Hybrid differential defocus phase contrast

Abstract

To provide advanced techniques of digital phase contrast microscopy.SOLUTION: Phase contrast images are calculated by digitally post-processing microscope images acquired at different angled illumination configurations and defocus values.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] Various examples of the present disclosure generally relate to digital phase contrast techniques that determine a phase contrast image by digitally post-processing multiple microscope images. In particular, techniques are disclosed that enhance the cumulative phase transfer function based on the use of multiple angle illumination arrangements and multiple amounts of defocus. [Background technology]

[0002] When light interacts with a specimen of interest, such as biological tissue, two main contrast mechanisms leave a mark on the incident light. First, the specimen can attenuate the incident light through absorption. Second, the specimen can modify the wavefront of the incident light, leaving behind phase contrast. For thin, unlabeled biological specimens, absorption is generally negligible. In these situations, phase contrast microscopy is used to generate specimen images.

[0003] Phase-sensitive techniques have a long history, including Zernike phase contrast imaging [1] (Non-Patent Document 1), Gabor in-line homography [2] (Non-Patent Document 2), and Nomarski differential interferometry (DIC) [3] (Non-Patent Document 3). While phase-sensitive, these methods are generally not quantitative, and the final images are prone to artifacts not originating from the specimen itself. For example, halo artifacts observed at phase discontinuities in Zernike phase contrast imaging hinder direct phase quantification. Gabor in-line homography suffers from so-called double image artifacts, while Nomarski DIC requires additional hardware components such as phase-shifting elements and polarization optics. The latter issue poses hurdles for microscope users in terms of cost, complexity, and calibration difficulties.

[0004] More recently, quantitative phase imaging systems have moved towards a data-driven approach: here, typically, multiple images are recorded and numerically combined into a single phase-contrast image using first principles of physical image formation. This type of technique is therefore sometimes called digital phase contrast: the phase contrast is obtained by digital post-processing of the acquired intensity images. Prominent examples are the transport of intensity equation (TIE) [4] and the differential phase contrast method (DPC) [5]. To acquire a TIE dataset, the specimen is translated in the optical axis (z-direction) and a so-called z-stack consisting of at least two images is recorded.

[0005] The data is then converted into a phase-contrast image by solving a diffusion-type partial differential equation. For example, US 2020 / 209604 A1 discloses annular illumination combined with TIE (i.e., image acquisition with a non-zero defocus amount) and accurate phase transfer function (PTF) calculation. In DPC, the specimen is illuminated from at least three different directions (angular illumination) while maintaining its unique z-position. Possible sources of angular illumination include any type of segmented illumination source, such as a segmented diode [5] (Non-Patent Document 5), a light-emitting diode (LED) array [6] (Non-Patent Document 6), a digital micromirror device (DMD), a liquid crystal display (LCD), or a variable condenser iris. The recorded data is then converted into a phase-contrast image by solving a deconvolution problem.

[0006] TIE and DPC have fundamental drawbacks: (1) TIE typically employs a point source. To improve the lateral resolution achievable with an optical system, a radiation source that is extended laterally relative to the optical axis is desirable. (2) The performance of DPC degrades when the numerical apertures (NA) of the illumination and detection are mismatched [6, 7]. The latter is particularly problematic when the illumination NA is smaller than the detection NA. In such a situation, the phase image lacks contrast.

[0007] A possible solution to problem (1) has recently been reported by Zuo and coworkers [7]. In this work, the specimen is illuminated sequentially by individual LEDs, which are simultaneously defocused. Unfortunately, sequentially using each LED of a large LED matrix, combined with defocusing, requires acquiring hundreds of images, making this technique time-consuming and computationally complex, as the data must be recorded, transferred, processed, and stored.

[0008] A possible solution to problem (2) is to combine DPC with an improved objective, as shown for example in PCT / EP2020 / 050307. In the latter patent, the authors used an amplitude-modulated pupil ring in combination with a DPC acquisition scheme. Unfortunately, this has the drawback that some of the light entering the pupil is absorbed—an undesirable effect on the fluorescence image when combined with DPC without a change in the objective. [Prior art documents] [Non-patent literature]

[0009] [Non-Patent Document 1] Zernike, Frits. "Phase contrast, a new method for the microscopic observation of transparent objects part II." Physica 9.10 (1942): 974-986. [Non-patent document 2] Gabor, Dennis. "Microscopy by reconstructed wave-fronts." Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 197.1051 (1949): 454-487. [Non-patent document 3] Nomarski, Georges. "Microinterferometre differentiel a ondes polarisees." J. Phys. Rad. 16 (1955): 9S-13S. [Non-patent document 4] Streibl, Norbert. "Phase imaging by the transport equation of intensity." Optics com munications 49.1 (1984): 6-10. [Non-Patent Document 5] Mehta, Shalin B., and Colin JR Sheppard. "Quantitative phase-gradient imaging at high resolution with asymmetric illumination-based differential phase contrast." Optics letters 34.13 (2009): 1924-1926. [Non-patent document 6] Tian, ​​Lei, and Laura Waller. "Quantitative differential phase contrast imaging in an LED array microscope." Optics express 23.9 (2015): 11394-11403. [Non-Patent Document 7] Zhou, Shun, et al. "Transport-of-intensity Fourier ptychographic diffraction tomography: defying the matched illumination condition." Optica 9.12 (2022): 1362-1373. [Patent documents]

[0010] [Patent Document 1] International Publication No. 2020 / 144228 (PCT / EP2020 / 050307) Summary of the Invention [Problem to be solved by the invention]

[0011] Therefore, there is a need for an improved technique for digital phase contrast microscopy. A need exists to alleviate at least the limitations and drawbacks identified above. This need is met by the features of the independent claims. The features of the dependent claims define embodiments. [Means for solving the problem]

[0012] A digital phase contrast technique is disclosed below: Multiple microscope images are acquired at multiple settings, each characterized by a different amount of defocus and a different angular illumination arrangement. Various techniques are based on the discovery that both defocusing of the imaging plane and angular illumination of the imaging plane have the potential to obtain images that encode phase information. By combining angular illumination and defocusing, phase information can be reconstructed over a wider spatial frequency range than referenced techniques such as TIE and DPC. In this way, good-quality phase-contrast images can be obtained.

[0013] A method for determining a phase contrast image is disclosed, wherein the phase contrast image is determined based on a plurality of microscopic images acquired using a microscope.

[0014] The microscope images are intensity images, i.e., they are not acquired with phase contrast, but nevertheless contain encoded phase information that allows the phase of the imaged specimen to be reconstructed.

[0015] The microscope includes an illumination module configured to provide switchable angular illumination, i.e., drive different angular illumination configurations. The angular illumination provides a range of angles at which light is incident on the imaging plane of the microscope, and the angular spectrum of this angular illumination is fixed across the imaging plane.

[0016] The microscope further includes an optical system, which may include one or more optical elements, such as a lens. The optical system is configured to illuminate the imaging surface. The optical system is further configured to image the imaging surface onto at least one camera of the microscope.

