Rapid quantitative differential interference microscopy system and method based on holographic recording

Abstract

The invention discloses a rapid quantitative differential interference microscopy system and method based on holographic recording. The system comprises a partially coherent illumination module, and a microscope objective, a tube lens, a transmission grating, a first linear polarizer, a first thin lens, a half-wave plate, a shading plate, a phase-type spatial light modulator, a second thin lens, a second linear polarizer and an image acquisition module which are sequentially arranged along the optical axis direction of the partially coherent illumination module. According to the invention, the phase-type spatial light modulator is utilized to realize shearing offset in any direction and at any degree, so that the device is suitable for different types of application occasions; the system realizes holographic recording of differential interference by utilizing grating carrier frequency, realizes quantitative differential interference detection on a to-be-detected sample only by utilizing two acquired images, has very high time resolution, spatial resolution and imaging precision, and has a wide application prospect in biological imaging and industrial detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical microscopy imaging, and particularly relates to a fast quantitative differential interference microscopy system and method based on holographic recording. Background Art

[0002] Today, with the continuous development of science and technology, quantitative phase microscopy technology, as a new emerging technology that can achieve high-resolution and high-contrast detection without preprocessing the sample to be measured, is making remarkable new progress. Quantitative phase microscopy technology performs high-contrast imaging of transparent samples by restoring the phase change caused when the illuminating light passes through the sample. It is a label-free and non-invasive imaging method, and the detection process will not cause damage or affect the sample to be measured. Quantitative phase microscopy technology plays an important role in the fields of biomedicine, microbiology, materials science, drug research and development, etc., bringing great help and breakthroughs to scientific research and practical applications.

[0003] Quantitative differential interference microscopy technology is an advanced quantitative phase microscopy technology. It has the characteristics of high stability, high imaging quality, high axial resolution, etc., and is widely used in biological imaging and industrial inspection. Quantitative differential interference microscopy imaging can be achieved through various channels. Gradient light differential interference microscopy technology is a quantitative differential interference microscopy technology that couples a phase-type spatial light modulator to a traditional differential interference contrast microscope. It can perform high-quality quantitative phase imaging on thick tissue samples. It is very difficult to accurately determine the shear offset during the implementation of this method, so its imaging accuracy is greatly affected. Quantitative differential interference microscopy technology based on laser structured illumination uses a digital grating to perform structured illumination on the sample, and then images the sample on a certain defocus plane to achieve differential interference detection. To achieve quantitative phase imaging, this method combines a four-step phase shift operation and an angular spectrum transfer technique. However, in the process of defocus detection, it is very difficult to accurately determine the shear offset and the sample defocus amount, so it is very difficult to ensure the imaging accuracy of this method.

[0004] Quantitative differential interference microscopy based on pupil-plane amplitude grating (amplitude-type spatial light modulator) modulation is divided into two types. The first method realizes differential interference detection based on the 0th diffraction term and ±1st diffraction terms of the amplitude grating, and then combines four-step phase-shifting operation to obtain the phase distribution of the sample. This technique requires that the amplitude gradient of the sample is 0 everywhere. Therefore, the application range of this technique is greatly limited. The second method realizes differential interference detection based on the +1st diffraction term of the double-frequency amplitude grating, and then combines three-step phase-shifting operation to obtain the phase distribution of the sample. In this technique, the spatial light modulator needs to load two grating patterns simultaneously, and there is a very small difference in the periods of these two grating patterns. Therefore, this technique requires the use of complex random coding techniques to achieve differential interference detection. In addition, this technique requires a laser with a very narrow linewidth as the light source, and the image quality will be adversely affected by laser speckle. The latest quantitative differential interference microscopy technique realizes differential interference detection based on the polarization modulation characteristics of the phase-type spatial light modulator, which greatly improves the performance of quantitative differential interference microscopy. However, this technique requires four-step phase-shifting operation (8 original images) to achieve quantitative phase imaging of the sample to be measured, and the imaging speed is greatly limited.

[0005] The above quantitative differential interference microscopy techniques all require phase-shifting operations to achieve quantitative phase imaging, which means multiple phase-shifted intensity images need to be acquired. Therefore, the imaging speed is severely limited, and it is difficult to capture rapid dynamic changes. To improve the imaging speed of quantitative differential interference microscopy, researchers have proposed various methods. First, in the quantitative differential interference microscopy technique based on pupil-plane amplitude grating modulation, researchers achieved single-exposure collection of multiple differential interference phase-shifted images by restricting the imaging field of view and adding complex multi-frequency amplitude gratings, making the imaging speed of quantitative differential interference microscopy only limited by the camera exposure time. However, this method requires a laser with a very narrow linewidth as the illumination source, and the image quality is adversely affected by laser speckle. Additionally, the alignment degree between multiple differential interference phase-shifted images directly affects the imaging accuracy of this technique. Second, the quantitative differential interference microscopy technique based on four-wave shearing achieves single-exposure rapid quantitative phase imaging by placing a two-dimensional amplitude grating at a certain position in front of the imaging plane. However, this technique requires mechanically adjusting the axial distance of the two-dimensional amplitude grating relative to the imaging plane to achieve differential interference detection, and it is difficult to accurately determine the shear offset. Therefore, it is difficult to ensure the imaging accuracy with this method. Recently, researchers achieved single-exposure rapid quantitative phase imaging based on differential interference by placing a Wollaston prism on the imaging plane of a traditional differential interference contrast microscope. This method has a simple structure, high stability, high imaging quality, and the imaging speed is only affected by the camera exposure time. However, this method requires the shear plane of the Wollaston prism to be strictly coincident with the imaging plane of the traditional differential interference contrast microscope, and the shear offset direction caused by the Wollaston prism to be strictly consistent with the shear offset direction caused by the traditional differential interference contrast microscope. Based on this, there are great difficulties in the actual setup of this technique. Additionally, it is difficult to accurately determine the shear offset amount in this technique, so it is difficult to be popularized in practical applications. Summary of the Invention

[0006] To solve the above problems existing in the prior art, the present invention provides a fast quantitative differential interference microscopy system and method based on holographic recording. The technical problems to be solved by the present invention are achieved through the following technical solutions:

[0007] One aspect of the present invention provides a fast quantitative differential interference microscopy system based on holographic recording, including a partially coherent illumination module, and a microscope objective lens, a tube lens, a transmission grating, a first linear polarizer, a first thin lens, a half-wave plate, a phase-type spatial light modulator, a second thin lens, a second linear polarizer, and an image acquisition module sequentially arranged along the optical axis direction of the partially coherent illumination module, wherein,

[0008] The partial coherence illumination module is used to generate partially coherent illumination light; the sample is arranged at the front focal plane of the microscope objective, and the transmission grating is arranged at the confocal plane of the tube lens and the first thin lens; the first linear polarizer is arranged between the transmission grating and the first thin lens; the polarization direction of the first linear polarizer is along the Y-axis direction, and the first thin lens only collects the 0th order and ±1st order diffracted lights that carry the object light wave information and are polarized along the Y-axis direction;

[0009] The phase-type spatial light modulator is arranged at the confocal plane of the first thin lens and the second thin lens, and the working surface of the phase-type spatial light modulator only covers the spectral distributions of the 0th order and -1st order diffracted lights. The half-wave plate is arranged between the first thin lens and the phase-type spatial light modulator and is adjacent to the working surface of the phase-type spatial light modulator, and can make the spectral distribution of the -1st order diffracted light reaching the working surface of the phase-type spatial light modulator be linearly polarized along the X-axis direction. The X-axis direction and the Y-axis direction are perpendicular to each other and both are perpendicular to the optical axis direction of the partial coherence illumination module;

[0010] The phase-type spatial light modulator can perform phase modulation on the light field with polarization direction selectivity; the second linear polarizer is arranged between the second thin lens and the image acquisition module, and is used to perform polarization adjustment on the 0th order diffracted light and the -1st order diffracted light with the same polarization direction; the image acquisition module is used for image acquisition and recording.

[0011] Another aspect of the present invention provides a fast quantitative differential interference microscopy method based on holographic recording, including:

[0012] S1: Obtain the light intensity distribution of the sample by using the fast quantitative differential interference microscopy system described in any one of the above embodiments;

[0013] S2: Perform a spatial Fourier transform on the light intensity distribution to obtain the spectral distribution of the light intensity;

[0014] S3: According to the spectral distribution of the light intensity, obtain the phase distribution of the sample by using the holographic differential reconstruction method.

[0015] Compared with the prior art, the beneficial effects of the present invention are:

[0016] The present invention provides a fast quantitative differential interference microscopy system and method based on holographic recording, which has the following advantages: First, the optical structure of partial coherent illumination and coaxial interference enables the device to have high spatial phase sensitivity, high temporal phase sensitivity, high imaging stability, and high imaging quality simultaneously; Second, the microscopy system can accurately achieve shear offsets in any direction and to any degree by using a phase-type spatial light modulator, with very high imaging accuracy and being applicable to different types of application scenarios; In addition, the microscopy system realizes holographic recording of differential interference by using the grating carrier frequency, and only uses two images to achieve high-precision quantitative differential interference imaging of the sample to be measured, with very high temporal resolution and spatial resolution, and very high imaging accuracy at the same time. Finally, the microscopy system has a simple structure, is easy to set up, inherits the characteristics of high axial resolution of differential interference contrast microscopy, and can perform three-dimensional quantitative phase imaging on thick tissue samples. Therefore, the proposed fast quantitative differential interference microscopy system based on holographic recording can perform label-free, highly stable, highly sensitive, and high-resolution in-situ quantitative phase imaging on the sample to be measured, and has very good expandability in terms of structure and function, and has great application value in the fields of biomedicine and industrial inspection.

[0017] The following will further elaborate on the present invention in detail with reference to the drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a schematic structural diagram of a fast quantitative differential interference microscopy system based on holographic recording provided by an embodiment of the present invention;

[0019] Figure 2 is a schematic layout diagram of a half-wave plate, a phase-type spatial light modulator, and a light shield on the pupil plane provided by an embodiment of the present invention;

[0020] Figure 3 is the true phase distribution of the sample to be measured in a simulation experiment provided by an embodiment of the present invention;

[0021] Figure 4 is along Figure 3 the phase distribution diagram of the horizontal white dotted line in;

[0022] Figure 5 is the phase distribution diagram of the shear offset generated in the X-axis direction loaded on the phase-type spatial light modulator;

[0023] Figure 6 is the holographic differential interference intensity diagram of the shear offset in the X-axis direction collected by the image acquisition module;

[0024] Figure 7 is Figure 6 the frequency spectrum distribution diagram of the holographic differential interference intensity diagram of the shear offset in the X-axis direction in;

[0025] Figure 8 is the spectral distribution obtained after translating and filtering the spectral distribution shown in Figure 7 ;

[0026] Figure 9 is the phase gradient distribution along the X-axis direction obtained by performing a two-dimensional spatial inverse Fourier transform on the spectral distribution shown in Figure 8 ;

[0027] Figure 10 is the phase distribution map that generates a shear offset along the Y-axis direction loaded on the phase-type spatial light modulator;

[0028] Figure 11 is the holographic differential interference intensity map of the shear offset along the Y-axis direction collected by the image acquisition module;

[0029] Figure 12 is the spectral distribution of the holographic differential interference intensity map of the shear offset along the Y-axis direction;

[0030] Figure 13 is the spectral distribution obtained after translating and filtering the spectral distribution shown in Figure 12 ;

[0031] Figure 14 is the phase gradient distribution along the Y-axis direction obtained by performing a two-dimensional spatial inverse Fourier transform on the spectral distribution shown in Figure 13 ;

[0032] Figure 15 is the phase distribution recovered by using the phase gradient distribution along the X-axis direction and the phase gradient distribution along the Y-axis direction;

[0033] Figure 16 is the phase distribution along the Figure 15 horizontal white dashed line in

[0034] Figure 17 is the phase gradient distribution of COS7 cells along the X-axis direction;

[0035] Figure 18 is the phase gradient distribution of COS7 cells along the Y-axis direction;

[0036] Figure 19 is the COS7 cell phase distribution recovered by using the phase gradient distribution of COS7 cells along the X-axis direction and the phase gradient distribution along the Y-axis direction;

[0037] Figure 20 is the bright-field image of COS7 cells in the same field of view as Figure 19 ;

[0038] Explanation of reference numerals:

[0039] 1 - partially coherent illumination module; 2 - sample; 3 - microscope objective; 4 - tube lens; 5 - transmission grating; 6 - first linear polarizer; 7 - first thin lens; 8 - half-wave plate; 9 - light shield; 10 - phase-type spatial light modulator; 11 - second thin lens; 12 - second linear polarizer; 13 - image acquisition module. Detailed implementation manners

[0040] In order to further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following combines the accompanying drawings and specific implementation manners to elaborate in detail on a fast quantitative differential interference microscopy system and method based on holographic recording proposed according to the present invention.

