Implementing structured illumination microscopy on patterned substrates

Abstract

A structured illumination microscopy (SIM) system includes a light source, an optical structuring component for providing light from the light source in a SIM pattern for performing illumination of a sample on a substrate having a substrate pattern, the pitch of the SIM pattern being based on a characteristic of the substrate pattern, and an image sensor for detecting radiation generated by the sample in response to the illumination.

Description

[Technical field]

[0001] (CROSS REFERENCE TO RELATED APPLICATIONS) This application claims priority to U.S. Provisional Patent Application No. 63 / 200,639, filed March 19, 2021, entitled "PERFORMING STRUCTURED ILLUMINATION MICROSCOPY ON A PATTERNED SUBSTRATE," the contents of which are incorporated herein by reference. [Background technology]

[0002] Structured illumination microscopy (SIM) has been used to increase the resolution of images obtained from a sample. SIM utilizes several images of a sample with different fringe patterns such that different locations on the sample are exposed to a range of illumination intensities. In some cases, the procedure can be repeated by rotating the pattern orientation at separate angles about the optical axis. The captured images may be assembled into a single image with an extended spatial frequency bandwidth, which can be retransformed into real space to produce an image with higher resolution compared to those captured by conventional microscopes. Existing approaches to SIM may have one or more characteristics that increase the complexity, size, manufacturing costs, and / or operating costs of the system. Summary of the Invention

[0003] In a first aspect, a structured illumination microscopy (SIM) system comprises a light source, an optical structuring component for providing light from the light source in a SIM pattern for performing illumination of a sample on a substrate having a substrate pattern, the pitch of the SIM pattern being based on a characteristic of the substrate pattern, and an image sensor for detecting radiation generated by the sample in response to the illumination.

[0004] Implementations may include any or all of the following features: The substrate pattern includes a periodic pattern, and the pitch of the SIM pattern is based on the pitch of the periodic pattern. The pitch of the SIM pattern is greater than the pitch of the periodic pattern. The pitch of the SIM pattern is about 1.5 to about 2 times the pitch of the periodic pattern. The light structuring component includes a grating for generating the SIM pattern, and the grating corresponds to the pitch of the periodic pattern. The substrate pattern includes nanowells formed in the substrate. The substrate pattern includes the nanowells being arranged in a square array. The square array has nanowells arranged in linear rows and linear columns, the linear rows being substantially perpendicular to the linear columns. A first linear row or column is illuminated by the SIM pattern, and a second linear row or column is parallel and adjacent to the first linear row or column, and when the first linear row or column is illuminated by the SIM pattern, the second linear row or column is not illuminated by the SIM pattern. The light source includes at least one of a laser or a light emitting diode. The sample includes a biological material, and the image sensor is to detect fluorescence emitted by the sample in response to the illumination. The SIM system is configured to rotate the SIM pattern to modulation angles about an optical axis, and at least one of the illuminations is performed at each of the modulation angles of the SIM pattern. The substrate pattern is a periodic pattern, and the SIM system is configured to provide an offset for each of the modulation angles of the SIM pattern to form an offset modulation angle, none of the offset modulation angles corresponding to an angle of an axis of symmetry of the periodic pattern, and at least one of the illuminations is performed at each of the offset modulation angles of the SIM pattern. The substrate pattern includes a random pattern, and the pitch of the SIM pattern is based on a resolution associated with the random pattern. The pitch of the SIM pattern is approximately as large as the resolution associated with the random pattern.

[0005] A second aspect includes configuring a structured illumination microscopy (SIM) system for performing illumination of a sample on a substrate having a substrate pattern, selecting a pitch of a SIM pattern of the SIM system based on characteristics of the substrate pattern, performing illumination of a sample on the substrate with the SIM pattern, and detecting radiation generated by the sample in response to the illumination.

[0006] Implementations may include any or all of the following features: The substrate pattern includes a periodic pattern. The pitch of the SIM pattern is selected based on the pitch of the periodic pattern. Selecting the pitch of the SIM pattern includes configuring a SIM system with a grating for generating the SIM pattern, the grating corresponding to the pitch of the periodic pattern. The grating has a pitch that is about 1.5 to about 2 times the pitch of the periodic pattern. The sample includes a biological material, and detecting the emission includes detecting fluorescence emitted by the sample in response to the illumination.

[0007] In a third aspect, a structured illumination microscopy (SIM) system comprises a light source, an optical structuring component for providing light from the light source in a SIM pattern for performing illumination of a sample on a substrate having a periodic pattern, the optical structuring component being configured to rotate the SIM pattern to modulation angles about an optical axis and to provide offsets for each of the modulation angles of the SIM system to form offset modulation angles, none of the offset modulation angles corresponding to an angle of an axis of symmetry of the periodic pattern, and an image sensor for detecting radiation generated by the sample in response to the illumination.

[0008] Implementations may include any or all of the following features: An offset is provided such that each of the offset modulation angles is less than a corresponding modulation angle. An offset is provided such that each of the offset modulation angles is greater than a corresponding modulation angle. The offset is about 10-30 degrees. The offset is about 20 degrees. One of the modulation angles is about 45 degrees, and the offset modulation angle corresponding to one of the modulation angles is about 25 degrees. The periodic pattern includes nanowells formed in a substrate. The periodic pattern includes the nanowells being arranged in a square array. The square array has nanowells arranged in linear rows and linear columns, the linear rows being substantially perpendicular to the linear columns. A first nanowell is illuminated by the SIM pattern, and a second nanowell is adjacent to the first nanowell, and when the first nanowell is illuminated by the SIM pattern, the second nanowell is not illuminated by the SIM pattern. The light source includes at least one of a laser or a light emitting diode. The pitch of the SIM pattern is based on the pitch of the periodic pattern. The pitch of the SIM pattern is about 1.5 to about 2 times the pitch of the periodic pattern.

[0009] In a fourth aspect, a method includes configuring a structured illumination microscopy (SIM) system for rotating a SIM pattern to a modulation angle about an optical axis, the SIM system being configured to perform illumination of a sample on a substrate having a periodic pattern, providing an offset for each of the modulation angles of the SIM system to form an offset modulation angle, wherein none of the offset modulation angles corresponds to an angle of an axis of symmetry of the periodic pattern, performing illumination of the sample on the substrate with the SIM pattern at the offset modulation angle, and detecting radiation generated by the sample in response to the illumination. [Brief description of the drawings]

[0010] [Figure 1] FIG. 1 is a schematic diagram of an exemplary system that can facilitate structured illumination microscopy (SIM), in which a phase selector is placed after the reflective component. [Diagram 2] 1 shows an example of a SIM pattern. [Diagram 3] 1 shows an example of a substrate having a periodic pattern. [Figure 4] 4 shows an example of a combination of the SIM pattern of FIG. 2 and the substrate of FIG. [Diagram 5] 4 shows an example of a combination of a SIM pattern with the substrate of FIG. 3, where the pitch of the SIM pattern is selected based on the pitch of the periodic pattern of the substrate. [Figure 6] 13 shows a chart illustrating an example of the effect of SIM pattern pitch on sequencing error. [Figure 7] 4 shows an example of projection of SIM fringe excitation illumination light using a SIM pattern onto the substrate of FIG. 3, where the modulation angle of the SIM pattern is offset relative to the angle of the periodic pattern of the substrate. [Figure 8A] 13 illustrates an embodiment for providing an offset to the modulation angle of the SIM pattern to form an offset modulation angle. [Figure 8B] 13 illustrates an embodiment for providing an offset to the modulation angle of the SIM pattern to form an offset modulation angle. [Figure 8C] 13 illustrates an embodiment for providing an offset to the modulation angle of the SIM pattern to form an offset modulation angle. [Figure 9A] Examples of images captured without an offset to the modulation angle (FIG. 9A) and with an offset to the modulation angle (FIG. 9B) are shown. [Figure 9B] Examples of images captured without an offset to the modulation angle (FIG. 9A) and with an offset to the modulation angle (FIG. 9B) are shown. [Figure 10A] 10A and 10B show other examples of images captured without an offset to the modulation angle (FIG. 10A) and with an offset to the modulation angle (FIG. 10B). [Figure 10B]10A and 10B show other examples of images captured without an offset to the modulation angle (FIG. 10A) and with an offset to the modulation angle (FIG. 10B). [Figure 11] An embodiment of the method is given. [Figure 12] FIG. 1 is a schematic diagram of an exemplary system in which a phase selector is placed before a reflective component, which can facilitate SIM. [Figure 13] 13 is a schematic diagram of an exemplary system that may be used for biological and / or chemical analysis, where the system of FIG. 1 may be part of the system of FIG. [Figure 14] 1 shows an example of a substrate having a random pattern. [Figure 15] 2 illustrates an example of a rotating inline grating system (RIGS) having a rotatable mirror that may be implemented as part of the system of FIG. 1. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] This document describes examples of systems and techniques that can improve structured illumination by doing things including, but not limited to, providing structured illumination microscopy (SIM) with increased resolution and / or increased reliability. Such systems / techniques can provide one or more advantages over existing approaches, for example, as described below. The examples described herein are based on simulations unless otherwise noted.

[0012] SIM can be performed to achieve increased resolution (sometimes referred to as "super-resolution") of a substrate. One or more of several different types of samples can be analyzed. For other types of analysis, whether biological or non-biological, the substrate can be periodically patterned. However, the optical aspects of the SIM pattern, such as the pitch and its angle, are generally selected taking into account the optical system (e.g., numerical aperture, pixel size, etc.), and whether the substrate has a periodic pattern, or in particular does not have any characteristics of such a periodic pattern.