[0017] The method includes controlling a lighting module to drive a plurality of angular lighting arrangements, in at least some examples, at least one of the plurality of angular lighting arrangements including a range of lighting directions, i.e., the at least one angular lighting arrangement each comprising an extended angular spectrum (rather than just a single lighting angle).

[0018] Only one of the multiple angle lighting arrangements may include a range of lighting directions. Each of the multiple angle lighting arrangements may include a range of lighting directions. If all of the multiple angle lighting arrangements do not include a range of lighting directions, the remaining angle lighting arrangements include one lighting direction. The multiple angle lighting arrangements may each have angular spectra with different widths. For example, a first angle lighting arrangement has a first angular spectrum and a second angle lighting arrangement has a second angular spectrum with a different second width. A wider angular spectrum can be used with a narrower angular spectrum. The narrower angular spectrum can have the minimum width achievable for each lighting module (i.e., a single lighting direction).

[0019] For example, each of the multiple angular illumination arrangements (indexed by j) may be assigned a respective illumination numerical aperture (NA), NA i,j The illumination NA defines the angular range over which the imaging plane is illuminated. The higher the NA, the inarrows the angle range at which light is incident, so NA i Increasing generally increases the coherence of the illumination, effectively narrowing the light source and increasing spatial coherence.

[0020] The detection optical system, such as the objective lens or objective lens system, has a NA (Numerical Aperture) of 0.1 . d The NA of a detector is defined by the objective lens or lens system. The NA of a detector affects how fine the details in an image can be resolved. The higher the NA of a detector, the more light it can collect from a wider angle, improving resolution.

[0021] Each illumination numerical aperture (associated with each of the multiple angle illumination arrangements) is smaller than the detection numerical aperture, e.g., the ratio is at least 2, and σ=NA i,j / NA d where σ≦½ for all j. σ is sometimes called the coherence parameter, i.e., σ can be less than or equal to ½ for any image acquired and post-processed.

[0022] Although the above examples disclose at least one of the multiple angle lighting arrangements as including a range of lighting directions, this is generally arbitrary. In some examples, each of the multiple angle lighting arrangements includes a single lighting angle. By "single lighting angle," we mean that the width of each of the lighting angle distributions is as small as achievable using the lighting module. Generally, this means that a single light source, e.g., a single LED in each array, is switched on.

[0023] The method further includes controlling at least one camera to capture multiple images at multiple angular illumination arrangements and multiple amounts of defocus.

[0024] The method further includes combining the multiple images to determine a phase-contrast image. In principle, combining two or more images may include calculating pairwise differences. Combining two or more images may also include calculating the phase, i.e., a complex-valued representation of the sum of the two or more image combinations, with each phase shift applied to a separate image.

[0025] Each of the multiple images can be combined with each of the additional images. In some scenarios, multiple subsets of images may be formed, each including only some of the images. Each image in a given subset is then combined with any other image in that subset. This approach is particularly applicable when multiple phase reconstruction algorithms are used and run on separate subsets.

[0026] A phase contrast image can have quantitative phase contrast, i.e., the contrast can quantitatively encode the phase shift imparted by the object.

[0027] While in the above, at least one camera and illumination module are controlled to acquire an image, in other scenarios, multiple images can be pre-acquired, with multiple defocus amounts and multiple angular illumination configurations, loaded from a database or image archive, and then combined to determine a phase contrast image.

[0028] The computer device includes a processor and a memory. The memory stores program code. The processor loads the program code and executes the program code. When the processor executes the program code, the computer device performs the method disclosed above.

[0029] The computer program or computer-readable storage medium includes program code that is loaded and executed by a processor, which, when executed, performs the methods disclosed above.

[0030] It is to be understood that the features mentioned above and those to be described below can be used not only in the respective combinations shown, but also in other combinations or alone, without departing from the scope of the invention. [Brief explanation of the drawings]

[0031] [Figure 1] 1A and 1B are schematic diagrams illustrating a system including a microscope and a computer according to various examples. [Figure 2] 1 shows a schematic diagram of a DPC digital phase contrast technique according to a prior art implementation. [Figure 3] 1 shows a schematic diagram of a prior art implementation of the TIE digital phase contrast technique. [Figure 4] 1A-1C are schematic diagrams illustrating various examples of phase contrast techniques; [Figure 5] 5 is a comparison of the phase transfer functions of the phase contrast techniques according to FIGS. 2, 3 and 4. [Figure 6] 1 is a flowchart of a method according to various examples. [Figure 7] 10 shows the angular spectra of various example multiple angle illumination arrangements. DETAILED DESCRIPTION OF THE INVENTION

[0032] Some embodiments of the present disclosure generally provide a plurality of circuits or other electrical devices. References to circuits, other electrical devices, and functionality provided by each are not intended to be limiting, encompassing only those shown and described in the specification. While various disclosed circuits and other electrical devices may be labeled with specific reference numerals, such reference numerals do not limit the scope of operation of the circuits or other electrical devices. Such circuits and other electrical devices may be combined with each other and / or separated in any manner based on the particular type of electrical implementation desired. It is understood that any circuit or other electrical device disclosed herein may include any number of microcontrollers, graphic processor units (GPUs), integrated circuits, memory devices (e.g., flash memory, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or other suitable variations thereof), and software that cooperate with others to perform the operations disclosed herein. Additionally, any one or more electrical devices may be configured to execute program code embodied in a non-transitory computer-readable medium to perform any number of functions as disclosed.

[0033] Hereinafter, the embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be understood that the following description of the embodiments is not to be taken in a limiting sense. The scope of the present invention is not intended to be limited by the embodiments or drawings described below, which are merely examples.

[0034] The drawings should be considered schematic representations, and the components shown in the drawings are not necessarily drawn to scale. Rather, the various components are depicted so that their functions and general purpose will be apparent to those skilled in the art. Connections or couplings between functional blocks, devices, components, or other physical or functional units shown in the drawings or described herein may be implemented by indirect connections or couplings. Couplings between components may also be established via wireless connections. Functional blocks may be implemented in hardware, firmware, software, or a combination thereof.

[0035] The technique disclosed herein can be called "hybrid differential defocus (HDD) phase contrast." HDD phase contrast combines the advantages of TIE and DPC while addressing the drawbacks of each technique. In HDD, the specimen is defocused and illuminated with an asymmetric illumination pattern. Unlike Reference [7], the disclosed technique does not exclusively employ individual LED illumination, which would result in a large number of images being acquired. HDD instead utilizes, at least to some extent, multiplexing of illumination directions, for example, by simultaneously illuminating multiple facets (e.g., multiple LEDs) of a programmable light source. For example, half-pupil illumination can be used. That is, a split light source is used, with exactly half of the light source switched on in terms of area (e.g., top half vs. bottom half, or left half vs. right half). The split is symmetrical with respect to the optical axis, and the pupil itself can be square, rectangular, elliptical, circular, or annular. More generally, multiple illumination arrangements are activated, at least one of which encompasses a range of illumination angles at the imaging plane.

