A method for accurate correction of light source position combined with pupil function

Abstract

The present invention discloses a method for accurately correcting the position of a light source in conjunction with a pupil function, applicable to a Fourier stacked microscope system. The method comprises: reconstructing K pupil function images using different numbers of low-resolution images; searching for directions α1 and α2 corresponding to the maximum and minimum distances from the location where the pupil function intensity value sharply drops to the image center; executing a circular contour search algorithm along α1 and α2 in the K pupil function images to obtain two sets of distances from the location where the intensity value sharply drops to the image center, and determining the position deviation from the two sets of distances; determining the ideal position of the corner LED unit in the LED array corresponding to the obtained frequency domain position deviation based on the interval of α1 and α2, calculating the actual position of the corner LED corresponding to the sub-aperture in the frequency domain; and solving the spatial position of the LED array to complete the spatial position correction of the LED array. The present invention achieves accurate spatial position correction of the LED array.

Description

Technical Field

[0001] The present invention relates to the technical field of Fourier stack microscopy, and in particular to a method for accurately correcting the position of a light source in combination with a pupil function. Background Art

[0002] High-throughput imaging is crucial for biomedical applications such as cell monitoring, drug screening, and pathological diagnosis. In traditional optical microscopy platforms, dyes and fluorescent proteins are widely used to enhance the contrast of sample information so that the recorded optical intensity images can clearly visualize the tissue morphology of biological samples. However, this invasive labeling method makes tissue section imaging susceptible to photobleaching and phototoxicity. At the same time, the imaging flux of traditional optical microscopy technology follows the Lagrange invariance theorem, making it difficult to simultaneously take into account imaging resolution and field of view. These challenges limit the observation of transparent biological samples and create a demand for microscopic imaging technology with subcellular scale resolution within a wide field of view.

[0003] Thanks to advances in optical modulation technology and computational imaging algorithms, quantitative phase imaging techniques have enabled non-invasive quantitative phase reconstruction of living biological samples by converting phase information into intensity contrast. Phase information represents the objective optical path delay of target features and can provide quantitative support for further measurements of the refractive index distribution and deep structure of transparent samples. Among quantitative phase imaging techniques using partially coherent illumination modulation, Fourier ptychographic microscopy (FPM) has attracted considerable attention for its high-throughput imaging performance. Compared to spatial stitching methods that extend the imaging field of view, FPM uses angular illumination scanning to record sample information at different spatial frequencies. The recorded low-resolution images are then used to iteratively update the corresponding sub-spectral information in the Fourier domain, ultimately stitching them together to form a higher equivalent numerical aperture. By effectively combining synthetic aperture, phase retrieval, and optimization theory, this technique achieves imaging resolution comparable to that of high numerical aperture techniques while retaining the original wide field of view of low numerical aperture techniques.

[0004] LED (Light-emitting Diode) arrays are widely used as illumination sources in Fourier stack microscopy systems due to their high brightness, low coherence, ease of programmability, and low cost. However, spatial position deviations of individual LEDs caused by misaligned illumination modules can lead to misplaced subapertures in the frequency domain during reconstruction, compromising the quality of the recovered high-resolution image. Therefore, precise correction of the illumination spatial position is crucial for ensuring high-quality reconstruction. Existing position correction methods fall into two main categories: algorithmic self-correction methods and physical model-based methods. Algorithmic self-correction methods combine the FPM reconstruction process with position parameter optimization. Using the difference between the estimated and true images as a reference, they iteratively approach the correct subaperture frequency domain position through optimization search methods such as simulated annealing and particle swarm optimization. Physical model-based methods directly solve for position parameters using representations of actual positions, such as the bright-dark field transition boundary in low-resolution images, the zero-order autocorrelation spectrum of bright-field low-resolution images, and offset targets in bright-field low-resolution images with a defocused objective. However, due to the presence of sample information and various errors in low-resolution images, such as system aberrations, background noise, LED intensity fluctuations, and model misalignment, the position parameters calibrated by algorithmic self-correction methods are not accurate. Furthermore, methods based on physical models are only applicable to corrections in the bright field area and often require special system parameter configurations or additional precision mechanical displacement components to ensure effective implementation. Summary of the Invention

[0005] Since the algorithm self-correction method based on the reconstruction process is easily affected by the quality of low-resolution images collected and the accuracy of the optimization search algorithm, and the method based on the physical model cannot accurately characterize the dark field illumination position, the present invention provides a method for accurately correcting the light source position in combination with the pupil function. By utilizing the relationship between the pupil function and the dark field illumination position deviation, a position deviation judgment standard and a circle center search algorithm are introduced to achieve accurate correction of the spatial position of the LED array.