[0013] As disclosed herein, when the substrate has a periodic pattern, one or more characteristics of the SIM pattern can be selected to produce an advantageous net combined effect. For example, a particular instance or range of the pitch of the SIM pattern and / or the angle of the SIM pattern can significantly improve the achieved resolution. Thus, the problem of inefficient SIM resolution enhancement of a periodically patterned substrate (e.g., a patterned flow cell) can be solved by the selection of the pitch and / or angle of the SIM pattern used to illuminate the sample. In some implementations, the SIM pattern can be selected to be different (e.g., not identical in at least one characteristic) from the periodic pattern of the substrate. For example, the modulation angle of the SIM pattern can be selected to be different (e.g., not coincident) with the axis of symmetry of the periodic pattern, and / or the pitch of the SIM pattern can be selected to be different (e.g., larger) than the pitch of the periodic pattern of the substrate. When the substrate has a random pattern, the pitch of the SIM pattern can be selected to be approximately of the same order of magnitude as the microstructural resolution of the substrate pattern.

[0014] Imaging (e.g., using SIM) can be performed to analyze samples of any of a plurality of materials. In some implementations, SIM imaging or another type of imaging can be performed as part of a biological analysis of biological materials or a chemical analysis of any material. For example, a process of sequencing genetic materials can be performed. In one example, the process can be a DNA sequencing process, such as sequencing-by-synthesis or next-generation sequencing (also known as high-throughput sequencing). In another example, the process can be used to enable genotyping. Genotyping involves determining differences in an individual's genetic makeup (genotype) by examining the individual's DNA sequence using a biological assay and comparing it to the sequence of another individual or a reference sequence. Such a process can include fluorescent imaging, in which a sample of genetic material is subjected to an excitation light (e.g., a laser beam) to trigger a fluorescent emission response by one or more markers associated with the genetic material. Some nucleotides can have fluorescent tags associated with the nucleotides to fluoresce in response to exposure to an excitation energy source. The wavelength spectrum of the fluorescent emission response can be used to determine the presence of the corresponding nucleotide. The fluorescent emission response can be detected during the sequencing process and used to construct a record of the nucleotides in the sample.

[0015] SIM imaging is based on spatially structured light. For example, the structure can consist of or include a pattern of illumination light that helps to increase the resolution of the acquired image. In some implementations, the structure can include a pattern of stripes. The light stripes can be generated by impinging a light beam on a diffraction grating (referred to as a diffraction grating for simplicity) so that reflective or transmissive diffraction occurs. The structured light can be impinged on the fluorescent tag associated with the sample, illuminating the fluorescent tag associated with the sample according to the respective stripes, which may occur according to some periodicity. For example, images of fluorescent emission from the fluorescent tag associated with the sample can be acquired at different phases of the structured light stripes, which may be referred to as respective pattern phases of the image. This allows various locations of the fluorescent tag associated with the sample to be exposed to multiple illumination intensities. The structured light pattern can be rotated relative to the sample, and the aforementioned images can be captured at each of the rotation angles. The SIM system can provide light in one or more SIM patterns for impinging on the fluorescent tag associated with the sample or substrate. The SIM patterns can differ from each other in terms of pitch, meaning the distance between adjacent stripes of the SIM pattern. The SIM system can be used with one or more excitation light sources. To name a few examples, a single mode laser, a light-emitting diode (LED), or a multi-mode laser can be used.

[0016] Imaging can be performed as part of the process of analyzing the sample material. This can involve fluorescent imaging, such as when a sample of genetic material is subjected to light (e.g., a laser beam) to trigger a fluorescent response by one or more markers associated with the genetic material. Some nucleotides can be fluorescently tagged and paired with complementary nucleotides in the sample genetic material, allowing the presence of the nucleotide in the sample genetic material to be determined by applying excitation light to the sample and examining the fluorescent response from the sample. The fluorescent response can be detected throughout the analysis process by detecting the wavelength emission spectrum and used to build a record of the nucleotides in the sample.

[0017] Examples herein refer to a substrate. Substrate may refer to any material that provides a substantially rigid structure or a structure that retains the shape of a container in contact with it rather than taking on the shape of the container. The material may have a surface to which another material can be attached, including, for example, smooth supports (e.g., metal, glass, plastic, silicon, and ceramic surfaces), as well as textured and / or porous materials. Possible substrates include, but are not limited to, glass and modified or functionalized glass, plastics (including acrylics, polystyrene and copolymers of styrene and other materials, polypropylene, polyethylene, polybutylene, polyurethane, Teflon™, etc.), polysaccharides, nylon or nitrocellulose, resins, silica or silica-based materials including silicon and modified silicon, carbon, metals, inorganic glasses, plastics, fiber optic bundles, and various other polymers. Generally, the substrate allows for optical detection and does not detectably fluoresce itself.

[0018] Examples herein refer to a substrate having a periodic pattern. The periodic pattern includes one or more types of structures that are repeated at least once. The distance between the repeating structures may be referred to as the pitch of the periodic pattern. In some implementations, the periodic pattern includes nanowells formed in the substrate. The nanowells may be periodically arranged in rows and / or columns. The periodic pattern may form one or more arrays. The array may include a hexagonal array, a square array, or another array according to a Cartesian system with periodicity.

[0019] Examples herein refer to substrates having random patterns, in which the relative locations of a subset of wells (or other structures) in one region of the substrate surface are not known or predictable from the locations of the subset of wells (or other structures) in another region of the substrate surface. Random patterns generally do not include multiple repetitions of any subpattern.

[0020] The embodiments described herein refer to a flow cell. A flow cell is a substrate that can be used in preparing and containing or carrying one or more samples in at least one stage of an analytical process. A flow cell is made of a material that can be used with both the sample genetic material and the illumination and chemical reactions to which it is exposed. The substrate can have one or more channels in which the sample genetic material can be deposited. A substance (e.g., a liquid) can be flowed through the channel in which the sample genetic material is present to trigger one or more chemical reactions and / or remove unwanted materials. The flow cell can enable imaging by facilitating that the sample in the flow cell channel can be subjected to illumination excitation light and a fluorescent emission response from the sample can be detected. Some implementations of the system can be designed to be used with at least one flow cell, but may not include a flow cell during one or more stages, such as during shipping or when delivered to a customer. For example, the flow cell can be installed in the implementation at the customer's facility to perform the analysis.

[0021] In some implementations, different types of gratings can be used to provide the SIM pattern. The grating can include one or more forms of periodic structures. In some implementations, the grating can be formed by removing or omitting physical material from the substrate. In other implementations, optical filters or other non-physical materials can be implemented to form the grating. For example, a substrate can be provided with a set of slits and / or grooves therein to form the grating. In some implementations, the grating can be formed by adding material to the substrate. For example, the periodically spaced structures can be formed on the substrate by the same or different materials.

[0022] The embodiments described herein may provide advantages over previous approaches. In some implementations, image quality of a SIM system may be improved. In some implementations, sample analysis by SIM may be improved. In some implementations, resolution of a SIM system may be improved. In some implementations, throughput of a SIM system for sample analysis may be increased. In some implementations, crosstalk between adjacent nanowells or adjacent rows or columns of nanowells may be reduced or eliminated. In some implementations, a substrate for holding samples in SIM analysis may be provided with a more spatially dense pattern. In some implementations, aliasing in a SIM system may be reduced or eliminated.

[0023] 1 illustrates generally an example of a system 100 that can facilitate SIM imaging. System 100 can be used with one or more of the other embodiments described herein. Some components of this and other embodiments are illustrated conceptually as blocks or other general components. Such components can be implemented in the form of one or more separate or integrated components to perform the indicated functionality.

[0024] The system 100 includes a light source 102. The light source 102 can be selected based on the type of sample to which the system 100 is to be implemented, its coherence, and / or its power output. For example, a multimode laser can be used as the light source 102. As another example, a single mode laser can be used as the light source 102. As another example, an LED or several LEDs can be used as the light source 102.

[0025] The system 100 includes an optical structuring component 104 that receives light from the light source 102. In some implementations, the optical structuring component 104 facilitates the received light impinging on one or more gratings to generate a pattern of light stripes. The optical structuring component 104 can include a grating. One or more reflecting components can be used to direct the light to the appropriate grating. In some implementations, the optical structuring component 104 can select, or can be used to select, the pitch of the SIM pattern that the system 100 should apply to the sample. In some implementations, the optical structuring component 104 can provide, or can be used to provide, an offset to the modulation angle, thereby affecting the rotation of the SIM pattern about the optical axis of the system 100. A beam 106 extending between the light source 102 and the optical structuring component 104 illustrates the propagation of light in a schematic manner. The optical structuring component 104 can generate structured light and provide the structured light to subsequent components in the system 100. The light structuring element 104 can include structures such as gratings for implementing any of the SIM patterns 200, 502, 702 described herein.

[0026] In some implementations, the next component is a phase selector 108 in the system 100. The phase selector 108 can receive light from the light structuring component 104. The phase selector 108 is used to select a pattern phase at which an image is captured. In some implementations, the phase selector 108 can facilitate selection between multiple candidate pattern phases according to a desired illumination of the sample or a degree of resolution required. In some implementations, the pattern phase can correspond to a relative position between the SIM pattern and the sample. For example, the phase selector 108 can translate a grating to a position corresponding to the respective pattern phase upon illumination of the sample at each pattern phase.

[0027] System 100 includes a projection lens 110 that can receive light from phase selector 108. Such light can be referred to as phase-selected light to indicate that the light corresponds to a particular pattern phase selection made, such as by phase selector 108. Projection lens 110 can include one or more optical elements, such as lenses, that condition the phase-selected light before it impinges on a next stage in system 100.

