optical system according to any of the prior embodiments, wherein the processor uses the tilt angle when determining the focus shift. 60. The optical system according to any of the prior embodiments, wherein the autofocus module comprises an illumination source and a detector. 61. The optical system according to any of the prior embodiments, wherein the illumination source is configured to irradiate at least a portion of the substrate, and the detector is configured to image the portion of the substrate. 62. An optical system according to any of the prior embodiments, wherein the inclination angle is approximately 0.01 to approximately 89 degrees. 63. An optical system according to any of the prior embodiments, wherein the inclination angle is approximately 0.05 to approximately 15 degrees. 64. An optical system according to any of the prior embodiments, wherein the determination is performed using the image and without using additional images. 65. An optical system according to any of the prior embodiments, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 400 nanometers (nm). 66. An optical system according to any of the prior embodiments, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 100 nanometers (nm). 67. An optical system according to any of the prior embodiments, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 50 nanometers (nm). 68. The optical system according to any of the prior embodiments, wherein the autofocus module comprises one or more of the following: an autofocus illumination source, an autofocus sensor, an autofocus tube lens, a dichroic filter, or a beam splitter. 69. The optical system according to any of the prior embodiments, wherein the optical system comprises one or more image sensors. 70. An optical system according to any of the prior embodiments, wherein one or more image sensors are used for both imaging the substrate and focusing the optical system. 71. An optical system according to any of the prior embodiments, wherein the image is acquired by the autofocus module, and the autofocus module is configured solely for autofocusing, and not for imaging the substrate after autofocusing is complete. 72. A method for autofocusing an optical system, The process involves tilting the sample stage of an optical system by a certain angle, with the sample fixed on the sample stage. The optical system's image sensor obtains an image of the sample on a tilted sample stage, The processor determines the z-shift based on the tilt angle and the xy-plane shift from the center of the image, wherein the xy-plane shift is determined based on the focused region of the image. A method comprising moving a sample stage by a determined z-shift relative to the focal plane of the objective lens of an optical system, thereby focusing on the sample. 73. A method for autofocusing an optical system, The optical system's image sensor is tilted by an angle, Obtaining an image of a sample by an inclined image sensor of an optical system, wherein the sample is fixed on a sample stage. The processor determines the z-shift based on the tilt angle and the xy-plane shift from the center of the image, wherein the xy-plane shift is determined based on the focused region of the image. A method comprising moving a sample stage by a determined z-shift relative to the focal plane of the objective lens of an optical system, thereby focusing on the sample. 74. A method for autofocusing an optical system, The process involves tilting the sample stage of an optical system by a certain angle, with the sample fixed on the sample stage. An autofocus (AF) sensor for an optical system, distinct from the image sensor of the optical system, obtains an image of a sample on an inclined sample stage using the AF sensor. The processor determines the z-shift based on the tilt angle and the xy-plane shift from the center of the image, wherein the xy-plane shift is determined based on the focused region of the image. A method comprising moving a sample stage by a determined z-shift relative to the focal plane of the objective lens of an optical system, thereby focusing on the sample. 75. A method for autofocusing an optical system, An AF sensor for an optical system, which is different from the image sensor of an optical system, involves tilting the AF sensor by a certain angle. The process involves obtaining an image of a sample using an AF sensor in an optical system, where the sample is fixed on a sample stage. The processor determines the z-shift based on the tilt angle and the xy-plane shift from the center of the image, wherein the xy-plane shift is determined based on the focused region of the image. A method comprising moving a sample stage by a determined z-shift relative to the focal plane of the objective lens of an optical system, thereby focusing the sample with the optical system. 76. The method is A method according to any of the prior embodiments, further comprising calibrating the pivot point of an optical system. 77. Calibrating the pivot point of the optical system, The sample stage, image sensor, or AF sensor is tilted by the tilt angle or a second tilt angle, Acquiring a calibration image of the sample immobilized on the sample stage using an AF sensor or image sensor, The processor determines the swivel point offset based on the region center of the focused area of ​​the calibration image and the image center of the calibration image, A method according to any of the prior embodiments, comprising de-tilting a sample stage, image sensor, or AF sensor by a tilt angle or a second tilt angle. 78. The method is The method according to any of the prior embodiments, further comprising untilting the tilted sample stage by the tilt angle. 