Super-resolution imaging system and super-resolution method based on phase coding

Abstract

The invention discloses a super-resolution imaging system and a super-resolution method based on phase coding, which are used for improving the imaging resolution and the imaging signal-to-noise ratio of a visible light imaging system. The system is composed of an imaging main lens 1, a first 4f relay lens 2, a phase mask plate 3, a second 4f relay lens 4, a camera 5 and an electric rotating table 6, and a system transfer function has anisotropy on a certain frequency component by optimally designing a phase function of the phase mask plate. The phase mask plate 3 is controlled to rotate and regulate through the electric rotating table 6, a series of coded low-resolution images are collected through the camera 5, combined constraint iteration of the spatial domain and the frequency domain is combined, the collected images are reconstructed until algorithm convergence is achieved, and a reconstructed image breaking through Nyquist sampling is obtained. Compared with the method based on intensity mask coding, the method has the advantages that anisotropy regulation and control of the point spread function can be realized under the condition that luminous flux is not lost, and the imaging resolution is improved by more than 2.5 times.

Description

Technical Field

[0001] The present invention belongs to the field of computational optical imaging technology, and in particular to a super-resolution imaging system and a super-resolution method based on phase encoding. Background Art

[0002] Super-resolution imaging is an imaging technology that recovers the details of the target scene by collecting single or multiple low-resolution images, thereby improving the detail resolution ability of the detector. However, the essence of limiting the resolution of the detector is that the pixel size is too large, resulting in insufficient Nyquist sampling, and the high-frequency information of the image is mixed into the low frequency, resulting in the phenomenon of image mosaic. One way to improve the image resolution is to reduce the physical size of the pixel. Although reducing the pixel can improve the resolution, the signal-to-noise ratio drops sharply due to the reduction in the amount of light entering per unit area. In addition, the way to improve the pixel resolution from the hardware level has reached the physical limit and it is difficult to continue to break through. At present, a specific pattern can be added to the aperture plane of the imaging system to change the pupil shape to achieve the change of the point spread function, and the resolution can also be improved after collecting multiple frames of coded patterns and reconstructing them through algorithms. However, the coded mask currently used is based on the intensity mask, which sacrifices a certain amount of light flux in exchange for the anisotropic regulation of the point spread function. Therefore, how to achieve the coding regulation of the imaging system without losing the light flux has become an urgent problem to be solved in the aperture coded super-resolution imaging system.

[0003] Wavefront coding technology modulates the wavefront by adding a specially designed phase mask to the aperture plane of the optical imaging system. The optical transfer function or point spread function of the imaging system is insensitive to defocus, so a blurred intermediate image with little difference is formed on the detector, and a clear image is restored by digital filtering. The phase mask added for wavefront coding is usually obtained by etching quartz crystal, which can achieve coding control without basically losing light flux. The parameters of the phase mask are designed to meet the super-resolution sub-pixel light intensity control, but wavefront coding is generally used to expand the depth of field of the imaging system and has not been applied to super-resolution imaging control. Summary of the invention

[0004] The purpose of the present invention is to provide a super-resolution imaging system and a super-resolution method based on phase encoding. The invention builds a super-resolution imaging system based on phase encoding, and optimizes the form of the encoded phase function to provide anisotropic point spread function control without losing light flux, thereby achieving a 2.5-fold increase in pixel resolution under high signal-to-noise ratio control.

[0005] The technical scheme for achieving the purpose of the present invention is as follows: a super-resolution imaging system based on phase encoding, comprising an imaging main lens 1, a 4f relay lens 2, a phase mask plate 3, a 4f relay lens 4, a camera 5, and an electric rotating stage 6, wherein the aperture plane of the imaging main lens 1 is relay imaged to the phase mask plate 3, the phase mask plate 3 is located on the back focal plane of the 4f relay lens 2, the phase mask plate 3 is rotated by the electric rotating stage 6 to realize modulation of the aperture plane of the imaging main lens 1 and reduce the aberration of the imaging system, the relay lens 2 is arranged between the imaging main lens 1 and the phase mask plate 3, the 4f relay lens 4 is arranged between the phase mask plate 3 and the camera 5, the camera 5 is located on the back focal plane of the 4f relay lens 4, the imaging main lens 1, the phase mask plate 3, and the camera 5 are respectively fixedly mounted on an optical platform, when adjusting the focal length of the imaging main lens, the positions of the camera 5 and the phase mask plate 3 relative to the imaging main lens 1 remain unchanged, and the primary image plane of the imaging main lens imaging the object falls on the front focal plane of the 4f relay lens 1.