[0028] System 100 includes a mirror 112 that at least partially reflects light from the projection lens 110 toward the objective lens 114. In some implementations, mirror 112 provides selective transmission such that it reflects a portion of the illumination light reaching it from the projection lens 110 and transmits at least a portion of the imaging light reaching it from the objective lens 114. For example, mirror 112 can be a dichroic mirror.

[0029] The objective lens 114 receives the illumination light from the mirror 112. The objective lens 114 may include one or more optical elements, such as lenses, that condition the light from the projection lens 110 (as it is reflected by the mirror 112) before the light impinges on the next stage in the system 100.

[0030] The objective lens 114 directs light onto the sample 116. In some implementations, the sample 116 includes one or more materials to be analyzed. For example, the sample 116 may include genetic or biological materials (e.g., cellulose) that are illuminated for detection of a fluorescent response of a fluorescent tag associated with the sample 116. The sample 116 may be held on a suitable substrate, including, but not limited to, a flow cell that allows liquids or other fluids to be selectively flowed through the sample. For example, the sample 116 may be subjected to one or more reagents including one or more nucleotides with associated fluorescent tags prior to illumination, followed by image capture and analysis. The substrate may have a periodic pattern. For example, one or more arrays of nanowells may be formed on the substrate.

[0031] The sample 116 can be held by a stage 118 of the system 100. The stage 118 can provide one or more types of manipulations to the sample 116. In some implementations, physical movement of the sample 116 can be provided. For example, the stage 118 can translationally and / or rotationally reposition the sample 116 relative to at least one other component of the system 100. In some implementations, thermal treatment of the sample 116 can be provided. For example, the stage 118 can heat and / or cool the sample 116.

[0032] Phase selection can be facilitated by stage 118. In some implementations, stage 118 can translate sample 116 a distance relative to the stationary light stripes to achieve phase selection (e.g., using a piezoelectric actuator in stage 118). For example, phase selector 108 can then be bypassed in system 100 or eliminated from system 100.

[0033] The light generated by the light source 102, conditioned in the described components, can propagate through the objective lens 114 and then be directed to the fluorescent tag associated with the sample 116 for illumination. Any light emitted by the fluorescent tag associated with the sample 116 can traverse the objective lens 114 in the opposite direction and be partially or totally transmitted through the mirror 112. The system 100 can include a filter component 120 that receives light from the objective lens 114 through the mirror 112. The filter component 120 can filter such light in one or more ways. For example, the filter component 120 can pass some specific wavelength spectrums above or below a predetermined level and / or block (or reflect) other specific wavelength spectrums above or below a predetermined level. In some implementations, the mirror 112 can incorporate the filter component 120 as part of the mirror, such as by positioning the filter component 120 on the back surface of the mirror 112.

[0034] Light that exceeds the filter component 120 can enter a camera system 122 in the system 100. The camera system 122 can include one or more image sensors that can detect electromagnetic radiation of a type relevant to the analysis to be performed. The camera system 122 and / or another image sensor can detect radiation generated by a fluorescent tag associated with the sample 116 in response to illumination. In some implementations, the camera system 122 is configured to capture images of fluorescent radiation emitted by the fluorescent tag in response to an excitation light. For example, the camera system 122 can include a charge-coupled device, a complementary metal oxide semiconductor device, or other image capture device. In some implementations, the camera system 122 can detect fluorescence emitted by a fluorescent tag associated with the sample 116 in response to one or more excitation illuminations. The camera system 122 can generate output in digital and / or analog form. For example, data corresponding to images captured by the camera system 122 can be stored by the camera system 122 or can be transmitted to a separate component (e.g., a computer system or other device) for storage and / or analysis. In some implementations, the camera system 122 may be supplemented or replaced by a detector in or at the substrate on which the sample 116 is located. For example, on-chip microscopy may be performed using sensor pixels in the substrate to detect emissions from fluorescent tags associated with the sample 116.

[0035] As one example, use of system 100 may involve configuring a SIM system (e.g., system 100) to illuminate a sample (e.g., sample 116) on a substrate having a periodic pattern, selecting the pitch of the SIM pattern (e.g., in optical structuring component 104) of the SIM system based on the pitch of the periodic pattern of the substrate on which the sample is positioned, illuminating (e.g., by objective lens 114) fluorescent tags associated with the sample on the substrate with the SIM pattern, and detecting (e.g., using camera system 122) radiation generated by the fluorescent tags associated with the sample in response to the illumination.

[0036] As another example, use of system 100 may involve performing a method including configuring a SIM system (e.g., system 100) to rotate a SIM pattern (e.g., in optical structuring component 104) about an optical axis to a modulation angle, where the SIM system is configured to perform illumination of a sample (e.g., sample 116) on a substrate having a periodic pattern, providing an offset (e.g., in optical structuring component 104) for each of the modulation angles of the SIM system to form an offset modulation angle, such that none of the offset modulation angles corresponds to the angle of a symmetry axis of the periodic pattern of the substrate on which the sample is positioned, performing illumination (e.g., by objective lens 114) of fluorescent tags associated with the samples on the substrate with the SIM pattern at the offset modulation angle, and detecting (e.g., using camera system 122) radiation generated by the fluorescent tags associated with the samples in response to the illumination.

[0037] FIG. 2 shows an example of a SIM pattern 200. The SIM pattern 200 can be used with one or more other examples described elsewhere herein. Here, the SIM pattern 200 is shown as a relatively bright area visible against any background of relatively dark areas. The SIM pattern 200 can be generated by directing light onto one or more gratings. The SIM pattern 200 includes SIM stripes 200A, here parallel to each other, separated by bands 202 that block the excitation illumination light from illuminating the background. The bands 202 and SIM stripes 200A can be formed such that the physical grating blocks the excitation illumination light to form the bands 202, and the illumination can pass through to form the SIM stripes 200A. The SIM pattern 200 can form a periodic pattern with a specific pitch defined based on the distance between adjacent SIM stripes 200A or bands 202. In some implementations, the SIM pattern 200 can distribute the SIM stripes 200A to form a sinusoidal distribution of light. For example, the pitch of the SIM pattern 200, the distance from one of the SIM stripes 200A to the adjacent one, may be about 400 nanometers (nm). In some implementations, the pitch of the SIM pattern 200 may be about 200 nanometers to 1600 nanometers. Larger or smaller values ​​of pitch may be used.

[0038] One or more directions can be used as a reference to describe the orientation of the SIM pattern 200. In some implementations, the orientation of the SIM pattern 200 can be defined relative to a reference axis 204, which here extends horizontally in the plane of the figure. For example, the reference axis 204 can correspond to a camera pixel direction (e.g., vertical or horizontal). Here, the SIM pattern 200 forms an angle with respect to the reference axis 204 that is about 45 degrees. In some implementations, the angle of the SIM pattern 200 can be between about 0 degrees and 90 degrees. Larger or smaller values ​​of the angle can be used.

[0039] FIG. 3 illustrates an example of a substrate 300 having a periodic pattern 302. The substrate 300 and / or the periodic pattern 302 may be a structure to which the sample 116 of FIG. 1 is aligned and / or used with one or more other examples described elsewhere herein. The substrate 300 may include one or more materials suitable for holding or otherwise containing at least one sample to be analyzed. The samples may be distributed over some or all of the substrate 300. Here, sample 304A is shown using a first shading, sample 304B is shown using a second shading, and sample 304C is shown using a third shading. For example, the different shading of samples 304A-304C may represent the fact that samples 304A-304C may be determined as specific nucleotides based on fluorescent emission from fluorescent tags associated with the samples in response to excitation illumination. The samples of the substrate 300 (including the samples 304A-304C) may be located at distinct locations due to the presence of the periodic pattern 302 in the substrate 300. In some implementations, the samples 304A-304C may be polyclonal (e.g., having two or more genetic material sequences). In some implementations, the periodic pattern 302 may include wells (e.g., nanowells) formed in the substrate 300, which may hold well / nanowell biological material therein. For example, the genetic material may be deposited and / or amplified in each of the multiple nanowells of the substrate 300. The purpose of the analysis may be to detect fluorescence emitted by a fluorescent tag associated with each sample 304A-304C, thereby determining the identity of at least one nucleotide that is part of the corresponding sample 304A-304C.

[0040] The nanowells can be arranged in one or more arrays in a periodic pattern 302. Here, the nanowells containing samples of the substrate 300 (including samples 304A-304C) are arranged in a square array. For example, here, box 306 encloses four of the samples to illustrate the spatial arrangement. The periodic pattern can include linear rows and / or linear columns. Here, a linear row can be defined as a series of samples aligned along a direction indicated by arrow 308. Here, a linear column can be defined as a series of samples aligned along a direction indicated by arrow 310. The linear rows are here substantially perpendicular to the linear columns. Other orientations of the linear rows and / or columns can be used. The linear rows and linear columns of the periodic pattern 302 here both form an angle with respect to the reference axis 204, which is about 45 degrees. In some implementations, the angle of the periodic pattern 302 can be about 0 degrees to 90 degrees. Larger or smaller values ​​of the angle can be used. The pitch of the periodic pattern 302 may also be defined as the distance from one of the linear rows to an adjacent one, or from one of the linear columns to an adjacent one. For example, the pitch may be about 400 nm. In some implementations, the pitch of the periodic pattern 302 may be about 200 nanometers to 1600 nanometers. Larger or smaller values ​​of pitch may be used.