79. The method is The method according to any of the prior embodiments, further comprising de-tilting a tilted image sensor by the tilt angle. 80. The method is The method according to any of the prior embodiments, further comprising de-tilting a tilted AF sensor by the tilt angle. 81. The method according to any of the prior embodiments, wherein the sample stage of the optical system is tilted by an angle of inclination, which is around the x-axis or the y-axis. 82. The method according to any of the prior embodiments, wherein the sample stage of the optical system is tilted by an inclination angle and is located in the xz plane or the yz plane. 83. The method according to any of the prior embodiments, wherein the AF sensor or image sensor of the optical system is tilted by an angle of inclination, which is around the x-axis or y-axis. 84. The method according to any of the prior embodiments, wherein the AF sensor or image sensor of the optical system is tilted by an angle of inclination in the xz plane or the yz plane. 85. The method according to any of the prior embodiments, wherein the inclination angle is in the range of 0.01 degrees to 89 degrees. 86. The method according to any of the prior embodiments, wherein the inclination angle is in the range of 0.05 degrees to 15 degrees. 87. The method according to any of the prior embodiments, wherein the inclination angle is clockwise around the x-axis or y-axis. 88. The method according to any of the prior embodiments, wherein the inclination angle is counterclockwise around the x-axis or y-axis. 89. The method according to any of the prior embodiments, wherein the image of the sample obtained by the AF sensor or image sensor comprises a single image. 90. The method according to any of the prior embodiments, wherein the AF sensor is used solely to acquire a signal for autofocusing the optical system. 91. The method according to any of the prior embodiments, wherein an image sensor is used to autofocus an optical system and to take an image using the optical system after autofocusing. 92. The method of any of the prior embodiments, wherein the optical system is used solely for autofocus and not for imaging, and lacks an AF illumination source. 93. A method for autofocusing an optical system, according to any of the prior embodiments, which is completed in 100 to 990 milliseconds. 94. A method for autofocusing an optical system, as described in any of the prior embodiments, which is completed in less than 600 milliseconds. 95. The method according to any of the prior embodiments, wherein the image includes a field of view (FOV) that is identical in size to the image sensor or AF sensor along the x-axis or y-axis. 96. The method according to any of the prior embodiments, wherein the image includes a length or width within the range of 0.1 mm to 5 cm. 97. The method according to any of the prior embodiments, wherein the image includes a length or width within the range of 0.5 mm to 9 mm. 98. The method according to any of the prior embodiments, wherein the image includes a field of view (FOV) identical to the size of the image sensor or AF sensor along the x-axis when the tilt angle is around the x-axis and along the y-axis, and when the tilt angle is around the y-axis. 99. The method according to any of the prior embodiments, wherein the AF illumination source includes a laser. 100. The method according to any of the prior embodiments, wherein the image includes a fluorescence signal from the sample. 101. The sample is One or more surfaces and one or more substrates, At least one hydrophilic polymer coating layer, Multiple oligonucleotide molecules attached to at least one hydrophilic polymer coating layer, The method according to any of the prior embodiments, comprising a flow cell comprising at least one distinct region of one or more surfaces, which includes a plurality of clone-amplified sample nucleic acid molecules immobilized on a plurality of attached oligonucleotide molecules, wherein the plurality of immobilized clone-amplified sample nucleic acid molecules are located at a distance of less than λ / (2*NA), where λ is the central wavelength of the excitation energy source and NA is the numerical aperture of the optical system. 102. The method according to any of the prior embodiments, wherein the sample includes a bead-shaped flow cell. 103. The method according to any of the prior embodiments, wherein the bead-shaped flow cell includes a surface coated with chemically immobilized fluorescent beads. 104. The method according to any of the prior embodiments, wherein fluorescent beads are randomly distributed on a surface. 105. The method according to any of the prior embodiments, wherein the fluorescent beads include one, two, three, four, five, or six different types of beads that emit different colors in response to laser excitation. 106. The method according to any of the prior embodiments, wherein fluorescent beads emit fluorescent light of one or more wavelengths in response to laser excitation. 107. The method according to any of the prior embodiments, wherein the sample includes a test target. 108. The method according to any of the prior embodiments, wherein the test target includes a coating of a predetermined geometric shape or pattern that is spatially repeatable. 109. The method according to any of the prior embodiments, wherein a predetermined geometric pattern or shape is repeated in one or two dimensions. 110. The method according to any of the prior embodiments, wherein the test target lacks a flow cell and liquid. 111. The method according to any of the prior embodiments, wherein the test target comprises one or more substrates having a predetermined refractive index. 112. The method according to any of the prior embodiments, wherein the test target includes a top substrate having a predetermined refractive index. 