Phase encoding-based super-resolution imaging system and super-resolution method

Abstract

Disclosed in the present invention are a phase encoding-based super-resolution imaging system and a super-resolution method, used for improving the imaging resolution and imaging signal-to-noise ratio of a visible light imaging system. The super-resolution imaging system consists of a main imaging lens, a first 4f relay lens, a phase mask, a second 4f relay lens, a camera, and an electric rotating stage. By optimizing a phase function of the phase mask, a transfer function of the super-resolution imaging system has anisotropy on a certain frequency component. The electric rotating stage controls the rotation regulation of the phase mask and the camera captures a series of encoded low-resolution images. By mean of joint spatial- and frequency-domain constraint iteration, the captured images are reconstructed until an algorithm converges, so as to obtain reconstructed images that break through Nyquist sampling. Compared with being based on intensity mask encoding, the method can implement the regulation and control of the anisotropy of a point spread function without losing luminous flux, thereby achieving an imaging resolution improvement of more than 2.5 times.

Description

A phase-encoded super-resolution imaging system and super-resolution method Technical Field

[0001] This invention belongs to computational optical imaging technology, specifically a phase-encoded super-resolution imaging system and super-resolution method. Background Technology

[0002] Super-resolution imaging is an imaging technique that improves the detail resolution of a detector by acquiring single or multiple frames of low-resolution images to restore details of the target scene. However, the fundamental limitation on detector resolution is that excessively large pixel sizes lead to insufficient Nyquist sampling, causing high-frequency information to alias with low frequencies, resulting in image mosaic. One way to improve image resolution is to reduce the physical size of pixels. While reducing pixel size can improve resolution, it also drastically reduces the signal-to-noise ratio due to the decrease in light intake per unit area. Furthermore, methods to improve pixel resolution at the hardware level have reached their physical limits and are difficult to further break through. Currently, specific patterns can be added to the aperture plane of the imaging system to change the pupil shape and thus alter the point spread function. Improving resolution can also be achieved by acquiring multiple frames of coded patterns and reconstructing them using algorithms. However, the current coded masks are based on intensity masks, which sacrifice some light throughput for anisotropic control of the point spread function. Therefore, how to achieve coded control of the imaging system without sacrificing light throughput has become a pressing problem for aperture-coded super-resolution imaging systems.

[0003] Wavefront coding technology modulates the wavefront by adding a specially designed phase mask to the aperture plane of an optical imaging system. The optical transfer function or point spread function of the imaging system is insensitive to defocusing, thus forming a blurred intermediate image with minimal difference on the detector. A clear image is then recovered through digital filtering. The phase mask used in wavefront coding is typically obtained by etching a quartz crystal, which allows for coding and modulation with minimal loss of light throughput. The parameters of the phase mask are designed to meet super-resolution sub-pixel intensity control requirements. However, wavefront coding is generally used to extend the depth of field of imaging systems and has not been applied to super-resolution imaging control. Summary of the Invention

[0004] The purpose of this invention is to provide a phase-encoded super-resolution imaging system and super-resolution method. This invention establishes a phase-encoded super-resolution imaging system. By optimizing the design of the encoded phase function, anisotropic point spread function modulation is achieved without sacrificing luminous flux, thereby achieving a 2.5-fold increase in pixel resolution under high signal-to-noise ratio modulation.

[0005] The technical solution to achieve the purpose of this invention is as follows: a super-resolution imaging system based on phase encoding, comprising an imaging main lens, a 4f relay lens one, a phase mask, a 4f relay lens two, a camera, and an electric rotary stage. The aperture plane of the imaging main lens is relayed onto the phase mask, which is located on the back focal plane of the 4f relay lens one. The phase mask is rotated by the electric rotary stage to modulate the aperture plane of the imaging main lens and reduce the aberrations of the imaging system. The 4f relay lens one is positioned between the imaging main lens and the phase mask, and the 4f relay lens two is positioned between the phase mask and the camera. The camera is located on the back focal plane of the 4f relay lens two. The imaging main lens, the phase mask, and the camera are respectively fixedly mounted on an optical platform. When adjusting the focal length of the imaging main lens, the positions of the camera and the phase mask relative to the imaging main lens remain unchanged. The first-order image plane of the imaging main lens falls on the front focal plane of the 4f relay lens one.