[0041] In this embodiment, the substrate pattern (e.g., periodic pattern 302) forms an angle of approximately 45 degrees with respect to the camera. Other orientations having larger or smaller angles with respect to the camera can be used. For example, the substrate pattern (e.g., periodic pattern 302) can substantially match the pixel pattern of the camera.

[0042] 4 shows an embodiment 400 of the projection of excitation illumination light of SIM stripes 200A using the SIM pattern 200 of FIG. 2 on the substrate 300 of FIG. 3. The embodiment 400 illustrates that the SIM pattern 200 and the periodic pattern 302 of the substrate 300 both form an angle of about 45 degrees with respect to the reference axis 204. The embodiment 400 also illustrates that both the SIM pattern 200 and the periodic pattern 302 have a pitch of about 400 nm. As a result, the SIM stripes 200A of the excitation illumination light here spatially correlate with and substantially overlap the linear rows of the periodic pattern 302. That is, when one of the linear rows or columns is illuminated by a first SIM stripe 200A of the SIM pattern 200, another one of the linear rows or columns parallel to and adjacent to the linear row or column is also illuminated by a second adjacent SIM stripe 200A of the SIM pattern 200. This situation may result in increased crosstalk between adjacent linear rows and / or columns of the periodic pattern 302.

[0043] The result of this is that in embodiment 400, substantially all of the wells in substrate 300 (e.g., nanowells in a flow cell) are illuminated by SIM stripes 200A from SIM pattern 200. The resulting images of emission from fluorescent tags associated with samples contained in the wells may then be the same as those obtained using wide-field illumination. That is, the projected SIM stripes 200A will not provide any enhanced resolution by projecting some excitation illumination onto a subset or portion of wells and blocking excitation illumination from other subsets or portions of wells. For example, if capturing six images of emission from fluorescent tags associated with samples in substrate 300 using two modulation angles and three pattern phases at each of the modulation angles, some or all of the six images may appear as wide-field images with different net intensities (depending on whether the well centers and illumination peaks overlap). The resulting SIM reconstructions may be less effective at distinguishing or differentiating adjacent wells. The situation where the SIM pattern 200 overlaps with some of the linear rows (or columns) of the periodic pattern 302 may be referred to as aliasing, and aliasing where the linear rows (or columns) of the SIM pattern 200 and the periodic pattern 302 completely overlap each other may be referred to as total aliasing. The systems and techniques described herein may reduce or eliminate the undesirable occurrence of aliasing and / or total aliasing.

[0044] Figure 5 illustrates an example embodiment 500 of projecting SIM stripes of excitation illumination light onto the substrate 300 of Figure 3 using a SIM pattern 502, where the pitch of the SIM pattern 502 is selected based at least in part on the pitch of the periodic pattern 302 of the substrate 300. The SIM pattern 502 may be used in conjunction with one or more of the other examples described elsewhere herein.

[0045] At least one aspect of the SIM pattern 502 may differ from a corresponding aspect of the periodic pattern 302. Here, the SIM pattern 502 and the periodic pattern 302 may have the same angle with respect to the reference axis 204. For example, the angle may be about 45 degrees. However, the pitch of the SIM pattern 502 may differ from the pitch of the periodic pattern 302. Here, the SIM pattern 502 includes SIM stripes that appear as relatively bright bands against the background of the substrate 300. The SIM stripes include a first SIM stripe 502A and a second SIM stripe 502B, where the first SIM stripe 502A is adjacent to and parallel to the second SIM stripe 502B. In some implementations, the pitch of the SIM pattern 502, shown in this example as the distance between the first SIM stripe 502A and the second SIM stripe 502B, may be selected at least in part based on the pitch of the periodic pattern 302. For example, it is demonstrated that the pitch of the SIM pattern 502 can be selected such that the distance between the first SIM stripe 502A and the second SIM stripe 502B is greater than the pitch of the periodic pattern 302. As another example, it is demonstrated that the pitch of the SIM pattern 502 can be selected such that the distance between the first SIM stripe 502A and the second SIM stripe 502B is less than the pitch of the periodic pattern 302. In some implementations, the pitch of the SIM pattern 502 can be about 200 nanometers to 1600 nanometers. Here, the pitch of the SIM pattern 502 is about 479 nm, which is greater than the pitch of the periodic pattern 302 of the substrate 300, which is about 400 nm. In some implementations, the pitch of the SIM pattern 502 can be selected or changed by configuring the light structuring components of the SIM system. For example, a grating having a particular spacing corresponding to the intended pitch of the SIM pattern can be selected for the SIM system.

[0046] The illumination of the substrate 300 in the embodiment 500 may have reduced aliasing when compared to that in the embodiment 400 due to the selection of the pitch of the SIM pattern 502. In some implementations, one linear row of the periodic pattern 302 may be illuminated by the first SIM stripe 502A. Another linear row parallel and adjacent to the just mentioned linear row may not be currently illuminated or may only be partially illuminated. For example, the second SIM stripe 502B may not illuminate any of the latter linear rows or may only partially illuminate them. Thus, the amount of crosstalk between the emission of the sample in these linear rows may be reduced or eliminated. Thus, an image reconstructed from several SIM images may be improved, such as by allowing for less aliasing and thus achieving a higher resolution.

[0047] 6 shows a diagram 600 illustrating examples of the effect of SIM pattern pitch on sequencing errors. These examples relate to sequencing genetic material by fluorescence analysis using a SIM system. Diagram 600 can be used in conjunction with one or more of the other examples described elsewhere herein.

[0048] Diagram 600 shows error rate with reference to the vertical axis as a function of SIM pitch with reference to the horizontal axis (e.g., in nm). The error rate is represented here by data 602. The error rate can be any metric that indicates the proportion of errors occurring during sequencing, including but not limited to mismatch rate ("MMR"). In some implementations, the mismatch rate is a predefined metric made available by the system providing the sequencing analysis. For example, the mismatch rate can be defined as the number of matched reads with a particular mismatch pattern divided by the total number of matched reads. Diagram 600 relates to sequencing errors that occur when analyzing a substrate (e.g., a flow cell) with wells spaced apart by about 400 nm.

[0049] Data 602 of chart 600 shows that SIM pattern pitch affects sequencing errors. It is demonstrated that the error rate is low when the SIM pattern pitch is about 600 nm to about 800 nm. For example, the pattern pitch can be about 650 nm to about 750 nm. This range includes SIM pattern pitches that are about 1.5 times to about 2 times the pitch of the periodic pattern of the substrate. For example, the pattern pitch can be about 1.65 times to about 1.85 times the pitch of the periodic pattern of the substrate. The relatively low error rate may continue, at least in part, because when one linear row of wells is illuminated, the next row of wells on the substrate may not be illuminated or may be less illuminated. Thus, fluorescent crosstalk from unilluminated or low-illuminating rows of wells is reduced.

[0050] Figure 7 shows an example embodiment 700 of projecting SIM stripes of excitation illumination light onto the substrate 300 of Figure 3 using a SIM pattern 702, where the modulation angle of the SIM pattern 702 is offset relative to the angle of the periodic pattern 302 of the substrate 300. The SIM pattern 702 can be used in conjunction with one or more of the other examples described elsewhere herein.

[0051] The SIM pattern 702 includes SIM stripes including a first SIM stripe 702A and a second SIM stripe 702B. The substrate 300 here includes samples including a sample 704A, a sample 704B, and a sample 704C. In some implementations, the samples 704A-704C can be positioned in wells that make up the periodic pattern 302 of the substrate 300. For example, the wells can be nanowells. The linear rows and columns of the periodic pattern 302 form an angle with respect to the reference axis 204. For example, the angle can be about 45 degrees. However, the SIM stripes of the SIM pattern 702 can form a different angle with respect to the reference axis 204 than the linear rows and columns of the periodic pattern 302. For example, the angle of the SIM stripes can be larger or smaller than the angle of the linear rows and columns of the periodic pattern 302. In some implementations, the angle of the SIM stripes of the SIM pattern 702 can be selected to be offset from +10 degrees to +80 degrees relative to the angle of the periodic pattern 302 with respect to the reference axis 204, or the angle of the SIM stripes of the SIM pattern 702 can be selected to be offset from -10 degrees to -80 degrees relative to the angle of the periodic pattern 302 with respect to the reference axis 204, where the angle of the SIM pattern is offset by about 20 degrees relative to the angle of the periodic pattern 302 with respect to the reference axis 204. For example, the SIM pattern can be selected to have an angle of about 25 degrees with respect to the reference axis 204, while the periodic pattern 302 is selected to have an angle of about 45 degrees with respect to the reference axis 204.

[0052] The SIM pattern 702 can have any of a number of values ​​for the pitch between adjacent ones of the SIM stripes. In some implementations, the pitch of the SIM pattern 702 can be between about 200 nanometers and 1600 nanometers. In some implementations, the pitch of the SIM pattern 702 can be selected to be different from the pitch of the periodic pattern 302 of the substrate 300. For example, the SIM pattern 702 can have a pitch of about 479 nm. The periodic pattern 302 can have any of a number of values ​​for the pitch between adjacent linear rows or adjacent linear columns. In some implementations, the pitch of the periodic pattern 302 can be between about 200 nanometers and 1600 nanometers. For example, the periodic pattern 302 can have a pitch of about 400 nm, while the pitch of the SIM pattern 702 has a pitch of about 479 nm. In some implementations, the angle and pitch for the SIM pattern 702 can be selected to be different from the angle and pitch of the periodic pattern 302 of the substrate 300.