[0041] The foregoing and other technical contents, features, and effects of the present invention can be clearly presented in the following detailed description in conjunction with the accompanying drawings. Through the description of the specific implementation manners, a more in-depth and specific understanding of the technical means and effects adopted by the present invention to achieve the predetermined purpose can be obtained. However, the accompanying drawings are only provided for reference and illustration, and are not used to limit the technical solution of the present invention.

[0042] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including", or any other variant is intended to cover non-exclusive inclusion, so that an article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed. Without more limitations, an element defined by the statement "including a..." does not exclude the existence of another identical element in the article or device including the said element.

[0043] Embodiment 1

[0044] Please refer to Figure 1 , Figure 1It is a schematic structural diagram of a fast quantitative differential interference microscopy system based on holographic recording provided by an embodiment of the present invention. The fast quantitative differential interference microscopy system includes a partially coherent illumination module 1, and a microscopic objective lens 3, a tube lens 4, a transmission grating 5, a first linear polarizer 6, a first thin lens 7, a half-wave plate 8, a phase-type spatial light modulator 10, a second thin lens 11, a second linear polarizer 12, and an image acquisition module 13 arranged in sequence along the optical axis direction of the partially coherent illumination module 1. Among them, the partially coherent illumination module 1 is used to generate partially coherent illumination light; the sample 2 is arranged at the front focal plane of the microscopic objective lens 3, and the transmission grating 5 is arranged at the confocal plane of the tube lens 4 and the first thin lens 7; the first linear polarizer 6 is arranged between the transmission grating 5 and the first thin lens 7; the polarization direction of the first linear polarizer 6 is along the Y-axis direction, and the first thin lens 7 only collects the 0th order and ±1st order diffracted lights carrying the object light wave information and polarized along the Y-axis direction; the phase-type spatial light modulator 10 is arranged at the confocal plane of the first thin lens 7 and the second thin lens 11, and the working surface of the phase-type spatial light modulator 10 only covers the spectral distributions of the 0th order and -1st order diffracted lights. The half-wave plate 8 is arranged between the first thin lens 7 and the phase-type spatial light modulator 10 and is adjacent to the working surface of the phase-type spatial light modulator 10, and can make the spectral distribution of the -1st order diffracted light reaching the working surface of the phase-type spatial light modulator 10 be linearly polarized along the X-axis direction. The X-axis direction and the Y-axis direction are perpendicular to each other and both are perpendicular to the optical axis direction of the partially coherent illumination module 1; the phase-type spatial light modulator 10 can perform phase modulation with polarization direction selectivity on the light field; the second linear polarizer 12 is arranged between the second thin lens 11 and the image acquisition module 13, and is used to perform polarization adjustment with the same polarization direction on the 0th order diffracted light and the -1st order diffracted light; the image acquisition module 13 is used for image acquisition and recording.

[0045] Specifically, the partially coherent illumination module 1 of this embodiment is composed of a plurality of light-emitting diodes evenly distributed in a ring, and each light-emitting diode has the same spectral bandwidth. The microscopic objective lens 3 and the tube lens 4 form a confocal system. The tube lens 4 and the first thin lens 7 form a confocal system, and a transmission grating 5 is placed at the confocal plane of the tube lens 4 and the first thin lens 7 for modulating the object light wave after low-pass filtering. The quasi-plane wave emitted by each light-emitting diode of the partially coherent illumination module 1 performs large-angle oblique illumination on the sample 2 located at the front focal plane of the microscopic objective lens 3, thereby generating an object light wave carrying the sample information. After being magnified and imaged by the confocal system composed of the microscopic objective lens 3 and the tube lens 4, the object light wave is propagated to the confocal plane of the tube lens 4 and the first thin lens 7. During this process, the object light wave undergoes two spatial Fourier transform effects of the microscopic objective lens 3 and the tube lens 4 successively, and its spectral distribution is limited by the finite aperture of the microscopic objective lens 3. Therefore, the object light wave propagated to the confocal plane of the tube lens 4 and the first thin lens 7 is actually the result of low-pass filtering. At the same time, the transmission grating 5 placed at the confocal plane of the tube lens 4 and the first thin lens 7 is used to modulate the object light wave after low-pass filtering. Under the spectral splitting effect of the transmission grating 5, multiple diffracted lights carrying the object light wave information are generated at the front focal plane of the first thin lens 7. Due to the finite aperture of the first thin lens 7, only the 0th-order and ±1st-order diffracted lights are collected by the first thin lens 7.

[0046] Since the light emitted by the partially coherent illumination module 1 is non-polarized, but the subsequent optical path needs to perform polarization modulation of the light field, a first linear polarizer 6 is placed between the transmission grating 5 and the first thin lens 7. The polarization direction of the first linear polarizer 6 is along the Y-axis direction. Therefore, the 0th-order and ±1st-order diffracted lights entering the first thin lens 7 are linearly polarized along the Y-axis direction. Specifically, after the 0th-order and ±1st-order diffracted lights carrying the object light wave information undergo the spatial Fourier transform effect of the first thin lens 7, their spectral information is evenly distributed at the confocal plane of the first thin lens 7 and the second thin lens 11. It should be noted that the spectral distributions of the 0th-order and ±1st-order diffracted lights appear as three completely identical circular regions at the confocal plane of the first thin lens 7 and the second thin lens 11, and there is no overlap between them, as Figure 2 shown.