[0006] A phase-encoded super-resolution imaging method, the specific steps of which are as follows:

[0007] Step 1: Construct the phase-encoded super-resolution imaging system described above, and control the rotation of the phase mask by an electric rotary stage to sequentially record N phase-encoded low-resolution images and their corresponding optical transfer functions;

[0008] Step 2: Sum and average all phase-coded low-resolution images, then upsample to obtain the initial high-resolution object amplitude, and perform a Fourier transform on the initial high-resolution object amplitude to obtain the initial high-resolution object spectrum.

[0009] Step 3: Select the k-th optical transfer function to encode the spectrum of the high-resolution object to obtain the spectrum of the high-resolution modulated image, and then perform an inverse Fourier transform on the spectrum of the high-resolution modulated image and downsample it to obtain a low-resolution modulated image.

[0010] Step 4: Calculate the ratio of the low-resolution coded modulation image to the phase-coded low-resolution image as the low-resolution update matrix, and upsample the low-resolution update matrix to obtain the high-resolution update matrix;

[0011] Step 5: Use the high-resolution update matrix to perform spatial constraints on the high-resolution modulated image to obtain the high-resolution updated modulated image, and perform Fourier transform to obtain the spectrum of the high-resolution updated modulated image.

[0012] Step 6: Subtract the spectrum of the high-resolution modulated image before spatial constraints from the spectrum of the high-resolution modulated image after spatial constraints to obtain the spectrum increment of the modulated image. Then, use an adaptive step size to adjust the ratio of the spectrum increment of the coded image to the deconvolution of the optical transfer function to update the spectrum of the high-resolution object.

[0013] Step 7: Repeat steps 3 to 6 for the next phase-coded low-resolution image and the next optical transfer function until all phase-coded low-resolution images have been traversed once.

[0014] Step 8: Repeat steps 3 to 7 until the mean square error of the phase-coded low-resolution image and the low-resolution modulated image is less than the convergence threshold.

[0015] Preferably, the parameters of the phase mask in the phase-encoded super-resolution imaging system are determined according to the following method:

[0016] The expression for the phase mask function W(x,y) is determined as follows: W(x,y)=αx 2 +βy n

[0017] In the formula, n is the power exponent parameter, α and β are the phase mask parameters, and (x,y) are the xy coordinate axes.

[0018] The values ​​of the power exponent parameter n and the phase mask parameters α and β are designed to set the shape of the optical transfer function of the imaging system to a single-slit shape.

[0019] Preferably, the phase mask is rotated N times at an angle ω, and the corresponding coding patterns are recorded sequentially. k Rotation angle and the corresponding optical transfer function (OTF) k The expression is:

[0020] Among them, R (Pattern) k ) indicates the pattern k Perform autocorrelation operation, max(...) represents the maximum value operation, Pattern k For the k-th encoded pattern, OTF k Let ω be the optical transfer function of the k-th frame, ω be the rotation angle, and N be the number of rotations.

[0021] Preferably, the high-resolution object amplitude in step 2 is specifically:

[0022] In the formula, imresize(A,B,C) means transforming the image A to size B according to the interpolation format C, and F(...) represents the Fourier transform. This represents the high-resolution object amplitude corresponding to the k=1th phase encoding in the iter=1th iteration, i.e., the initialized high-resolution object amplitude. To encode low-resolution images for phase encoding, This represents the high-resolution object spectrum corresponding to the k=1th phase encoding in the iter=1th iteration, i.e. the initialized high-resolution object spectrum. HRsize is the high-resolution image size, and 'nearest' is the nearest neighbor interpolation format.

[0023] Preferably, a high-resolution update matrix is ​​used. High-resolution modulated images The specific formula for obtaining a high-resolution updated modulated image by performing spatial constraints is as follows:

[0024] In the formula, It represents the high-resolution updated modulation image corresponding to the k-th phase-coded image in the iter-th iteration.