[0006] The present invention discloses a method for accurately correcting the position of a light source in combination with a pupil function, which is applicable to a Fourier stack microscope system and includes:

[0007] Step 1: Light up the LED units in the programmable LED array in the Fourier stacking microscope system one by one under a low numerical aperture objective lens, collect a series of low-resolution intensity images at different illumination positions, and reconstruct K pupil function images using different numbers of low-resolution images through the stacking iterative engine algorithm;

[0008] Step 2: First, in the pupil function image reconstructed using the largest number of low-resolution images, set an omnidirectional search interval to search for the directions α1 and α2 corresponding to the maximum and minimum distances from the location where the pupil function intensity value drops sharply to the image center; in K pupil function images, perform a circular contour search algorithm along α1 and α2 to obtain two sets of distances from the location where the intensity value drops sharply to the image center, and determine the position deviation based on these two sets of distances;

[0009] Step 3: Determine the ideal position of the corner LED unit in the LED array corresponding to the obtained frequency domain position deviation based on the intervals of α1 and α2, and calculate the actual position of the sub-aperture corresponding to the corner LED in the frequency domain;

[0010] Step 4: Solve the spatial position of the LED array: According to the sub-aperture position calculation formula, a set of spatial position parameters can be solved for every two position coordinates. Finally, the average value of the multiple sets of parameters obtained is taken to complete the spatial position correction of the LED array.

[0011] Furthermore, the collecting of a series of low-resolution intensity images at different lighting positions includes:

[0012] A rectangular N×N LED array is used as the illumination source. The interval between adjacent LED units is represented by d. If the LED array is translated (Δx, Δy) and rotated (θ) on the horizontal plane, the spatial position r of the LED unit in the mth row and nth column on the array is m,n It can be expressed as:

[0013]

[0014] Where x m,n with y m,n represents the two-dimensional coordinate component value of the LED unit on the plane in the airspace, 1≤m≤N,1≤n≤N. Assuming that the distance h from the light source to the sample is far enough, the illumination light wave with a central wavelength of λ irradiated on the two-dimensional thin sample can be approximated as a plane wave, where the illumination wave vector can be expressed as:

[0015]

[0016] Where k x,m,n With k y,m,n Represents the two-dimensional coordinate component value of the wave vector in the frequency domain;

[0017] Illumination waves with different wave vectors scan different spatial frequency information on the sample spectrum, which is equivalent to shifting the center of the sample spectrum to k m,n At , the outgoing sub-spectrum is low-pass filtered by the coherent transfer function defined by the objective lens. The relevant process can be expressed as:

[0018] G m,n (k)=F{o(r)exp(ik m,n r)}P(k)=O(kk m,n )P(k)

[0019] Where o(r) represents the complex transmission function of the sample in the spatial domain, i represents the imaginary unit 1, F{·} represents the two-dimensional Fourier transform, and P(k) represents the pupil function of the objective lens. Finally, the information propagated to the camera image plane is collected and converted into a low-resolution intensity image The relevant process can be expressed as:

[0020]

[0021] Where, F -1 {·} represents the two-dimensional inverse Fourier transform, g m,n (r) represents the complex amplitude of the sample on the image plane; by lighting up the LED units in the array one by one and using a camera to capture images, a series of low-resolution intensity images of the sample can be obtained.

[0022] Furthermore, the method of reconstructing K pupil function images using different numbers of low-resolution images through a stacked iterative engine algorithm includes:

[0023] 1) Spectrum initialization: The interpolated result of the low-resolution image collected by the LED unit at the center of the array under normal incident illumination is selected as the initial value of the reconstructed amplitude part, and the phase part is set to zero;

[0024] 2) Target complex amplitude generation: corresponding to the incident wave vector k m,n The illumination light wave is captured by the circular pupil function of the objective lens to intercept the spectrum information in a sub-aperture of the initial high-resolution spectrum of the sample, and generate the target complex amplitude under the corresponding LED;

[0025] 3) Complex amplitude estimation update: Keeping the phase of the target complex amplitude image unchanged, the amplitude part of the target complex amplitude image is updated with the actual low-resolution image acquired under the corresponding illumination position sequence (m, n);