113. A system according to any one of the prior embodiments, wherein the test target includes a bottom substrate. 114. The method according to any of the prior embodiments, wherein at least a portion of a first or second substrate is coated having a predetermined geometric pattern or shape. 115. The method according to any of the prior embodiments, wherein the thickness of the first substrate is configured to simulate the presence of a first virtual flow cell. 116. The method according to any of the prior embodiments, wherein the thickness of the top substrate is configured to enable imaging of the bottom surface of the first channel of a virtual first flow cell. 117. The method according to any of the prior embodiments, wherein the coating of a predetermined geometric shape or pattern includes optically opaque portions and transparent portions. 118. The method according to any of the prior embodiments, wherein the optical system includes one, two, three, four, five, or six detection channels. 119. The optical system, after autofocus of the optical system, 1.0mm 2 A method according to any of the prior embodiments, configured to acquire a flow cell image having a field of view greater than or equal to a certain extent. 120. The optical system The objective lens, Image sensor and, Numerical aperture (NA) less than 0.6, The method according to any of the prior embodiments, comprising: a processor configured to process a flow cell image to correct optical aberrations and to generate an optical resolution that is substantially identical within the flow cell image. 121. The method according to any of the prior embodiments, wherein the optical system further comprises one or more illumination sources, the one or more illumination sources lacking an AF laser configured solely for the autofocus of the optical system. 122. The method according to any of the prior embodiments, wherein the method for autofocusing an optical system is configured to focus the optical system for imaging sample nucleic acid molecules immobilized in a flow cell during a first flow cycle and a second flow cycle in a sequencing run. 123. The method according to any of the prior embodiments, wherein the method for autofocusing an optical system is configured to focus the optical system for imaging sample nucleic acid molecules immobilized on a first surface in a first flow cycle of a sequencing run, and to refocus the optical system for imaging sample nucleic acid molecules immobilized on the first or second surface in a second flow cycle of a sequencing run. 124. A method for autofocusing an optical system, according to any of the prior embodiments, comprising focusing an optical system for imaging sample nucleic acid molecules immobilized on a first surface in a first flow cycle of a sequencing run, and refocusing an optical system for imaging sample nucleic acid molecules immobilized on a second surface in a first or second flow cycle of a sequencing run. 125. The method according to any of the prior embodiments, wherein the method for autofocusing an optical system is configured to focus at least along the z-axis. 126. The sample stage of the optical system can be tilted by an inclination angle. A method according to any of the prior embodiments, comprising moving the sample stage in the xy plane and simultaneously tilting the sample stage of the optical system by an inclination angle. 127. A method according to any of the prior embodiments, wherein moving the sample stage in the xy plane includes moving the sample stage to a predetermined spatial location. 128. To untilt a tilted sample stage by the tilt angle, A method according to any of the prior embodiments, comprising moving the sample stage by a determined z-shift relative to the focal plane of the objective lens, and simultaneously untilting the inclined sample stage by the inclination angle. 129. To de-tilt a tilted image sensor by the tilt angle, The method according to any of the prior embodiments, further comprising moving the sample stage by a determined z-shift and simultaneously untilting the tilted image sensor by the tilt angle. 130. To un-tilt a tilted AF sensor by the tilt angle, The method according to any of the prior embodiments, further comprising moving the sample stage by a determined z-shift and simultaneously untilting the tilted AF sensor by the tilt angle. 131. The method according to any of the prior embodiments, wherein the error in the autofocus of the optical system is within the range of -400 nm to +400 nm. 132. The method according to any of the prior embodiments, wherein the error in the autofocus of the optical system is within the range of -100 nm to +100 nm. 133. The method according to any of the prior embodiments, wherein the error in the autofocus of the optical system is within the range of -50 nm to +50 nm. 134. The method according to any of the prior embodiments, wherein the sample stage is an electrically operated stage that automatically tilts by a predetermined angle provided by the user. 135. The method according to any of the prior embodiments, wherein an image sensor or AF sensor is fixed on an electric stage that automatically tilts by a predetermined angle provided by the user. 136. The method according to any of the prior embodiments, wherein the objective lens is fixed on a z-stage that is movable along the z-axis. 137. The method according to any of the prior embodiments, wherein moving the sample stage relative to the focal plane of the objective lens of an optical system by a determined z-shift includes moving the objective lens, thereby moving the focal plane of the objective lens by a determined z-shift. 