[0006] A super-resolution imaging method based on phase encoding, the specific steps are:

[0007] Step 1: constructing the phase-encoding-based super-resolution imaging system as claimed in claim 1, controlling the rotation of the phase mask plate 3 by the electric rotating stage 6 and sequentially recording N phase-encoded low-resolution images and corresponding optical transfer functions;

[0008] Step 2: Sum and average all phase-encoded low-resolution images and then upsample them to obtain the initialized high-resolution object amplitude, and perform Fourier transform on the initialized high-resolution object amplitude to obtain the initialized high-resolution object spectrum;

[0009] Step 3: Select the kth optical transfer function to encode the high-resolution object spectrum to obtain a high-resolution modulated image spectrum, and perform inverse Fourier transform on the high-resolution modulated image spectrum and then 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 a low-resolution update matrix, and upsample the low-resolution update matrix to obtain a high-resolution update matrix;

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

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

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

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

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

[0016] Determine the expression of the phase mask function W(x,y), specifically:

[0017] W(x,y)=αx 2 +βy n

[0018] Where n is the power exponent parameter, α, β are phase mask parameters, and (x, y) is the xy coordinate axis.

[0019] The power index parameter n of the phase mask plate 3 and the values ​​of the phase mask parameters α and β are designed to set the optical transfer function shape of the imaging system to a single slit shape.

[0020] Preferably, the phase mask plate 3 is rotated N times at equal angles ω and the corresponding coding patterns Pattern are recorded in sequence. k , rotation angle And the corresponding optical transfer function OTF k The expression is:

[0021]

[0022] in, Indicates the Pattern k Perform autocorrelation operation, max(...) means to take the maximum value operation, Pattern k is the kth coding pattern, OTF k is the kth optical transfer function, ω is the rotation angle, and N is the number of rotations.

[0023] Preferably, the high-resolution object amplitude in step 2 is specifically:

[0024]

[0025] In the formula, imresize(A,B,C) means transforming image A to size B according to the C interpolation format. represents the Fourier transform, represents the high-resolution object amplitude corresponding to the k=1th phase encoding in the iter=1th iteration, that is, the initialized high-resolution object amplitude, is a phase-encoded low-resolution image, It represents the high-resolution object spectrum corresponding to the k=1th phase encoding in the iter=1th iteration, that is, the initialized high-resolution object spectrum. HRsize is the size of the high-resolution image, and 'nearest' is the nearest neighbor interpolation format.

[0026] Preferably, a high-resolution update matrix is ​​used For high resolution modulated images The specific formula for obtaining a high-resolution updated modulated image by performing spatial constraints is:

[0027]

[0028] In the formula, It is represented as the high-resolution updated modulation image corresponding to the k-th phase code in the iter-th iteration.

[0029] Preferably, the high-resolution updated modulated image spectrum after spatial domain constraint is subtracted from the high-resolution modulated image spectrum before spatial domain constraint to obtain the modulated image spectrum increment, and the ratio of the coded image spectrum increment to the optical transfer function deconvolution is adjusted by an adaptive step size to obtain the specific formula of the updated high-resolution object spectrum:

[0030]

[0031] Among them, ΔImage iter,k represents the modulated image spectrum increment corresponding to the kth phase code in the iterth iteration, represents the high-resolution updated modulated image spectrum corresponding to the k-th phase encoding in the iter-th iteration, represents the high-resolution modulated image spectrum corresponding to the kth phase encoding in the iterth iteration, represents the high-resolution updated object spectrum corresponding to the k-th phase encoding in the iter-th iteration, represents the high-resolution object spectrum corresponding to the kth phase encoding in the iterth iteration, OTF k represents the k-th optical transfer function, stepsize represents the adaptive step size parameter, and ε represents the regularization parameter.