[0026] 4) Sub-aperture region update within the spectrum: Use Fourier transform to obtain the updated spectrum of the target complex amplitude distribution And use the spectrum to update the information in the corresponding sub-aperture in the sample high-resolution spectrum;

[0027] 5) Repeat steps 2) to 4) to update the spectra within the sub-aperture corresponding to all position sequences {(m,n)|1≤m≤N,1≤n≤N};

[0028] 6) Repeat iterative steps 2) to 5) until the high-resolution complex amplitude of the sample converges, thereby finally obtaining the transformed pupil function;

[0029] 7) Reduce the number of low-resolution images used to reconstruct the pupil function, and repeat steps 1) to 6) to obtain a total of K pupil function images.

[0030] Furthermore, spectrum initialization can be expressed as:

[0031]

[0032] In the formula, O0(k) represents the initial value of the reconstructed sample spectrum, R(·) represents the interpolation operation of the image, Indicates the initial zero phase of the setting.

[0033] Furthermore, the target complex amplitude under the corresponding LED is expressed as:

[0034]

[0035] Where j represents the current iteration number, 1≤j≤j max , pupil function P j The initial value of (k) is set to the passband A circular low-pass filter with 1 inside, NA obj Indicates the numerical aperture of the objective lens;

[0036] The complex amplitude estimate update is expressed as:

[0037]

[0038] Where, represents the updated target complex amplitude distribution corresponding to the LED with position sequence (m,n) at the jth iteration.

[0039] Furthermore, updating the sub-aperture region within the spectrum involves solving a non-convex optimization problem, updating the spectrum information and pupil function simultaneously. The update formula is:

[0040]

[0041]

[0042] Where α and β represent the update step size and are generally set to 1, * represents the complex conjugate operation, corresponding to the currently updated subaperture, and the updated complex amplitude The actual wave vector contained in With the target complex amplitude The ideal wave vector contained in The difference in the position of the ideal subaperture will cause the reconstruction to shift, and the center of the pupil function will shift to

[0043] Furthermore, due to bright field illumination The low-frequency self-cancellation effect of the phase transfer function of the pupil function is that the pupil function is a multi-center The superposition state of the sub-pupils, where N1×N1 represents the number of LEDs located in the bright field;

[0044] Furthermore, the step 2 includes:

[0045] In the K-frame pupil function image, the distance from the position where the two sets of intensity values ​​drop sharply along α1 and α2 to the center of the image is and like and At this time, the influence of translation in the position deviation parameter of LED array is greater, and the translation direction is the same as α2. It is used to represent the frequency domain position deviation of the sub-aperture corresponding to the corner LED in the LED array along the translation direction. represents the radius of the pupil, p img Indicates the pixel size of the image sensor, N img ×N img represents the number of pixels of the pupil function image, and Mag represents the magnification of the objective lens;

[0046] like At this time, the influence of rotation on the position deviation parameter of the LED array is greater. According to the interval where α1 is located, select the array Used to represent the frequency domain position deviation of the sub-aperture corresponding to the corner LED in a certain area of ​​the LED array; with the coordinate system from left to right and from top to bottom as the positive direction, when the rotation angle of the LED array is positive, if 0°<α1<90°, the obtained position deviation corresponds to the corner LED located in the lower left area of ​​the LED array; if 90°<α1<180°, the obtained position deviation corresponds to the corner LED located in the upper left area of ​​the LED array; if -90°<α1<0°, the obtained position deviation corresponds to the corner LED located in the lower right area of ​​the LED array; if -180°<α1<-90°, the obtained position deviation corresponds to the corner LED located in the upper right area of ​​the LED array.

[0047] Furthermore, the step 3 includes:

[0048] Convert the polar coordinates of the sub-aperture position deviation corresponding to the corner LED into two-dimensional frequency domain coordinates, and calculate the ideal frequency domain position of the corresponding sub-aperture according to its arrangement position in the LED array. By adding the frequency domain position deviation and the ideal frequency domain position, the actual frequency domain positions of K sub-apertures are obtained.

[0049] Furthermore, the step 4 includes:

[0050] Based on the corresponding formula between the spatial position parameters of the LED array and the illumination wave vector, and in accordance with the principle that the number of known results is greater than the unknown quantity to be solved, a set of equations for the spatial position parameters (Δx, Δy, θ) can be established for the actual positions of every two sub-apertures. The actual positions of the K sub-apertures can be solved in total. Group space position parameters; Take the average value to obtain the corrected LED array spatial position parameters.