[0025] Preferably, the modulated image spectrum increment is obtained by subtracting the modulated image spectrum before spatial constraint from the modulated image spectrum after spatial constraint, and the ratio of the coded image spectrum increment to the optical transfer function deconvolution is adjusted using an adaptive step size to update the high-resolution object spectrum. The specific formula is as follows:

[0026] Wherein, ΔImage iter,k This represents the spectral increment of the modulated image corresponding to the k-th phase-coded image in the iter-th iteration. This represents the spectrum of the high-resolution updated modulated image corresponding to the k-th phase-coded image in the iter-th iteration. This represents the spectrum of the high-resolution modulated image corresponding to the k-th phase-coded image in the iter-th iteration. This represents the high-resolution updated object spectrum corresponding to the k-th phase code in the iter-th iteration. OTF represents the high-resolution object spectrum corresponding to the k-th phase code in the iter-th iteration. k Let represent the optical transfer function of the k-th frame, stepsize represent the adaptive step size parameter, and ε represent the regularization parameter.

[0027] Compared with existing technologies, this invention has significant advantages: Compared to intensity-coded mask-based super-resolution imaging systems, this invention can obtain anisotropic modulation of the point spread function without sacrificing signal energy. Its improved resolution is comparable to intensity-coded mask modulation, thus achieving high-resolution, high-signal-to-noise ratio imaging by breaking through the Nyquist sampling frequency barrier. Furthermore, compared to general micro-scanning-based super-resolution imaging systems, this invention's super-resolution imaging system has a simpler structure, faster measurement speed, and easier operation. It achieves stable resolution improvement without the need for complex mechanical scanning devices, ultimately increasing the resolution of the imaging target by more than 2.5 times.

[0028] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0029] Figure 1 is a structural diagram of the phase-encoded super-resolution imaging system of the present invention.

[0030] Figure 2 shows the phase encoding pattern used in this invention.

[0031] Figure 3 shows the point spread function and optical transfer function patterns used in this invention. Figure 3(a) shows the point spread function corresponding to the rotating phase encoding pattern, and Figure 3(b) shows the optical transfer function corresponding to the rotating phase encoding pattern.

[0032] Figure 4 is a schematic diagram of the super-resolution method of the present invention.

[0033] Figure 5 shows the simulation experiment of the USAF resolution target. Figure 5(a) shows the low-resolution image and spectrum of the present invention using phase coding, and Figure 5(b) shows the super-resolution image and spectrum of the present invention using phase coding.

[0034] Figure 6 shows a comparison experiment of real-world super-resolution imaging of an ISO12233 resolution target. Figure 6(a) is a low-resolution image captured using phase coding according to the present invention. Figure 6(b) is a super-resolution image reconstructed using phase coding. Figure 6(c) is a low-resolution image captured using intensity coding mask. Figure 6(d) is a super-resolution image reconstructed using intensity coding mask.

[0035] Figure 7 shows the experimental results of super-resolution imaging in complex scenes. Figure 7(a) is the test scene, Figure 7(b) is the low-resolution image of the first test scene region, Figure 7(c) is the super-resolution image of the first test scene region, Figure 7(d) is the low-resolution image of the second test scene region, and Figure 7(e) is the super-resolution image of the second test scene region.

[0036] Figure 8 shows a physical image of the phase mask. Detailed Implementation