[0032] Compared with the prior art, the present invention has significant advantages: compared with the super-resolution imaging system based on intensity coding mask, the present invention can obtain the anisotropic regulation of the point spread function without losing signal energy, and its improved resolution is no less than that of intensity coding mask regulation, thereby breaking through the Nyquist sampling frequency to achieve high-resolution and high signal-to-noise ratio imaging. In addition, compared with the general super-resolution imaging system based on micro-scanning, the super-resolution imaging system of the present invention has a simple structure, fast measurement, and easy operation. It can achieve stable resolution improvement without adding a complex mechanical scanning device, and can ultimately improve the resolution of the imaging target by more than 2.5 times.

[0033] The present invention is further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a structural diagram of the super-resolution imaging system based on phase encoding of the present invention.

[0035] Figure 2 This is the phase encoding pattern used in the present invention.

[0036] Figure 3 Point spread function and optical transfer function pattern used in the present invention. Figure 3 (a) is the point spread function corresponding to the rotation phase encoding pattern, Figure 3 (b) is the optical transfer function corresponding to the rotational phase encoding pattern.

[0037] Figure 4 Schematic diagram of the super-resolution method of the present invention.

[0038] Figure 5 For the simulation experiment of USAF resolution target, Figure 5 (a) is a low-resolution image and spectrum using phase encoding in the present invention, Figure 5 (b) is the super-resolution image and spectrum using phase encoding of the present invention.

[0039] Figure 6 This is a real-shot super-resolution imaging comparison experiment on an ISO12233 resolution target. Figure 6 (a) is a low-resolution image taken by the present invention using phase encoding. Figure 6 (b) is the super-resolution image obtained by phase encoding reconstruction. Figure 6 (c) is a low-resolution image taken with an intensity-coded mask. Figure 6 (d) is the super-resolution image reconstructed using the intensity-encoded mask.

[0040] Figure 7 Experimental results of super-resolution imaging for complex scenes, Figure 7 (a) is the test scene. Figure 7 (b) is a low-resolution image of the selected test scene area 1. Figure 7 (c) is the super-resolution image of the selected test scene area 1. Figure 7 (d) is a low-resolution image of the test scene area 2. Figure 7 (e) is the super-resolution image of test scene area 2.

[0041] Figure 8 This is a physical picture of the phase encoding mask. DETAILED DESCRIPTION

[0042] like Figure 1 As shown, a super-resolution imaging system based on phase encoding includes an imaging main lens 1, a 4f relay lens 2, a phase mask plate 3, a 4f relay lens 4, a camera 5, and an electric rotating stage 6. A transmission optical path structure based on a 4f system is adopted, and the transmission optical path structure is composed of a 4f relay lens 1 3 and a 4f relay lens 2 5. In this optical path structure, the aperture plane of the imaging main lens 1 is relayed and imaged to the phase mask plate 3, and the phase mask plate 3 is located on the back focal plane of the 4f relay lens 1 2. The phase mask plate 3 is rotated by the electric rotating stage 6 to realize the modulation of the aperture plane of the imaging main lens 1 and reduce the aberration of the imaging system. The relay lens 1 2 is arranged between the imaging main lens 1 and the phase mask plate 3, and the 4f relay lens 2 4 is arranged between the phase mask plate 3 and the camera 5. The camera 5 is located on the back focal plane of the 4f relay lens 2 4. The imaging main lens 1 is CANON (100-400mm), the focal length is adjusted to 400mm, the 4f relay lens 1 2 and the 4f relay lens 2 4 are CANON LENS EF 50mmF1.4, and the camera 5 has a camera size of 5.5×5.5μm. The imaging main lens 1, the phase mask plate 3, and the camera 5 are fixedly mounted on the optical platform respectively. When the focal length of the imaging main lens is adjusted, the positions of the camera 5 and the phase mask plate 3 relative to the imaging main lens 1 remain unchanged, and the primary image plane of the imaging main lens imaging the object falls on the front focal plane of the 4f relay lens 1.