[0051] Due to the adoption of the above technical solution, the present invention has the following advantages:

[0052] 1) The pupil function is used to accurately characterize the dark field illumination position deviation from the physical model, avoiding falling into the local optimum due to the limitations of the optimization search algorithm. The calibration reference is changed from the global image to the local contour, which enhances the robustness to noise and does not put forward new requirements for the system parameter configuration.

[0053] 2) The precise correction of the corner LED units further constrains and enhances the alignment of the entire LED array, avoiding a large amount of residual deviation in the dark field after bright field correction. By comparing multiple pupil function images, the contribution of translation and rotation angle to the misalignment deviation of the illumination position is analyzed, providing a reference for determining the current main correction parameters.

[0054] 3) The present invention realizes the global spatial position correction of the LED array through the pupil function. The proposed position deviation judgment standard can determine the contribution comparison of different position deviation parameters. It not only overcomes the shortcomings of the previous algorithm self-correction method in which the correction process and the reconstruction process are inseparable, but also realizes the visualization of the dark field illumination position deviation, which is easy to operate and highly robust. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments described in the embodiments of the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0056] Figure 1 Schematic diagram of a flow chart of a method for accurately correcting the position of a light source in combination with a pupil function according to an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The present invention will be further described with reference to the accompanying drawings and embodiments. The embodiments described are only a part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by those skilled in the art should fall within the scope of protection of the embodiments of the present invention.

[0058] See also Figure 1 The present invention provides an embodiment of a method for accurately correcting the position of a light source in combination with a pupil function, which is applicable to a Fourier stack microscope system and includes the following steps:

[0059] 1. FPM acquisition process:

[0060] A rectangular N×N LED array is used as the illumination source. The interval between adjacent LED units is represented by d. If the LED array is translated (Δx, Δy) and rotated (θ) on the horizontal plane, the spatial position r of the LED unit in the mth row and nth column (1≤m≤N, 1≤n≤N) on the array board is m,n It can be expressed as:

[0061]

[0062] Where x m,n with y m,n represents the two-dimensional coordinate component value of the LED unit on the plane in the airspace. Assuming that the distance h from the light source to the sample is far enough, the illumination light wave with a central wavelength of λ irradiating the two-dimensional thin sample can be approximated as a plane wave, where the illumination wave vector can be expressed as:

[0063]

[0064] Where k x,m,n With k y,m,n Represents the two-dimensional coordinate component value of the wave vector in the frequency domain.

[0065] Illumination waves with different wave vectors scan different spatial frequency information on the sample spectrum, which is equivalent to shifting the center of the sample spectrum to k m,n At , the outgoing sub-spectrum is low-pass filtered by the coherent transfer function defined by the objective lens. The relevant process can be expressed as:

[0066] G m,n (k)=F{o(r)exp(ik m,n r)}P(k)=O(kk m,n )P(k)

[0067] Where o(r) represents the complex transmission function of the sample in the spatial domain, i represents the imaginary unit 1, F{·} represents the two-dimensional Fourier transform, and P(k) represents the pupil function of the objective lens. Finally, the information propagated to the camera image plane is collected and converted into a low-resolution intensity image The relevant process can be expressed as:

[0068]

[0069] Where, F -1 {·} represents the two-dimensional inverse Fourier transform, g m,n (r) represents the complex amplitude of the sample on the image plane. By lighting up the LED units in the array one by one and using a camera to capture images, a series of low-resolution intensity images of the sample can be obtained.

[0070] 2. Pupil function reconstruction process:

[0071] The pupil function reconstruction algorithm based on the FPM stacking iterative engine is implemented in the following 7 steps:

[0072] 1) Spectrum initialization: The interpolated result of the low-resolution image collected by the LED unit at the center of the array under normal incident illumination is selected as the initial value of the reconstructed amplitude part, and the phase part is set to zero. The process can be expressed as:

[0073]

[0074] In the formula, O0(k) represents the initial value of the reconstructed sample spectrum, R(·) represents the interpolation operation of the image, Indicates the initial zero phase of the setting.