[0037] As shown in Figure 1, a phase-encoded super-resolution imaging system includes a main imaging lens 1, a 4f relay lens 2, a phase mask 3, a second 4f relay lens 4, a camera 5, and an electrically driven rotary stage 6. It employs a transmissive optical path structure based on a 4f system, which is composed of the first 4f relay lens 2 and the second 4f relay lens 4. In this optical path structure, the aperture plane of the main imaging lens 1 is relayed onto the phase mask 3. The phase mask 3 is located on the back focal plane of the first 4f relay lens 2. The electric rotary stage 6 rotates the phase mask 3 to modulate the aperture plane of the main imaging lens 1 and reduce aberrations in the imaging system. The first 4f relay lens 2 is positioned between the main imaging lens 1 and the phase mask 3, and the second 4f relay lens 4 is positioned between the phase mask 3 and the camera 5. The camera 5 is located on the back focal plane of the second 4f relay lens 4. The main imaging lens 1 is a CANON (100-400mm) with a focal length adjusted to 400mm. The 4f relay lenses 2 and 4f relay lens 4 are CANON LENS EF 50mm F1.4. The camera 5 is a 5.5×5.5μm camera. Figure 8 shows the physical diagram of the phase mask 3, a quartz glass element with a diameter of 24.5mm and a thickness of 2mm, with a pre-designed phase mask function etched in a circular area with a central diameter of 9mm. The main imaging lens 1, phase mask 3, and camera 5 are fixedly mounted on the optical platform. When adjusting the focal length of the main imaging lens, the positions of the camera 5 and phase mask 3 relative to the main imaging lens 1 remain unchanged. The first-order image plane of the main imaging lens falls on the front focal plane of the 4f relay lens 1.

[0038] As shown in Figure 4, a super-resolution imaging method based on a phase-coded imaging system comprises the following steps:

[0039] Step 1: Construct a phase-encoded super-resolution imaging system. Control the rotation of the phase mask 3 using an electric rotary stage 6 and sequentially record N phase-encoded low-resolution images. and the corresponding optical transfer function (OTF) k , k = 1...N.

[0040] First, determine the expression for the phase mask function W(x,y). The phase mask function W(x,y) is composed of a weighted sum of a quadratic power function and a higher power function, and its expression is: W(x,y)=αx 2 +βy n

[0041] The power-law parameter n of the phase mask 3 and the phase mask parameters α and β are designed to set the shape of the optical transfer function (OTF) of the imaging system to a single-slit shape. The generalized pupil function P(x,y) is autocorrelated and normalized, and denoted as the phase-encoded OTF(u,v,n). The phase mask parameters α and β are separated to investigate the influence of parameter selection on the OTF. Its expression is: P(x,y)=pupil(x,y)×exp(jkW(x,y))

[0042] Here, `pupil(x,y)` represents the pupil function of the aperture plane. Analysis of the parameter-separated optical transfer function (OTF(u,v,n)) reveals that in the x-direction, the value of the phase parameter α is inversely proportional to the overall coefficient. When α decreases, the width of the OTF increases, and vice versa. In the y-direction, the value of the phase parameter β is also inversely proportional to the overall length coefficient. When β decreases, the width of the OTF increases, and vice versa. However, due to the relatively large value of `n`, the influence of β on the length direction of the single slit is small, so the overall impact of β on the result is relatively small. Because of the influence of the aperture stop OTF, the changes in its length and width are limited, and their limits do not exceed the autocorrelation boundary of the circular aperture stop itself. Because of the influence of a high-power exponent n in the y-direction, its length changes much faster than its width. Therefore, in the final OTF shape, the y-direction is always constrained by length first. Thus, the values ​​of parameters α and β can be controlled to control the phase modulation shape of the phase mask, making the resulting optical transfer function approach that of a single slit. For this purpose, n = 6, α = 190λ, and β = 3λ are chosen.

[0043] Secondly, the phase mask 3 is rotated N times at an angle ω, and the corresponding coding patterns are recorded sequentially. k Rotation angle and the corresponding optical transfer function (OTF) k The expression is:

[0044] Where R(A) represents the autocorrelation operation on A, max(...) represents the maximum value operation, and Pattern k For the k-th encoded pattern, OTF k Let ω be the optical transfer function of the k-th frame, ω be the rotation angle, and N be the number of rotations. Here, N = 16 is chosen.