[0047] ]>At the same time, the phase-type spatial light modulator 10 is placed at the confocal plane of the first thin lens 7 and the second thin lens 11, and its working surface only covers the spectral distributions of the 0th-order and -1st-order diffracted lights, as Figure 2 shown. The spectral distribution of the +1st-order diffracted light is blocked by the light-shielding plate 9 located at the confocal plane of the first thin lens 7 and the second thin lens 11 and cannot enter the subsequent optical path. Before reaching the phase-type spatial light modulator 10, the spectral distribution of the -1st-order diffracted light is modulated by the half-wave plate 8, as Figure 1 and 2As shown. The half-wave plate 8 is placed as close as possible to the working surface of the phase-type spatial light modulator 10, and it only covers the spectral distribution of the -1st order diffracted light. At the same time, the fast axis direction of the half-wave plate 8 makes a 45-degree angle with the positive X-axis direction (such as Figure 1 outward along the paper surface in Figure 1 and the positive Y-axis direction (such as upward along the paper surface in

[0048] ). Therefore, the spectral distribution of the -1st order diffracted light reaching the working surface of the phase-type spatial light modulator 10 is linearly polarized only along the X-axis direction. At the same time, the spectral distribution of the 0th order diffracted light reaching the working surface of the phase-type spatial light modulator 10 is linearly polarized only along the Y-axis direction. The phase-type spatial light modulator 10 has polarization direction selectivity in modulating the light field. In the present invention, the phase-type spatial light modulator only acts on the linearly polarized light along the Y-axis direction and does not act on the linearly polarized light along the X-axis direction. Therefore, the phase-type spatial light modulator 10 only performs phase modulation on the spectral distribution of the 0th order diffracted light and does not perform phase modulation on the spectral distribution of the -1st order diffracted light. Finally, the spectral distribution of the modulated 0th order diffracted light and the spectral distribution of the unmodulated -1st order diffracted light are coherently superimposed and recorded by the image acquisition module 13 after the spatial Fourier transform of the second thin lens 11. It should be noted that the second linear polarizer 12 is placed between the second thin lens 11 and the image acquisition module 13, and its polarization direction makes a 45-degree angle with the positive Y-axis direction and the negative X-axis direction at the same time, so that the 0th order diffracted light and the -1st order diffracted light reaching the image acquisition module 13 have the same polarization direction.

[0049] Preferably, in the partial coherent illumination module 1 of this embodiment, the wavelength range of the light-emitting diodes is 488 ± 10 nm, and the power is 60 mW; the microscopic objective lens 3 is an immersion objective lens with a magnification of 100X and a numerical aperture NA = 1.44 (planar field apochromatic objective lens); the focal length of the tube lens 4 is 200 mm; the grating constant of the transmission grating 5 is 8.47 μm; the wavefront deformation of the light wave after passing through the first linear polarizer 6 and the second linear polarizer 12 is less than 1 / 4 wavelength; the first thin lens 7 is a double-glued achromatic lens with a focal length of 200 mm; the half-wave plate 8 has an achromatic function; the light shield 9 is made of opaque light-shielding paper; the phase modulation resolution of the phase-type spatial light modulator 10 is 8 bits, its liquid crystal switching time is 2 ms, the pixel range is 1920 × 1152, and the size of a single pixel is 9.2 μm × 9.2 μm; the second thin lens 11 is a double-glued achromatic lens with a focal length of 250 mm; the image acquisition module 13 is selected as a CMOS camera, and the size of a single pixel is 2.4 μm × 2.4 μm.Furthermore, the partially coherent illumination module 1 of the present invention is composed of a light-emitting diode with a certain spectral bandwidth, the central wavelength of which is represented by λ. For the convenience of calculation, the axis of the rapid quantitative differential interference microscopy system of this embodiment is set as the Z axis (the horizontal left direction in the paper is the positive direction), the intersection of the axis of the system and the sample surface is the origin O, the vertical outward direction of the paper is the positive direction of the X axis, and the vertical upward direction in the paper is the positive direction of the Y axis. Let the focal length and numerical aperture of the microscope objective lens 3 be f respectively. obj and NA; the focal length of the tube lens 4 is f tube ; The grating constant (period) of the transmission grating 5 is d; the focal length of the first thin lens 7 is f1; the focal length of the second thin lens 11 is f2; the pixel size of the image acquisition module 13 is pixelsize; the width and length of the working surface of the phase-type spatial light modulator 10 are SLM_width and SLM_height respectively.

[0050] The sample 2 located at the front focal plane of the microscope objective 3 generates an object light wave carrying sample information under the illumination of the partially coherent illumination module 1, which is expressed as Among them, (x, y) represents the horizontal spatial coordinate, a(x, y) represents the amplitude information of the sample, Represents the phase information of the sample. After the object light wave undergoes the spatial Fourier transform of the microscope objective 3, the filtering of the pupil aperture of the microscope objective 3, and the spatial Fourier transform of the tube lens 4, a low-pass filtered object light wave is generated at the confocal plane of the tube lens 4 and the first thin lens 7. Its light field distribution is expressed as:

[0051]

[0052] in, Represents the convolution operation; E(x,y) represents the ideal light field distribution generated by the object light wave s(x,y) at the rear focal plane of the tube lens 4 after passing through the confocal system composed of the microscope objective 3 and the tube lens 4, that is, the ideal magnified image of s(x,y); h(x,y) is the complex amplitude point spread function of the confocal system composed of the microscope objective 3 and the tube lens 4, which represents the light field distribution generated at the rear focal plane of the tube lens 4 by an infinitesimal point source at the front focus of the microscope objective 3 after passing through the confocal system composed of the microscope objective 3 and the tube lens 4. The complex amplitude point spread function h(x,y) is also the system coherence transfer function (pupil function of the microscope objective 3) CTF(ξ,η) which is the light field distribution generated at the rear focal plane of the tube lens 4 after the spatial Fourier transform. Here, (ξ,η) represents the spectral coordinates corresponding to the spatial coordinates (x,y). CTF(ξ,η) is only present at ξ 2 +η 2 ≤(NA / λ) 2 Ideally, all values are 1 within the valid range.