[0043] like Figure 4 As shown, a super-resolution imaging method based on a phase encoding imaging system, the specific steps are as follows:

[0044] Step 1: Construct a super-resolution imaging system based on phase encoding, control the rotation of the phase mask plate 3 through the electric rotating stage 6 and record N phase-encoded low-resolution images in sequence And the corresponding optical transfer function OTF k , k=1...N.

[0045] First, determine the expression of 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 high-order power function. Its expression is:

[0046] W(x,y)=αx 2 +βy n

[0047] The power index parameter n of the phase mask plate 3 is designed, and the phase mask parameters α and β set the optical transfer function shape of the imaging system to a single slit shape. The generalized pupil function P(x, y) is autocorrelated normalized and recorded as the phase-encoded optical transfer function OTF(u, v, n), and the phase mask parameters α and β are separated to explore the influence of the parameter selection on the optical transfer function. The expression is:

[0048]

[0049] P(x,y)=pupil(x,y)×exp(jkW(x,y))

[0050]

[0051] Among them, pupil(x,y) is the pupil function of the aperture plane. Analysis of the optical transfer function OTF(u,v,n) with parameter separation shows that in the x direction, the value of its phase parameter α is inversely proportional to the size of the overall coefficient. When the value of α decreases, the width of the optical transfer function increases. Conversely, when the value of α increases, the width of the optical transfer function decreases. In the y direction, the value of its phase parameter β is also inversely proportional to the overall length coefficient. When the value of β decreases, the width of the optical transfer function increases. Conversely, when the value of β increases, the width of the optical transfer function decreases. However, due to the large value of n, the value of β has little effect on the length direction of the single slit, so the value of β has a relatively small impact on the result overall. Due to the influence of the aperture stop OTF, the changes in its length and width are limited, and its limit does not exceed the boundary of the autocorrelation of the circular aperture stop itself. However, due to the influence of the high-order power index n in the y direction, the length changes much faster than the width, so in the final OTF shape, the y direction is always limited by the length first. Therefore, the values ​​of the parameters α and β can be controlled to control the phase control shape of the phase mask, so that the obtained optical transfer function approaches a single slit. For this, n = 6, α = 190λ, β = 3λ are selected.

[0052] Secondly, the phase mask plate 3 is rotated N times at an equal angle ω and the corresponding coding patterns Pattern are recorded in sequence. k , rotation angle And the corresponding optical transfer function OTF k The expression is:

[0053]

[0054] in, Indicates the autocorrelation operation on A, max(...) indicates the maximum value operation, Pattern k is the kth coding pattern, OTF k is the kth optical transfer function, ω is the rotation angle, N is the number of rotations, and N=16 is selected here.

[0055] Step 2: Sum and average all phase-encoded low-resolution images and upsample them to obtain the initialized high-resolution object amplitude And perform Fourier transform on it to obtain the initialized high-resolution object spectrum Its expression is:

[0056]

[0057] Among them, imresize(A,B,C) means transforming image A to size B according to the C interpolation format. represents the Fourier transform, represents the high-resolution object amplitude corresponding to the k=1th phase encoding in the iter=1th iteration, that is, the initialized high-resolution object amplitude, represents the high-resolution object spectrum corresponding to the k=1th phase encoding in the iter=1th iteration, that is, the initialized high-resolution object spectrum;

[0058] Step 3: Select the kth optical transfer function OTF k High-resolution object spectrum Encode to obtain high-resolution modulated image spectrum Then perform inverse Fourier transform and downsample to obtain a low-resolution modulated image. Its expression is:

[0059]

