A phase encoding based super-resolution imaging system and method

Abstract

The application discloses a kind of super-resolution imaging system and super-resolution method based on phase coding, for improving the imaging resolution and imaging signal-to-noise ratio of visible light imaging system.The system is composed of imaging main lens 1, 4f relay lens one 2, phase mask plate 3, 4f relay lens two 4, camera 5, motorized rotary table 6, by optimizing the phase function of phase mask plate, so that the system transfer function has anisotropy on a certain frequency component, by motorized rotary table 6 control phase mask plate 3 rotation control and through camera 5 acquisition a series of coded low-resolution image, combined with the joint constraint iteration of space domain and frequency domain, the reconstructed image is acquired by the collected image until the algorithm converges, to obtain the reconstruction image that breaks through Nyquist sampling.Compared with the method based on intensity mask coding, the anisotropy of point spread function can be controlled without losing light flux, and the imaging resolution is improved by more than 2.5 times.

Description

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 scheme for achieving the object of the application is: a phase coding-based super-resolution imaging system, 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 a motorized rotary table 6; the aperture plane of the imaging main lens 1 is relayed 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 motorized rotary table 6 to realize modulation of the aperture plane of the imaging main lens 1 and reduce aberration of the imaging system; the 4f 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, and the imaging main lens 1, the phase mask plate 3, and the camera 5 are respectively fixedly installed 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, and a first image plane of the imaging main lens for imaging an object falls on the front focal plane of the 4f relay lens 1.

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

[0007] Step 1: constructing a phase coding-based super-resolution imaging system, rotating the phase mask plate 3 by the motorized rotary table 6 and sequentially recording N phase coding low-resolution images and corresponding optical transfer functions;

[0008] Step 2: summing and averaging all the phase coding low-resolution images to obtain an initialized high-resolution object amplitude, and performing Fourier transform on the initialized high-resolution object amplitude to obtain an initialized high-resolution object spectrum;

[0009] Step 3: selecting the kth optical transfer function to code the high-resolution object spectrum to obtain a high-resolution modulation image spectrum, and performing inverse Fourier transform on the high-resolution modulation image spectrum and then down-sampling to obtain a low-resolution modulation image;

[0010] Step 4: obtaining a low-resolution update matrix by dividing the low-resolution coded modulation image by the phase coding low-resolution image, and up-sampling the low-resolution update matrix to obtain a high-resolution update matrix;

[0011] Step 5: using the high-resolution update matrix to perform spatial domain constraint on the high-resolution modulation image to obtain a high-resolution updated modulation image, and performing Fourier transform to obtain a high-resolution updated modulation image spectrum;

[0012] Step 6: subtracting the high-resolution updated modulation image spectrum after spatial domain constraint from the high-resolution modulation image spectrum before spatial domain constraint to obtain a modulation image spectrum increment, and adjusting the proportion of the coded image spectrum increment and the optical transfer function deconvolution by using an adaptive step to update the high-resolution object spectrum;

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

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

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

[0016] The expression of the phase mask function W(x, y) is determined, specifically as follows:

[0017] W(x, y) = αx 2 + βy n

[0018] In the formula, n is a power index parameter, α and β are phase mask parameters, and (x, y) is an x-y coordinate axis.

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

[0020] Preferably, the phase mask plate 3 is rotated at an equal angle ω for N times and the corresponding encoding patterns Pattern k , the rotation angle and the corresponding optical transfer functions OTF k are recorded in sequence, and the expression is as follows:

[0021]

[0022] Wherein, represents the autocorrelation operation on Pattern k , max(...) represents the maximum value operation, Pattern k is the kth encoding 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 as follows:

[0024]

[0025] In the formula, imresize(A, B, C) represents transforming the image of A to the size of B according to the C interpolation format, represents the Fourier transform, HRkiter=1represents the high-resolution object amplitude corresponding to the kth phase-encoded image in the first iteration, i.e. the initialized high-resolution object amplitude, represents the phase-encoded low-resolution image, HRkiter=1represents the high-resolution object spectrum corresponding to the kth phase-encoded image in the first iteration, i.e. the initialized high-resolution object spectrum, HRsize represents the high-resolution image size, and 'nearest' represents the nearest interpolation format.