138. The sample stage of the optical system can be tilted by an angle of inclination. The motor coupled to the sample stage accepts the tilt angle, 139. A method according to any of the prior embodiments, comprising tilting a sample stage by an inclination angle using a motor. A method for autofocusing an optical system, The optical system acquires one or more flow cell images of the first tile or subtile of the sample during the sequence determination flow cycle, The sample stage is moved to position the second tile or subtile next to the first tile or subtile sample relative to the optical system, Repeating the method for autofocusing an optical system in any one of the prior embodiments, A method comprising: acquiring one or more flow cell images of a second tile or subtile of a sample in a flow cycle of sequencing execution using an optical system. 140. An optical system, The objective lens, Sample stage and An image sensor wherein at least one of the sample stage and the image sensor is tiltable by a certain angle, Numerical aperture (NA) less than 0.6, A processor configured to determine a z-shift based on the tilt angle and the xy-plane shift from the center of an image acquired by at least one image sensor, An optical system comprising a processor, wherein the xy-plane shift is determined based on the focused region of the image, and the z-shift of the sample stage is configured to focus the sample stage on the focal plane of the objective lens. 141. An optical system, The objective lens, Sample stage and Image sensor and, An AF sensor wherein at least one of the sample stage and the AF sensor is tiltable by a certain angle. Numerical aperture (NA) less than 0.6, A processor configured to determine the z-shift based on the tilt angle and the xy-plane shift from the center of the image acquired by the AF sensor, An optical system comprising a processor, wherein the xy-plane shift is determined based on the focused region of the image, and the z-shift of the sample stage is configured to focus the sample stage on the focal plane of the objective lens. 142. An optical system according to any of the prior embodiments, wherein a sample stage, an AF sensor, an image sensor, or a combination thereof is tiltable around the x-axis or y-axis. 143. An optical system according to any of the prior embodiments, wherein a sample stage, an AF sensor, an image sensor, or a combination thereof is tiltable in the xz plane or the yz plane. 144. An optical system according to any of the prior embodiments, wherein a sample stage, an AF sensor, an image sensor, or a combination thereof is tiltable by motors connected thereto. 145. An optical system according to any of the prior embodiments, wherein the inclination angle is in the range of 0.01 degrees to 89 degrees. 146. An optical system according to any of the prior embodiments, wherein the inclination angle is in the range of 0.05 degrees to 15 degrees. 147. An optical system according to any of the prior embodiments, wherein the inclination angle is clockwise around the x-axis or y-axis. 148. An optical system according to any of the prior embodiments, wherein the inclination angle is counterclockwise around the x-axis or y-axis. 149. An optical system according to any of the prior embodiments, wherein the image of a sample obtained by an AF sensor or image sensor comprises a single image. 150. An optical system according to any of the prior embodiments, wherein the AF sensor is used solely to acquire a signal for autofocusing the optical system. 151. An optical system according to any of the prior embodiments, wherein an image sensor is used to autofocus the optical system and to take an image using the optical system after autofocusing. 152. An optical system according to any of the prior embodiments, which is used solely for autofocus and not for imaging, and lacks an AF illumination source. 153. An optical system according to any of the prior embodiments, wherein the AF illumination source includes a laser. 154. An optical system according to any of the prior embodiments, wherein the optical system is configured to complete the autofocus of the optical system in 100 to 990 milliseconds. 155. An optical system according to any of the prior embodiments, wherein the optical system is configured to complete the autofocus of the optical system in less than 600 milliseconds. 156. An optical system according to any of the prior embodiments, wherein the image includes a field of view (FOV) that is identical in size to the image sensor or AF sensor along the x-axis or y-axis. 157. An optical system according to any of the prior embodiments, wherein the image includes a length or width within the range of 0.1 mm to 5 cm. 158. An optical system according to any of the prior embodiments, wherein the image includes a length or width within the range of 0.5 mm to 9 mm. 159. An optical system according to any of the prior embodiments, wherein the image includes a field of view (FOV) identical to the size of the image sensor or AF sensor along the x-axis when the tilt angle is around the x-axis and along the y-axis, and when the tilt angle is around the y-axis. 160. An optical system according to any of the prior embodiments, wherein the image includes a fluorescence signal from a sample. 161. An optical system according to any of the prior embodiments, wherein the sample stage includes a sample immobilized thereon during imaging of the sample using the optical system. 162. The sample is One or more surfaces and one or more substrates, At least one hydrophilic polymer coating layer, Multiple oligonucleotide molecules attached to at least one hydrophilic polymer coating layer, An optical system according to any of the prior embodiments, comprising a flow cell including at least one distinct region of one or more surfaces, which includes a plurality of clone-amplified nucleic acid molecules immobilized on a plurality of attached oligonucleotide molecules, wherein the plurality of immobilized clone-amplified sample nucleic acid molecules are located at a distance of less than λ / (2*NA), where λ is the central wavelength of the excitation energy source and NA is the numerical aperture of the imaging system. 