[0075] 2) Target complex amplitude generation: corresponding to the incident wave vector k m,n The circular pupil function of the objective lens is used to intercept the spectrum information in a sub-aperture of the initial high-resolution spectrum of the sample, and generate the target complex amplitude under the corresponding LED:

[0076]

[0077] Where j represents the current number of iterations (1≤j≤j max ), pupil function P j The initial value of (k) is set to the passband A circular low-pass filter with 1 inside, NA obj Indicates the numerical aperture of the objective lens.

[0078] 3) Complex amplitude estimation update: Keeping the phase of the target complex amplitude image unchanged, update the amplitude part of the target complex amplitude image with the actual low-resolution image acquired under the corresponding illumination position sequence (m, n):

[0079]

[0080] Where, represents the updated target complex amplitude distribution corresponding to the LED with position sequence (m,n) at the jth iteration.

[0081] 4) Sub-aperture region update within the spectrum: Use Fourier transform to obtain the updated spectrum of the target complex amplitude distribution This low-resolution spectrum is used to update the information in the corresponding sub-aperture in the sample high-resolution spectrum. This process involves solving a non-convex optimization problem, updating the spectrum information and pupil function at the same time. The update formula is:

[0082]

[0083]

[0084] Where α and β represent the update step size and are generally set to 1, * represents the complex conjugate operation, corresponding to the currently updated subaperture, and the updated complex amplitude The actual wave vector contained in With the target complex amplitude The ideal wave vector contained in The difference in the position of the ideal subaperture will cause the reconstruction to shift, and the center of the pupil function will shift to

[0085] 5) Repeat steps 2) to 4) to update the frequency spectra within the sub-aperture corresponding to all position sequences {(m,n)|1≤m≤N,1≤n≤N}.

[0086] 6) Repeat steps 2) to 5) until the high-resolution complex amplitude of the sample converges, thereby finally obtaining the transformed pupil function. The low-frequency self-cancellation effect of the phase transfer function of the pupil function is that the pupil function is a multi-center The superposition state of the sub-pupils, where N1×N1 represents the number of LEDs located in the bright field.

[0087] 7) Reduce the number of low-resolution images used to reconstruct the pupil function and repeat steps 1) to 6) to obtain a total of Image of pupil function.

[0088] 3. Judgment of position deviation:

[0089] Shift the pupil center Δk in the frequency domain coordinate system m,n =(Δk x,m,n ,Δk y,m,n ) is converted into the positioning problem of Δk in the polar coordinate system m,n =(R m,n ,α m,n) is a two-parameter search problem. In a pupil function image acquired using the largest number of low-resolution images, a search interval ranging from 0 to ±180° with appropriate spacing is set, and multiple radial lines originating from the image center are generated. Within these radial lines, the two directions α1 and α2 corresponding to the maximum and minimum distances from the image center at which the pupil function intensity drops sharply are determined.

[0090] In the K-frame pupil function image, the distance from the position where the two sets of intensity values ​​drop sharply along α1 and α2 to the center of the image is and like and At this time, the influence of translation in the position deviation parameter of LED array is greater, and the translation direction is the same as α2. It is used to represent the frequency domain position deviation of the sub-aperture corresponding to the corner LED in the LED array along the translation direction. represents the radius of the pupil, p img Indicates the pixel size of the image sensor, N img ×N img represents the number of pixels of the pupil function image, and Mag represents the magnification of the objective lens.

[0091] like At this time, the influence of rotation on the position deviation parameter of the LED array is greater. According to the interval where α1 is located, select the array This parameter represents the frequency domain position deviation of the subaperture corresponding to the corner LEDs in a region of the LED array. With the coordinate system pointing from left to right and from top to bottom as the positive direction, when the rotation angle of the LED array is positive, if 0° < α1 < 90°, the resulting position deviation corresponds to the corner LED in the lower left region of the LED array; if 90° < α1 < 180°, the resulting position deviation corresponds to the corner LED in the upper left region of the LED array; if -90° < α1 < 0°, the resulting position deviation corresponds to the corner LED in the lower right region of the LED array; and if -180° < α1 < -90°, the resulting position deviation corresponds to the corner LED in the upper right region of the LED array.

