A single-frame coded phase retrieval system and parameter calibration method based on iterative filtering inversion

Abstract

This invention discloses a single-frame coded phase retrieval system and parameter calibration method based on iterative filtering inversion, belonging to the field of lensless computational microscopy imaging technology. It solves the problems of mismatch between single-frame coded phase retrieval algorithms and complex coding scenarios, difficulty in balancing noise suppression and resolution, large system diffraction distance estimation errors, and inaccurate wavefront lateral offset calibration, leading to low imaging accuracy and poor stability. This invention constructs a system including a light source, replaceable amplitude / phase coding, CMOS imaging, one-dimensional electric displacement drive, and a built-in IrCPR algorithm control module, along with a process of "multi-distance calibration of coding functions → Z1 / Z2 calibration using ToG / SG according to coding board type → cross-correlation spectrum registration." This invention improves the accuracy of coding function calibration and diffraction distance estimation, achieves pixel-level alignment of the coded wavefront, and completes complex amplitude reconstruction with a single frame acquisition. The system has strong adaptability and stability, making it suitable for high-precision microscopy imaging scenarios.

Description

Technical Field

[0001] This invention relates to the field of lensless computational microscopy imaging technology, and in particular to a single-frame coded phase recovery system and parameter calibration method based on iterative filtering inversion. Background Technology

[0002] Lensless computational microscopy has significant application value in portable detection due to its advantages such as not requiring optical lenses and having a compact structure. Among them, single-frame coded phase retrieval technology can overcome the phase singularity problem of traditional lensless imaging by adding a coding element between the sample and the image sensor. However, existing technologies have key defects in both algorithm and system parameter calibration, which seriously restrict the imaging accuracy and stability. At the level of single-frame coded phase retrieval algorithms, existing mainstream algorithms cannot simultaneously achieve both model adaptability and reconstruction accuracy. The SPICA algorithm, based on amplitude coding, originates from the single-frame aperture coding phase retrieval approach proposed by the Horisaki team. Although it uses a binary coding plate as a strong constraint to solve for the wavefront function of the transmission plane of the amplitude coding plate using the GS algorithm, this algorithm relies on the binary amplitude coding plate, simplifying the coding function to a 0 / 1 binary real matrix. It ignores the fact that the actual amplitude coding function should be a complex number—the phase information of the actual coding function retains the phase fluctuations of the illumination background light. If this phase information is ignored, the algorithm model cannot fully match the actual system, easily leading to image distortion in the reconstructed image. While the BCPR algorithm borrows the idea of ​​image completion to integrate the encoding and decoding processes into a unified optimization, improving image reconstruction quality compared to the SPICA algorithm, it is still insufficient. While the algorithm offers advantages in wavefront inversion, its computational architecture still requires the encoding function to be a binary real matrix, containing only "0" and "1" elements. This makes it unsuitable for real-world complex encoding scenarios. Furthermore, if the encoding plane and the observation plane are not strictly parallel, forcibly binarizing the encoding function will result in the loss of some information, also leading to image distortion. The SPAR algorithm based on phase encoding uses sparse optimization as its technical approach, introducing the BM3D algorithm for light field block operations and spatial filtering to eliminate twin images and background noise. However, this algorithm uses a simple conjugate multiplication method to complete the wavefront inversion of the encoding plane, ignoring the difficulty in achieving an ideal phase encoding plate where only the phase changes and the amplitude is assumed to be 1 in actual production. It does not consider the amplitude deviation of the phase encoding plate, leading to deviations in amplitude reconstruction. Additionally, due to the encapsulation effect of the phase, a phase unpacking algorithm is required, significantly reducing the reconstruction speed. Moreover, all the above algorithms are prone to speckle noise during wavefront inversion. Directly filtering out noise can easily lead to a loss of resolution in the reconstructed image, making it difficult to achieve a balance between "noise suppression and resolution preservation."

[0003] Furthermore, the core parameters of the coded diffraction imaging system (diffraction distance and coded wavefront registration) directly affect the reconstruction accuracy. However, existing parameter calibration methods also have significant drawbacks: On the one hand, the system diffraction distance includes the distance Z1 from the sample to the coded plate and the distance Z2 from the coded plate to the image sensor. Traditional methods estimate the distance using a single sharpness function (such as the SG function). However, the optical field characteristics of the amplitude coded plate and the phase coded plate differ greatly, and a single sharpness function is prone to multi-peak misjudgment—for example, when estimating Z2 of the amplitude coded plate, the SG function is prone to multi-peak phenomena when the coded pixel size is 20μm and 40μm. If the distance search range is too small, it is easy to lead to misjudgment of the maximum value. The G function and ToG function exhibit numerous maxima during Z2 estimation using the phase-encoded plate, with the maxima on the left side of the curve significantly exceeding the sharpness value at the actual collimation distance, leading to misjudgment of distance. Furthermore, Z1 estimation is more complex, requiring the loading of a sample before capturing an coded diffraction image. The modulation effect of the coded plate on the sample is similar to speckle modulation, causing random perturbations in the subsequent diffraction field. If digital collimation is directly performed on the coded modulated diffraction image, the inverse diffraction image stack will be covered by speckle, making it impossible to assess image clarity or sharpness. Existing algorithms also lack optimized filtering strategies for wavefront decoupling in Z1 estimation, resulting in insufficient sharpness at the edge of the decoupled incident wavefront, further increasing the distance estimation error. On the other hand, there is a two-dimensional lateral offset between the coding function calibrated when the sample is unloaded and the coding function after the sample is loaded. The samples are mostly slices or glass products with non-negligible thickness. When the incident parallel laser illuminates the sample at a certain angle, the difference in refractive index between the sample and the surrounding air will cause the emitted beam to shift laterally. The offset range is about a dozen pixels. Existing hardware adjustment methods (such as mechanical fine-tuning of the coding plate or sensor) are extremely difficult to achieve pixel-level alignment, which leads to the failure of coding constraints. The coding function cannot match the sample diffraction field. For example, without adding wavefront registration, the true image of the resolution target amplitude image reconstructed directly using the IrCPR algorithm cannot be distinguished, which seriously affects the imaging quality. Summary of the Invention