163. An optical system according to any of the prior embodiments, wherein the sample includes a bead-shaped flow cell. 164. An optical system according to any of the prior embodiments, wherein a bead-shaped flow cell includes a surface coated with chemically immobilized fluorescent beads. 165. An optical system according to any of the prior embodiments, wherein fluorescent beads are randomly distributed on a surface. 166. An optical system according to any of the prior embodiments, wherein the fluorescent beads include one, two, three, four, five, or six different types of beads that emit different colors in response to laser excitation. 167. An optical system according to any of the prior embodiments, wherein fluorescent beads emit fluorescent light of one or more wavelengths in response to laser excitation. 168. An optical system according to any of the prior embodiments, wherein the sample includes a test target. 169. An optical system according to any of the prior embodiments, wherein the test target includes a coating of a predetermined geometric shape or pattern that is spatially repeatable. 170. An optical system according to any of the prior embodiments, wherein a predetermined geometric pattern or shape is repeated in one or two dimensions. 171. An optical system according to any of the prior embodiments, wherein the test target lacks a flow cell and liquid. 172. An optical system according to any of the prior embodiments, wherein the test target comprises one or more substrates having a predetermined refractive index. 173. An optical system according to any of the prior embodiments, wherein the test target includes a top substrate having a predetermined refractive index. 174. An optical system according to any of the prior embodiments, wherein the test target includes a bottom substrate. 175. An optical system according to any of the prior embodiments, wherein at least a portion of a first or second substrate includes a coating having a predetermined geometric pattern or shape. 176. An optical system according to any of the prior embodiments, wherein the thickness of the first substrate is configured to simulate the presence of a first virtual flow cell. 177. An optical system according to any of the prior embodiments, wherein the thickness of the top substrate is configured to enable imaging of the bottom surface of a first channel of a virtual first flow cell. 178. An optical system according to any of the prior embodiments, wherein a coating of a predetermined geometric shape or pattern includes optically opaque portions and transparent portions. 179. An optical system according to any of the prior embodiments, wherein the optical system includes one, two, three, four, five, or six detection channels. 180. The optical system, after autofocus of the optical system, 1.0mm 2 An optical system according to any of the prior embodiments, configured to acquire a flow cell image having a field of view (FOV) greater than or equal to a certain value. 181. An optical system according to any of the prior embodiments, wherein the optical system is configured to focus before imaging the sample nucleic acid molecules immobilized in the flow cell during the first and second flow cycles of the sequencing run. 182. An optical system according to any of the prior embodiments, wherein the optical system is configured to focus the optical system before imaging sample nucleic acid molecules immobilized on a first surface in a first flow cycle of sequencing execution, and to refocus the optical system before imaging sample nucleic acid molecules immobilized on the first or second surface in a second flow cycle of sequencing execution. 183. An optical system according to any of the prior embodiments, wherein the optical system is configured to focus an optical system for imaging sample nucleic acid molecules immobilized on a first surface in a first flow cycle of sequencing execution, and to refocus an optical system for imaging sample nucleic acid molecules immobilized on a second surface in a first or second flow cycle of sequencing execution. 184. An optical system according to any of the prior embodiments, wherein the optical system is configured to focus the optical system along at least the z-axis. 185. An optical system according to any of the prior embodiments, wherein the error in the autofocus of the optical system is within the range of -400 nm to +400 nm. 186. An optical system according to any of the prior embodiments, wherein the error in the autofocus of the optical system is within the range of -100 nm to +100 nm. 187. An optical system according to any of the prior embodiments, wherein the error in the autofocus of the optical system is within the range of -50 nm to +50 nm. 188. An optical system according to any of the prior embodiments, wherein the sample stage is an electrically operated stage that automatically tilts by a predetermined angle provided by the user. 189. An optical system according to any of the prior embodiments, wherein an image sensor or AF sensor is fixed on an electrically operated stage that automatically tilts at a predetermined angle. 190. An optical system according to any of the prior embodiments, wherein the objective lens is fixed on a z-stage that is movable along the z-axis. 191. An optical system according to any of the prior embodiments, wherein the optical system further comprises one or more illuminating sources.