[0036] Additionally, HDD uses a variable pattern displayed by a programmable light source instead of TIE, which exclusively uses a point light source. While DPC holds the specimen at a fixed position on the focal plane, HDD uses axial movement of the specimen to achieve improved phase contrast. Because the imaging plane is uniformly illuminated in the spatial domain with an angular spectrum (i.e., the angular spectrum does not depend on the lateral position relative to the optical axis within the associated aperture), angular illumination configurations should not be confused with, for example, light-sheet microscopy, in which only a sheet of light from a portion of the specimen is illuminated.

[0037] The various techniques are based on the discovery that combining defocusing with a multiple angle illumination arrangement results in a phase contrast modality that improves lateral resolution compared to TIE while not suffering from the NA mismatch that leads to low phase contrast seen in DPC. Also, by multiplexing multiple LEDs in parallel, HDD allows data acquisition protocols to be orders of magnitude faster than conventional techniques [7].

[0038] 1 is a schematic diagram of a system 70 according to various examples. The system 70 includes a microscope 90 and a computer 80. The microscope 90 includes an illumination module 91, an optical system 92, and a detection module 93.

[0039] The detection module 93 includes a detection optics. d The detection module 93 further includes one or more cameras for capturing the microscopic images.

[0040] The illumination module 91 is configured to provide switchable / reconfigurable angular illumination of an imaging plane defined along the optical path 94 of the system 70. This means that the illumination angle is controllable. In addition to controlling the main illumination angle, it is also possible to control the angular spectrum, e.g., width or contributions. For example, multiple illumination arrangements with angular spectra of different widths can be driven. Sometimes only a single illumination direction is driven (angular spectrum with smallest width), and sometimes multiple illumination directions are superimposed (angular spectrum with larger width).

[0041] Optical system 92 is configured to illuminate the imaging surface and further image the imaging surface onto at least one camera of detection module 93 .

[0042] The microscope 90 further includes a control module 95 configured to control various components of the microscope. For example, the control module 95 can be implemented using a CPU, a field programmable gate array (FPGA), or an application-specific integrated circuit (ASIC). The control module 95 can include memory. The control module 95 can be configured to control an illumination module that drives a multiple-angle illumination arrangement. The control module 95 can also be configured to control the detection module 93, and in particular, at least one camera of the detection module 93, to acquire multiple images. Optionally, the control module 95 can be configured to control the optical system 92, for example, to move a sample holder configured to hold a sample to implement multiple amounts of defocus.

[0043] Also shown is a computer 80 that includes an interface 84 configured to communicate with the microscope 90, and specifically, a control module 95. For example, a processor 81, e.g., a CPU, FPGA, ASIC, of ​​the computer 80, provides control data to the control module 95 to perform control functions, such as triggering image acquisition, triggering the activation of a certain angle illumination arrangement, triggering the implementation of a particular amount of defocus, etc. The processor 81 can also acquire image data from the microscope 90 through the interface 84 and post-process the image data. The processor 81 can also load image data from a database or image archive.

[0044] Processor 81 is configured to load and execute program code from memory 83 to perform such techniques. Specifically, processor 81 can perform digital post-processing to determine phase contrast based on a plurality of intensity images acquired from microscope 90. Computer 80 can also include a user interface 82, e.g., a GUI, for outputting the phase contrast thus determined.

[0045] 1 shows a situation in which the computer architecture is split between control module 95 and computer 80, in some situations digital post-processing of image data may be performed by control module 95. Alternatively, or additionally, component-level control of various components of microscope 90 may be at least partially delegated to computer 80.

[0046] 2, 3, and 4 illustrate the differential phase contrast (DPC), transport of intensity equation (TIE), and hybrid differential defocus (HDD) schemes, respectively.

[0047] The DPC (Figure 2) uses a programmable illumination unit (PIU) 201. To generate a phase-contrast image of the specimen, at least three focal plane images must be acquired while varying illumination patterns 202. Specifically, these variable illumination patterns 202 correspond to different angular illumination configurations that illuminate the imaging plane 203 at different angles while the specimen is held in a fixed position. Each pattern 202 includes LEDs driven with different asymmetric distributions about the optical axis 207 (dashed lines and open circles). That is, each illumination configuration includes multiple illumination directions (defined by the LEDs being driven). An objective lens 204 and a tube lens 205 are used to image the imaging plane 203 onto a pixel detector 206 (camera) (part of the optical system, see Figure 1: optical system 92). Different LEDs are driven for different variable illumination patterns 202. A subsequent numerical deconvolution routine converts the recorded images into a phase-contrast image of the specimen (see [6]). Details related to such a DPC phase reconstruction algorithm are provided below.

[0048] Assume that a minimum of three images are recorded from equiangular directions (azimuth angles) spaced 120° apart (this angle represents the azimuth position of the average angular spectrum, for example, when using a semicircular illumination pattern centered at that azimuth angle). These images are all acquired with the same amount of defocus, i.e., in this example, the defocus amount is nominally zero so that the sample is in the imaging plane. These three images are included in the DPC subset. The two-dimensional (2D) raw images are referred to here as I 0° , I 120° , I 240° These can be generated, for example, by three equally angularly spaced LEDs, with or without a diffuser to extend the angular range. Alternatively, any angularly separated light source (digital micromirror device, spatial light modulator, etc.) can be used. Details regarding illumination module 91 are provided above in connection with FIG. 1. A complex-valued real-space phase image is then calculated as the combination of these three images in the DPC subset.

[0049]

number

[0050] The DPC phase contrast image is calculated using the formula of the phase reconstruction algorithm.

number

[0051] H DPC (k)=exp(j·arctan(k y / k x )) is the Hilbert transform kernel (see Kieran G. Larkin and Peter A. Fletcher, "Isotropic scalar image visualization of vector differential image data using the inverse Riesz transform," Biomed. Opt. Express 5, 907-920 (2014), and the appendix), and imag[...] selects the imaginary part of a complex number. Instead of using the Hilbert transform kernel, one can also employ a DPC transform function using the "weak object transfer function" (WOTF) formula: Equation 6. Since the WOTF itself requires the computation of at least two Fourier transforms, the Hilbert transform is an approximation but is faster. Meanwhile, it has been observed that the loss in accuracy is very limited for relevant spatial frequencies.

[0052] DPC phase-contrast images suffer from artifacts induced by shadows cast by scatterers located outside the imaging plane (out-of-focus scatterers). Shadow projections are sensitive to angular illumination and are preserved in the real-space phase and image when performing the above calculations. Examples of scatterers outside the imaging plane include scratches on optical elements in the optical path and dust on the backside of the slide in the specimen holder. These shadows cast in DPC phase-contrast images are generally poorly localized, i.e., limited to a small spatial frequency.