[0004] This invention proposes a single-frame coded phase retrieval system and parameter calibration method based on iterative filtering inversion. By constructing an integrated system including a light source module, a replaceable amplitude / phase coding module, a CMOS imaging module, a one-dimensional electric displacement drive module, and a control module with a built-in iterative filtering inversion (IrCPR) algorithm, the system executes a parameter calibration process of "multi-distance acquisition to calibrate the coding function → selecting ToG / SG sharpness function according to the coding board type to calibrate the diffraction distance Z1 / Z2 → cross-correlation spectrum to achieve coding wavefront registration". This invention solves the problems in the prior art, such as the mismatch between the single-frame coded phase retrieval algorithm model and the actual complex coding scenario, the difficulty in balancing speckle noise suppression and resolution preservation, and the problems of large diffraction distance estimation error of the coding imaging system and the inability to accurately calibrate the transverse offset of the coding wavefront after sample loading, which lead to low imaging accuracy and poor stability.

[0005] A single-frame coded phase recovery system based on iterative filtering inversion includes a light source module, a coding module, an imaging module, a driving module, and a control module. The coding module is set on the parallel coherent light emission path of the light source module, the imaging module is set on the light emission path of the coding module and is fixedly connected to the driving module, and the control module is electrically and signal connected to the light source module, the driving module, and the imaging module.

[0006] Furthermore, the light source module includes a fiber laser, a pinhole, and a double-laminated collimating lens. The pinhole and the double-laminated collimating lens are sequentially arranged on the light output path of the fiber laser to convert the beam emitted by the fiber laser into parallel coherent light. The encoding module, which is a replaceable amplitude encoding plate or phase encoding plate, is used to modulate the diffraction field of the sample with a wavefront and encode it into a random scattering field, thus forming an encoded diffraction intensity image. The imaging module is a CMOS image sensor with its outer casing removed, used to acquire encoded diffraction intensity images, providing raw data support for encoding function calibration and sample complex amplitude reconstruction; The drive module is a one-dimensional electric displacement stage used to drive the imaging module to move along the axial direction; The control module is used to control the switching of the light source module, the movement of the drive module, and the image acquisition of the imaging module. The control module has a built-in iterative filtering and inversion single-frame encoded phase recovery algorithm, which is used to process the acquired encoded diffraction intensity image, reconstruct the complex amplitude of the sample, and thus complete the image restoration of the sample.

[0007] Furthermore, the fiber laser has a wavelength of 532nm, the collimating doublet has a focal length of 200mm, the amplitude encoder has a pixel size range of 2.5μm-40μm, the phase encoder has a pixel size of 10μm, and the CMOS image sensor has a pixel size of 1.85μm.

[0008] A parameter calibration method for a single-frame coded phase retrieval system based on iterative filtering inversion, the method comprising the following steps, based on the aforementioned single-frame coded phase retrieval system based on iterative filtering inversion: S1. Control the sample to be unloaded, drive the imaging module to move along the axis through the driving module, and acquire 11 axial diffraction intensity images of the encoding module at a sampling interval of 0.5 mm. Input the 11 images into the multi-distance phase recovery algorithm to reconstruct the encoding function. S2. Perform inverse diffraction transmission on the 11 axial diffraction intensity images acquired in S1 to generate a wavefront stack. If the encoding module is an amplitude encoding board, the ToG sharpness function is used to calculate the sharpness value of the wavefront stack, and the distance corresponding to the maximum sharpness value is taken as the distance Z2 from the encoding module to the imaging module. If the encoding module is a phase encoding board, the SG sharpness function is used to calculate the sharpness value of the wavefront stack, and the distance corresponding to the minimum sharpness value is taken as Z2. The control drive module fixes the imaging module at Z2. S3. Load the sample, acquire one coded diffraction intensity image of the sample, input the coded diffraction intensity image into the wavefront decoupling model, decouple to obtain the incident wavefront of the coded module, perform inverse diffraction transmission on the incident wavefront of the coded module, select the ToG sharpness function to calculate the sharpness value, and take the distance corresponding to the maximum sharpness value as the distance Z1 from the sample to the coded module. S4. Input the encoded diffraction intensity image into a single-frame phase retrieval algorithm based on nonlinear optimization, calculate the reference light field of the encoding module plane, calculate the cross-correlation spectrum between the encoding function and the reference light field of the encoding module plane, obtain the lateral offset based on the peak position of the cross-correlation spectrum, perform pixel-level translation on the encoding function to obtain the aligned encoding function, and then perform image reconstruction.