[0045] Step 2: Summate and average all phase-encoded low-resolution images, then upsample to obtain the initialized high-resolution object amplitude. A Fourier transform is then performed on the spectrum to obtain the initialized high-resolution object spectrum. Its expression is:

[0046] Here, `imresize(A,B,C)` means transforming image A to size B according to interpolation format C, and `F(...)` represents Fourier transform. This represents the high-resolution object amplitude corresponding to the k=1th phase encoding in the iter=1th iteration, i.e., the initialized high-resolution object amplitude. This represents the high-resolution object spectrum corresponding to the k=1th phase code in the iter=1th iteration, i.e., the initialized high-resolution object spectrum;

[0047] Step 3: Select the k-th optical transfer function (OTF) k High-resolution object spectrum Encoding yields the high-resolution modulated image spectrum. After performing an inverse Fourier transform, the image was downsampled to obtain a low-resolution modulated image. Its expression is:

[0048] Where imresize(A,B,C) means transforming image A to size B according to interpolation format C, and F -1 (...) represents the inverse Fourier transform. OTF represents the spectrum of the high-resolution modulated image corresponding to the k-th phase-coded image in the iter-th iteration. k Let k be the optical transfer function. This represents the high-resolution object spectrum corresponding to the k-th phase code in the iter-th iteration. This represents the low-resolution coded modulation image corresponding to the k-th phase code in the iter-th iteration;

[0049] Step 4: Calculate the low-resolution coded modulation image Phase-coded low-resolution images The ratio is the low-resolution update matrix. Upsample the low-resolution update matrix Obtain the high-resolution update matrix Its expression is:

[0050] Here, `imresize(A,B,C)` means transforming image A to size B using interpolation format C. This represents the low-resolution update matrix corresponding to the k-th phase code in the iter-th iteration. This represents the low-resolution modulated image corresponding to the k-th phase-coded image in the iter-th iteration. This represents the high-resolution update matrix corresponding to the k-th phase code in the iter-th iteration;

[0051] Step 5: Update the matrix using high resolution High-resolution modulated images Spatial constraints are applied to obtain a high-resolution updated modulated image. The high-resolution updated modulated image spectrum is obtained by performing a Fourier transform. Its expression is:

[0052] Where F(...) denotes the Fourier transform, This represents the high-resolution updated modulation image corresponding to the k-th phase-coded image in the iter-th iteration. This is represented as the high-resolution updated modulated image spectrum corresponding to the k-th phase-coded image in the iter-th iteration;

[0053] Step 6: Update the modulated image spectrum with high resolution after spatial constraints. High-resolution modulated image spectrum before spatial constraints Subtraction yields the modulated image spectral increment ΔImage iter,k And an adaptive step size adjustment is used to adjust the spectral increment ΔImage of the encoded image. iter,k Optical Transfer Function (OTF) k The deconvolution ratio is used to update the high-resolution object spectrum. Its expression is:

[0054] Wherein, ΔImage iter,k This represents the spectral increment of the modulated image corresponding to the k-th phase-coded image in the iter-th iteration. This represents the spectrum of the high-resolution updated modulated image corresponding to the k-th phase-coded image in the iter-th iteration. This represents the spectrum of the high-resolution modulated image corresponding to the k-th phase-coded image in the iter-th iteration. This represents the high-resolution updated object spectrum corresponding to the k-th phase code in the iter-th iteration. OTF represents the high-resolution object spectrum corresponding to the k-th phase code in the iter-th iteration. k Let represent the optical transfer function of the kth frame, stepsize represent the adaptive step size parameter, and ε represent the regularization parameter to avoid zero values ​​in the denominator;

[0055] Step 7: Let k = k + 1, and select the next optical transfer function (OTF). k Repeat steps 3-6 until all phase-encoded low-resolution images are obtained. Iterate through each one once.

[0056] Step 8: Set iter = iter + 1, and repeat steps 3 to 7 until the phase-coded low-resolution image is obtained. With low-resolution modulated images The mean square error is less than the convergence threshold T, which is typically 0.001.

[0057] To test the effectiveness of the super-resolution method based on phase-coded imaging system of this invention, two sets of experiments were selected for illustration.

[0058] Figure 2 shows the phase encoding pattern used in this invention. By setting the phase plate parameters, phase encoding patterns at different angles are obtained by rotating the plate sequentially. Figure 3 shows the point spread function and optical transfer function patterns used in this invention. The point spread function and optical transfer function of the imaging system are calculated from Figure 2. Figure 3(a) shows the point spread function corresponding to the rotated phase encoding pattern, and Figure 3(b) shows the optical transfer function corresponding to the rotated phase encoding pattern. As can be seen from the figures, the shape of the optical transfer function is a single-slit shape.