[0092] 4. Dark field illumination position deviation acquisition and actual position calculation:

[0093] The polar coordinates of the sub-aperture position deviation corresponding to the corner LED are converted into two-dimensional frequency domain coordinates, and the ideal frequency domain position of the corresponding sub-aperture is calculated according to its arrangement position in the LED array. The actual positions of K sub-apertures are obtained by adding the two

[0094] 5. Solving the spatial position of LED array:

[0095] Based on the corresponding formula between the spatial position parameters of the LED array and the illumination wave vector, and in accordance with the principle that the number of known results is greater than the unknown quantity to be solved, a set of equations for the spatial position parameters (Δx, Δy, θ) can be established for the actual positions of every two sub-apertures. The actual positions of the K sub-apertures can be solved in total. Group spatial position parameters. Take the average value to obtain the corrected LED array spatial position parameters.

[0096] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A method for accurate correction of light source position in combination with pupil function, applicable to Fourier stacking microscopy system, characterized in that: include: Step 1: Light up the LED units in the programmable LED array in the Fourier stacking microscope system one by one under a low numerical aperture objective lens, collect a series of low-resolution intensity images at different illumination positions, and reconstruct K pupil function images using different numbers of low-resolution images through the stacking iterative engine algorithm; Step 2: First, in the pupil function image reconstructed using the largest number of low-resolution images, set an omnidirectional search interval to search for the directions α1 and α2 corresponding to the maximum and minimum distances from the location where the pupil function intensity value drops sharply to the image center; in K pupil function images, perform a circular contour search algorithm along α1 and α2 to obtain two sets of distances from the location where the intensity value drops sharply to the image center, and determine the position deviation based on these two sets of distances; Step 3: Determine the ideal position of the corner LED unit in the LED array corresponding to the obtained frequency domain position deviation based on the intervals of α1 and α2, and calculate the actual position of the sub-aperture corresponding to the corner LED in the frequency domain; Step 4: Solve the spatial position of the LED array: According to the sub-aperture position calculation formula, a set of spatial position parameters can be solved for every two position coordinates. Finally, the average value of the multiple sets of parameters obtained is taken to complete the spatial position correction of the LED array.

2. The method according to claim 1, characterized in that The method collects a series of low-resolution intensity images at different lighting positions, including: A rectangular N×N LED array is used as the illumination source. The interval between adjacent LED units is represented by d. If the LED array is translated (Δx, Δy) and rotated (θ) on the horizontal plane, the spatial position r of the LED unit in the mth row and nth column on the array is m，n It can be expressed as: Where x m,n with y m,n represents the two-dimensional coordinate component value of the LED unit on the plane in the airspace, 1≤m≤N,1≤n≤N. Assuming that the distance h from the light source to the sample is far enough, the illumination light wave with a central wavelength of λ irradiated on the two-dimensional thin sample can be approximated as a plane wave, where the illumination wave vector can be expressed as: Where k x,m,n With k y,m,n Represents the two-dimensional coordinate component value of the wave vector in the frequency domain; Illumination waves with different wave vectors scan different spatial frequency information on the sample spectrum, which is equivalent to shifting the center of the sample spectrum to k m,n At , the outgoing sub-spectrum is low-pass filtered by the coherent transfer function defined by the objective lens. The relevant process can be expressed as: G m,n (k)=F{o(r)exp(ik m,n r)}P(k)=O(kk m,n )P(k) Where o(r) represents the complex transmission function of the sample in the spatial domain, i represents the imaginary unit 1, F{·} represents the two-dimensional Fourier transform, and P(k) represents the pupil function of the objective lens. Finally, the information propagated to the camera image plane is collected and converted into a low-resolution intensity image The relevant process can be expressed as: Where, F -1 {·} represents the two-dimensional inverse Fourier transform, g m,n (r) represents the complex amplitude of the sample on the image plane; by lighting up the LED units in the array one by one and using a camera to capture images, a series of low-resolution intensity images of the sample can be obtained.

3. The method according to claim 2, characterized in that The method of reconstructing K pupil function images using different numbers of low-resolution images through a stacked iterative engine algorithm includes: 1) Spectrum initialization: The interpolated result of the low-resolution image collected by the LED unit at the center of the array under normal incident illumination is selected as the initial value of the reconstructed amplitude part, and the phase part is set to zero; 2) Target complex amplitude generation: corresponding to the incident wave vector k m,n The circular pupil function of the objective lens is used to intercept the spectrum information in a certain sub-aperture of the initial high-resolution spectrum of the sample, and generate the target complex amplitude under the corresponding LED; 3) Complex amplitude estimation update: Keeping the phase of the target complex amplitude image unchanged, the amplitude part of the target complex amplitude image is updated with the actual low-resolution image acquired under the corresponding illumination position sequence (m, n); 4) Sub-aperture region update within the spectrum: Use Fourier transform to obtain the updated spectrum of the target complex amplitude distribution And use the spectrum to update the information in the corresponding sub-aperture in the sample high-resolution spectrum; 5) Repeat steps 2) to 4) to update the spectra within the sub-aperture corresponding to all position sequences {(m,n)|1≤m≤N,1≤n≤N}; 6) Repeat iterative steps 2) to 5) until the high-resolution complex amplitude of the sample converges, thereby finally obtaining the transformed pupil function; 7) Reduce the number of low-resolution images used to reconstruct the pupil function, and repeat steps 1) to 6) to obtain a total of K pupil function images.