[0053] The embodiment 700 illustrates that crosstalk due to emission of fluorescent tags associated with adjacent samples (e.g., in the wells of a flow cell) can be reduced by relative rotation between the SIM pattern 702 and the linear rows or columns of the periodic pattern 302. Here, when one central well is relatively well illuminated by the SIM pattern 702, adjacent wells (e.g., in the same linear row or column) are not illuminated or are illuminated to a lesser extent. This can reduce crosstalk between adjacent wells. For example, sample 704A is shown illuminated by the first SIM stripe 702A. Sample 704B is adjacent to sample 704A (e.g., samples 704A and 704B are located in wells that are in the same linear column). Meanwhile, when sample 704A is illuminated, sample 704B is partially illuminated by the SIM pattern 702 (e.g., sample 704B is not illuminated as much as sample 704A). As another example, sample 704C is also adjacent to sample 704A (e.g., samples 704A and 704C are located in wells in the same linear row), while when sample 704A is illuminated, sample 704C is also partially illuminated by SIM pattern 702 (e.g., sample 704C is less illuminated than sample 704A). As a result, crosstalk based on emission from fluorescent tags associated with samples 704B and 704C relative to emission from fluorescent tags associated with sample 704A can be reduced or eliminated.

[0054] Table 1 below shows examples of results for the relative rotation of the SIM pattern and the periodic pattern on a substrate having a periodic pattern of flow cells with a substrate pattern pitch of about 300 nm, where the periodic pattern of flow cells forms an angle with respect to an arbitrary reference axis that is about 45 degrees. For example, the arbitrary reference axis may correspond to the camera pixel direction (e.g., vertical or horizontal). In some implementations, the angle of the periodic pattern of flow cells may be about 0 degrees to 90 degrees. The SIM angles illustrated in Table 1 are measured with respect to a reference axis. The pitch of the SIM pattern may be about 470 to 490 nm (e.g., about 479 nm). In some implementations, the pitch of the SIM pattern may be between about 200 nanometers and 1600 nanometers.

[0055] [Table 1]

[0056] Table 1 includes two metrics that may be affected by the relative angle. The first metric is the percentage of clusters that pass the filter in the sequencing analysis, sometimes referred to as %PF. For example, the pass filter percentage may be a predefined metric made available by the system providing the sequencing analysis. Here, Table 1 shows that when the angle of the SIM pattern is offset by 20 degrees, a higher percentage (82.6%) of clusters pass the filter compared to the %PF (74.7%) without the offset. That is, providing an offset can increase the percentage of clusters that pass the filter.

[0057] The second metric is the error rate, which may reflect the rate at which errors occur in sequencing. For example, the error rate was determined here based on 150 cycles. Here, Table 1 shows that when the angle of the SIM pattern is offset by 20 degrees, a lower error rate (0.22%) can be obtained with the offset compared to the error rate (0.69%) without the offset. That is, by providing an offset, the error rate can be reduced.

[0058] In some examples above, a substrate with a periodic pattern is described, which is a square pattern. In some implementations, the SIM pattern can be applied at one or more distinct angles (sometimes called and at modulation angles), and one or more pattern phases can be used. For example, two modulation angles can be used, and at each angle, three pattern phases can be applied. Other approaches can be used. Any of such approaches can be applied with other types of substrate patterns. For example, the substrate pattern can include a hexagonal pattern (e.g., a pattern with three hexagons intersecting at each vertex). As another example, more than two modulation angles can be used.

[0059] 8A-8C show embodiments 800, 800', and 800'' for providing an offset to the modulation angle of the SIM pattern to form an offset modulation angle. Embodiments 800, 800', and / or 800'' may be used with one or more of the other embodiments described elsewhere herein.

[0060] The embodiments 800, 800', and 800'' are shown relative to a reference axis 802. In some implementations, the reference axis 802 may be similar to the reference axis 204 (FIGS. 2-5 and 7). For example, the reference axis 802 may be selected as an arbitrary reference for purposes of defining the angle of the SIM pattern.

[0061] The example 800 shows a modulation angle 804 shown relative to a reference axis 802. The modulation angle 804 can be measured in a counterclockwise direction from the rightmost end of the reference axis 802. In some implementations, the modulation angle 804 corresponds to how much the SIM pattern rotates around the optical axis of the SIM system when a particular illumination is performed. The SIM imaging may use two or more such modulation angles when capturing a SIM image. For example, prior to the development of the subject matter, the SIM imaging may use an angle of 45 degrees as one of the modulation angles. Thus, the modulation angle 804 is shown to be about 45 degrees in this example for illustrative purposes.

[0062] The embodiment 800 also shows that an offset 806 is provided to the modulation angle 804 to form an offset modulation angle 808. In the embodiment 800, the offset 806 is defined in a clockwise direction from the modulation angle 804. In some implementations, providing the offset 806 can correspond to using the SIM pattern 502 (FIG. 5) to using the SIM pattern 702 (FIG. 7). As a result of the offset 806 being provided, the offset modulation angle 808 does not correspond to any axis of symmetry of the periodic pattern of the substrate holding the sample. For example, the SIM pattern 702 in FIG. 7 does not correspond to (e.g., is not parallel to) any of the linear rows or linear columns of the periodic pattern 302, which are the axes of symmetry of the periodic pattern 302.

[0063] The offset 806 can be any numerical value of angle. Providing the offset can include rotating the SIM pattern in either direction about its optical axis by an amount corresponding to that angle (e.g., by adjusting a grating, or another component of the optical structuring component). The offset 806 angle of the SIM stripes of the SIM pattern can be selected from ±10 degrees to ±80 degrees with respect to the angle of the periodic pattern of the substrate with respect to the reference axis 802. For example, here the offset 806 is about 20 degrees from the 45 degree angle of the modulation angle 804, so that the offset modulation angle 808 is about 25 degrees. Thus, the embodiment 800 corresponds to the embodiment described above with reference to Table 1.

[0064] Example 800' shows that a modulation angle 804 is shown relative to a reference axis 802. The modulation angle 804' can be measured in a counterclockwise direction from the rightmost end of the reference axis 802. In some implementations, the modulation angle 804' corresponds to how much the SIM pattern rotates about the optical axis of the SIM system when a particular illumination is performed. SIM imaging may use two or more such modulation angles in capturing a SIM image. Here, example 800' also shows that a modulation angle 804'' is shown relative to the reference axis 802. The modulation angle 804'' can be measured in a counterclockwise direction from the rightmost end of the reference axis 802. In some implementations, the modulation angle 804'' corresponds to how much the SIM pattern rotates about the optical axis of the SIM system when another particular illumination is performed. More or fewer modulation angles than shown may be used.

[0065] The embodiment 800' also shows that an offset 806' is provided to the modulation angle 804' to form an offset modulation angle 808'. In the embodiment 800', the offset 806' is defined in a counterclockwise direction from the modulation angle 804'. In some implementations, providing the offset 806' can correspond to going from using the SIM pattern 502 (FIG. 5) to using the SIM pattern 702 instead (FIG. 7). As a result of the offset 806' being provided, the offset modulation angle 808' does not correspond to any axis of symmetry of the periodic pattern of the substrate holding the sample. For example, the SIM pattern 702 of FIG. 7 does not correspond to (e.g., is not parallel to) any of the linear rows or linear columns of the periodic pattern 302, which are the axes of symmetry of the periodic pattern 302.

[0066] Example 800' also shows that an offset 806'' is provided to modulation angle 804'' to form offset modulation angle 808''. In some implementations, providing offset 806'' can correspond to switching from using SIM pattern 502 (FIG. 5) to instead using SIM pattern 702 (FIG. 7). As a result of offset 806'' being provided, offset modulation angle 808'' does not correspond to any axis of symmetry of the periodic pattern of the substrate holding the sample. For example, SIM pattern 702 in FIG. 7 does not correspond to (e.g., is not parallel to) any of the linear rows or linear columns of periodic pattern 302, which are the axes of symmetry of periodic pattern 302.

[0067] Each of offsets 806, 806', and / or 806'' can be any numerical value of angle. Providing offsets 806, 806', and / or 806'' can include rotating the SIM pattern in either direction about its optical axis by an amount corresponding to that angle (e.g., by adjusting a grating, or another component of the optical structuring component).

[0068] Referring now also to FIG. 8C, embodiment 800'' illustrates that the offset modulation angle can be formed within an offset range 810 that includes angles less than modulation angle 804''. That is, the offset can be defined in a clockwise or counterclockwise direction relative to modulation angle 804'' and can have any of a number of values ​​within offset range 810. In some implementations, offset range 810 can include angles equal to or greater than about 5-15 degrees from modulation angle 804''. For example, a minimum offset angle within offset range 810 can be about 10 degrees from modulation angle 804''. In some implementations, offset range 810 can include angles equal to or less than about 25-35 degrees from modulation angle 804''. For example, a maximum offset angle within offset range 810 can be about 30 degrees from modulation angle 804''.

[0069] Example 800'' also illustrates that the offset modulation angles can be formed within an offset range 810' that includes angles greater than modulation angle 804''. In some implementations, offset range 810' can include angles equal to or greater than about 5-15 degrees from modulation angle 804''. For example, a minimum offset angle within offset range 810' can be about 10 degrees from modulation angle 804''. In some implementations, offset range 810' can include angles equal to or less than about 25-35 degrees from modulation angle 804''. For example, a maximum offset angle within offset range 810' can be about 30 degrees from modulation angle 804''.