[0053] Referring now to Figure 3, TIE phase reconstruction is based on a diffusion equation relating the axial intensity derivative to the phase of the specimen. The axial intensity derivative is approximated by recording at least two images with the imaging plane and specimen axially moved closer to the focal plane, allowing for multiple amounts of defocus 311. The illumination unit can be fully coherent, such as an on-axis point source 301 or an on-axis collimated laser. Alternatively, partially coherent illumination may be used. After recording images under varying defocus (also known as a z-stack), sufficient information is available to solve the underlying diffusion equation to yield the specimen's phase information [4].

[0054] The TIE subset contains two images, and these two images are I ―ΔZ , I +ΔZ The images are acquired at two different defocus amounts, given by ΔZ=c λ / NA 2 is the distance to the focal plane of the specimen. Thus, positive and negative defocus amounts are used, equidistant from the focal plane. λ and NA are the central wavelength of the illumination and the numerical aperture used. The c parameter therefore refers to the magnitude of defocus relative to the depth of field of the detection optics. In practice, the c parameter (for the images in the TIE subset) is selected between 1 and 10 to control the defocus distance. The two images for the TIE subset are acquired with the same illumination configuration, e.g., on-axis illumination. With such on-axis illumination, the angular spectrum is centered at the apex and partially coherent. This can be achieved by driving only a single light source centered on the optical axis 207 for an array of light sources, as shown in Figure 3 for light source 301 centered on the optical axis 207. However, a range of illumination directions can also be used. For example, for images post-processed using TIE reconstruction, σ≦1 / 3, specifically, 1 / 10≦σ≦1 / 3. The TIE phase-contrast image φ of the specimen TIE is then generated by the formula given by the TIE reconstruction algorithm.

number

[0055] H TIE (k)=k x 2 +k Y 2 is a second-order transfer function, and FFT denotes the 2D Fast Fourier Transform. This simple form of the transfer function is preferable to the calculation of the WOTF transfer function, which is numerically less efficient and provides only a small improvement at high spatial frequencies. This optical transfer function H TIE (k) is -H DPC (k) but is a simplified transfer function that is predefined and does not depend on any microscope properties, i.e., only on the k-space position.

[0056] As previously discussed in relation to the DPC phase reconstruction algorithm, TIE phase-contrast images, unlike DPC phase-contrast images, are less affected by shadowing artifacts caused by out-of-focus scatterers such as impurities, dust, and scratches. This is because the TIE phase reconstruction algorithm removes angle-sensitive shadowing from pairwise difference images according to Equation 3 above, without changing the illumination geometry. On the other hand, high image frequencies are not preserved in TIE phase-contrast images, which results in blurred edges and reduced image resolution.

[0057] According to some examples, two separate phase reconstruction algorithms can be implemented, one based on the DPC subset and Equation 2, and one based on the TIE subset and Equation 3.

[0058] In this scheme, two temporary phase-contrast images are acquired and calculated based on the TIE phase reconstruction algorithm and the DPC phase reconstruction algorithm, respectively. The image information associated with these two temporary phase-contrast images can then be combined to obtain a final phase-contrast image. For example, a low-pass filter can be applied to the temporary phase-contrast image acquired from the TIE phase reconstruction algorithm, and a high-pass filter can be applied to the temporary phase-contrast image acquired from the DPC phase reconstruction algorithm. The filtered representations of these respective temporary phase-contrast images, i.e., the low-pass and high-pass filtered image information, can then be combined pixel-by-pixel to obtain a final phase-contrast image. Thus, the temporary phase-contrast image φ TIE and φ DPC Given the above calculation steps, the final HDD phase contrast image is calculated using optional high-pass-low-pass filters.

number

[0059] In this way, high-pass filtered image information obtained from the DPC phase-contrast image is combined with low-pass filtered image information obtained from the TIE phase-contrast image. The kernel width of the Gaussian filter is controlled by the parameter σ, and the complementary transfer weight function (1-w(k)) is selected to be at least large enough to filter background artifacts such as dust from the DPC temporal phase-contrast image. The scalar parameter d is selected to ensure continuity of the combined DPC and TIE spectra in the circular spatial frequency annulus given by Equation 5.

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[0060] The combination of the DPC and TIE phase reconstruction algorithms and subsequent TIE and DPC temporal phase-contrast images provides a final phase-contrast image with superior characteristics compared to the DPC temporal phase-contrast image and the TIE temporal phase-contrast image. In particular, angle-sensitive shadowing due to out-of-focus scatter in the imaging path, as seen in the DPC phase-contrast image, is not observed in the final phase-contrast image because high-pass filtering is applied to the DPC phase-contrast image. In this way, blurring artifacts resulting from out-of-focus scatter in the imaging path are eliminated. Meanwhile, low spatial frequencies that are not well preserved by the TIE phase-contrast algorithm are filtered from the TIE phase-contrast image, so most of the image information is obtained from the DPC phase-contrast image. Thus, the resulting HDD phase-contrast image does not have the same background artifacts as the DPC phase-contrast image, while at the same time exhibiting good image contrast across all spatial frequencies. Furthermore, it is sufficient to acquire a total of five different images: two images from the TIE subset at two different defocus amounts and three images from the DPC subset at three different angular illumination configurations. The acquisition time is significantly reduced compared to competing approaches such as [7], requiring only five images, or less than 10 if multiple acquisitions are used to improve the signal-to-noise ratio. Furthermore, the exposure of the specimen to light is reduced, which is favorable for certain light-sensitive specimens, such as cellular structures.

[0061] The images acquired and their association with the two subsets are shown below. [Table 1]

[0062] Table 1: DPC and TIE subsets are based on a total of five images. The subsets are non-overlapping, i.e., no image belongs to both subsets. The c parameter of the images in the TIE subset can range from 1 to 10. For the images used for DPC, semicircular illumination and σ = 1 / 2 are used, and for the images used for TIE, σ = 1 / 3 is used.

[0063] The above discloses an HDD scheme employing two separate phase reconstruction algorithms, one for acquiring temporary DPC phase-contrast images and one for acquiring temporary TIE phase-contrast images. The DPC and TIE phase-contrast images are then fused through selective high-pass and low-pass digital signal processing. In another variation, a joint HDD reconstruction algorithm can be employed. This is described in connection with FIG. 4.

[0064] Now, referring to Figure 4, such a joint HDD reconstruction algorithm combines the working principles of DPC (see Figure 2) and TIE (see Figure 3) in accordance with the disclosed technique.