[0059] Figure 5 shows a simulation experiment on a USAF resolution target to quantitatively analyze the effectiveness of the super-resolution algorithm. Figure 5(a) shows the low-resolution image and its spectrum, which resolves to the -1-1 line pairs with a line pair width of 1000μm. Figure 5(b) shows the image and its spectrum after super-resolution reconstruction using phase coding. After super-resolution, it can resolve to the 0-3 line pairs with a line pair width of 396.85μm, and the super-resolution is improved by 1000 / 396.85 = 2.519 times.

[0060] Figure 6 shows a super-resolution imaging comparison experiment of an ISO12233 resolution target. Figure 6(a) is a low-resolution image taken using phase encoding in this invention, and Figure 6(b) is a low-resolution image taken using an intensity-coded mask. The optical transfer function obtained by the phase encoding parameters used in this invention is basically the same as the optical transfer function obtained by the optimal slit width of the intensity-coded mask design. However, it can be seen from the images that the phase encoding used in this invention can achieve similar modulation effects. Only 300 lines can be identified in the low-resolution image, but the signal-to-noise ratio of phase encoding is significantly better than that of intensity-coded mask. Figure 6(c) is a super-resolution image reconstructed using phase encoding, and Figure 6(d) is a super-resolution image reconstructed using intensity-coded mask. It can be seen that both phase encoding and intensity encoding can resolve to between 700 and 800 lines, with a resolution improvement of more than 2.3 times. Moreover, the signal-to-noise ratio of phase encoding reconstruction is better than that of intensity encoding.

[0061] Figure 7 shows the experimental results of super-resolution imaging in complex scenes. Figure 7(a) shows the test of a complex scene and two regions selected for super-resolution reconstruction. Figures 7(b) and 7(d) are low-resolution images of regions one and two, respectively. It can be seen that the letters and human figures in the low-resolution images show obvious mosaic effects, the edges of the target objects are blurred, and the details of the letters cannot be identified. After phase encoding, as shown in Figures 7(c) and 7(e), the details are clearly restored and the resolution is effectively improved.

[0062] In summary, the phase-coded super-resolution imaging system of this invention can effectively overcome the limitations of insufficient Nyquist sampling. Especially in the case of insufficient illumination, light flux is particularly important for imaging. Phase coding can achieve anisotropic control with almost no loss of light flux, thereby increasing the imaging resolution by 2.5 times and meeting a wider range of application needs.

Claims

1. A phase-encoded super-resolution imaging system, characterized in that, The system includes a main imaging lens (1), a 4f relay lens one (2), a phase mask (3), a 4f relay lens two (4), a camera (5), and an electric rotary stage (6). The aperture plane of the main imaging lens (1) is relayed onto the phase mask (3). The phase mask (3) is located on the back focal plane of the 4f relay lens one (2). The phase mask (3) is rotated by the electric rotary stage (6) to modulate the aperture plane of the main imaging lens (1) and reduce aberrations in the imaging system. The 4f relay lens one (2) is positioned between the main imaging lens (1) and the phase mask (3). The second relay lens (4) is set between the phase mask (3) and the camera (5). The camera (5) is located on the back focal plane of the second relay lens (4). The imaging main lens (1), the phase mask (3), and the camera (5) are fixedly mounted on the optical platform. When adjusting the focal length of the imaging main lens, the positions of the camera (5) and the phase mask (3) relative to the imaging main lens (1) remain unchanged. The first-order image plane of the imaging main lens falls on the front focal plane of the first relay lens (2). The parameters of the phase mask of the phase-encoded super-resolution imaging system are determined according to the following method: The expression for the phase mask function W(x,y) is determined as follows: W(x,y)=αx 2 +βy n In the formula, n is the power exponent parameter, α and β are the phase mask parameters, and (x,y) are the xy coordinate axes; The values ​​of the power exponent parameter n and the phase mask parameters α and β of the phase mask plate (3) are designed to set the shape of the optical transfer function of the imaging system to a single slit shape. Rotate the phase mask (3) by an equal angle ω N times and record the corresponding coding patterns in sequence. k Rotation angle and the corresponding optical transfer function (OTF) k The expression is: Among them, R (Pattern) k ) indicates the pattern k Perform autocorrelation operation, max(...) represents the maximum value operation, Pattern k For the k-th encoded pattern, OTF k Let N be the optical transfer function of the k-th frame, and N be the number of rotations.