[0026] Preferably, the high-resolution update matrix is The high-resolution modulation image is updated The specific formula for obtaining the high-resolution update modulation image by spatial constraint is:

[0027]

[0028] In the formula, HRkiterrepresents the high-resolution update modulation image corresponding to the kth phase-encoded image in the iterth iteration.

[0029] Preferably, the modulation image spectrum increment is obtained by subtracting the high-resolution update modulation image spectrum after spatial constraint from the high-resolution modulation image spectrum before spatial constraint, and the proportion of the encoded image spectrum increment and the optical transfer function deconvolution is adjusted by using an adaptive step size to update the high-resolution object spectrum. The specific formula is:

[0030]

[0031] where ΔImage iter,k represents the modulation image spectrum increment corresponding to the kth phase-encoded image in the iterth iteration, represents the high-resolution update modulation image spectrum corresponding to the kth phase-encoded image in the iterth iteration, represents the high-resolution modulation image spectrum corresponding to the kth phase-encoded image in the iterth iteration, represents the high-resolution update object spectrum corresponding to the kth phase-encoded image in the iterth iteration, represents the high-resolution object spectrum corresponding to the kth phase-encoded image in the iterth iteration, OTF k represents the kth optical transfer function, stepsize represents the adaptive step size parameter, and ε represents the regularization parameter.

[0032] Compared with the prior art, the present application has the following advantages: compared with the intensity coding mask super-resolution imaging system, the present application can obtain the anisotropic regulation of the point spread function without losing signal energy, and the improved resolution capability is not inferior to the intensity coding mask regulation, thereby breaking through the Nyquist sampling frequency to realize high-resolution and high signal-to-noise ratio imaging. In addition, compared with the general micro-scan based super-resolution imaging system, the super-resolution imaging system of the present application has the advantages of simple structure, fast measurement and easy operation, and can realize stable resolution improvement without adding a complex mechanical scanning device, and finally can improve the imaging target resolution by more than 2.5 times.

[0033] The present application will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 The figure is a structural diagram of the phase coding based super-resolution imaging system of the present application.

[0035] Figure 2 The figure is a phase coding pattern used in the present application.

[0036] Figure 3 The figure is a point spread function and optical transfer function pattern used in the present application. Figure 3 (a) is a point spread function corresponding to a rotating phase coding pattern, Figure 3 (b) is an optical transfer function corresponding to a rotating phase coding pattern.

[0037] Figure 4 The figure is a flowchart of the super-resolution method of the present application.

[0038] Figure 5 The figure is a simulation experiment on a USAF resolution target, Figure 5 (a) is a low-resolution image and spectrum using phase coding in the present application, Figure 5 (b) is an image and spectrum after super-resolution using phase coding in the present application.

[0039] Figure 6 The figure is a real super-resolution imaging comparison experiment on an ISO12233 resolution target, Figure 6 (a) is a low-resolution image using phase coding in the present application, Figure 6 (b) is a super-resolution image obtained by reconstruction using phase coding, Figure 6 (c) is a low-resolution image using intensity coding mask, Figure 6 (d) is a super-resolution image obtained by reconstruction using intensity coding mask.

[0040] Figure 7 The figure is an experimental result of super-resolution imaging of a complex scene, Figure 7 (a) is a test scene,Figure 7 (b) is a low-resolution image of the test scene area 1. Figure 7 (c) is a super-resolution image of the selected test scene region one. Figure 7 (d) is a low-resolution image of test scene region two. Figure 7 (e) is the super-resolution image of test scene region two.

[0041] Figure 8 This is a physical image of the phase-encoding mask. Detailed Implementation

[0042] like Figure 1 As shown, a phase-encoded super-resolution imaging system includes an imaging main lens 1, a 4f relay lens 2, a phase mask 3, a 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 a first 4f relay lens 3 and a second 4f relay lens 5. In this optical path structure, the aperture plane of the imaging main 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 imaging main lens 1 and reduce aberrations in the imaging system. The first 4f relay lens 2 is positioned between the imaging main 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 imaging main lens 1 is a CANON (100-400mm) with a focal length adjusted to 400mm. The 4f relay lens 1 (2) and 4f relay lens 2 (4) are CANON LENS EF 50mm F1.4 lenses. The camera 5 is a 5.5×5.5μm camera. The imaging main lens 1, phase mask 3, and 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 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 4f relay lens 1.

[0043] like Figure 4 As shown, a super-resolution imaging method based on a phase-coded imaging system comprises the following steps:

[0044] 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.