[0065] In the illustrated example, the illumination module 91 is implemented by the PIU 201 and includes an LED array including multiple LEDs positioned at different angles and distances relative to the optical axis 207. The multiple LEDs are driven separately, for example, by the control module 95 (see FIG. 1 ). Driving multiple LEDs, for example, according to asymmetric patterns, creates different illumination patterns 202, as described above in connection with FIG. 2 . Each of the multiple illumination patterns 202 includes multiple driven LEDs, implementing a wide angular spectrum of illumination angles and simultaneously driving multiple illumination directions. The asymmetric arrangement of the illumination patterns 202 results in an average of angular spectra tilted relative to the optical axis 207. It should be noted that while FIG. 4 shows a semicircular angular spectrum, other illumination patterns are also contemplated. Furthermore, the HDD is not limited to being implemented by the PIU 201 shown in FIG. 4 . In principle, the illumination module may include at least one of a programmable LED array, a digital micromirror device, a liquid crystal display, a variable condenser iris, an angular diffuser, and an aperture wheel.

[0066] For example, a digital micromirror device can be illuminated by a light source, and depending on the orientation of each mirror of the digital micromirror device, each illumination spot in the illumination pupil plane can be actuated or de-actuated—which is equivalent to switching on versus off an LED in a programmable LED array of programmable illumination unit 201. This allows control of both the dominant angle of illumination (i.e., the average of the angular spectrum) as well as further characteristics of the angular spectrum such as width and side peaks.

[0067] A similar effect can be achieved with a liquid crystal display with a suitably illuminated background. Individual pixels of the liquid crystal display are activated and deactivated. A variable capacitor iris can contain multiple apertures that can be selectively opened and closed.

[0068] An angular diffuser can be placed between the imaging plane 203 and the illumination pupil plane to help widen the aperture.

[0069] The HDD is not limited to lighting arrangements including multiple lighting angles, such as that shown in lighting pattern 202 of FIG. 4, and one or more angle lighting arrangements including a single lighting direction may be used in addition to lighting arrangements including multiple lighting directions.

[0070] In accordance with the scenario and HDD technology of Figure 4, a multiple angle illumination arrangement is implemented in combination with multiple defocus amounts 311. While the schematic of Figure 4 illustrates two defocus amounts (zero defocus and offset by Δz), larger count value defocus amounts are contemplated.

[0071] Furthermore, in the scenario of FIG. 4, multiple defocus amounts are implemented by shifting the sample stage to reposition the specimen along the optical path, specifically along the optical axis 207. For example, this can be implemented by motorizing the sample stage of the optical system 92, with the motorized sample stage controlled by the control module (see FIG. 1). This is just one option for using multiple defocus amounts. In other scenarios, multiple cameras combined with a beam splitter can be used. Multiple cameras are positioned at different distances relative to the sample surface along the optical axis. The use of multiple cameras has the advantage of multiplexing image acquisition at multiple defocus positions. This reduces the overall measurement time required to acquire all images that will be post-processed. Alternatively or additionally, electrically adjustable lenses with variable focal lengths can be used. This eliminates the need for multiple cameras and allows for a more compact arrangement. Because electrically adjustable lenses can focus quickly, they can reduce the overall measurement time required for image acquisition, for example, when compared to a sample repositioning scheme.

[0072] Furthermore, further reductions in measurement time can be achieved by multiplexing multiple angular illumination configurations in polarization space and / or wavelength space. For example, a multicolor illumination module 91 (e.g., red-green-blue) can be used, which can drive different angular illumination configurations at different wavelengths. This can then be combined with a wavelength-selective detection module 93, which can simultaneously acquire images at different wavelengths. Similar combinations for different polarizations are conceivable.

[0073] The above describes various aspects related to the hardware implementation of microscope 90, as well as its various components and image acquisition and measurement methods. Next, we discuss aspects related to the digital post-processing of the joint phase reconstruction algorithm. In particular, we explain how the combination of multiple intensity images associated with different combinations of multiple angular illumination arrangements and multiple defocus amounts can be implemented to obtain a phase-contrast image.

[0074] Various aspects are based on the following findings: several issues must be addressed in digitally post-processing acquired HDD microscopy images: (1) the typical transfer function deconvolution analysis used for DPC data with the specimen fixed in the focal plane is no longer valid; (2) the diffusion equation underlying TIE is not valid under partially coherent illumination such as that produced by PIU; moreover, TIE assumes a stable illumination pattern, whereas illumination patterns change; and (3) the transfer function analysis of [7] for individual point sources is not valid, since multiple points in the PIU are switched on simultaneously.

[0075] To solve these problems, multiple images acquired with different combinations of defocus amounts and angular illumination configurations are subtracted from each other, allowing for background subtraction. Furthermore, for each of these pairs, the difference between the phase transfer functions is calculated (thereby obtaining a so-called differential phase transfer function). Based on the information from the difference image and the differential phase transfer function, the phase of the specimen can then be recovered, for example, using deconvolution analysis, which recovers the phase of the object given by the optical system. An optimization problem can be formulated to obtain the specimen phase, i.e., a phase-contrast image, based on the difference image and the differential phase transfer function. While deconvolution analysis is one option for solving such optimization problems, other scenarios are possible, particularly iterative approaches. Sometimes, such iterative approaches are more robust to noise or provide robust convergence.

[0076] Furthermore, various options are available for determining the phase transfer function. One particular scheme, detailed below, is based on the weak object transfer function formula. The "weak object" assumption is used when dealing with objects that only slightly modulate the phase and amplitude of light passing through them. WOTF is a concept used under this weak object. WOTF involves the Fourier transform of an object with a weak phase or amplitude. It describes how the object affects the phase and amplitude of light in frequency space, assuming that these effects are relatively small. For a weak object, the outgoing wave just beyond the object is approximately the sum of the incident wave and a small perturbation due to the object itself. The WOTF formula allows for the incorporation of partially coherent illumination conditions generated by the PIU and defocusing due to axial specimen movement. However, other options different from the WOTF formula are also available. For example, a predefined parametrized template can be used, retrieved from a database and instantiated for a specific combination of angular illumination configuration and defocus amount. It is also possible to use the Hirbert transform to determine the phase transfer function.

[0077] The WOTF format - see [4] - provides the generalized transfer function (complex valued) of an optical system as follows:

number

[0078] k=(k x ,k y ) and k'=(k' x ,k' y ) denotes the spatial frequency, S is the light source 92 (i.e., the illumination pattern at the illumination pupil), and P is the focused pupil of the optical system. Alternative formulations, such as using a two-dimensional integral over the illumination angle present at the focused pupil, are possible. Because HDD phase contrast imaging uses defocus and a variable light source pattern, two metrics are needed to represent the changing illumination and defocus conditions of the system. We define bimodal weak object transfer as follows:

number

[0079] The indices m and n allow distinguishing between different light source patterns and defocus states, respectively. Here, S(k) denotes the mth illumination pattern displayed on the PIU (however, as noted above, this can be formulated similarly for various optical modules, e.g., by integrating the illumination angles provided by a particular optical module). Conversely, the amount of defocus can be included in this description by adding an appropriate phase to the pupil. Below is an example of a spherical phase correction, but other phase corrections are also possible, e.g., a quadratic approximation.

number

[0080] where Zn denotes the relative movement of the specimen with respect to the focal plane at the nth axial acquisition plane. The modulated amplitude (ATF) and phase (PTF) contrast functions are defined as follows:

number

[0081] For weakly absorbing samples and aberration-free optical systems, the ATF can be neglected (see [6]). However, in some scenarios, aberrations in the optical system can be taken into account, e.g., spherical aberration, coma, astigmatism, etc.