[0070] 9A and 9B show examples of an image 900 captured without an offset to the modulation angle (FIG. 9A) and an image 910 captured with an offset to the modulation angle (FIG. 9B). Images 900 and / or 910 can be used with one or more other examples described elsewhere herein. Images 900 and 910 in this example are simulations generated based on sample data, where the sample data is the same in both images. For example, images 900 and 910 can be generated separately using the same input conditions except for the SIM angle (e.g., the sample data in images 900 and 910 can be statistically the same). Images 900 and 910 can be captured when the periodic pattern of the substrate has a pitch of about 275 nm. In some implementations, image 900 can be captured with the SIM pattern forming a 45 degree angle with respect to a reference axis. For example, image 900 can be similar to the first scenario listed in Table 1 above (e.g., without providing an offset to the modulation angle). Image 900 may be a SIM reconstruction of multiple images of fluorescence captured from a sample, including various relatively bright and dark regions, including brighter image portions 902A and darker image portions 902B. Analysis may be performed on the brighter image portions 902A and / or darker image portions 902B, among other things, to obtain information about the sample. The usefulness of each of the brighter and darker image portions 902A and 902B in such analysis depends in part on the amount of crosstalk affecting the image content (e.g., fluorescence) that makes up the respective brighter and darker image portions 902A and 902B. For example, Table 1 above illustrates %PF and error rates that may be associated with SIM images generated without the benefit of the present subject matter.

[0071] In some implementations, the image 910 may be captured with a SIM pattern that forms an angle of 25 degrees with respect to the reference axis. For example, the image 910 may be similar to the second scenario listed in Table 1 above (e.g., by providing an offset to the modulation angle). The image 910 may be a SIM reconstruction of multiple images of fluorescence captured from the sample, including various relatively bright and relatively dark regions, including brighter image portions 904A and darker image portions 904B. Analysis may be performed on the brighter image portions 904A and / or darker image portions 904B, among others, to obtain information about the sample. The usefulness of each of the brighter image portions 904A and darker image portions 904B in such analysis depends in part on the amount of crosstalk affecting the image content (e.g., fluorescence) that constitutes the respective brighter image portions 904A and darker image portions 904B. For example, Table 1 above shows that the %PF and error rate that may be associated with SIM images may be improved in accordance with the present subject matter.

[0072] Table 2 below shows example results for the analysis of a sample based on images 900 and 910.

[0073] [Table 2]

[0074] Table 2 includes three metrics that may be affected by the relative angle. The first metric is the pass filter percentage, or %PF. The second metric is the align percentage, sometimes referred to as %Align. For example, %Align may reflect the percentage of pass filter clusters aligned to the genome being sequenced. The third metric is the mismatch rate (e.g., MMR-150). Here, Table 2 shows that when the angle of the SIM pattern is offset by 20 degrees, a higher percentage (83.54%) of clusters pass the filter compared to the %PF (61.30%) without the offset. Here, Table 2 shows that when the angle of the SIM pattern is offset by 20 degrees, a higher percentage (99.85%) of clusters are aligned compared to the %Align (97.83%) without the offset. Here, Table 2 also shows that when the angle of the SIM pattern is offset by 20 degrees, a lower mismatch rate (0.266) can be achieved compared to the mismatch rate (1.524) without the offset. That is, providing an offset can improve the quality of the analysis.

[0075] 10A and 10B show other examples of an image 1000 captured without an offset to the modulation angle (FIG. 10A) and an image 1010 captured with an offset to the modulation angle (FIG. 10B). Images 1000 and / or 1010 can be used with one or more other examples described elsewhere herein. Images 1000 and 1010 in this example are simulations generated based on sample data, where the sample data is the same in both images. For example, images 1000 and 1010 can be generated separately using the same input conditions except for the SIM angle (e.g., the sample data in images 1000 and 1010 can be statistically the same). Images 1000 and 1010 can be captured when the periodic pattern of the substrate has a pitch of about 250 nm. For example, other than the substrate pitch (e.g., about 250 nm compared to about 275 nm), the sample data in images 1000 and 1010 can correspond to the sample data in images 900 and 910 in FIGS. 9A and 9B. In some implementations, the image 1000 may be captured with a SIM pattern that forms a 45 degree angle with respect to the reference axis. For example, the image 1000 may be similar to the first scenario listed in Table 1 above (e.g., without providing an offset to the modulation angle). The image 1000 may be a SIM reconstruction of multiple images of fluorescence captured from a sample, including various relatively bright and relatively dark regions, including brighter image portions 1002A and darker image portions 1002B. Analysis may be performed on the brighter image portions 1002A and / or darker image portions 1002B, among others, to obtain information about the sample. The usefulness of each of the brighter image portions 1002A and darker image portions 1002B in such analysis depends in part on the amount of crosstalk affecting the image content (e.g., fluorescence) that constitutes the respective brighter image portions 1002A and darker image portions 1002B. For example, Table 1 above shows %PF and error rates that may be associated with SIM images generated without the benefit of the present subject matter.

[0076] In some implementations, the image 1010 may be captured with a SIM pattern that forms an angle of 25 degrees with respect to the reference axis. For example, the image 1010 may be similar to the second scenario listed in Table 1 above (e.g., by providing an offset to the modulation angle). The image 1010 may be a SIM reconstruction of multiple images of fluorescence captured from a sample, including various relatively bright and relatively dark regions, including brighter image portions 1004A and darker image portions 1004B. Analysis may be performed on the brighter image portions 1004A and / or darker image portions 1004B, among others, to obtain information about the sample. The usefulness of each of the brighter image portions 1004A and darker image portions 1004B in such analysis depends in part on the amount of crosstalk affecting the image content (e.g., fluorescence) that constitutes the respective brighter image portions 1004A and darker image portions 1004B. For example, Table 1 above shows that the %PF and error rate that may be associated with SIM images may be improved in accordance with the present subject matter.

[0077] Table 3 below shows example results for images 1000 and 1010.

[0078] [Table 3]

[0079] Table 3 includes three metrics that may be affected by the relative angle. The first metric is the pass filter percentage, or %PF. The second metric is the align percentage, sometimes referred to as %Align. For example, %Align may reflect the percentage of pass filter clusters aligned to the genome being sequenced. The third metric is the mismatch rate (e.g., MMR-150). Here, Table 3 shows that when the angle of the SIM pattern is offset by 20 degrees, a higher percentage (73.25%) of clusters pass the filter compared to the %PF (34.97%) without the offset. Here, Table 3 shows that when the angle of the SIM pattern is offset by 20 degrees, a higher percentage (99.51%) of clusters are aligned compared to the %Align (91.27%) without the offset. Here, Table 3 also shows that when the angle of the SIM pattern is offset by 20 degrees, a lower mismatch rate (0.784) can be achieved compared to the mismatch rate (3.134) without the offset. That is, providing an offset can improve the quality of the analysis.

[0080] That is, the angular offset of the SIM pattern can provide useful improvements in analysis using a SIM system. This can be beneficial when the substrate has a periodic pattern with a relatively small pitch. For example, when the camera pixel spacing is relatively low (e.g., about 220-230 nm), it may not be possible to visually observe the SIM pattern. This can occur for periodic patterns (e.g., flow cells) with a pitch of less than about 300 nm, to give one example. However, because of the reduced fluorescence crosstalk, SIM reconstructions can still be performed in a reliable manner and provide useful results.

[0081] 11 illustrates an example embodiment of a method 1100. Method 1100 may be used with one or more of the other embodiments described elsewhere herein. More or fewer operations may be performed than shown. Two or more operations may be performed in a different order unless otherwise noted.

[0082] At operation 1110, method 1100 may involve configuring a SIM system (e.g., system 100 of FIG. 1) to perform illumination of a sample on a substrate (e.g., substrate 300 of FIG. 3) having a substrate pattern (e.g., periodic pattern 302 of FIG. 3 or random pattern 1401 of FIG. 14). For example, a sample may be prepared in which the sample material is associated with a fluorescent tag that produces fluorescent emission in response to illumination with excitation light.

[0083] At operation 1120, method 1100 may involve selecting a pitch of a SIM pattern (e.g., SIM pattern 502 of FIG. 5 or SIM pattern 702 of FIG. 7) of a SIM system based on at least one characteristic of the substrate pattern. In some implementations, the pitch of the SIM pattern may be between about 200 nanometers and 1600 nanometers. If the substrate pattern is a periodic pattern, the pitch of the SIM pattern may be selected to be larger or smaller than the pitch of the periodic pattern. As another example, if the substrate pattern is a random pattern, the pitch of the SIM pattern may be selected based on the microstructural resolution of the random pattern of the substrate.

[0084] At operation 1130, method 1100 may involve providing an offset (e.g., offsets 806, 806', and / or 806'') to each of the modulation angles of the SIM system to form offset modulation angles (e.g., offset modulation angles 808, 808', and / or 808''). In some implementations, the offset may be selected from ±10 degrees to ±80 degrees relative to the modulation angle. For example, the modulation angle may be defined with respect to a reference axis. The offset may be defined in a clockwise or counterclockwise direction relative to the modulation angle. Operation 1130 may be performed when the substrate pattern is a periodic pattern. None of the offset modulation angles may correspond to (e.g., align with) the angle of an axis of symmetry of the periodic pattern.

[0085] In operation 1140, the method 1100 may involve performing illumination of the substrate sample with a SIM pattern (e.g., as shown in FIG. 5 and / or FIG. 7). For example, the illumination may be performed using one or more lasers and / or one or modes of LEDs.

[0086] At operation 1150, the method 1100 may involve detecting radiation (e.g., images 910 and / or 1010) generated by the sample in response to the illumination. For example, fluorescent radiation produced by a fluorescent tag associated with the sample material may be detected.