[0009] Furthermore, in S1, the optimization model of the multi-distance phase retrieval algorithm is as follows:

[0010] In the formula, Indicates the first j The estimated value of the encoding function under the next iteration. n Represents the location index in multi-distance acquisition. N The total number of multi-distance intensity images acquired. The first time when the sample is unloaded n Each collection distance ( The diffraction intensity image of the coding element under ) Denotes the total variation priors, For the corresponding regularization coefficient, The iterative formula for the multi-distance phase retrieval algorithm can be derived as follows:

[0011] In the above formula, The gradient operator is expressed as follows: , x and y It is an image spatial index. Nx and Ny yes x and y Total number of pixels in the direction.

[0012] Furthermore, in S2, the expression for the ToG sharpness function is:

[0013] The expression for the SG sharpness function is:

[0014] In the above formula, the operator 'std' represents calculating the variance of the matrix. The nuclear norm of a matrix is ​​defined as the weighted sum of the singular values ​​of the matrix.

[0015] Furthermore, in S3, the optimization objective of the wavefront decoupling model is: .

[0016] The iterative process of the wavefront decoupling model includes:

[0017]

[0018]

[0019]

[0020] In the above formula, Represents the filter coefficients With a guide filter of 0.01, after 50 iterations, the above iterative formula achieves effective decoupling of the coded plane wavefront.

[0021] Furthermore, in S4, the following formulas are executed sequentially to reconstruct the image:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] in, Indicates the filter parameters are Image filtering function, Indicates the filter parameters are Image filtering function, and These are the incident and transmitted wavefront functions of the encoding plane at the k-th iteration, respectively.

[0028] A storage medium storing a computer program, which, when executed by a processor, implements the parameter calibration method of the single-frame coded phase recovery system based on iterative filtering inversion described above.

[0029] A computer device, characterized in that it comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described parameter calibration method for a single-frame coded phase recovery system based on iterative filtering inversion.

[0030] The beneficial effects of this invention are as follows: The single-frame coded phase retrieval system and parameter calibration method based on iterative filtering inversion proposed in this invention effectively solves the problems of mismatch between existing single-frame coded phase retrieval algorithms and actual complex coding scenarios, and the difficulty in balancing speckle noise suppression and resolution preservation. This is achieved through a design of "stacked inversion wavefront separation + real-imaginary part collaborative filtering + adaptive updating of the coding function." The resulting sample amplitude reconstruction structure similarity (SSIM) is significantly higher than that of traditional algorithms, and the phase reconstruction results maintain a high degree of consistency with the true value. In the accompanying parameter calibration process, the diffraction distance calibration adopts a classification strategy of "coding plate type - sharpness function," with the amplitude coding plate adapted to the ToG function and the phase coding plate adapted to the SG function, ensuring the accuracy of Z1 and Z2 distance estimation. Wavefront registration is achieved based on the peak shift of the cross-correlation spectrum. Pixel-level alignment successfully solves the lateral offset problem of the encoded wavefront after sample loading, allowing the encoding constraints to be effectively implemented. The system supports the replacement of amplitude encoding plates and phase encoding plates, which can be adapted to encoding elements of different pixel sizes without adjusting the core algorithm framework. Furthermore, by calibrating the encoding function through multi-distance acquisition combined with the MDPR-PnP algorithm, it can adapt to different illumination conditions, avoiding model mismatch caused by laser intensity attenuation and differences in calibration and testing conditions, thus improving the stability of the system in long-term operation. At the same time, this invention only requires a single frame acquisition of the sample encoded diffraction image to complete the complex amplitude reconstruction, without the need for multi-frame scanning. Combined with an automated parameter calibration process, the imaging efficiency is high. Moreover, the system hardware uses conventional fiber lasers, CMOS sensors, and electric displacement stages, which are easy to implement in engineering and are suitable for various high-precision microscopic imaging scenarios such as biological slice observation and micro-nano structure detection. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the structure of a coded imaging system; Figure 2 The results of single-frame reconstruction using different coding boards are shown below. Figure 2 (ae) is the reconstructed image corresponding to amplitude encoders with pixel sizes of 2.5μm, 5μm, 10μm, 20μm, and 40μm. Figure 2 (f) is the reconstructed image corresponding to a phase encoder with a pixel size of 10μm; Figure 3 This is a comparison chart of the results of the amplitude-encoded phase retrieval algorithm, where... Figure 3 (a1) Figure 3 (b1) Figure 3 (c1) Figure 3 (d1) and Figure 3 (e1) is the reconstructed image of the SPICA algorithm with amplitude encoder pixel sizes of 2.5μm, 5μm, 10μm, 20μm and 40μm respectively; Figure 3 (a2) Figure 3 (b2) Figure 3 (c2) Figure 3 (d2) and Figure 3 (e2) are the reconstructed images of the BCPR algorithm with amplitude encoder pixel sizes of 2.5μm, 5μm, 10μm, 20μm and 40μm respectively; Figure 3 (a3) Figure 3 (b3) Figure 3 (c3) Figure 3 (d3) and Figure 3 (e3) is the reconstructed image of the IFCPR algorithm with amplitude encoder pixel sizes of 2.5μm, 5μm, 10μm, 20μm and 40μm respectively; Figure 4 The image shows a comparison of the phase encoding and phase retrieval algorithm results. Figure 4 (a1) is the reconstructed image of the CMI algorithm without adding pinhole constraints. Figure 4 (b1) and Figure 4 (c1) are the reconstructed images using the SPAR algorithm with BM3D and TNRD as filters, respectively. Figure 4 (d1) is the reconstructed image using the IFCPR algorithm. Figure 4 (a2) Figure 4 (b2) Figure 4 (c2) and Figure 4 (d2) are respectively Figure 4 (a1) Figure 4 (b1) Figure 4 (c1) and Figure 4 (d1) partial magnified view; Figure 5 This is a flowchart of the encoder calibration process based on multi-distance acquisition.

