Diffraction imaging system and image restoration method based on SPGD algorithm

Abstract

The invention discloses a diffraction imaging system and an image restoration method based on an SPGD algorithm. The FZP imaging system comprises a monochromatic extended light source, an imaging target film, a far-field lens, an FZP, a beam shrinking lens and an imaging detection camera. According to the FZP, a series of concentric rings with different diameters are etched on a special optical material, modulation of the incident light wave front phase is achieved, and then light beam focusing and imaging are achieved; the provided image restoration method comprises the following steps: firstly, acquiring an FZP diffraction efficiency measurement value eta 1 and PSF1 corresponding to a main order, then optimizing an equivalent point spread function (PSFn) and diffraction efficiency of other orders through SPGD iteration, and then substituting the point spread function and the diffraction efficiency of the optimal point into an inverse filter which is based on an imaging model and is capable of adjusting a filtering radius and a frequency component threshold value, so as to restore the image. The image restoration method of the FZP imaging system is high in reliability, easy to implement and high in real-time performance, and can be better used for enhancing and restoring the image parameters of the imaging system.

Description

Technical Field

[0001] This invention belongs to the field of thin-film diffraction imaging technology, specifically relating to a diffraction imaging system and an image restoration method based on the SPGD algorithm. Background Technology

[0002] Fresnel zone plates (FZPs) offer advantages such as ultra-large aperture, lightweight design, relaxed tolerances, and ease of deployment and folding, making them a crucial development direction for space-based ultra-large telescopes. Driven by international projects like Eyeglass, MORIE, and Falcon 7, thin-film diffraction imaging has made significant progress. However, no thin-film diffraction imaging telescope is currently operational in orbit. Related research indicates that the imaging performance of thin-film diffraction imaging systems still lags behind their space applications. Specifically, multi-order diffraction by the FZP diffraction element degrades the imaging signal-to-noise ratio, wavefront aberrations reduce image resolution, and the coupling problem between these two factors urgently needs to be addressed. Non-imaging-order diffracted light becomes strong background noise, severely reducing the signal-to-noise ratio and hindering the realization of wavefront aberration correction to improve imaging system resolution.

[0003] The FZP consists of a series of stepped concentric ring micro / nano substructures. These stepped micro / nano substructures modulate the phase of the incident beam. While aiming for focused imaging, they inevitably introduce non-designed order light, which becomes strong background noise in the designed order imaging light, thus reducing the diffraction efficiency of the FZP. The relationship between the number of steps and the diffraction efficiency is as follows:

[0004]

[0005] Where N is the number of steps in the FZP annular structure, λ0 is the design wavelength, λ is the working wavelength, and m is the diffraction order. Theoretically, the diffraction efficiency of a two-step FZP is 40.5%, that of a four-step FZP is 81%, and that of an eight-step FZP can reach over 98%. However, due to processing errors, the actual diffraction efficiency further decreases.

[0006] On the other hand, the wavefront of the FZP imaging beam is distorted due to factors such as FZP components, system errors, and operating environment, which in turn causes the point spread function (PSF) of the FZP imaging system to diffuse, ultimately reducing the imaging resolution. The specific expression for the effect of wavefront distortion is as follows:

[0007]

[0008] Where (x,y) are the focal plane coordinates, (x′,y′) are the pupil plane coordinates, A(x′,y′) is the beam amplitude, Φ(x′,y′) is the beam wavefront distortion, z is the transmission distance, and k is the wavenumber. The model of the FZP imaging system is as follows:

[0009]

[0010] In the formula, I represents the actual image of the target, I0 represents the ideal image of the target, η1 represents the diffraction efficiency of the imaging order, and PSF1 and PSF2 represent the diffraction efficiency of the target. n are the point spread functions of the primary and secondary beams, respectively, and w is the noise.

[0011] Therefore, FZP imaging is subject to the dual effects of multi-order diffraction and wavefront distortion coupling, resulting in a sharp degradation of imaging quality. To address this problem, this invention proposes a stochastic parallel gradient descent (SPGD) optimization method to iteratively optimize the optimal PSF of FZP imaging and achieve rapid image enhancement based on the imaging model. Summary of the Invention

[0012] To address the problem in the prior art where multi-order diffraction in FZP imaging systems leads to a degradation in the imaging signal-to-noise ratio, thus restricting the correction of wavefront distortion and the improvement of imaging resolution, this invention aims to provide a diffraction imaging system and an image restoration method based on the SPGD algorithm. This method equates the noise and wavefront distortion caused by multi-order diffraction to a noise PSF (Power-Sensitive Filter). n The PSF of FZP is obtained by optimizing the SPGD algorithm. n Simultaneously, based on the FZP imaging model, rapid image enhancement is achieved. The imaging system utilizes a point light source, a monochromatic extended light source, an equivalent lens, FZP, a beam-shrinking lens, an imaging acquisition camera, and a computer control system to implement the imaging system. This provides the prerequisites for subsequent optimization of the PSF and image enhancement of the FZP imaging system. It is applicable to image post-processing and restoration of thin-film diffraction imaging systems such as Fresnel lenses, photon sieves, and mosaic diffraction telescopes, as well as the measurement and optimization of the point spread function of diffraction imaging systems.