[0053] Although s L (x, y) is the convolution between the ideal light field distribution E(x, y) and the complex amplitude point spread function h(x, y). Its spatial resolution is limited by the finite aperture of the microscope objective 3, but it still accurately carries the phase information and amplitude information of the sample 2. At the same time, a two-dimensional transmission grating 5 with a grating constant of d is placed at the confocal plane of the tube lens 4 and the first thin lens 7, and its diffraction direction is along the Y-axis direction. Theoretically, under the spectral splitting action of the transmission grating 5, multiple diffracted lights carrying the object light wave information will be generated at the front focal plane of the first thin lens 7. However, the first thin lens 7 has a finite aperture, and only the 0th and ±1st order diffracted lights can enter the first thin lens 7 in the fast quantitative differential interference microscopy system of the present invention. Therefore, the modulation function of the transmission grating 5 on the light field can be expressed as g(x, y) = 1 + cos(2πy / d). Therefore, after the light field distribution shown in formula (1) is modulated by the transmission grating 5, a new light field is generated at the confocal plane of the tube lens 4 and the first thin lens 7, which is expressed as:

[0054] e g (x, y) = s L (x, y)·g(x, y) (2)

[0055] Since the polarization direction of the first linear polarizer 6 is along the Y-axis direction, the light field distribution shown in formula (2) is further represented by the Jones vector as:

[0056]

[0057] Subsequently, after the spatial Fourier transform of the first thin lens 7, the spectral information of the light field distribution shown in formula (3) is distributed at the confocal plane of the first thin lens 7 and the second thin lens 11. As described above, the spectral distribution presents three completely identical circular regions at the confocal plane of the first thin lens 7 and the second thin lens 11. These three circular regions are evenly distributed along the Y-axis and there is no overlap between them. Among them, the spectral distribution of the +1st order diffracted light is blocked by the light shield 9 located at the confocal plane of the first thin lens 7 and the second thin lens 11 and cannot enter the subsequent optical path. Therefore, the spectral distribution at the confocal plane of the first thin lens 7 and the second thin lens 11 is expressed as:

[0058]

[0059] Among them, (ξ, η) represents the spectral coordinates corresponding to the spatial coordinates (x, y), and ~ represents the two-dimensional spatial Fourier transform of the corresponding variable. For example, represents the two-dimensional spatial Fourier transform of s L (x, y). It should be noted that Among them, represents the two-dimensional Fourier transform of the ideal light field distribution E(x,y), and P(ξ,η) represents the The circular function is valid within the range of the circle, and its value is all 1 within the valid range of the circle, and all 0 outside the valid range of the circle, where f obj represents the focal length of the microscope objective 3, f tube Indicates the focal length of the tube lens 4 .

[0060] Furthermore, in order to modulate the spectrum distribution shown in formula (4), the phase-type spatial light modulator 10 is placed at the confocal plane of the first thin lens 7 and the second thin lens 11, and its working surface only covers the spectrum distribution of the 0th and -1st order diffracted light, as shown in FIG. Figure 1 and Figure 2 As shown. At the same time, a half-wave plate 8 is placed in front of the phase-type spatial light modulator 10, and it is adjacent to the working surface of the phase-type spatial light modulator 10. The half-wave plate 8 only covers the spectral distribution of the -1 order diffraction light and is used to modulate the spectral distribution of the -1 order diffraction light. The fast axis direction of the half-wave plate 8 is 45 degrees to the positive direction of the X-axis and the positive direction of the Y-axis. Therefore, after being modulated by the half-wave plate 8, the spectral distribution of the -1 order diffraction light reaching the working surface of the phase-type spatial light modulator 10 is only linearly polarized along the X-axis direction. At this time, the spectral distribution shown in formula (4) is expressed as:

[0061]

[0062] In order to realize differential interference detection, the working surface of the phase-type spatial light modulator 10 is loaded with a desired phase modulation pattern, which is expressed in spatial coordinates as follows:

[0063]

[0064] Wherein, x0 and y0 represent the offset distances generated on the image acquisition module 13 along the X-axis direction and the Y-axis direction, respectively, and are constants.

[0065] It should be noted that the phase range that can be modulated by each pixel of the phase-type spatial light modulator 10 is between 0 and 2π, which means that the phase distribution finally loaded on the phase-type spatial light modulator 10 must be between 0 and 2π to ensure accurate light field modulation. Considering that the phase modulation function of the light field is a periodic function with 2π as the basic period, it is only necessary to perform phase wrapping processing on the original phase distribution shown in formula (6) to obtain a phase distribution that meets the requirements. Therefore, the phase distribution actually loaded by the phase-type spatial light modulator 10 is the result obtained after phase wrapping processing on the original phase distribution. According to the spatial Fourier transform effect of the lens, the spatial frequency (ξ, η) and the position coordinates (x, y) at the front focal plane of the second thin lens 11 exist. The relationship. Therefore, the phase distribution shown in formula (6) can be expressed in terms of frequency coordinates as:

[0066] θ(ξ, η) = 2π(ξ·x0 + η·y0) (7)

[0067] Therefore, the modulation function of the phase-type spatial light modulator 10 on the optical field can be expressed as Mod(ξ, η) = e jθ(ξ,η) , where j represents the imaginary unit. Under the polarization modulation of the phase-type spatial light modulator 10, the spectral distribution shown in formula (5) is further expressed as:

[0068]

[0069] Finally, under the spatial Fourier transform of the second thin lens 11 and the polarization modulation of the second linear polarizer 12, an optical field distribution with a holographic differential interference effect is generated at the rear focal plane of the second thin lens 11, which is expressed as:

[0070]

[0071] where E c (x, y) is the ideal optical field distribution generated at the rear focal plane of the second thin lens 11 after the object light wave s(x, y) passes through the confocal system composed of the microscopic objective lens 3, the tube lens 4, the first thin lens 7, and the second thin lens 11, that is, the ideal magnified image of s(x, y), and h r (x, y) represents the complex amplitude point spread function of the confocal system composed of the first thin lens 7 and the second thin lens 11, and s c (x - x0, y - y0) represents the function after s c (x, y) is translated along the (x0, y0) vector.

[0072] Compared with E c (x, y), s c (x, y) still accurately carries the phase information and amplitude information of the sample 2, but their spatial resolution is limited. Therefore, s c (x, y) = A(x, y)·e jφ(x,y) , where A(x, y) and φ(x, y) are the magnified images of the sample amplitude information a(x, y) and the sample phase information respectively, but the spatial resolution of A(x, y) and φ(x, y) is limited. Therefore, obtaining the distribution of φ(x, y) means obtaining the phase distribution of the sample. The optical field distribution shown in formula (9) is finally detected by the image acquisition module 13 located at the rear focal plane of the second thin lens 11, and its intensity distribution is expressed as:

[0073]

[0074] Example Two

[0075] On the basis of Example One, this example provides a fast quantitative differential interference microscopy method based on holographic recording, including:

[0076] S1: Obtain the light intensity distribution of the sample by using the fast quantitative differential interference microscopy system described in Example One. The expression of this intensity distribution is as shown in formula (10).