[0032] Among them, 1 is the power supply module, 2 is the encoding module, 3 is the imaging module, and 4 is the driving module. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] A single-frame coded phase recovery system based on iterative filtering inversion includes a light source module 1, a coding module 2, an imaging module 3, a driving module 4, and a control module. The coding module 2 is disposed on the parallel coherent light emission path of the light source module 1, the imaging module 3 is disposed on the light emission path of the coding module 2 and is fixedly connected to the driving module 4, and the control module is electrically and signal connected to the light source module 1, the driving module 4, and the imaging module 3.

[0035] Furthermore, refer to Figure 1 As shown, the light source module 1 includes a fiber laser, a pinhole, and a double-cemented collimating lens. The pinhole and the double-cemented collimating lens are sequentially arranged on the light output path of the fiber laser to convert the beam emitted by the fiber laser into parallel coherent light. Encoding module 2 is a replaceable amplitude encoding plate or phase encoding plate, used to modulate the diffraction field of the sample with a wavefront and encode it into a random scattering field, that is, to form an encoded diffraction intensity image. Imaging module 3 is a CMOS image sensor with its outer casing removed, used to acquire encoded diffraction intensity images, providing raw data support for encoding function calibration and sample complex amplitude reconstruction; Drive module 4 is a one-dimensional electric displacement stage used to drive imaging module 3 to move along the axial direction; The control module is used to control the switching of the light source module 1, the movement of the drive module 4, and the image acquisition of the imaging module 3. The control module has a built-in iterative filtering and inversion single-frame encoded phase recovery algorithm, which is used to process the acquired encoded diffraction intensity image, reconstruct the complex amplitude of the sample, and thus complete the image restoration of the sample.

[0036] Furthermore, the fiber laser has a wavelength of 532nm, the collimating doublet has a focal length of 200mm, the amplitude encoder has a pixel size range of 2.5μm-40μm, the phase encoder has a pixel size of 10μm, and the CMOS image sensor has a pixel size of 1.85μm.

[0037] Specifically, in this embodiment, a fiber laser with a wavelength of 532nm is used as a coherent light source. Its emitted beam passes through a pinhole and a double cemented lens with a focal length of 200mm to form a parallel beam to illuminate the coding board. The coding board is selected from two types: binary amplitude and binary phase. The minimum light-transmitting pixels of the amplitude board are 2.5μm, 5μm, 10μm, 20μm and 40μm, respectively, and the minimum light-transmitting pixel of the phase board is 10μm. The amplitude coding board is made by coating a reflective film, while the phase coding board is made by etching depth. The CMOS image sensor module (IMX226, pixel size 1.85μm, Sony) with the shell removed is mounted on a one-dimensional stepper motor displacement stage (GCD-203200M, Daheng Optoelectronics) for axial multi-distance image acquisition. (4) With an axial sampling interval of 0.5mm, 11 axial intensity images are acquired for image reconstruction.