[0013] To solve the technical problem, the technical solution of the present invention is as follows:

[0014] A diffraction imaging system, the imaging system comprising: a point source and monochromatic extended light sources arranged sequentially along the optical axis of the point source, an imaging target film, a far-field lens, a Fresnel lens (FZP), a beam-shrinking lens, and an imaging detection camera;

[0015] The system also includes: a computer; the imaging detection camera is signal-connected to the computer.

[0016] Furthermore, the light beam emitted by the point light source or monochromatic extended light source passes through the imaging target film and the far-field lens to reach the Fresnel lens FZP, and then passes through the beam-shrinking lens to enter the imaging detection camera for imaging.

[0017] Furthermore, the computer is pre-configured with an image restoration processing unit, which is used to acquire the FZP diffraction efficiency measurement value η1 and the PSF1 corresponding to the principal order, and then optimize the equivalent point spread function PSF of other orders through SPGD iteration. n By combining the diffraction efficiency with the point spread function and diffraction efficiency at the optimal point, and then incorporating these into an inverse filter based on the imaging model with adjustable filter radius and frequency component thresholds, image restoration of the FZP imaging system can be achieved.

[0018] An image restoration method based on the SPGD algorithm, the method being applied to the system described in any one of the above-mentioned methods, the method comprising:

[0019] Step 1: Switch the light source and imaging target film to point light source, and use the camera to acquire the focal plane image of the principal order diffraction light of FZP, i.e., FZP principal order PSF1;

[0020] Step 2: Equivalent all non-imaging-order diffraction imaging systems to PSF n The FZP imaging model is established by initializing with a zero matrix and substituting the point spread function PSF1 and diffraction efficiency corresponding to the primary and secondary beams of the imaging into η1.

[0021]

[0022] In the formula, I represents the image acquired by the camera from the FZP imaging system, I0 represents the imaging target, and w represents the imaging noise. To represent convolution, the above expression... Perform a Fourier transform, simplify, and then perform an inverse Fourier transform to obtain:

[0023]

[0024] Further modifications yield the relevant imaging model:

[0025]

[0026] In the formula, FFT2 and IFFT2 are the two-dimensional Fourier transforms and inverse transforms, respectively. The FZP imaging system can acquire the actual image I, the principal-level spot spread function PSF1, and the corresponding diffraction efficiency η1. The PSF1 is iteratively optimized using the SPGD algorithm. n The correction value for the diffraction efficiency η1 is used below to optimize the equivalent point spread function and diffraction efficiency of multi-level diffraction using SPGD.

[0027] Step 3: Based on the corresponding imaging model parameters and SPGD, generate random disturbances Δη1 and ΔPSF. n Based on the generated random interference, positive and negative interference are further generated. The specific generation expressions and related processes are as follows:

[0028] Generate positive interference:

[0029] η1=η1+Δη1

[0030] PSF pos =η1×PSF0+(1-η1)×(PSF) n +ΔPSF n )

[0031] Generate negative interference:

[0032] η1=η1-Δη1

[0033] PSF neg =η1×PSF0+(1-η1)×(PSF) n -ΔPSF n )

[0034] Step 4: After determining the generation of positive and negative interference, obtain the image under positive interference through inverse filtering. and images under negative interference Further calculations yielded the positive performance index J. + and negative performance index J - The relevant calculations are as follows:

[0035] Positive performance metrics:

[0036]

[0037] Negative performance metrics:

[0038]

[0039] Step 5: After obtaining the positive and negative performance metrics, further iteratively update the PSF and η of the image to find the optimal path. The specific expressions for the relevant iterative updates are as follows:

[0040] PSF n (k+1) =PSF n (k) +γ1×(J +(k) -J -(k) )×ΔPSF n (k)

[0041] η1 (k+1) =η1 (k) +γ2×(J +(k) -J -(k) )×Δη1 (k)

[0042] In the above expression, It refers to the point spread function at time k+1 during the iteration process. This refers to the point spread function at time k during the iteration process, while This refers to the random perturbation at iteration k, and J in the above equation... +(k) With J -(k) They represent the passage at time k. and The evaluation metric for the recovered image after inverse filtering is defined as follows: The image evaluation metric J is defined as...