4. The method according to claim 3, characterized in that Spectrum initialization can be expressed as: In the formula, O0(k) represents the initial value of the reconstructed sample spectrum, R(·) represents the interpolation operation of the image, Indicates the initial zero phase of the setting.

5. The method according to claim 4, characterized in that The target complex amplitude under the corresponding LED is expressed as: Where j represents the current iteration number, 1≤j≤j max , pupil function P j The initial value of (k) is set to the passband A circular low-pass filter with 1 inside, NA obj Indicates the numerical aperture of the objective lens; The complex amplitude estimate update is expressed as: Where, represents the updated target complex amplitude distribution corresponding to the LED with position sequence (m,n) at the jth iteration.

6. The method according to claim 5, characterized in that Updating the sub-aperture region within the spectrum involves solving a non-convex optimization problem, updating the spectrum information and pupil function at the same time. The update formula is: Where α and β represent the update step size and are generally set to 1, * represents the complex conjugate operation, corresponding to the currently updated subaperture, and updates the complex amplitude The actual wave vector contained in With the target complex amplitude The ideal wave vector contained in The difference in the position of the pupil shifts the center of the pupil function to 7. The method according to claim 6, characterized in that Due to bright field illumination The low-frequency self-cancellation effect of the phase transfer function of the pupil function is that the pupil function is a multi-center The superposition state of the sub-pupils, where N1×N1 represents the number of LEDs located in the bright field; 8. The method according to claim 1, characterized in that The step 2 includes: In the K-frame pupil function image, the distance from the position where the two sets of intensity values ​​drop sharply along α1 and α2 to the center of the image is and like and At this time, the influence of translation in the position deviation parameter of LED array is greater, and the translation direction is the same as α2. It is used to represent the frequency domain position deviation of the sub-aperture corresponding to the corner LED in the LED array along the translation direction. represents the radius of the pupil, p img Indicates the pixel size of the image sensor, N img ×N img represents the number of pixels of the pupil function image, and Mag represents the magnification of the objective lens; like At this time, the influence of rotation on the position deviation parameter of the LED array is greater. According to the interval where α1 is located, select the array Used to represent the frequency domain position deviation of the sub-aperture corresponding to the corner LED in a certain area of ​​the LED array; with the coordinate system from left to right and from top to bottom as the positive direction, when the rotation angle of the LED array is positive, if 0°<α1<90°, the obtained position deviation corresponds to the corner LED located in the lower left area of ​​the LED array; if 90°<α1<180°, the obtained position deviation corresponds to the corner LED located in the upper left area of ​​the LED array; if -90°<α1<0°, the obtained position deviation corresponds to the corner LED located in the lower right area of ​​the LED array; if -180°<α1<-90°, the obtained position deviation corresponds to the corner LED located in the upper right area of ​​the LED array.

9. The method according to claim 1, characterized in that The step 3 includes: Convert the polar coordinates of the sub-aperture position deviation corresponding to the corner LED into two-dimensional frequency domain coordinates, and calculate the ideal frequency domain position of the corresponding sub-aperture according to its arrangement position in the LED array. By adding the frequency domain position deviation and the ideal frequency domain position, the actual frequency domain positions of K sub-apertures are obtained.

10. The method according to claim 1, characterized in that The step 4 comprises: Based on the corresponding formula between the spatial position parameters of the LED array and the illumination wave vector, and in accordance with the principle that the number of known results is greater than the unknown quantity to be solved, a set of equations for the spatial position parameters (Δx, Δy, θ) can be established for the actual positions of every two sub-apertures. The actual positions of the K sub-apertures can be solved in total. Group space position parameters; Take the average value to obtain the corrected LED array spatial position parameters.

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