[0038] A parameter calibration method for a single-frame coded phase retrieval system based on iterative filtering inversion, the method comprising the following steps, based on the aforementioned single-frame coded phase retrieval system based on iterative filtering inversion: S1. Control the sample to be unloaded, drive the imaging module 3 to move along the axis through the driving module 4, and acquire 11 axial diffraction intensity images of the encoding module 2 at a sampling interval of 0.5 mm. Input the 11 images into the multi-distance phase recovery algorithm to reconstruct the encoding function. S2. Perform inverse diffraction transmission on the 11 axial diffraction intensity images acquired in S1 to generate a wavefront stack. If the encoding module 2 is an amplitude encoding board, the ToG sharpness function is used to calculate the sharpness value of the wavefront stack, and the distance corresponding to the maximum sharpness value is taken as the distance Z2 from the encoding module 2 to the imaging module 3. If the encoding module 2 is a phase encoding board, the SG sharpness function is used to calculate the sharpness value of the wavefront stack, and the distance corresponding to the minimum sharpness value is taken as Z2. Control the drive module 4 to fix the imaging module 3 at Z2. S3. Load the sample, acquire one coded diffraction intensity image of the sample, input the coded diffraction intensity image into the wavefront decoupling model, decouple to obtain the incident wavefront of the coded module 2, perform inverse diffraction transmission on the incident wavefront of the coded module 2, select the ToG sharpness function to calculate the sharpness value, and take the distance corresponding to the maximum sharpness value as the distance Z1 from the sample to the coded module 2. S4. Input the encoded diffraction intensity image into a single-frame phase retrieval algorithm based on nonlinear optimization, calculate the reference light field of the encoding module 2 plane, calculate the cross-correlation spectrum between the encoding function and the reference light field of the encoding module 2 plane, obtain the lateral offset based on the peak position of the cross-correlation spectrum, perform pixel-level translation on the encoding function to obtain the aligned encoding function, and then perform image reconstruction.

[0039] Specifically, based on, for example Figure 1The data measurement and calculation process of the iterative filtering inversion coded imaging system shown can be summarized as follows: (1) Without placing the sample, place the CMOS image sensor close to the coding board to form an on-chip coding structure. Move the image sensor by the axial displacement stage to measure 11 multi-distance diffraction images of the coding board and input them into the MDPR-PnP algorithm to reconstruct the coding function; (2) After the measurement is completed, move the image sensor back to its original position and fix the positions of the coding board and the image sensor. Since the coding board has been calibrated, the coding board and the image sensor do not need to be changed; (3) Place the sample and measure the single-frame coded diffraction image of the sample. Then, after digital focusing, wavefront registration and IrCPR algorithm respectively, the final sample reconstruction is completed.

[0040] Using a resolution target as the sample, Figure 2 The images show single-frame reconstruction results using different encoding boards. Comparing the results, it's clear that amplitude coding produces different imaging effects depending on the pixel size of the encoding board. For example... Figure 2 As shown in (a) and 2(e), neither excessively large nor excessively small coded pixels can reconstruct sample information with high quality. When the coded pixel size is 2.5 μm, although the multi-distance phase retrieval algorithm can effectively reconstruct the coded function, the pixel size of this coded image is close to the pixel limit of the image sensor (pixel size is 1.85 μm). Therefore, the binary distribution shown by the reconstructed coded function has a large error, which leads to obvious image distortion of the corresponding reconstructed resolution target. When the coded pixel size is 40 μm, the light field range truncated at the '0' position is large, and the random modulation effect of the amplitude coded plate is severely weakened. Therefore, the reconstructed resolution target image produces local image distortion. (Comparison) Figure 2 As shown in (b), 2(c), and 2(d), the high-resolution regions reconstructed by the three encoding boards are not significantly different. Figure 2 (d1) There is still residual noise at the first line pair of the fourth group, therefore the appropriate pixel size for the amplitude coding board is 5μm and 10μm. Compared with the reconstruction results of amplitude coding, phase coding has the best reconstruction effect, and its image contrast in the high-resolution area is significantly better than other images.

[0041] In summary, the IrCPR algorithm can simultaneously perform both amplitude coding and phase coding; therefore, this paper compares and analyzes it with existing coding phase retrieval algorithms. To ensure a fair comparison between algorithms, this paper uses the coding function reconstructed by the MDPR-PnP algorithm for use by various phase retrieval algorithms, thus guaranteeing that all algorithms can be compared under the same coding function. The comparison results between the IrCPR algorithm and the single-frame amplitude coding phase retrieval algorithm are as follows: Figure 3 As shown. Figure 3(a1-e1) represents the reconstruction resolution chart of the SPICA algorithm at coded pixel sizes of 2.5μm, 5μm, 10μm, 20μm, and 40μm. As shown in the figure, the SPICA algorithm can only reconstruct partial information at 5μm, 10μm, and 20μm, but its high-resolution areas are still submerged in noise and cannot be distinguished. The SPICA algorithm simply introduces total variation as a sparse prior, but it ignores an important fact: the inverse problem of coded imaging is similar to a speckle demodulation problem. If only edge sparsity is used as a constraint, it will inevitably fail to effectively separate the random noise introduced by coded modulation. The BCPR algorithm considers the above problem and performs image reconstruction in a dual-loop manner. The inner loop uses guided filtering for complex amplitude completion, while the outer loop uses alternating projection for sample reconstruction. Figure 3 As shown in (a2-e2), the BCPR algorithm has a higher imaging resolution than the SPICA algorithm, but it still cannot completely eliminate the influence of background or speckle noise. Furthermore, the BCPR algorithm is only effective with small pixels; when the encoded pixels are larger than 10μm, the reconstructed image information becomes severely distorted. In contrast, the IrCPR algorithm proposed in this paper presents significantly better reconstruction quality than other algorithms. Moreover, the IrCPR algorithm is not sensitive to the pixel size of the encoding board, thus maximizing the flexibility of coded imaging applications.