[0045] Firstly, the expression of the phase mask function W(x, y) is determined, which is composed of a quadratic function and a high-order function weighted sum, and 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. By normalizing the autocorrelation of the generalized pupil function P(x, y) to the phase encoding optical transfer function OTF(u, v, n), and separating the phase mask parameters α and β to explore the influence of the selection of the parameters on the optical transfer function, its expression is:

[0048]

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

[0050]

[0051] Wherein, pupil(x, y) is the pupil function of the aperture plane, and the analysis of the optical transfer function OTF(u, v, n) after parameter separation shows that in the x direction, the value of the phase parameter α is inversely proportional to the size of the integral coefficient, and when the value of α decreases, the width of the optical transfer function increases, and vice versa, when the value of α increases, the width of the optical transfer function decreases. In the y direction, the value of the phase parameter β is also inversely proportional to the length coefficient as a whole. When the value of β decreases, the width of the optical transfer function increases, and vice versa, 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 relatively small effect on the result as a whole. Due to the influence of the aperture stop OTF, the length and width change is limited, and the limit does not exceed the autocorrelation boundary of the circular aperture stop itself. 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 finally presented OTF shape, the y direction is always limited by the length. Therefore, the values of the parameters α and β can be controlled to control the phase control shape of the phase mask plate, so that the obtained optical transfer function tends to be a single slit. For this, n = 6, α = 190λ, and β = 3λ are selected.

[0052] Secondly, the phase mask plate 3 is rotated by an angle ω for N times, and the corresponding encoding patterns Pattern k , the rotation angle and the expression of the corresponding optical transfer function OTF k are recorded in turn.

[0053]

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

[0055] Step 2: Sum and average all the phase-coded low-resolution images to obtain the initialized high-resolution object amplitude and perform Fourier transform to obtain the initialized high-resolution object spectrum The expression is:

[0056]

[0057] where, imresize(A, B, C) represents transforming A to the size of B according to the C interpolation format, represents the Fourier transform, represents the kth phase-coded high-resolution object amplitude in the first iteration, that is, the initialized high-resolution object amplitude, represents the kth phase-coded high-resolution object spectrum in the first iteration, that is, the initialized high-resolution object spectrum;

[0058] Step 3: Select the kth optical transfer function OTF k to the high-resolution object spectrum to obtain the high-resolution modulation image spectrum and perform inverse Fourier transform to obtain the low-resolution modulation image The expression is:

[0059]

[0060] where, imresize(A, B, C) represents transforming A to the size of B according to the C interpolation format, represents the inverse Fourier transform, represents the kth phase-coded high-resolution modulation image spectrum in the iter iteration, OTF k represents the kth optical transfer function, represents the kth phase-coded high-resolution object spectrum in the iter iteration, represents the kth phase-coded low-resolution coded modulation image in the iter iteration;

[0061] Step 4: Obtain low resolution update matrix from the ratio of the phase encoded low resolution image and upsample the low resolution update matrix to obtain high resolution update matrix The expression is:

[0062]

[0063] where imresize(A, B, C) means to transform the image A to size B with C interpolation format, represents the low resolution update matrix corresponding to the kth phase encoding in the iterth iteration, represents the low resolution modulation image corresponding to the kth phase encoding in the iterth iteration, represents the high resolution update matrix corresponding to the kth phase encoding in the iterth iteration;

[0064] Step 5: Obtain high resolution modulation image from the high resolution update matrix and perform spatial constraint to obtain high resolution updated modulation image and perform Fourier transform to obtain high resolution updated modulation image spectrum The expression is:

[0065]

[0066] where, represents Fourier transform, represents the high resolution updated modulation image corresponding to the kth phase encoding in the iterth iteration, represents the high resolution updated modulation image spectrum corresponding to the kth phase encoding in the iterth iteration;

[0067] Step 6: Obtain modulation image spectrum increment ΔImage from the high resolution updated modulation image spectrum after spatial constraint and the high resolution modulation image spectrum iter,k before spatial constraint, and adjust the encoding image spectrum increment ΔImage iter,k with adaptive step size, k and deconvolve the updated high resolution object spectrum with the optical transfer function OTF The expression is:

[0068]

[0069]

[0070] where ΔImage iter,k represents the modulation image spectrum increment of the kth phase encoding in the iterth iteration, represents the high-resolution updated modulation image spectrum of the kth phase encoding in the iterth iteration, represents the high-resolution modulation image spectrum of the kth phase encoding in the iterth iteration, represents the high-resolution updated object spectrum of the kth phase encoding in the iterth iteration, represents the high-resolution object spectrum of the kth phase encoding in the iterth iteration, OTF k represents the kth 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, select the next optical transfer function OTF k , repeat the iteration steps 3-6 until all phase encoding low-resolution images are traversed once.