[0060] Among them, imresize(A,B,C) means transforming image A to size B according to the C interpolation format. represents the inverse Fourier transform, represents the high-resolution modulated image spectrum corresponding to the kth phase encoding in the iterth iteration, OTF k represents the kth optical transfer function, represents the high-resolution object spectrum corresponding to the k-th phase encoding in the iter-th iteration, represents the low-resolution coded modulation image corresponding to the k-th phase code in the iter-th iteration;

[0061] Step 4: Calculate the low-resolution coded modulation image Phase-encoded low-resolution images The ratio is the low resolution update matrix And upsample the low resolution update matrix Get the high-resolution update matrix Its expression is:

[0062]

[0063] Among them, imresize(A,B,C) means transforming image A to size B according to the C interpolation format. represents the low-resolution update matrix corresponding to the k-th phase encoding in the iter-th iteration, represents the low-resolution modulated image corresponding to the k-th phase encoding in the iter-th iteration, represents the high-resolution update matrix corresponding to the k-th phase encoding in the iter-th iteration;

[0064] Step 5: Update the matrix with high resolution For high resolution modulated images Apply spatial constraints to obtain high-resolution updated modulated images And perform Fourier transform to obtain high-resolution updated modulated image spectrum Its expression is:

[0065]

[0066] in, represents the Fourier transform, It is represented as the high-resolution updated modulation image corresponding to the k-th phase encoding in the iter-th iteration, It is represented as the high-resolution updated modulated image spectrum corresponding to the k-th phase code in the iter-th iteration;

[0067] Step 6: Update the modulated image spectrum with high resolution after spatial constraints High-resolution modulation image spectrum before spatial constraints Subtract to get the modulated image spectrum increment ΔImage iter,k , and an adaptive step size is used to adjust the coded image spectrum increment ΔImage iter,k and the optical transfer function OTF k Deconvolution scale to update high-resolution object spectrum Its expression is:

[0068]

[0069]

[0070] Among them, ΔImage iter,k represents the modulated image spectrum increment corresponding to the kth phase code in the iterth iteration, represents the high-resolution updated modulated image spectrum corresponding to the k-th phase encoding in the iter-th iteration, represents the high-resolution modulated image spectrum corresponding to the kth phase encoding in the iterth iteration, represents the high-resolution updated object spectrum corresponding to the k-th phase encoding in the iter-th iteration, represents the high-resolution object spectrum corresponding to the kth phase encoding in the iterth iteration, OTF k represents the k-th optical transfer function, stepsize represents the adaptive step size parameter, and ε represents the regularization parameter to avoid zero value in the denominator;

[0071] Step 7: Let k = k + 1 and select the next optical transfer function OTF k Repeat iterative steps 3 to 6 until all phase-encoded low-resolution images Go through them all once.

[0072] Step 8: Set iter = iter + 1, and repeat steps 3 to 7 until the phase-encoded low-resolution image With low resolution modulated image The mean square error is less than the convergence threshold T, and the value of T is generally 0.001.

[0073] In order to test the effectiveness of the super-resolution method based on the phase-encoded imaging system of the present invention, two groups of experiments are selected for illustration.

[0074] Figure 2 This is the phase encoding pattern used in the present invention. Phase encoding patterns of different angles are obtained by setting phase plate parameters and rotating them in sequence. Figure 3 The point spread function and optical transfer function pattern used in the present invention are given by Figure 2 Calculate the point spread function and optical transfer function of the imaging system, Figure 3 (a) is the point spread function corresponding to the rotation phase encoding pattern, Figure 3 (b) is the optical transfer function corresponding to the rotation phase encoding pattern. As can be seen from the figure, the shape of the optical transfer function is a single slit shape.

[0075] Figure 5 In order to conduct simulation experiments on USAF resolution targets to quantitatively analyze the effectiveness of super-resolution algorithms, Figure 5 (a) is a low-resolution image and its spectrum, which is resolved to -1-1 line pairs with a line pair width of 1000μm Figure 5 (b) is the image and its spectrum after phase encoding super-resolution reconstruction. After super-resolution, it can resolve to 0-3 line pairs, with a line pair width of 396.85 μm, and the super-resolution is improved by 1000 / 396.85=2.519 times.