[0042] Figure 4 This is a comparison of the IrCPR algorithm and the single-frame phase coding phase recovery algorithm. Figure 4 (a) shows the reconstruction result of the CMI algorithm. It should be noted that the CMI imaging used in this study did not include a pinhole in the experimental optical path; therefore, the CMI algorithm could not converge effectively, and the reconstructed image contained a large amount of noise. This also indirectly confirms the role of the pinhole in coherent modulation imaging; the introduction of the pinhole becomes a very strong physical constraint. Without the pinhole constraint, coherent modulation imaging cannot reconstruct sample information using only the wavefront separation mechanism of ePIE. If a pinhole is introduced, the imaging field of view will be reduced, while the algorithm in this paper is designed for full-field imaging. Figure 4 (b) and Figure 4 (c) shows the reconstruction results of the SPAR algorithm using the BM3D and TNRD filters, respectively. BM3D is the filter used in the original SPAR algorithm paper. The results show that the SPAR algorithm fails to effectively reconstruct sample information using either of these filters. In contrast, the IrCPR algorithm significantly outperforms the other algorithms in reconstruction quality. Interestingly, Figure 4 The results shown are exactly the ablation analysis of each module of the IrCPR algorithm. Figure 4 (a) Wavefront separation mechanism using only stacked imaging. Figure 4 (b) and Figure 4(c) Instead of using the separation mechanism, the conjugate cancellation approach is adopted, and a filter is used for noise suppression. The IrCPR algorithm includes elements such as stacked wavefront separation, coding function update, and joint filtering of real and imaginary parts. It can effectively reconstruct sample information and does not have strict requirements on the type of coding plate.

[0043] Furthermore, in S1, the multi-distance phase retrieval algorithm corresponds to the wavefront source tracing problem of multi-frame intensity data. Its optimization model has various iterative models depending on the application scenario. In this embodiment, the multi-distance phase retrieval algorithm based on plug-and-play regularization (MDPR-PnP) is selected for encoding function calibration. Its corresponding optimization model is shown below:

[0044] In the formula, Indicates the first j The estimated value of the encoding function under the next iteration. n Represents the location index in multi-distance acquisition. N The total number of multi-distance intensity images acquired. The first time when the sample is unloaded n Each collection distance ( The diffraction intensity image of the coding element under ) Denotes the total variation priors, For the corresponding regularization coefficient, The iterative formula for the multi-distance phase retrieval algorithm can be derived as follows:

[0045] In the above formula, The gradient operator is expressed as follows: , x and y It is an image spatial index. Nx and Ny yes x and y Total number of pixels in the direction.

[0046] Specifically, the calibration process of the multi-distance coding function is as follows: Figure 5 As shown. The parameter settings of the MDPR-PnP algorithm are as follows: (1) The gradient descent coefficient τ is 0.005, =0.25; (2) The filter uses a guided filter with a filter coefficient of 0.005 and a filter kernel size of 3×3; (3) The number of iterations is 50.

[0047] Furthermore, in S2, the expression for the ToG sharpness function is:

[0048] The expression for the SG sharpness function is:

[0049] In the above formula, the operator 'std' represents calculating the variance of the matrix. The nuclear norm of a matrix is ​​defined as the weighted sum of the singular values ​​of the matrix.

[0050] Furthermore, in S3, the present invention uses the ToG function to estimate the distance of the amplitude encoding board and obtains Z2 by means of maxima optimization. Its expression can be written in the following form:

[0051] For the phase encoder, this paper uses the SG function to obtain Z2 by minimization, and its expression can be written in the following form:

[0052] The calibration process for Z2 can refer to the digital focusing method of holographic imaging, which is simple to operate. Unlike Z2, the estimation of Z1 is more complex, requiring the loading of the sample and the capture of a sample-encoded diffraction image before calibration. Since the modulation effect of the encoding plate on the sample is similar to speckle modulation, the addition of speckle will cause random perturbations in the subsequent diffraction field. Furthermore, if digital focusing is still performed on the encoded modulated diffraction image, the inverse diffraction image stack will be covered by speckle, making it impossible to assess image sharpness or clarity. Therefore, the calibration of Z1 should be divided into two steps: first, designing a wavefront inversion algorithm to eliminate the modulation effect of the encoding plate and reconstruct the incident wavefront of the encoding plane; then, using the digital focusing principle to perform inverse propagation calculation on the decoupled incident wavefront to determine the specific value of Z1 based on the image sharpness function. Using the IrCPR algorithm, this invention calculates the incident wavefront... For the purpose of optimization, the formula is summarized as follows: .