[0277] Preferred embodiments of the present invention are shown and described herein, but it will be apparent to those skilled in the art that such embodiments are provided only as examples. The breadth and scope of this disclosure should not be limited by any of the above exemplary embodiments. Numerous variations, modifications, and substitutions will be conjured here upon those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be used in the practice of the invention. The following claims define the scope of the invention, and methods and structures within the scope of these claims and their equivalents are intended to be encompassed thereby.

Claims

1. A method for focusing an optical system, (a) Receiving an image of the substrate of the optical system, wherein a portion of the image but less than the entirety of the image is in focus, and the portion of the focused image is offset from the center of the image; (b) Using at least the portion of the focused image and the distance from the center of the image to determine the amount of focus shift in the image, (c) A method comprising adjusting the parameters of the optical system in order to correct the focus shift.

2. The method according to claim 1, wherein the image is an image of a flow cell, and the substrate is a flow cell.

3. The method according to claim 1, wherein the adjustment in (c) is an automatic adjustment.

4. The method according to claim 1, wherein the aforementioned image is received from an autofocus element.

5. The method according to claim 1, wherein the determination is made in a maximum of about 600 milliseconds (ms).

6. The method according to claim 1, wherein the determination is made within a maximum of approximately 100 ms.

7. The method according to claim 1, further comprising imaging a substrate using a light source and a detector to generate the image before (a).

8. The method according to claim 1, wherein the determination is performed using the image and without using additional images.

9. The method according to claim 1, wherein the image includes a length or width in the range of about 0.1 millimeters (mm) to about 5 centimeters (cm).

10. The method according to claim 1, wherein the image includes a length or width within the range of approximately 0.5 mm to approximately 9 mm.

11. The method according to claim 1, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 400 nanometers (nm).

12. The method according to claim 1, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 100 nanometers (nm).

13. The method according to claim 1, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 50 nanometers (nm).

14. The method according to claim 1, wherein the center of the focused region is determined using an image processing algorithm.

15. The method according to claim 14, wherein the image processing algorithm includes separating the image into a predetermined number of regions and determining the center of the focused region by using the sum or average intensity of each region to identify the location of the focused region.

16. The method according to claim 1, wherein the image intensity or spatial frequency information of the location in the focused region is used to locate the center of the focused region.

17. The method according to claim 1, wherein information regarding the geometric pattern in the image determines the image processing algorithm.

18. A method for focusing an optical system, (a) Using a detector to image a substrate tilted at a certain angle, wherein the image of the substrate includes both in-focus and out-of-focus portions. (b) Using a processor to determine the focus shift of the optical system, at least partially based on the tilt angle and the distance of the focused portion from the center of the image, (c) Adjusting the substrate in order to eliminate the inclination angle, (d) A method comprising adjusting the substrate by the focus misalignment, thereby focusing the optical system.

19. The method of claim 18, further comprising using a vector from the center of the image of the focused portion of (b) the determination of (b).

20. The method according to claim 18, further comprising a motor coupled to the substrate configured to impart the aforementioned tilt angle.