[0082] Under the assumption that the ATF is zero, in a partially coherent microscope, the spatial two-dimensional Fourier transform FT[I] of the observed image can be modeled as Equation 9:

number

[0083] where b is a constant offset and φ is the unknown phase of the specimen in the estimated imaging plane. Note that the latter is a set of equations; i.e., a separate equation for each combination of source pattern (m) (or more general angular illumination configuration) and defocus amount (n).

[0084] The background terms need to be removed from these equations, so to obtain equation 10, we calculate the difference between the equations with paired indices (m,n) and (m',n').

number

[0085] The image intensity difference (eg, the difference between acquired microscopic images, ie, image combination) is obtained as Equation 11, and the PTF difference (differential phase contrast function; Equation 12).

number

number

[0086] Equation 10 defines the optimization problem, which allows the latter set of equations to be written as a least-squares problem.

number

[0087] The optimization problem can be solved for the phase φ (i.e., to determine the phase contrast image) via numerical iterative techniques or deconvolution. For example, the optimal phase estimate is given by:

number

[0088] iFT[…] denotes the Fourier transform, and for simplicity of notation, dPTF at the spatial frequency vector k * m,n,m’,n’ and FT[dI m,n,m’,n’ ] dependency, which corresponds to a Wiener filter.

[0089] Modeling known aberrations in the PTF and / or ATF can increase the robustness of the reconstruction.

[0090] The main challenge in performing the deconvolution of the last equation is primarily the denominator term (Equation 16), which may have zero crossings.

number

[0091] Division by a value close to or equal to zero leads to noise amplification and numerical problems. To prevent division by zero, a regularization term (α>0) is added to the denominator.

number

[0092] If the regularization term is too large, the deconvolution process attenuates low spatial frequencies, resulting in poor phase contrast and lateral resolution. Conversely, if the regularization term is too small, values ​​near zero in the denominator amplify noise. To avoid excessive regularization and the resulting attenuation of spatial frequencies, the form of the denominator d(k) should ideally be adjusted to minimize zero regions.

[0093] Figure 5 shows the PTF and associated achievable numerical aperture (NA) coverage for different phase contrast techniques - DPC, TIE, and HDD. Example phase images 501-503 for each technique are shown.

[0094] 5 shows the adjustment process of the spatial frequency coverage of d(k). Hereinafter, the quantity of Equation 18 will be referred to as the cumulative NA coverage.

number

[0095] The first row in Figure 5 shows the DPC (see Figure 2) under mismatched illumination conditions (numerical aperture NAi = 0.3 in the illumination part of the optical system, and numerical aperture NAd = 0.6 in the detection part of the optical system). Although the DPC is essentially able to reach a cumulative NA radius of NAi + NAd (the radius of the dashed line in the middle of the first row in Figure 5), a hole of approximately radius NAd - NAi appears in the NA coverage, resulting in a loss of low-frequency coverage. This leads to a lower contrast in the obtained phase reconstruction (as evident in the phase-contrast image 501).

[0096] TIE (see Figure 3) employs axial defocusing—as shown in the second row of Figure 5. Evaluating the corresponding phase transfer function (second row of Figure 5, left column) reveals that the NA coverage reaches a smaller value in the k-space interval compared to DPC (simply put, the black dots around the center of k-space are smaller). This improves the contrast in the final phase reconstruction (see phase-contrast image 502) compared to DPC. However, since only an on-axis point source is used (see Figure 3), the illumination NA vanishes in standard TIE phase-contrast systems. Thus, the NA coverage only reaches the bandwidth of NAd (simply put, the radius of the white donut is limited), which is a disadvantage compared to DPC in terms of the achievable lateral resolution (given by λ / [NAi + NAd], where λ is the wavelength). Better NA coverage can be achieved by combining both the TIE and DPC phase reconstruction algorithms using appropriate bandpass filters (see Equation 4).

[0097] The HDD (see Figure 4) is shown in the third row of Figure 5. By synthesizing the PTF from both the variable illumination pattern and the defocus, a wider range of spatial frequencies can be covered (the donuts in the middle column have a smaller inner hole and a wider radius). The resulting phase contrast (right column) features superior phase contrast compared to the DPC and reaches higher resolution compared to the TIE (see phase contrast image 503). The dark areas in the PTF require regularization.

[0098] 6 is a flowchart of a method according to various examples, which relates to determining a phase-contrast image. This is based on the HDD technique disclosed herein, which uses digital post-processing of multiple intensity microscopy images to reconstruct a phase-contrast image.

[0099] The method of Figure 6 can be implemented using a processor based on program code loaded from memory. For example, the method of Figure 6 can be implemented by processor 81 of computer 80 by loading and executing program code stored in memory 83.

[0100] Optional box 605 loads a specimen onto the microscope. For example, a biological sample including a cell culture may be loaded onto the microscope. Loading the specimen onto the microscope involves holding the sample on the sample stage of the microscope.

[0101] Optional box 610 drives an angular illumination arrangement. Depending on the specific implementation of the illumination module, box 610 can take different forms. For example, an aperture wheel can be positioned at a rotational position. A certain LED pattern of the LED array of the PIU can also be driven according to, for example, a desired angular spectrum. Digital micromirrors of a DMD (Digital Micromirror Device) can also be reconfigured. Pixels of a liquid crystal display can be switched on and off. The angular illumination arrangement driven in box 610 provides full illumination of the imaging surface under a range of illumination angles. In this way, the brightness level does not vary significantly across the imaging surface (within the system's aperture), and the illumination angle observed at different area positions perpendicular to the optical axis does not change.

[0102] Box 610 can drive multiple types of angular illumination arrangements, each characterized by a different width of its angular spectrum. For example, a first type of angular illumination arrangement that can be driven by box 610 includes a range of illumination directions. The angular spectrum is therefore relatively wide. A second type of angular illumination arrangement that can be driven by box 610 includes a single illumination direction. The angular spectrum is therefore relatively narrow. This is illustrated in FIG. 7, which shows multiple angular spectra 701, 702, 711-714. The angular spectrum indicates the distribution of angles at which light is incident across the imaging plane (in the set in FIG. 7, light 762 is incident on imaging plane 761, and respective angle 763 is highlighted).

[0103] 7 shows that angular spectra 701, 702 include a range of illumination directions. Here, "range of illumination directions" means that the illumination modules used can provide illumination using a smaller angular spectrum, but the illumination modules are controlled to illuminate the imaging surface using a wider angular spectrum, i.e., combining multiple illumination directions that can be individually switched by the illumination modules. For example, in an LED array scenario, this means that multiple LEDs (each defining a single illumination direction) are switched on simultaneously.