[0077] S2: Perform a spatial Fourier transform on the light intensity distribution to obtain the spectral distribution of the light intensity.

[0078] Step S2 of this example specifically includes:

[0079] S2.1: Transform the expression of the light intensity distribution to obtain the transformed expression:

[0080]

[0081] where * represents the conjugate of the variable; B(x, y) = |s c (x, y)| 2 +|s c (x - x0, y - y0)| 2 ,

[0082]

[0083] Perform a spatial Fourier transform on both sides of formula (11) to obtain the spectral distribution of I c (x, y):

[0084]

[0085] S3: According to the spectral distribution of the light intensity, use the holographic differential reconstruction method to obtain the phase distribution of the sample.

[0086] This step uses a method similar to digital holographic reconstruction to obtain the distribution of e<00Spatial Fourier transform on both sides of formula (11) to obtain the spectral distribution of I(x, y):Perform a spatial Fourier transform on both sides of formula (11) to obtain the spectral distribution of I c (x, y):

[0084]

[0085] S3: According to the spectral distribution of the light intensity, use the holographic differential reconstruction method to obtain the phase distribution of the sample.

[0086] This step uses a method similar to digital holographic reconstruction to obtain the distribution of e d (x, y), which is denoted here as the holographic differential reconstruction method. Specifically, it includes the following steps:

[0087] S3.1: Move the entire spectral distribution shown in formula (12) in the reverse direction along the η coordinate axis by a distance of k to obtain a new spectral distribution c

[0088] S3.2: Set a circular mask Mask(ξ, η) centered at the origin (0, 0) of the spectral coordinates. The radius of this circular mask is It takes the value of 1 within the circular region and 0 in other regions. It should be noted that the circular region with a radius of is the effective range of the spectrum of e d (x, y).

[0089] S3.3: Multiply the spectrum distribution by the circular mask Mask(ξ, η) to obtain the distribution of . Subsequently, perform an inverse spatial Fourier transform on the obtained distribution to obtain the distribution of e d (x, y), thereby obtaining the distribution of φ(x, y) - φ(x - x0, y - y0).

[0090] S3.4: In the phase modulation pattern shown in formula (6), when y0 = 0 and , the gradient distribution of φ(x, y) along the X-axis direction is obtained:

[0091]

[0092] Similarly, in the phase modulation pattern shown in formula (6), when x0 = 0 and , the gradient distribution of φ(x, y) along the Y-axis direction is obtained:

[0093]

[0094] S3.5: Using the Frankot-Chellappa phase integration algorithm, the phase distribution of the sample to be measured can be quantitatively obtained:

[0095]

[0096] where represents the two-dimensional spatial Fourier transform operation, represents the two-dimensional inverse spatial Fourier transform operation, and ε represents the regularization coefficient, which is defaulted to 0.0001.

[0097] Since the fast quantitative differential interference microscopy system of the present invention accurately realizes shear offset in any direction and to any degree by using a phase-type spatial light modulator, the imaging accuracy is very high and it is applicable to different types of application scenarios. It should be noted that in order to enable the fast quantitative differential interference microscopy system proposed by the present invention to achieve accurate quantitative phase imaging, the following requirements need to be met among various devices:

[0098] (1) In order to perform different processing on the spectrum distributions of the 0th-order and ±1st-order diffraction lights at the confocal plane of the first thin lens 7 and the second thin lens 11, it is required that the spectrum distributions of the 0th-order and ±1st-order diffraction lights do not overlap with each other at the confocal plane of the first thin lens 7 and the second thin lens 11. Therefore, it is necessary to satisfy:

[0099] (2) In order to filter and select the correct spectral distribution with a circular mask during the holographic differential reconstruction process, it is required that there is no overlap between the three spectral distributions on the right side of formula (12). Therefore, it is necessary to satisfy:

[0100] (3) In order to make the working surface of the phase-type spatial light modulator 10 only cover the spectral distributions of the 0th-order and -1st-order diffracted lights at the confocal plane of the first thin lens 7 and the second thin lens 11, so as to achieve selective phase modulation. Therefore, it is necessary to satisfy: and

[0101] (4) In order to satisfy the sampling theorem and obtain a high-quality original image, it is required that the lateral spatial resolution of the system under vertical illumination occupies at least four pixels of the image acquisition module 13. Therefore, it is necessary to satisfy:

[0102] (5) In order to satisfy the sampling theorem and achieve high-quality holographic recording of differential interference, it is required that the interference fringes occupy at least four pixels of the image acquisition module 13. Therefore, it is necessary to satisfy:

[0103] (6) In order to satisfy the sampling theorem during the holographic differential reconstruction process, that is, the signal with the maximum frequency in the holographic differential interference intensity map is collected by at least two pixels of the image acquisition module 13, it is required that the three spectral distributions on the right side of formula (12) do not exceed the edge of the spectral image. Therefore, it is necessary to satisfy:

[0104] The effects of the fast quantitative differential interference microscopy system based on holographic recording proposed by the present invention are further illustrated through simulation experiments below.

[0105] In the simulation process, the sample to be measured is set as a pure phase object, and its true phase distribution is as shown in Figure 3 and Figure 4 gives the phase distribution along the horizontal white dotted line in Figure 3 . At the same time, the transmission grating 5 is set to diffract along the Y-axis direction. In order to realize the holographic differential interference detection along the X-axis direction, the phase-type spatial light modulator 10 is loaded with the phase distribution as shown in Figure 5 . At this time, on the image acquisition module 13, the 0th-order object light wave generates a shear offset along the X-axis direction relative to the -1st-order object light wave carrying the carrier wave vector, and the holographic differential interference intensity map of the shear offset along the X-axis direction collected by the image acquisition module 13 is as shown in Figure 6 .