[0053] Furthermore, unlike the solution process of the IrCPR algorithm, the above equation requires decoupling the wavefront and obtaining the incident light field of the encoding plate, which is still the diffraction fringes of the sample. Therefore, the solution of the above equation should maintain the consistency of the fringes as much as possible and should not use overly fine image filters. In addition, since the image evaluation function of digital focusing evaluates edge sharpness information, the above equation does not need to introduce the modulation function update mechanism of the IrCPR algorithm. Based on the above analysis, the filtering prior in the above equation can be constructed by a self-referenced guided filter, the purpose of which is to highlight the edge information in a self-similar guided filtering manner so that the subsequent image sharpness function can more accurately estimate the diffraction distance Z1. Based on the above analysis, the above equation can be solved as follows:

[0054]

[0055]

[0056]

[0057] In the above formula, Represents the filter coefficients With a guide filter of 0.01, after 50 iterations, the above iterative formula achieves effective decoupling of the coded plane wavefront.

[0058] Furthermore, in S4, the following formulas are executed sequentially to reconstruct the image:

[0059]

[0060]

[0061]

[0062]

[0063] In practical applications, this invention uses a TNRD filter based on a nonlinear diffusion model to simultaneously filter the incident wavefront and the coding function. The relevant algorithm parameters are set as follows: =0.0002, =0.0001, =0.1, =0.5, =0.25.

[0064] A storage medium storing a computer program, which, when executed by a processor, implements the parameter calibration method of the single-frame coded phase recovery system based on iterative filtering inversion described above.

[0065] Specifically, the storage medium of this invention, by storing the corresponding computer program, enables the processor to accurately implement the parameter calibration method of a single-frame coded phase retrieval system based on iterative filtering inversion. Relying on the complete process of "multi-distance acquisition and calibration of the coding function → selection of ToG / SG sharpness function according to coding board type to calibrate diffraction distance Z1 / Z2 → cross-correlation spectrum to achieve coding wavefront registration," this effectively solves the problems in existing technologies such as the mismatch between the coding phase retrieval algorithm and the actual complex coding scenario, the difficulty in balancing speckle noise suppression and resolution preservation, large diffraction distance estimation errors, and inaccurate lateral offset of the coding wavefront. The calibration issue ensures the accuracy of the coding function calibration and the reliability of the diffraction distance estimation, achieving pixel-level alignment of the coding wavefront and effectively implementing coding constraints. Simultaneously, this storage medium facilitates program storage, transmission, and deployment, enabling different computer devices to conveniently apply the parameter calibration method of this invention without repeated development of core logic. This ensures the consistency and stability of the calibration process and enhances the practicality and scalability of the technical solution of this invention, helping the single-frame coded phase recovery system based on iterative filtering inversion to function efficiently in high-precision microscopic imaging scenarios such as biological slice observation and micro / nano structure detection.

[0066] A computer device, characterized in that it comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described parameter calibration method for a single-frame coded phase recovery system based on iterative filtering inversion.

[0067] Specifically, the computer device of this invention stores the corresponding computer program in its memory and executes the program via a processor. This enables precise parameter calibration of a single-frame coded phase retrieval system based on iterative filtering inversion. It fully replicates the calibration process of "multi-distance acquisition to calibrate the coding function → selecting ToG / SG sharpness functions according to the coding board type to calibrate diffraction distances Z1 / Z2 → cross-correlation spectrum to achieve coding wavefront registration." This effectively solves the problems of mismatch between the single-frame coded phase retrieval algorithm and the actual complex coding scenario, difficulty in balancing speckle noise suppression and resolution preservation, and large diffraction distance estimation errors in coded imaging systems in existing technologies. This addresses the issue of inaccurate calibration of the transverse offset of the encoded wavefront after loading, ensuring the accuracy of the encoding function calibration, the reliability of the diffraction distance estimation, and pixel-level alignment with the encoded wavefront, thus effectively implementing the encoding constraints. Furthermore, this computer device eliminates the need for repeated development of the core logic for parameter calibration; the calibration process can be quickly initiated simply by the processor calling the program in memory. This ensures the consistency and stability of the calibration operation while lowering the technical application threshold, making it easily adaptable to the needs of single-frame encoded phase retrieval systems based on iterative filtering inversion in various high-precision microscopic imaging scenarios such as biological slice observation and micro / nano structure detection.

[0068] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A single-frame coded phase retrieval system based on iterative filtering inversion, characterized in that, It includes a light source module (1), an encoding module (2), an imaging module (3), a driving module (4), and a control module. The encoding module (2) is set on the parallel coherent light emission path of the light source module (1). The imaging module (3) is set on the light emission path of the encoding module (2) and is fixedly connected to the driving module (4). The control module is electrically and signal connected to the light source module (1), the driving module (4), and the imaging module (3).

2. The single-frame coded phase retrieval system based on iterative filtering inversion according to claim 1, characterized in that, The light source module (1) includes a fiber laser, a pinhole and a double-cemented collimating lens. The pinhole and the double-cemented collimating lens are sequentially arranged on the light output path of the fiber laser to convert the light beam emitted by the fiber laser into parallel coherent light. The encoding module (2) is a replaceable amplitude encoding plate or phase encoding plate, used to modulate the diffraction field of the sample with a wavefront and encode it into a random scattering field, that is, to form an encoded diffraction intensity image. The imaging module (3) is a CMOS image sensor with its outer shell removed, used to acquire the encoded diffraction intensity image, providing raw data support for encoding function calibration and sample complex amplitude reconstruction; The drive module (4) is a one-dimensional electric displacement stage used to drive the imaging module (3) to move along the axial direction; The control module is used to control the switching of the light source module (1), the movement of the drive module (4), and the image acquisition of the imaging module (3). The control module has a built-in iterative filtering and inversion single-frame encoded phase recovery algorithm, which is used to process the acquired encoded diffraction intensity image, reconstruct the complex amplitude of the sample, and then complete the image restoration of the sample.