[0076] Figure 6 For the super-resolution imaging comparison experiment of ISO12233 resolution target, Figure 6 (a) is a low-resolution image taken by the present invention using phase encoding. Figure 6 (b) is a low-resolution image taken with an intensity coding mask. The optical transfer function obtained by the phase coding parameters used in the present invention is basically consistent with the optical transfer function obtained by the optimal slit width designed for the intensity coding mask. However, it can be seen from the image that the phase coding used in the present invention can obtain a similar modulation effect. Only 300 lines can be identified in the low-resolution image, but the signal-to-noise ratio of the phase coding is significantly better than that of the intensity coding mask. Figure 6 (c) is the super-resolution image obtained by phase encoding reconstruction. Figure 6 (d) is the super-resolution image reconstructed using the intensity coding mask. It can be seen that both the phase coding and intensity coding super-resolution results can resolve between 700 lines and 800 lines, with the resolution improved by more than 2.3 times. In addition, the phase coding reconstruction signal-to-noise ratio is better than that of the intensity coding.

[0077] Figure 7 Experimental results of super-resolution imaging for complex scenes, Figure 7 (a) To test a complex scene, two regions are selected for super-resolution reconstruction. Figure 7 (b) and Figure 7 (d) are low-resolution images of area 1 and area 2. It can be seen that the letters and portraits in the low-resolution images have obvious mosaic effects, the edges of the target objects are blurred, and the details of the letters cannot be recognized. After phase encoding, Figure 7 (c) and Figure 7 As shown in (e), the details are clearly restored and the resolution is effectively improved.

[0078] In summary, the phase-encoded super-resolution imaging system of the present invention can effectively break through the limitation of insufficient Nyquist sampling, especially in the case of insufficient light. The light flux is particularly important for imaging. Phase encoding can achieve anisotropic regulation with almost no loss of light flux, and the imaging resolution can be increased to 2.5 times, which has a wider application demand.

Claims

1. A super-resolution imaging system based on phase encoding, characterized in that: The imaging system comprises an imaging main lens 1, a 4f relay lens 2, a phase mask plate 3, a 4f relay lens 4, a camera 5, and an electric rotating stage 6. The aperture plane of the imaging main lens 1 is relayed and imaged to the phase mask plate 3. The phase mask plate 3 is located on the rear focal plane of the 4f relay lens 1. The phase mask plate 3 is rotated by the electric rotating stage 6 to realize modulation of the aperture plane of the imaging main lens 1 and reduce the aberration of the imaging system. The relay lens 1 2 is arranged between the imaging main lens 1 and the phase mask plate 3. The 4f relay lens 2 4 is arranged between the phase mask plate 3 and the camera 5. The camera 5 is located on the rear focal plane of the 4f relay lens 2 4. The imaging main lens 1, the phase mask plate 3, and the camera 5 are respectively fixedly mounted on an optical platform. When the focal length of the imaging main lens is adjusted, the positions of the camera 5 and the phase mask plate 3 relative to the imaging main lens 1 remain unchanged. The primary image plane of the imaging main lens imaging the object falls on the front focal plane of the 4f relay lens 1.