[0104] Instead, each of the angular spectra 711-714 includes a single illumination direction. Nevertheless, each angular spectrum 711-714 has a width 751 that is significantly smaller than the width 752 of the angular spectra 701 and 702. This finite width 751 results from the extension of the minimum optical aperture of the light source module at the illumination pupil plane, for example, the extension of the emission area of ​​a light-emitting diode, the pixel size of a liquid crystal display, or the micromirrors of a micromirror device. The hardware of the optical module does not allow providing illumination arrangements with widths narrower than the angular spectra 711-714, and therefore they can be said to include a single illumination direction.

[0105] The bottom of FIG. 7 shows the illumination pattern 202 of a programmable light source (LED array) for angular spectra 701, 702, 711-714 (the optical axis 207 is shown as the open circle in each of these plots).

[0106] As can be seen, the illumination configurations associated with angular spectra 701 and 702 correspond to DPC-type illumination, while the illumination configurations associated with angular spectra 711-714 correspond to TIE-type illumination. This type of technology is based on the following discovery: illumination configurations that provide a range of illumination directions and illumination configurations that provide a single illumination direction (or more generally, wide and narrow angular spectra) have different advantages and disadvantages. A wide angular spectrum provides high resolution in phase-contrast images. A narrow angular spectrum provides high contrast in phase-contrast images. Combining a wide and narrow angular spectrum allows for a combination of high contrast and high resolution.

[0107] In option box 615, one or more components of the microscope are controlled to drive a certain amount of defocus. For example, box 615 may involve repositioning a sample stage for holding a specimen along the optical path or optical axis, i.e., performing a Z-position change. However, this is not necessary in all scenarios to drive a certain amount of defocus. In some scenarios, multiple cameras may acquire images of the imaging plane at different offsets relative to the imaging plane, thereby implementing different amounts of defocus. As a further option, an electrically configurable lens, such as an objective lens or a tube lens, may be used in box 615 to implement a certain amount of defocus.

[0108] An image is then acquired in box 620. The image is acquired at some combination of angular illumination arrangement and amount of defocus, as precedented by the execution of boxes 610 and 615. Generally, it should be noted that box 620 is optional, since in some scenarios image reconstruction (discussed below in connection with box 635) may be performed on pre-acquired images. An example series of images that may be acquired is disclosed above in connection with Table 1.

[0109] Box 625 checks whether more defocus is needed; if so, a further iteration 626 of boxes 615 and 620 is performed to select another defocus amount. This corresponds to incrementing index n in the equation above.

[0110] If all defocus amounts have been obtained for a certain angular illumination configuration, the method begins at box 630. Here, index n is reinitialized, followed by checking whether more angular illumination configurations are needed in box 630. If so, a further iteration 631 of boxes 610, 615, 620, and 625 is performed. Also, index m in the formula is incremented.

[0111] In the scenario of FIG. 6, loop 626 is the inner loop and loop 631 is the outer loop, and other scenarios are possible that switch between different defocus amounts and angular illumination arrangements.

[0112] Once all images have been acquired in box 620 (ie, all different combinations of index m and index n), image reconstruction begins in box 635 .

[0113] Several options are available for implementing box 635. In one example (box 636), a joint phase reconstruction includes images acquired with different illumination configurations and different defocus amounts. This involves solving an optimization problem, e.g., using deconvolution analysis as described above. An example optimization problem is described above in connection with Equation 14 and FIG. 4. Optional regularization can be considered. In another example (box 637), separate phase reconstruction algorithms are performed for each of the image subsets, i.e., the TIE subset and the DPC subset (as described above in connection with FIGS. 2 and 3). A downstream combination of the TIE phase-contrast and DPC-contrast images can then be performed to obtain a final phase-contrast image.

[0114] Thereafter, once the phase contrast image has been determined, the phase contrast image can be optionally output to a user in box 640, for example, via a computer screen or by uploading the image to a server.

[0115] In summary, at least the following examples are disclosed:

[0116] Example 1 1. A method for determining a phase contrast image based on a plurality of microscopic images acquired using a microscope, comprising: the microscope comprises an illumination module configured to provide switchable angle illumination of an imaging plane of the microscope, the microscope further comprising an optical system for illuminating the imaging plane and imaging the imaging plane onto at least one camera of the microscope; The method comprises: controlling the lighting module to drive a plurality of angular lighting arrangements, at least one of the angular lighting arrangements including a corresponding range of lighting directions; controlling at least one camera to acquire a plurality of images at a plurality of angular illumination arrangements and a plurality of amounts of defocus; and combining the multiple images to determine a phase contrast image.

[0117] Example 2 2. The method of example 1, further comprising applying multiple amounts of defocus by at least one of moving a sample stage along the optical path of the optical system, using multiple cameras positioned along the optical path of the optical system, or controlling an electrically adjustable lens.

[0118] Example 3 3. The method of example 1 or 2, wherein at least some of the plurality of angular illumination arrangements are multiplexed in polarization space or wavelength space.

[0119] Example 4 10. The method of any one of the preceding Examples, wherein the illumination module comprises at least one of a programmable LED array, a digital micromirror device, a liquid crystal display, a variable condenser diaphragm, an angular diffuser, and an aperture wheel.

[0120] Example 5 combining the plurality of images includes calculating pairwise differences between each of the plurality of images included in the first subset using a first phase reconstruction algorithm to obtain a first temporary phase-contrast image; combining the plurality of images further comprises calculating pairwise differences between each of the plurality of images included in the second subset using a second phase reconstruction algorithm to obtain a second temporary phase contrast image; The method comprises: 10. The method of any one of the preceding examples, further comprising combining first image information associated with the first temporary phase-contrast image and second image information associated with the second temporary phase-contrast image to obtain the phase-contrast image.

[0121] Example 6 applying a low pass filter to the first temporary phase contrast image to obtain the first image information; 6. The method of example 5, further comprising applying a high-pass filter to the second temporary phase-contrast image to obtain the second image information.

[0122] Example 7 the first subset consists of a first image of the plurality of images and a second image of the plurality of images; the first image included in the first subset has a positive defocus amount; the second image included in the second subset has a negative defocus amount; 7. The method of claim 5 or 6, wherein the first and second images included in the first subset are both acquired with the same angular illumination arrangement.

[0123] Example 8 the second subset consists of a first image of the plurality of images, a second image of the plurality of images, and a third image of the plurality of images; A method according to any one of Examples 5 to 7, wherein the first image included in the second subset, the second image included in the second subset, and the third image included in the second subset are all acquired with the same defocus amount but different angle illumination arrangements.

[0124] Example 9 A method described in any one of Examples 5 to 8, wherein at least one of the first phase reconstruction algorithm and the second phase reconstruction algorithm is based on a predefined optical transfer function that is independent of the properties of the microscope.