2. A super-resolution imaging method based on phase coding, characterized in that, The specific steps are as follows: Step 1: Construct the phase-encoded super-resolution imaging system as described in claim 1, and control the rotation of the phase mask (3) by an electric rotary stage (6) and sequentially record N phase-encoded low-resolution images and their corresponding optical transfer functions; Step 2: Sum and average all phase-coded low-resolution images, then upsample to obtain the initial high-resolution object amplitude, and perform a Fourier transform on the initial high-resolution object amplitude to obtain the initial high-resolution object spectrum. Step 3: Select the k-th optical transfer function to encode the spectrum of the high-resolution object to obtain the spectrum of the high-resolution modulated image, and then perform an inverse Fourier transform on the spectrum of the high-resolution modulated image and downsample it to obtain a low-resolution modulated image. Step 4: Calculate the ratio of the low-resolution coded modulation image to the phase-coded low-resolution image as the low-resolution update matrix, and upsample the low-resolution update matrix to obtain the high-resolution update matrix; Step 5: Use the high-resolution update matrix to perform spatial constraints on the high-resolution modulated image to obtain the high-resolution updated modulated image, and perform Fourier transform to obtain the spectrum of the high-resolution updated modulated image. Step 6: Subtract the spectrum of the high-resolution modulated image before spatial constraints from the spectrum of the high-resolution modulated image after spatial constraints to obtain the spectrum increment of the modulated image. Then, use an adaptive step size to adjust the ratio of the spectrum increment of the coded image to the deconvolution of the optical transfer function to update the spectrum of the high-resolution object. Step 7: Repeat steps 3 to 6 for the next phase-coded low-resolution image and the next optical transfer function until all phase-coded low-resolution images have been traversed once. Step 8: Repeat steps 3 to 7 until the mean square error of the phase-coded low-resolution image and the low-resolution modulated image is less than the convergence threshold.

3. The phase-encoded super-resolution imaging method according to claim 2, characterized in that, The high-resolution object amplitude in step 2 is specifically as follows: In the formula, imresize(A,B,C) means transforming the image A to size B according to the interpolation format C. This represents the high-resolution object amplitude corresponding to the first phase encoding in the first iteration, i.e., the initialized high-resolution object amplitude. For phase-coded low-resolution images, HRsize is the high-resolution image size, and 'nearest' is the nearest neighbor interpolation format.

4. The phase-encoded super-resolution imaging method according to claim 2, characterized in that, Update the matrix using high resolution High-resolution modulated images The specific formula for obtaining a high-resolution updated modulated image by performing spatial constraints is as follows: In the formula, It represents the high-resolution updated modulation image corresponding to the k-th phase-coded image in the iter-th iteration.

5. The phase-encoded super-resolution imaging method according to claim 2, characterized in that, The modulated image spectrum increment is obtained by subtracting the modulated image spectrum before spatial constraints from the spectrum after spatial constraints at a higher resolution. The specific formula for adjusting the ratio of the coded image spectrum increment to the deconvolution of the optical transfer function using an adaptive step size to update the spectrum of the high-resolution object is as follows: Wherein, ΔImage iter,k This represents the spectral increment of the modulated image corresponding to the k-th phase-coded image in the iter-th iteration. This represents the spectrum of the high-resolution updated modulated image corresponding to the k-th phase-coded image in the iter-th iteration. This represents the spectrum of the high-resolution modulated image corresponding to the k-th phase-coded image in the iter-th iteration. This represents the high-resolution updated object spectrum corresponding to the k-th phase code in the iter-th iteration. OTF represents the high-resolution object spectrum corresponding to the k-th phase code in the iter-th iteration. k Let represent the optical transfer function of the k-th frame, stepsize represent the adaptive step size parameter, and ε represent the regularization parameter.

Images