[0072] Step 8: Let iter = iter + 1, repeat steps 3-7 until the mean square error of the phase encoding low-resolution image and the low-resolution modulation image 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 encoding imaging system of the present application, two groups of experiments are selected for illustration.

[0074] Figure 2 is the phase encoding pattern adopted by the present application. By setting the phase plate parameters, different angle phase encoding patterns are obtained in turn. Figure 3 is the point spread function and optical transfer function pattern adopted by the present application, which is Figure 2 calculated from the point spread function and the optical transfer function of the imaging system, Figure 3 (a) is the point spread function corresponding to the rotated phase encoding pattern, Figure 3 (b) is the optical transfer function corresponding to the rotated phase encoding pattern. It can be observed from the figure that the shape of the optical transfer function is a single-slit shape.

[0075] Figure 5 is a simulation experiment on the USAF resolution target to quantitatively analyze the effectiveness of the super-resolution algorithm, Figure 5 (a) is a low-resolution image and its spectrum, which is resolved to -1-1 group of line pairs, and the line pair width is 1000 μmFigure 5 (b) is the image and its spectrum after super-resolution reconstruction by using phase coding, and after super-resolution, 0-3 line pairs can be distinguished, the line pair width is 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 on the ISO12233 resolution target, Figure 6 (a) is a low-resolution image of the actual shooting by using phase coding of the application, Figure 6 (b) is a low-resolution image of the actual shooting by using an intensity coding mask, the optical transfer function obtained by using the phase coding parameter of the application is basically consistent with the optical transfer function obtained by using the optimal slit width designed by the intensity coding mask, but it can be seen from the image that the phase coding used by the application can obtain similar modulation effect, and only 300 lines can be identified in the low-resolution image, but the signal-to-noise ratio of the phase coding is obviously better than that of the intensity coding mask; Figure 6 (c) is a super-resolution image obtained by using phase coding reconstruction, Figure 6 (d) is a super-resolution image obtained by using intensity coding mask reconstruction, it can be seen that the super-resolution results of both phase coding and intensity coding can distinguish between 700 lines and 800 lines, the resolution is improved by more than 2.3 times, and the signal-to-noise ratio of the phase coding reconstruction is better than that of the intensity coding.

[0077] Figure 7 The experimental results of super-resolution imaging for complex scenes, Figure 7 (a) is the test of a complex scene and the selection of two regions for super-resolution reconstruction, Figure 7 (b) and Figure 7 (d) are low-resolution images of region one and region two, respectively, it can be seen that the letters and portraits in the low-resolution image can see obvious mosaic effect, the target object edge is blurred, and the letter details cannot be identified, after phase coding, Figure 7 (c) and Figure 7 (e) shown, the details are clearly recovered, and the resolution is effectively improved.

[0078] In summary, the phase coding super-resolution imaging system based on the application can effectively break through the limitation of insufficient Nyquist sampling, especially in the case of insufficient light, light flux is particularly important for imaging, phase coding almost does not lose light flux and can realize anisotropic regulation, and the imaging resolution is improved by 2.5 times, and has wider application demand.