[0125] Example 10 5. The method according to any one of Examples 1 to 4, wherein combining the plurality of images comprises solving an optimization problem according to differences between pairs of the plurality of images and associated differences of respective phase transfer functions, the phase transfer functions being determined for each combination of the plurality of angular illumination arrangements and the plurality of defocus values.

[0126] Example 11 11. The method of example 10, further comprising determining a phase transfer function for each combination of a plurality of angular illumination configurations and a plurality of defocus amounts based on parameterized templates stored in a database.

[0127] Example 12 The method of Example 11 further comprises calculating a phase transfer function for each combination of the plurality of angular illumination configurations and the plurality of defocus amounts based on a weak object transfer function formula comprising a two-dimensional integral over an optical field at a pupil plane and a light source plane.

[0128] Example 13 13. The method of example 12, wherein the weak transfer function formula accounts for one or more aberrations of the optical system.

[0129] Example 14 14. The method of any one of Examples 10 to 13, wherein the optimization problem is solved using deconvolution analysis.

[0130] Example 15 The method of example 14, wherein the convolution analysis takes into account a regularization term.

[0131] Example 16 10. The method of any one of the preceding examples, wherein at least one of the plurality of angular illumination arrangements includes a single illumination direction.

[0132] Example 17 10. The method of any one of the preceding examples, wherein the multiple angular illumination arrangements have multiple widths of angular spectrum.

[0133] Example 18 10. The method according to any one of the preceding embodiments, wherein the magnitude of each of the plurality of defocus amounts is related to the depth of field of the detection optics of the microscope by a ratio in the range of 1 to 10.

[0134] Example 19 1. A method for determining a phase contrast image based on a plurality of microscopy images acquired using a microscope, the microscope comprising: an illumination module configured to provide switchable angle illumination of an imaging plane of the microscope; the microscope further comprising an optical system for illuminating the imaging plane and imaging the imaging plane onto at least one camera of the microscope; The method comprises: controlling the lighting module to drive a plurality of angular lighting configurations having a plurality of angular spectrum widths; controlling the at least one camera to acquire a plurality of images at a plurality of angular illumination arrangements and a plurality of amounts of defocus; combining the multiple images to determine a phase contrast image.

[0135] Example 20 at least one processing device, comprising: a memory storing program code; and a processor configured to read and execute the program code, The processing device, wherein the processor is configured to execute the method according to any one of Examples 1 to 19 when the processor executes the program code.

[0136] Example 21 20. Program code that is executed by a processor, the processor being configured to, when executing the program code, perform the method according to any one of claims 1 to 19.

[0137] While the present invention has been shown and described with reference to certain preferred embodiments, equivalents and modifications will occur to those skilled in the art upon reading and understanding the specification. The present invention includes all such equivalents and modifications, and is limited only by the scope of the appended claims.

[0138] For purposes of explanation, the above describes a scenario in which the multiple angle illumination arrangement includes at least one angle illumination arrangement that includes multiple illumination directions. More generally, the multiple angle illumination configurations used in combination with multiple defocus amounts may have angular spectra with different widths, e.g., a wide angular spectrum and a narrow angular spectrum (see FIG. 6).

[0139] Addendum Related to Equation 2, H DPC (k)=exp(j·arctan(k Y / k x )) is used as the Hirbert transform kernel. The equation is derived as follows:

[0140] First, consider 1D DPC. The raw images (e.g., left and right portions of an LED array) look like DIC images. DIC or DPC phase contrast images are related to the phase gradient. By subtracting the images from the left and right half illumination from each other, we get an approximate gradient dphase / dx. In the Fourier domain, this corresponds to multiplication by jk... i.e.,

number

[0141] An approximation is possible, the essential feature is that the pre-multiplier k changes sign at the origin of the coordinate system. This is the main feature of the transfer function. That is, approximately,

number

[0142] Then, in two dimensions,

number

Claims

1. 1. A method for determining a phase contrast image based on a plurality of microscopic images acquired using a microscope, comprising: the microscope comprises an illumination module configured to provide switchable angle illumination of an imaging plane of the microscope, the microscope further comprising an optical system for illuminating the imaging plane and imaging the imaging plane onto at least one camera of the microscope; The method comprises: controlling the lighting module to drive a plurality of angular lighting arrangements, at least one of the angular lighting arrangements including a corresponding range of lighting directions; controlling at least one camera to acquire a plurality of images at a plurality of angular illumination arrangements and a plurality of amounts of defocus; and combining the multiple images to determine a phase contrast image.

2. 10. The method of claim 1, further comprising applying multiple amounts of defocus by at least one of moving a sample stage along the optical path of the optical system, using multiple cameras positioned along the optical path of the optical system, or controlling an electrically adjustable lens.

3. The method of claim 1 , wherein at least some of the multiple angular illumination arrangements are multiplexed in polarization space or wavelength space.

4. The method of claim 1 , wherein the illumination module comprises at least one of a programmable LED array, a digital micromirror device, a liquid crystal display, a variable condenser iris, an angular diffuser, and an aperture wheel.

5. combining the plurality of images includes calculating pairwise differences between each of the images in the first subset of the plurality of images using a TIE (Transport of Intensity Equation) phase reconstruction algorithm to obtain a first temporary phase-contrast image; combining the images further comprises calculating pairwise differences between each of the images in the second subset of images using a DPC (differential phase contrast) phase reconstruction algorithm to obtain a second temporary phase contrast image; The method comprises:

2. The method of claim 1, further comprising combining first image information associated with the first temporary phase-contrast image and second image information associated with the second temporary phase-contrast image to obtain the phase-contrast image.

6. applying a low pass filter to the first temporary phase contrast image to obtain the first image information; The method of claim 5 , further comprising applying a high-pass filter to the second temporary phase-contrast image to obtain the second image information.

7. the first subset comprises a first image of the plurality of images and a second image of the plurality of images; the first image included in the first subset has a positive defocus amount; the second image included in the first subset has a negative defocus amount; The method of claim 5 , wherein the first and second images included in the first subset are both acquired with the same angular illumination arrangement.

8. the second subset consists of a first image of the plurality of images, a second image of the plurality of images, and a third image of the plurality of images; 6. The method of claim 5, wherein the first image in the second subset, the second image in the second subset, and the third image in the second subset were all acquired with the same amount of defocus but different angular illumination arrangements.

9. The method of claim 1 , wherein at least one of the plurality of angular illumination arrangements includes a single illumination direction.

10. The method of claim 1 , wherein the multiple angular illumination arrangements have multiple widths of angular spectrum.

11. 11. The method according to claim 1, wherein the magnitude of each of the plurality of defocus amounts is related to the depth of field of the detection optics of the microscope by a ratio in the range of 1 to 10.

12. at least one processing device, comprising: a memory storing program code; and a processor configured to read and execute the program code, A processing device, wherein the processor is configured to perform the method of any one of claims 1 to 10 when executing the program code.

13. 11. Program code that is executed by a processor, the processor being configured to, when executing the program code, perform the method of any one of claims 1 to 10.

Images