2. A super-resolution imaging method based on phase encoding, characterized in that: The specific steps are: Step 1: construct the phase-encoding-based super-resolution imaging system as claimed in claim 1, control the rotation of the phase mask plate 3 by the electric rotating stage 6 and sequentially record N phase-encoded low-resolution images and corresponding optical transfer functions; Step 2: Sum and average all phase-encoded low-resolution images and then upsample them to obtain the initialized high-resolution object amplitude, and perform Fourier transform on the initialized high-resolution object amplitude to obtain the initialized high-resolution object spectrum; Step 3: Select the kth optical transfer function to encode the high-resolution object spectrum to obtain a high-resolution modulated image spectrum, and perform inverse Fourier transform on the high-resolution modulated image spectrum and then 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 a low-resolution update matrix, and upsample the low-resolution update matrix to obtain a high-resolution update matrix; Step 5: Use the high-resolution update matrix to perform spatial domain constraints on the high-resolution modulated image to obtain a high-resolution updated modulated image, and perform Fourier transform to obtain a high-resolution updated modulated image spectrum; Step 6: Subtract the high-resolution updated modulated image spectrum after spatial domain constraint from the high-resolution modulated image spectrum before spatial domain constraint to obtain the modulated image spectrum increment, and use an adaptive step size to adjust the ratio of the coded image spectrum increment and the optical transfer function deconvolution to update the high-resolution object spectrum; Step 7: Repeat iterative steps 3 to 6 for the next phase-encoded low-resolution image and the next optical transfer function until all phase-encoded low-resolution images are traversed once. Step 8: Repeat steps 3 to 7 until the mean square error between the phase-encoded low-resolution image and the low-resolution modulated image is less than the convergence threshold.

3. The super-resolution imaging method based on phase encoding according to claim 2, characterized in that: The parameters of the phase mask of the super-resolution imaging system based on phase encoding are determined according to the following method: Determine the expression of the phase mask function W(x,y), specifically: W(x,y)=αx 2 +βy n Where n is the power exponent parameter, α, β are phase mask parameters, and (x, y) is the xy coordinate axis. The power index parameter n of the phase mask plate 3 and the values ​​of the phase mask parameters α and β are designed to set the optical transfer function shape of the imaging system to a single slit shape.

4. The super-resolution imaging method based on phase encoding according to claim 2, characterized in that: Rotate the phase mask plate 3 N times at equal angles ω and record the corresponding coding patterns Pattern in sequence k , rotation angle And the corresponding optical transfer function OTF k The expression is: in, Indicates the Pattern k Perform autocorrelation operation, max(...) means to take the maximum value operation, Pattern k is the kth coding pattern, OTF k is the kth optical transfer function, ω is the rotation angle, and N is the number of rotations.

5. The super-resolution imaging method based on phase encoding according to claim 2, characterized in that: The high-resolution object amplitude in step 2 is specifically: In the formula, imresize(A,B,C) means transforming image A to size B according to the C interpolation format. represents the Fourier transform, represents the high-resolution object amplitude corresponding to the k=1th phase encoding in the iter=1th iteration, that is, the initialized high-resolution object amplitude, is a phase-encoded low-resolution image, It represents the high-resolution object spectrum corresponding to the k=1th phase encoding in the iter=1th iteration, that is, the initialized high-resolution object spectrum. HRsize is the size of the high-resolution image, and 'nearest' is the nearest neighbor interpolation format.

6. The super-resolution imaging method based on phase encoding according to claim 2, characterized in that: Update the matrix with high resolution For high resolution modulated images The specific formula for obtaining a high-resolution updated modulated image by performing spatial constraints is: In the formula, It is represented as the high-resolution updated modulation image corresponding to the k-th phase code in the iter-th iteration.

7. The super-resolution imaging method based on phase encoding according to claim 2, characterized in that: The modulated image spectrum increment is obtained by subtracting the high-resolution updated modulated image spectrum after spatial domain constraint from the high-resolution modulated image spectrum before spatial domain constraint, and the ratio of the coded image spectrum increment and the optical transfer function deconvolution is adjusted by an adaptive step size to obtain the specific formula for the updated high-resolution object spectrum: Among them, ΔImage iter,k represents the modulated image spectrum increment corresponding to the kth phase code in the iterth iteration, represents the high-resolution updated modulated image spectrum corresponding to the k-th phase encoding in the iter-th iteration, represents the high-resolution modulated image spectrum corresponding to the kth phase encoding in the iterth iteration, represents the high-resolution updated object spectrum corresponding to the k-th phase encoding in the iter-th iteration, represents the high-resolution object spectrum corresponding to the kth phase encoding in the iterth iteration, OTF k represents the k-th optical transfer function, stepsize represents the adaptive step size parameter, and ε represents the regularization parameter.

Images