3. The single-frame coded phase retrieval system based on iterative filtering inversion according to claim 2, characterized in that, The fiber laser has a wavelength of 532nm, the collimating doublet has a focal length of 200mm, the amplitude encoder has a pixel size range of 2.5μm-40μm, the phase encoder has a pixel size of 10μm, and the CMOS image sensor has a pixel size of 1.85μm.

4. A parameter calibration method for a single-frame coded phase retrieval system based on iterative filtering inversion, based on the single-frame coded phase retrieval system based on iterative filtering inversion as described in any one of claims 1-3, characterized in that, The method includes the following steps: S1. Control the sample to be unloaded, drive the imaging module (3) to move along the axis through the driving module (4), and collect 11 axial diffraction intensity images of the encoding module (2) with a sampling interval of 0.5 mm. Input the 11 images into the multi-distance phase recovery algorithm to reconstruct the encoding function. S2. Perform inverse diffraction transmission on the 11 axial diffraction intensity images acquired in S1 to generate a wavefront stack. If the encoding module (2) is an amplitude encoding board, the ToG sharpness function is used to calculate the sharpness value of the wavefront stack, and the distance corresponding to the maximum sharpness value is taken as the distance Z2 from the encoding module (2) to the imaging module (3). If the encoding module (2) is a phase encoding board, the SG sharpness function is used to calculate the sharpness value of the wavefront stack, and the distance corresponding to the minimum sharpness value is taken as Z2. Control the driving module (4) to fix the imaging module (3) at Z2. S3. Load the sample, acquire one coded diffraction intensity image of the sample, input the coded diffraction intensity image into the wavefront decoupling model, decouple to obtain the incident wavefront of the coded module (2), perform inverse diffraction transmission on the incident wavefront of the coded module (2), use the ToG sharpness function to calculate the sharpness value, and take the distance corresponding to the maximum sharpness value as the distance Z1 from the sample to the coded module (2). S4. Input the encoded diffraction intensity image into a single-frame phase recovery algorithm based on nonlinear optimization, calculate the reference light field of the encoding module (2) plane, calculate the cross-correlation spectrum between the encoding function and the reference light field of the encoding module (2) plane, obtain the lateral offset based on the peak position of the cross-correlation spectrum, perform pixel-level translation on the encoding function, obtain the aligned encoding function, and then perform image reconstruction.

5. The parameter calibration method for a single-frame coded phase retrieval system based on iterative filtering inversion according to claim 4, characterized in that, In S1, the optimization model of the multi-distance phase retrieval algorithm is as follows: ， In the formula, Indicates the first j The estimated value of the encoding function under the next iteration. n Represents the location index in multi-distance acquisition. N The total number of multi-distance intensity images acquired. The first time when the sample is unloaded n Each collection distance ( The diffraction intensity image of the coding element under ) Denotes the total variation priors, For the corresponding regularization coefficient, The iterative formula for the multi-distance phase retrieval algorithm can be derived as follows: ， In the above formula, The gradient operator is expressed as follows: , x and y It is an image spatial index. Nx and Ny yes x and y Total number of pixels in the direction.

6. The parameter calibration method for a single-frame coded phase recovery system based on iterative filtering inversion according to claim 5, characterized in that, In S2, the expression for the ToG sharpness function is: , The expression for the SG sharpness function is: ， In the above formula, the operator 'std' represents calculating the variance of the matrix. The nuclear norm of a matrix is ​​defined as the weighted sum of the singular values ​​of the matrix.

7. The parameter calibration method for a single-frame coded phase recovery system based on iterative filtering inversion according to claim 6, characterized in that, In S3, the optimization objective of the wavefront decoupling model is: ， The iterative process of the wavefront decoupling model includes: ， ， ， ， In the above formula, Represents the filter coefficients With a guide filter of 0.01, after 50 iterations, the above iterative formula achieves effective decoupling of the coded plane wavefront.

8. The parameter calibration method for a single-frame coded phase recovery system based on iterative filtering inversion according to claim 7, characterized in that, In S4, the following formulas are executed sequentially to reconstruct the image: ， ， ， ， ， ， in, Indicates the filter parameters are Image filtering function, Indicates the filter parameters are Image filtering function, and These are the incident and transmitted wavefront functions of the encoding plane at the k-th iteration, respectively.

9. A storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the parameter calibration method for the single-frame coded phase recovery system based on iterative filtering inversion as described in any one of claims 4-8.

10. A computer device, characterized in that, include: The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the parameter calibration method for a single-frame coded phase recovery system based on iterative filtering inversion as described in any one of claims 4-8.

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