21. The method according to claim 18, wherein the detector is part of an autofocus element.

22. The method according to claim 18, wherein the optical system further comprises an additional detector configured to image the substrate.

23. The method according to claim 18, further comprising tilting the substrate to the inclination angle before (a).

24. The method according to claim 18, further comprising releasing the tilt of the substrate following (d).

25. The method according to claim 23, wherein the tilting is performed by tilting a plane perpendicular to the optical axis of the optical system.

26. The method according to claim 18, wherein the inclination angle is approximately 0.01 to approximately 89 degrees.

27. The method according to claim 18, wherein the inclination angle is approximately 0.05 to approximately 15 degrees.

28. The method according to claim 18, wherein the angular resolution of the inclination angle is about 0.001 degrees to about 0.2 degrees.

29. The method according to claim 18, wherein the angular resolution of the inclination angle is about 0.01 degrees to about 0.1 degrees.

30. The method according to claim 18, wherein the angular resolution of the inclination angle is about 0.01 degrees to about 0.08 degrees.

31. The method according to claim 18, wherein the determination is performed using the image and without using additional images.

32. The substrate includes a flow cell, and the flow cell is (a) One or more surfaces, (b) at least one hydrophilic polymer coating layer, (c) A plurality of oligonucleotide molecules attached to at least one hydrophilic polymer coating layer, (d) at least one separate region of one or more surfaces comprising a plurality of clone-amplified nucleic acid molecules immobilized on the plurality of attached oligonucleotide molecules, wherein the plurality of immobilized clone-amplified sample nucleic acid molecules are located at a distance of less than λ / (2*NA), where λ is the central wavelength of the excitation energy source and NA is the numerical aperture of the optical system.

33. The method according to claim 32, wherein the substrate includes bead-shaped flow cells.

34. The method according to claim 33, wherein the bead-shaped flow cell includes a surface containing fluorescent beads chemically immobilized on the substrate.

35. The method according to claim 34, wherein the fluorescent beads are randomly distributed on the surface.

36. The method according to claim 34, wherein the fluorescent beads include at least about four types of beads configured to emit different colors in response to excitation from a laser.

37. The method according to claim 18, wherein the error between the distance from the focal plane and the true distance from the focal plane is at most about 400 nanometers (nm).

38. The method according to claim 18, wherein the error between the distance from the focal plane and the true distance from the focal plane is at most about 100 nanometers (nm).

39. The method according to claim 18, wherein the error between the distance from the focal plane and the true distance from the focal plane is at most about 50 nanometers (nm).

40. (d) The method according to claim 32, wherein the optical system occurs before imaging the nucleic acid molecules immobilized on the substrate in the first flow cycle.

41. The method according to claim 32, further comprising repeating (a) to (d) for a second flow cycle in order to refocus the optical system.

42. A method for focusing an optical system, (a) Imaging a substrate using a detector tilted at a certain angle, wherein the image of the substrate includes both in-focus and out-of-focus portions. (b) Using a processor to determine the focus shift of the optical system, at least partially based on the tilt angle and the distance of the focused portion from the center of the image, (c) A method comprising adjusting the substrate by the focus misalignment, thereby focusing the optical system.

43. The method according to claim 42, further comprising adjusting the substrate by the aforementioned focus misalignment to bring the substrate into focus.

44. The method of claim 42, further comprising tilting the detector to the tilt angle before (a).

45. The method according to claim 42, further comprising releasing the tilt of the detector following (c).

46. The method according to claim 44, wherein the inclination is the inclination of a plane perpendicular to the optical axis of the optical system.

47. The method according to claim 42, wherein the inclination angle is approximately 0.01 to approximately 89 degrees.

48. The method according to claim 42, wherein the inclination angle is approximately 0.05 to approximately 15 degrees.

49. The method according to claim 42, wherein the determination is performed using the image and without using additional images.

50. The method according to claim 42, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 400 nanometers (nm).

51. The method according to claim 42, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 100 nanometers (nm).

52. The method according to claim 42, wherein the error in the amount of the focus shift from the true amount of the focus shift is at most about 50 nanometers (nm).

53. The method according to claim 42, further comprising calibrating the pivot point of the optical system.

54. The method according to claim 53, wherein the calibration of the pivot point includes releasing the tilt of the substrate, the detector, or the autofocus sensor.

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