[0087] FIG. 12 illustrates, in a schematic manner, another example of a system 1200 that can facilitate a SIM. The system 1200 can be used with one or more of the other embodiments described herein. Some components of this and other embodiments are illustrated conceptually as blocks or other general components. Such components can be implemented in the form of one or more separate or integrated components to perform the indicated functions. Components corresponding to components of the system 100 (FIG. 1) that are not explicitly mentioned can play the same or similar role in the system 1200.

[0088] The system 1200 includes a phase selector 108' positioned before the light structuring component 104'. In some implementations, the phase selector 108' can receive the beam 106 from the light source 102. The phase selector 108' can provide the phase-selected light to the light structuring component 104'. The light structuring component 104' can generate structured light and provide the structured light to a subsequent component in the system 1200. In some implementations, the subsequent component is a projection lens 110. Other approaches can be used.

[0089] In some implementations, the stage 118 can translate the sample 116 a distance relative to the stationary light stripes to achieve phase selection (e.g., using a piezoelectric actuator in the stage 118). For example, the phase selector 108' can then be bypassed in or eliminated from the system 1200.

[0090] FIG. 13 is a schematic diagram of an exemplary system 1300 that may be used for biological and / or chemical analysis. Systems and / or techniques described herein, including but not limited to system 100 (FIG. 1), system 1200 (FIG. 12), and / or method 1100 (FIG. 11), may be part of the system 1300 in some implementations. The system 1300 may be operated to obtain any information or data related to at least one biological and / or chemical substance. In some implementations, a carrier 1302 provides a material to be analyzed. For example, the carrier 1302 may include a cartridge or any other component that holds the material. In some implementations, the system 1300 has a receptacle 1304 for receiving the carrier 1302 at least during the analysis. The receptacle 1304 may form an opening in a housing 1306 of the system 1300. For example, some or all of the components of the system 1300 may be in the housing 1306.

[0091] The system 1300 can include an optical system 1308 for biological and / or chemical analysis of the material of the carrier 1302. The optical system 1308 can perform one or more optical operations, including, but not limited to, illuminating and / or imaging the material. For example, the optical system 1308 can include any or all of the systems described elsewhere herein. As another example, the optical system 1308 can perform any or all of the operations described elsewhere herein.

[0092] The system 1300 can include a thermal system 1310 for providing thermal processing for biological and / or chemical analysis. In some implementations, the thermal system 1310 thermally conditions at least a portion of the material to be analyzed and / or the carrier 1302.

[0093] The system 1300 can include a fluid system 1312 for managing one or more fluids associated with biological and / or chemical analysis. In some implementations, the fluids can be provided to the carrier 1302 or its materials. For example, fluids can be added to and / or removed from the materials of the carrier 1302.

[0094] The system 1300 includes a user interface 1314 that facilitates input and / or output related to the biological and / or chemical analysis. The user interface may be used to specify one or more parameters for operation of the system 1300 and / or to output results of the biological and / or chemical analysis, to name a few examples. For example, the user interface 1314 may include one or more display screens (e.g., a touch screen), a keyboard, and / or a pointing device (e.g., a mouse or track pad).

[0095] The system 1300 can include a system controller 1316 that can control one or more aspects of the system 1300 for performing biological and / or chemical analyses. The system controller 1316 can control the receptacle 1304, the optical system 1308, the thermal system 1310, the fluidic system 1312, and / or the user interface 1314. The system controller 1316 can include at least one processor and at least one storage medium (e.g., memory) having executable instructions for the processor.

[0096] FIG. 14 shows an example of a substrate 1400 having a random pattern 1401. The substrate 1400 can be used with one or more other examples described elsewhere herein. The random pattern 1401 of the substrate 1400 is formed here by a random or pseudorandom distribution of wells 1402 on the surface. The wells 1402 are represented here diagrammatically using circles and can have any shape. In some implementations, the wells 1402 can be nanowells or another structure suitable for holding a sample. For example, the sample can be a genetic material (not shown) distributed in some or all of the wells 1402 of the random pattern 1401.

[0097] With the substrate 1400 provided with the random pattern 1401, the optical system can obtain a certain resolution of the microstructures on the surface of the substrate 1400. In some implementations, a resolution 1404 of the microstructures of the random pattern 1401 on the substrate 1400 can be defined or determined. For example, the resolution 1404 can be expressed as a length corresponding to the smallest distance between two distinguishable features on the substrate 1400.

[0098] The optical system can perform SIM analysis of the sample on the substrate 1400. In doing so, the optical system can illuminate the substrate 1400 with one or more SIM patterns. In some implementations, a SIM pattern 1406 can be generated. Here, the SIM pattern 1406 is represented diagrammatically as four parallel bands of light incident on the surface of the substrate 1400. Other approaches can be used. For example, the SIM pattern 1406 can have more or fewer light bands and / or can be oriented in one or more other directions relative to the substrate 1400. The distance between the bands of the SIM pattern 1406 can be referred to as the pitch of the SIM pattern 1406. In some implementations, the pitch of the SIM pattern 1406 can be selected based on the characteristics of the random pattern 1401 of the substrate 1400. For example, the pitch of the SIM pattern 1406 can be selected based on the microstructural resolution of the random pattern 1401 of the substrate 1400. In some implementations, the pitch of the SIM pattern 1406 can be on the order of magnitude of the resolution 1404. For example, the pitch of the SIM pattern 1406 can be larger, such as on the order of several times the resolution 1404 (e.g., if the resolution 1404 is on the order of 100 nm, the pitch of the SIM pattern 1406 can be on the order of hundreds of nm). If the pitch of the SIM pattern 1406 is too large relative to the resolution 1404, the optical system may not be able to resolve the fine structures of the substrate 1400.

[0099] 15 illustrates an example of a system 1500 having a rotatable mirror 1502. The system 1500 can be used with one or more of the other examples described elsewhere herein. In some implementations, any of the systems or techniques described herein can be implemented as part of the system 1500. For example, one or more arrangements of SIM patterns 200, 502, 702 can be implemented as part of the system 1500. Individual components of the system 1500 can perform similar or identical functions as corresponding components described with reference to other examples in this description.

[0100] The system 1500 includes a light source 1504. In some implementations, the light source 1504 provides light that is in turn received through at least one fiber optic cable 1506. For example, the light source 1504 and the fiber optic cable 1506 can be collectively considered a fiber launch module.

[0101] The system 1500 includes a grating 1508 and a grating 1510. In some implementations, the grating 1508 and / or 1510 can function as a diffractive component with respect to light from the light source 1504. For example, the grating 1508 and / or 1510 can comprise a substrate having a periodic structure, the substrate being combined with a prism. The gratings 1508 and 1510 can be positioned relative to one another according to one or more arrangements, where the gratings 1508 and 1510 face one another in the system 1500. The gratings 1508 and 1510 can be substantially identical to one another or can have one or more differences. The size, periodicity, or other spatial aspects of one of the gratings 1508 and 1510 can be different from the size, periodicity, or other spatial aspects of the other. The grating orientation (i.e., the spatial orientation of the periodic structure) of one of the gratings 1508 and 1510 can be different from the grating orientation of the other. In some implementations, the grating orientations of each of the gratings 1508 and 1510 may be substantially perpendicular to each other or at any other angle relative to each other, with the gratings themselves pointing toward each other. In some implementations, the gratings 1508 and 1510 may be in an offset position relative to the rotatable mirror 1502. In some implementations, the gratings 1508 and / or 1510 may be in a fixed position relative to the light source 1504.

[0102] The system 1500 can include one or more components (e.g., as the phase selector 108 of FIG. 1) to facilitate phase selection for light to be applied to the sample (e.g., to the sample 116 of FIG. 1). Here, the system 1500 includes a piezoelectric stripe shifter 1512. In some implementations, the piezoelectric stripe shifter 1512 can receive light from the gratings 1508 and / or 1510 and perform phase selection for some or all of the light. For example, the piezoelectric stripe shifter 1512 can be used to control the phase of a structured light pattern to be used when a particular image is to be captured. The piezoelectric stripe shifter 1512 can include a piezoelectric actuator. For example, a piezoelectric piston system can be used to achieve phase selection. Other approaches can be used. For example, a tilted optical plate can be used for phase selection. For example, the system 1500 is implemented here on a board 1514, and one or more regions of the board 1514 can be tilted to achieve phase selection. As another example, one or more of the gratings 1508 and 1510 can be moved (e.g., translated) for phase selection, such as by a piezoelectric actuator. The light emitted from the piezoelectric stripe shifter 1512 may be referred to as phase-selected light to indicate that the light has been adjusted according to a particular phase selection. In some implementations, the gratings 1508 and / or 1510 may be in a fixed position relative to the light source 1504.

[0103] The system includes a projection lens 1516, which may include one or more optical components (e.g., lenses) for conditioning the light it receives from the piezoelectric fringe shifter 1512. For example, the projection lens 1516 may control properties of the light before it enters an objective lens (e.g., objective lens 114 in FIG. 1).

[0104] The rotatable mirror 1502 can be used to redirect at least one light beam to arrive toward and / or from one or more of the gratings 1508 or 1510. The rotatable mirror 1502 can include one or more materials to sufficiently reflect the electromagnetic waves with which the sample is illuminated. In some implementations, the light from the light source 1504 includes a laser beam of one or more wavelengths. For example, a metal-coated mirror and / or a dielectric mirror can be used. The rotatable mirror 1502 can be double-sided. For example, the rotatable mirror 1502 can be considered double-sided if it can perform reflection on at least a portion of its two sides (e.g., reflective at a first end for a first beam path and reflective at a second end opposite the first end for a second beam path).