[0106] For Figure 6Performing spatial Fourier transform to obtain the spectral distribution as shown in Figure 7 , and then using the holographic differential reconstruction method proposed in the present invention to obtain the spectral distribution as shown in Figure 8 . Performing spatial inverse Fourier transform and phase extraction operation on the spectral distribution shown in Figure 8 yields the phase difference distribution of the sample along the X-axis direction, and dividing this phase difference distribution by the shear offset along the X-axis direction gives the phase gradient distribution of the sample along the X-axis direction, as shown in Figure 9 . Further, to achieve holographic differential interference detection along the Y-axis direction, the phase-type spatial light modulator 10 is loaded with the phase distribution as shown in Figure 10 . At this time, on the image acquisition module 13, the 0th-order object light wave generates a shear offset along the Y-axis direction relative to the -1st-order object light wave carrying the carrier wave vector, and the holographic differential interference intensity map of the shear offset along the Y-axis direction collected by the image acquisition module 13 is as shown in Figure 11 . Performing spatial Fourier transform on Figure 11 to obtain the spectral distribution as shown in Figure 12 , and then using the holographic differential reconstruction method proposed in the present invention to obtain the spectral distribution as shown in Figure 13 . Performing spatial inverse Fourier transform and phase extraction operation on the spectral distribution shown in Figure 13 yields the phase difference distribution of the sample along the Y-axis direction, and dividing this phase difference distribution by the shear offset along the Y-axis direction gives the phase gradient distribution of the sample along the Y-axis direction, as shown in Figure 14 .

[0107] Finally, performing Frankot-Chellappa phase integration operation on Figure 9 and Figure 14 using formula (15) gives the sample phase distribution as shown in Figure 15 . Figure 16 shows the phase distribution along the horizontal white dashed line in Figure 15 . Comparing Figure 3 and Figure 15 and Figure 4 and Figure 16 , it can be seen that the fast quantitative differential interference microscopy system based on holographic recording proposed in the present invention accurately reconstructs the phase distribution of the sample only using two original images collected by the image acquisition module, with very high detection accuracy. It should be noted that in the simulation process, this embodiment takes into account the reality that the system objective lens has a finite numerical aperture. Therefore, the phase distributions shown in Figure 15 and Figure 16 have a resolution degradation problem compared to the true phase distributions shown in Figure 3 and Figure 4 .

[0108] Subsequently, the real-time rapid quantitative differential interference microscopy imaging of transparent living COS7 cells was performed using the rapid quantitative differential interference microscopy system of this embodiment, and high-quality phase images thereof were obtained, as Figures 17 to 19 shown. First, a phase distribution that generates a shear offset along the X-axis direction was loaded onto the phase-type spatial light modulator 10 to obtain the phase gradient distribution of COS7 cells along the X-axis direction, as Figure 17 shown. Subsequently, a phase distribution that generates a shear offset along the Y-axis direction was loaded onto the phase-type spatial light modulator 10 to obtain the phase gradient distribution of COS7 cells along the Y-axis direction, as Figure 18 shown. Finally, the Frankot-Chellappa phase integration operation was performed on the phase gradient distributions shown in Figure 17 and Figure 18 using formula (15) to obtain the phase distribution of COS7 cells shown in Figure 19 shown. In particular, Figure 20 shows the bright-field image of COS7 cells in the same field of view as Figure 19 . By comparing Figure 19 and Figure 20 , it can be seen that the rapid quantitative differential interference microscopy system based on holographic recording proposed in the present invention can perform high-quality quantitative phase imaging on organelles such as mitochondria, lipid droplets, and black vacuoles in transparent living cells, and can capture the structural changes of the organelles themselves and the interactions between different organelles, which proves the feasibility and effectiveness of the proposed invention device.

[0109] In summary, the fast quantitative differential interference microscopy system based on holographic recording proposed in the present invention combines the grating carrier frequency and the polarization modulation characteristics of the phase-type spatial light modulator to achieve fast quantitative differential interference microscopy imaging. The present invention uses partially coherent light as the illumination light to avoid the speckle noise caused by high-coherence light sources. Therefore, this microscopy system has high imaging quality and high spatial phase sensitivity. The present invention adopts an optical structure of coaxial interference, which has very strong immunity to external disturbances and has high imaging stability and high temporal phase sensitivity. Compared with the traditional quantitative differential interference microscopy technology, the present invention precisely realizes shear offsets in any direction and to any degree by using a phase-type spatial light modulator, with very high imaging accuracy and being applicable to different types of application scenarios. The present invention uses the grating carrier frequency to achieve holographic recording of differential interference, and only uses two images to achieve high-precision quantitative differential interference microscopy imaging of the sample to be measured. Therefore, the fast quantitative differential interference microscopy system of the present invention has very high temporal resolution and spatial resolution, and at the same time has very high imaging accuracy. The fast quantitative differential interference microscopy system of the present invention has a simple structure, is easy to build, inherits the advantages of high axial resolution of the traditional differential interference contrast microscope, and can perform three-dimensional quantitative phase imaging on thick tissue samples. Therefore, the proposed fast quantitative differential interference microscopy system based on holographic recording can perform label-free, highly stable, highly sensitive and high-resolution in-situ quantitative phase imaging on the sample to be measured, and has very good expandability in terms of structure and function, and has great application value in the fields of biomedicine and industrial inspection, etc.

[0110] In several embodiments provided by the present invention, it should be understood that the devices and methods disclosed in the present invention can be implemented in other ways. For example, the device embodiments described above are only illustrative. For example, the division of the modules is only a logical function division. In actual implementation, there may be other division methods. For example, multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0111] In addition, each functional module in various embodiments of the present invention can be integrated in a processing module, or each module can exist physically alone, or two or more modules can be integrated in one module. The above-mentioned integrated modules can be implemented in the form of hardware, or in the form of a combination of hardware and software functional modules.