Claims

1. A phase-encoded based super-resolution imaging system, characterized in that, The application relates to an imaging system based on phase coding super-resolution, which comprises an imaging main lens (1), a 4f relay lens (2), a phase mask plate (3), a 4f relay lens (2), a camera (5) and a motorized rotary table (6). The aperture plane of the imaging main lens (1) is relayed 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 motorized rotary table (6) to realize modulation of the aperture plane of the imaging main lens (1) and reduce aberration of the imaging system, the 4f 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 fixedly arranged 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, a first image plane of the imaging main lens is located on the front focal plane of the 4f relay lens (2), and the parameters of the phase mask plate of the phase coding super-resolution imaging system are determined according to the following method. The expression of the phase mask function W(x, y) is determined, and the expression is as follows: W(x, y) = ax + βy 2 + γ n In the formula, n is a power index parameter, alpha and beta are phase mask parameters, and (x, y) is an x-y coordinate axis. The power index parameter n and the phase mask parameters alpha and beta of the phase mask plate (3) are designed to set the shape of the optical transfer function of the imaging system as a single-slit shape. The phase mask (3) is rotated by an angle ω for N times and the corresponding encoding patterns Pattern are recorded in sequence k , the rotation angle and the expression of the corresponding optical transfer function OTF k are as follows: wherein, represents a self-correlation operation on Pattern k max(...) represents a maximum operation, Pattern k is the kth encoded pattern, OTF k is the kth optical transfer function, and N is the number of rotations.

2. A phase encoding based super-resolution imaging method, characterized in that, The specific steps are as follows: Step 1: constructing the phase coding super-resolution imaging system according to claim 1, rotating the phase mask plate (3) by the motorized rotary table (6) and sequentially recording N phase coding low-resolution images and corresponding optical transfer functions; Step 2: summing and averaging all the phase coding low-resolution images to obtain an initialized high-resolution object amplitude, and performing Fourier transform on the initialized high-resolution object amplitude to obtain an initialized high-resolution object spectrum; Step 3: selecting the kth optical transfer function to code the high-resolution object spectrum to obtain a high-resolution modulation image spectrum, and performing inverse Fourier transform on the high-resolution modulation image spectrum and then down-sampling to obtain a low-resolution modulation image; Step 4: obtaining a low-resolution update matrix by dividing the low-resolution coding modulation image by the phase coding low-resolution image, and up-sampling the low-resolution update matrix to obtain a high-resolution update matrix; Step 5: using the high-resolution update matrix to perform spatial domain constraint on the high-resolution modulation image to obtain a high-resolution updated modulation image, and performing Fourier transform to obtain a high-resolution updated modulation image spectrum; Step 6: subtracting the high-resolution updated modulation image spectrum after spatial domain constraint from the high-resolution modulation image spectrum before spatial domain constraint to obtain a modulation image spectrum increment, and adjusting the proportion of the coded image spectrum increment and the optical transfer function deconvolution with an adaptive step to update the high-resolution object spectrum. Step 7: Repeat iteration steps 3-6 for the next phase-encoding low-resolution image and the next optical transfer function until all phase-encoding low-resolution images are traversed once; Step 8: Repeat steps 3-7 until the mean square error of the phase-encoding low-resolution image and the low-resolution modulation image is less than a convergence threshold.

3. The phase-encoded super-resolution imaging method of claim 2, wherein, The high-resolution object amplitude in step 2 is specifically: where imresize(A,B,C) denotes the image resizing of A to size B with interpolation format C, represents the high resolution object amplitude corresponding to the first phase encoded image in the first iteration, i.e. the initialized high resolution object amplitude, is the phase encoded low resolution image, HRsize is the high resolution image size, and 'nearest' is the nearest neighbor interpolation format.

4. The phase-encoded super-resolution imaging method of claim 2, wherein, Updating a matrix with high resolution on high resolution modulation images The specific formula for obtaining a high resolution updated modulation image with spatial constraints is: wherein denotes the high resolution updated modulation image corresponding to the kth phase encoded pair in the iterth iteration.

5. The phase-encoded super-resolution imaging method of claim 2, wherein, The modulation image spectrum increment is obtained by subtracting the high-resolution modulation image spectrum after the spatial constraint from the high-resolution modulation image spectrum before the spatial constraint, and the proportion of the encoding image spectrum increment and the optical transfer function deconvolution is adjusted by using an adaptive step to update the high-resolution object spectrum, and the specific formula is: where ΔImage iter,k represents the modulation image spectrum increment corresponding to the kth phase encoding in the iterth iteration, represents the high-resolution updated modulation image spectrum corresponding to the kth phase encoding in the iterth iteration, represents the high-resolution modulation image spectrum corresponding to the kth phase encoding in the iterth iteration, represents the high-resolution updated object spectrum corresponding to the kth phase encoding in the iterth iteration, represents the high-resolution object spectrum corresponding to the kth phase encoding in the iterth iteration, OTF k represents the kth optical transfer function, stepsize represents an adaptive step size parameter, and ε represents a regularization parameter.

Images