[0105] The rotatable mirror 1502 may include an elongated member. The rotatable mirror 1502 may have any of a variety of form factors or other shape characteristics. The rotatable mirror 1502 may have a generally flat configuration. The rotatable mirror 1502 may have a substantially square or other rectangular shape. The rotatable mirror 1502 may have rounded corners. The rotatable mirror 1502 may have a substantially constant thickness. The reflective surface of the rotatable mirror 1502 may be substantially planar.

[0106] The rotatable mirror 1502 may be supported by a shaft 1518 of the system 1500. The shaft 1518 may allow the rotatable mirror 1502 to rotate in either or both directions about the shaft 1518. The shaft 1518 may be made of a material having sufficient rigidity to hold and manipulate the rotatable mirror 1502, including but not limited to metal. The shaft 1518 may be coupled substantially at the center of the rotatable mirror 1502. For example, the rotatable mirror 1502 may have an opening at the center or a notch from one side that reaches the center to facilitate coupling with the shaft 1518. As another example, the shaft 1518 may include separate shaft portions coupled to each side of the rotatable mirror 1502 without requiring any openings in the rotatable mirror 1502. The shaft 1518 may have at least one suspension 1520. Here, suspensions 1520 are positioned at the ends of shaft 1518 on either side of rotatable mirror 1502. Suspensions 1520 may include bearings or other features that facilitate low friction operation.

[0107] The rotatable mirror 1502 can be actuated to adopt one or more positions. Any form of motor or other actuator can be used to control the rotatable mirror 1502. In some implementations, a stepper motor 1522 is used. The stepper motor 1522 can be coupled to the shaft 1518 and can be used to rotate the shaft 1518, and thereby the rotatable mirror 1502, to adopt a desired position. In some implementations, the rotatable mirror 1502 rotates in the same direction (e.g., always clockwise or always counterclockwise about the axis of rotation of the shaft 1518) to a new position. In some implementations, the rotatable mirror 1502 reciprocates between two or more positions (e.g., alternately clockwise or counterclockwise about the axis of rotation of the shaft 1518).

[0108] The terms "substantially" and "about" used throughout this specification are used to describe and account for small variations, such as those due to processing variations. For example, they can refer to ±5% or less, such as ±2% or less, such as ±1% or less, such as ±0.5% or less, such as ±0.2% or less, such as ±0.1% or less, such as ±0.05% or less. Also, as used herein, indefinite articles such as "a" or "an" mean "at least one".

[0109] It should be understood that all combinations of the foregoing concepts and additional concepts discussed in more detail below (unless such concepts are mutually inconsistent) are contemplated as being part of the inventive subject matter disclosed herein. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the inventive subject matter disclosed herein.

[0110] Although several implementations have been described, it will be understood that various modifications can be made without departing from the spirit and scope of the invention.

[0111] Additionally, the logic flows depicted in the figures do not require the particular order shown, or sequential order, to achieve desired results. Additionally, other steps can be provided or eliminated from the described flows, and other components can be added to or removed from the described systems. Accordingly, other implementations are within the scope of the following claims.

[0112] While certain features of the described implementations have been illustrated as described herein, many modifications, substitutions, changes, and equivalents will occur to those skilled in the art. It should therefore be understood that the appended claims are intended to cover all such modifications and changes as fall within the scope of the implementations. It should be understood that these are presented by way of example only, and not by way of limitation, and that various changes in form and details may be made. Any portion of the apparatus and / or methods described herein may be combined in any combination, except in mutually exclusive combinations. The implementations described herein may include various combinations and / or subcombinations of the functions, components, and / or features of the different implementations described.

Claims

1. A structured illumination microscopy (SIM) system, comprising: a light source; an optical structuring component for providing light from the light source with a SIM pattern for illuminating a sample on a substrate having a substrate pattern, wherein a pitch of the SIM pattern is based on characteristics of the substrate pattern; an image sensor for detecting radiation generated by the sample in response to the illumination; The SIM system is configured to rotate the SIM pattern around an optical axis by a modulation angle, and at least one of the illuminations is performed at each of the modulation angles of the SIM pattern.

2. The SIM system according to claim 1, wherein the substrate pattern includes a periodic pattern, and the pitch of the SIM pattern is based on the pitch of the periodic pattern.

3. The SIM system according to claim 2, wherein the pitch of the SIM pattern is greater than the pitch of the periodic pattern.

4. The SIM system according to claim 3, wherein the pitch of the SIM pattern is about 1.5 to about 2 times the pitch of the periodic pattern.

5. The SIM system according to claim 2, wherein the optical structuring component includes a grating for generating the SIM pattern, and the grating corresponds to the pitch of the periodic pattern.

6. The SIM system according to claim 1, wherein the substrate pattern includes nanowells formed on the substrate.

7. The SIM system according to claim 6, wherein the substrate pattern includes that the nanowells are arranged in a square array.

8. The SIM system according to claim 7, wherein the square array has the nanowells arranged in linear rows and linear columns, and the linear rows are substantially perpendicular to the linear columns.

9. A first linear row or linear column is illuminated by the SIM pattern, and a second linear row or linear column is parallel and adjacent to the first linear row or linear column. When the first linear row or linear column is illuminated by the SIM pattern, the second linear row or linear column is not illuminated by the SIM pattern.

10. The SIM system according to claim 1, wherein the light source includes at least one of a laser or a light emitting diode.

11. The SIM system according to claim 1, wherein the sample includes a biological material, and the image sensor detects fluorescence emitted by the sample in response to the illumination.

12. The SIM system according to claim 1, wherein the substrate pattern is a periodic pattern, and the SIM system is configured to provide an offset for each of the modulation angles of the SIM pattern to form an offset modulation angle, wherein none of the offset modulation angles corresponds to an angle of a symmetry axis of the periodic pattern, and at least one of the illuminations is performed at each of the offset modulation angles of the SIM pattern.

13. The SIM system according to claim 1, wherein the substrate pattern includes a random pattern, and the pitch of the SIM pattern is based on a resolution related to the random pattern.

14. The SIM system according to claim 13, wherein the pitch of the SIM pattern is approximately the same magnitude as the resolution related to the random pattern.

15. A method comprising: configuring a structured illumination microscopy (SIM) system for illuminating a sample on a substrate having a substrate pattern; selecting a pitch of a SIM pattern or a grating of the SIM system based on characteristics of the substrate pattern; performing the illumination of the sample on the substrate with the SIM pattern; and detecting radiation generated by the sample in response to the illumination, wherein the substrate pattern includes a periodic pattern, the pitch is selected based on a pitch of the periodic pattern, and the grating has a pitch that is about 1.5 to about 2 times the pitch of the periodic pattern.

16. The method according to claim 15, wherein the sample includes a biological material, and detecting the radiation includes detecting fluorescence emitted by the sample in response to the illumination.

17. A structured illumination microscopy (SIM) system comprising: a light source, An optical structuring component for providing light from a light source with a SIM pattern for illuminating a sample on a substrate having a periodic pattern, wherein the optical structuring component is configured to rotate the SIM pattern about an optical axis by a modulation angle and to provide an offset for each of the modulation angles of the SIM system for forming an offset modulation angle, wherein none of the offset modulation angles corresponds to an angle of a symmetry axis of the periodic pattern. An image sensor for detecting radiation generated by the sample in response to the illumination, and a structured illumination microscopy (SIM) system comprising the same. **Claim 18** The SIM system according to claim 17, wherein the offset is provided such that each of the offset modulation angles is smaller than the corresponding modulation angle. **Claim 19** The SIM system according to claim 17, wherein the offset is provided such that each of the offset modulation angles is larger than the corresponding modulation angle. **Claim 20** The SIM system according to claim 17, wherein the offset is about 10 to 30 degrees. **Claim 21** The SIM system according to claim 20, wherein the offset is about 20 degrees. **Claim 22** The SIM system according to claim 21, wherein one of the modulation angles is about 45 degrees and the offset modulation angle corresponding to one of the modulation angles is about 25 degrees. **Claim 23** The SIM system according to claim 17, wherein the periodic pattern includes nanowells formed on the substrate. **Claim 24** The SIM system according to claim 23, wherein the periodic pattern includes that the nanowells are arranged in a square array. **Claim 25** The SIM system according to claim 24, wherein the square array has nanowells arranged in linear rows and linear columns, and the linear rows are substantially perpendicular to the linear columns. **Claim 26** The SIM system according to claim 23, wherein a first nanowell is illuminated by the SIM pattern, a second nanowell is adjacent to the first nanowell, and the second nanowell is not illuminated by the SIM pattern when the first nanowell is illuminated by the SIM pattern. **Claim 27** The SIM system according to claim 17, wherein the light source includes at least one of a laser or a light emitting diode.

28. The SIM system according to claim 17, wherein the pitch of the SIM pattern is based on the pitch of the periodic pattern.

29. The SIM system according to claim 28, wherein the pitch of the SIM pattern is about 1.5 to about 2 times the pitch of the periodic pattern.

30. A method comprising: Configuring a structured illumination microscopy (SIM) system for rotating a SIM pattern by a modulation angle about an optical axis, the SIM system being configured to illuminate a sample on a substrate having a periodic pattern. Providing an offset for each of the modulation angles of the SIM system for forming an offset modulation angle, none of the offset modulation angles corresponding to the angle of the symmetry axis of the periodic pattern. Illuminating the sample on the substrate with the SIM pattern of the offset modulation angle and Detecting radiation generated by the sample in response to the illumination.

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