[0112] The above content is a further detailed description of the present invention in combination with specific preferred implementation manners, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A fast quantitative differential interference microscopy system based on holographic recording, characterized in that, Comprising a partially coherent illumination module (1), a microscope objective lens (3), a tube lens (4), a transmission grating (5), a first linear polarizer (6), a first thin lens (7), a half-wave plate (8), a phase-type spatial light modulator (10), a second thin lens (11), a second linear polarizer (12), and an image acquisition module (13) arranged in sequence along the optical axis direction of the partially coherent illumination module (1), wherein, the partially coherent illumination module (1) is used to generate partially coherent illumination light; a sample (2) is arranged at the front focal plane of the microscope objective lens (3), and the transmission grating (5) is arranged at the confocal plane of the tube lens (4) and the first thin lens (7); the first linear polarizer (6) is arranged between the transmission grating (5) and the first thin lens (7); the polarization direction of the first linear polarizer (6) is along the Y-axis direction, and the first thin lens (7) only collects the 0th order and ±1st order diffracted lights carrying the object light wave information and polarized along the Y-axis direction; the phase-type spatial light modulator (10) is arranged at the confocal plane of the first thin lens (7) and the second thin lens (11), and the working surface of the phase-type spatial light modulator (10) only covers the spectral distributions of the 0th order and -1st order diffracted lights. The half-wave plate (8) is arranged between the first thin lens (7) and the phase-type spatial light modulator (10) and is adjacent to the working surface of the phase-type spatial light modulator (10), and can make the spectral distribution of the -1st order diffracted light reaching the working surface of the phase-type spatial light modulator (10) be linearly polarized along the X-axis direction. The X-axis direction and the Y-axis direction are perpendicular to each other and both are perpendicular to the optical axis direction of the partially coherent illumination module (1); the phase-type spatial light modulator (10) can perform phase modulation on the spectral distribution of the 0th order diffracted light; the second linear polarizer (12) is arranged between the second thin lens (11) and the image acquisition module (13), and is used to perform polarization adjustment on the 0th order diffracted light and the -1st order diffracted light with the same polarization direction; the image acquisition module (13) is used for image acquisition and recording.

2. The rapid quantitative differential interference microscopy system based on holographic recording according to claim 1, wherein It further includes a light shield (9) arranged at the confocal plane of the first thin lens (7) and the second thin lens (11), and the light shield (9) is used to block the spectral distribution of the +1st order diffracted light.

3. The rapid quantitative differential interference microscopy system based on holographic recording according to claim 1, characterized in that, The phase modulation pattern loaded on the working surface of the phase-type spatial light modulator (10) is represented by spatial coordinates as: wherein, x0 and y0 respectively represent the offset distances generated on the image acquisition module (13) along the X-axis direction and the Y-axis direction, λ represents the central wavelength of the light emitted by the partially coherent illumination module (1), and f2 represents the focal length of the second thin lens (11).

4. The rapid quantitative differential interference microscopy system based on holographic recording according to claim 1, wherein The parameters of the microscope objective lens (3), the tube lens (4), and the transmission grating (5) satisfy: where λ represents the central wavelength of the light emitted by the partially coherent illumination module (1), f obj and NA respectively represent the focal length and numerical aperture of the microscope objective lens (3), f tube represents the focal length of the tube lens (4), and d represents the grating constant of the transmission grating (5).

5. The rapid quantitative differential interference microscopy system based on holographic recording according to claim 4, wherein The width SLM_width and length SLM_height of the working surface of the phase-type spatial light modulator (10) satisfy: wherein, f1 represents the focal length of the first thin lens (7).

6. The rapid quantitative differential interference microscopy system based on holographic recording according to claim 5, wherein The pixel size of the image acquisition module (13) satisfies: wherein, f2 represents the focal length of the second thin lens (11).

7. A rapid quantitative differential interference microscopy method based on holographic recording, characterized in that, including: S1: obtaining the light intensity distribution of a sample by using the rapid quantitative differential interference microscopy system according to any one of claims 1 to 6; S2: performing a spatial Fourier transform on the light intensity distribution to obtain the spectral distribution of the light intensity; S3: obtaining the phase distribution of the sample by using a holographic differential reconstruction method according to the spectral distribution of the light intensity.

8. The rapid quantitative differential interference microscopy method based on holographic recording according to claim 7, characterized in that, The expression of the light intensity distribution detected by the image acquisition module (13) is: where, j represents the imaginary unit, represents the convolution operation, h(x, y) represents the complex amplitude point spread function of the confocal system composed of the microscope objective lens (3) and the tube lens (4), h r (x, y) represents the complex amplitude point spread function of the confocal system composed of the first thin lens (7) and the second thin lens (11); E c (x, y) is the ideal light field distribution generated by the object light wave s(x, y) on the rear focal plane of the second thin lens (11), (x, y) represents the transverse spatial coordinates, a(x, y) represents the amplitude information of the sample, represents the phase information of the sample; s c (x - x0, y - y0) represents s c (x, y) after being translated along the vector (x0, y0), d represents the grating constant of the transmission grating (5), f1 represents the focal length of the first thin lens (7), and f2 represents the focal length of the second thin lens (11).

9. The rapid quantitative differential interference microscopy method based on holographic recording according to claim 8, characterized in that The S2 includes: S2.1: transforming the expression of the light intensity distribution to obtain a transformed expression: where * denotes conjugate, B(x,y) = |s c (x,y)| 2 +|s c (x - x0, y - y0)| 2 , A(x,y) and φ(x,y) respectively represent the magnified images of the sample amplitude information a(x,y) and the sample phase information ; S2.2: performing a spatial Fourier transform on both sides of the transformed expression to obtain the spectral distribution of the light intensity: wherein, (ξ, η) represents the spectral coordinates corresponding to the spatial coordinates (x, y), and ~ represents the two-dimensional spatial Fourier transform of the corresponding variable.

10. The rapid quantitative differential interference microscopy method based on holographic recording according to claim 9, characterized in that, The S3 includes: S3.1: Shift the overall spectrum distribution along the negative direction of the η coordinate axis by k c distance to obtain a new spectrum distribution S3.2: Set a circular mask Mask(ξ,η) centered at the origin of the spectral coordinates. The circular mask takes a value of 1 within a circular region with a radius of and takes a value of 0 in other regions; S3.3: Multiply the new spectral distribution by the circular mask Mask(ξ,η) to obtain the distribution of. Perform an inverse spatial Fourier transform on the obtained distribution of to obtain the distribution of e d (x,y), thereby obtaining the distribution of φ(x,y) - φ(x - x0, y - y0); S3.4: In the phase modulation pattern loaded by the phase-type spatial light modulator (10), let y0 = 0 and Obtain the gradient distribution of φ(x, y) along the X-axis direction: In the phase modulation pattern loaded by the phase-type spatial light modulator (10), when x0 = 0 and the gradient distribution of φ(x, y) in the Y-axis direction is obtained: S3.5: quantitatively obtaining the phase distribution of the sample to be measured: Among them, represents a two-dimensional spatial Fourier transform operation, represents a two-dimensional inverse spatial Fourier transform operation, and ε represents a regularization coefficient.

Images