[0043]

[0044] In the formula, I(x,y) is the enhanced image gray level obtained by the first optimization, (x,y) is the image coordinate, and M and N are the resolutions of the image in the x and y directions;

[0045] Step 6: Calculate the fitness J for the random disturbance generated in Step 5, and find the optimal PSF. n and η1;

[0046] Step 7: Determine if the fitness J has reached the convergence condition. If it has not converged, repeat steps 4 to 6; if it has converged, obtain the PSF. n The optimal values ​​of η1;

[0047] Step 8: Replace the image with one of different details and grayscale distribution, and repeat steps 1 to 7 to obtain a new PSF. n The optimal values ​​of η1 and η1 are then calculated, and finally, the average of the obtained optimal values ​​is taken to obtain the result. as well as Substituting the obtained parameters into the following formula, we obtain the equivalent PSF of the FZP imaging system:

[0048]

[0049] Step 9: Based on the imaging model from Step 1, obtain a method for rapid image enhancement;

[0050]

[0051] Finally, the FZP image can be quickly restored by using a two-dimensional inverse fast Fourier transform.

[0052] Compared with the prior art, the advantages of the present invention are as follows:

[0053] This invention provides a diffraction imaging system and an image restoration method based on the SPGD algorithm. Specifically, it is a method for iterative optimization of the point spread function and image enhancement of an FZP imaging system based on stochastic parallel gradient descent (SPGD). This method is applicable to point spread function optimization and image enhancement of diffraction imaging systems such as Fresnel zone plates, photon sieves, and thin-film mosaic telescopes. For different diffraction imaging systems, the diffraction efficiency of the imaging order and the corresponding point spread function can be experimentally measured. The optimal diffraction efficiency and the equivalent point spread function of the non-imaging light are solved through an optimization algorithm, ultimately obtaining the optimal value of the point spread function of the diffraction imaging system. Based on the imaging model, rapid image enhancement is achieved using a two-dimensional inverse Fourier transform. This image enhancement method has advantages such as low algorithm complexity and high real-time performance. It reduces or even eliminates the influence of unavoidable manufacturing errors, material deformation, and random errors caused by the concentric circular structure of FZP in optical systems. This provides conditions for wavefront distortion correction and image post-processing in online thin-film diffraction imaging systems, improving the imaging quality of thin-film diffraction imaging systems. Attached Figure Description

[0054] Figure 1 A schematic diagram of the device for a diffraction imaging model acquisition and image enhancement method based on SPGD proposed in this embodiment;

[0055] Figure 2 An experimental diagram of the apparatus for a diffraction imaging model acquisition and image enhancement method based on SPGD proposed in this embodiment;

[0056] Figure 3 The point spread function corresponding to the principal diffracted light of the FZP imaging system;

[0057] Figure 4 The convergence curve of the equivalent point spread function corresponding to the non-imaging diffracted light of the FZP imaging system;

[0058] Figure 5 (a) to (d) are the equivalent point spread functions corresponding to the non-imaging diffraction light of the FZP imaging system for Jupiter, Forest 3, River 2 and Coast 2, respectively.

[0059] Figure 6 (a) to (d) are the equivalent point spread functions of the FZP imaging systems for Jupiter, Forest 3, River 2 and Coast 2, respectively.

[0060] Figure 7 These are actual FZP imaging images of Jupiter, Forest 3, River 2, and Coast 2, respectively.

[0061] Figure 8 A flowchart of iterative optimization of the equivalent point spread function in the diffraction imaging model based on SPGD;

[0062] Figure 9 These are fast-reconstructed images of Jupiter, Forest 3, River 2, and Coast 2 based on the FZP imaging model.

[0063] Figure label:

[0064] 1-Point light source; 2-Monochrome extended light source; 3-Imaging target film; 4-Far-field lens; 5-Fresnel lens; 6-Band-contraction lens; 7-Imaging detection camera; 8-Computer. Detailed Implementation

[0065] The specific implementation of the present invention is described below with reference to embodiments:

[0066] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0067] Furthermore, the terms such as "upper," "lower," "left," "right," "middle," and "one" used in this specification are merely for clarity of description and are not intended to limit the scope of the invention. Any changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0068] Example 1:

[0069] like Figure 1 and 2 As shown, in one embodiment, the experimental imaging system uses a monochromatic light source to illuminate the imaging object. The light beam passes through a remote lens, making the imaging target appear as if at infinity. The imaging beam is focused by an FZP (Focused Focusing Point), and a beam-shrinking lens adjusts the beam passing through the FZP to fit the target surface of the imaging camera. The camera acquires the image and uploads it to a control computer via Ethernet for image reconstruction.

[0070] like Figures 3-9 As shown, the specific implementation steps are as follows:

[0071] Step 1: Switch the light source and imaging target film to point light source, and use the camera to acquire the focal plane image of the principal order diffraction light of FZP, i.e., FZP principal order PSF1;

[0072] Step 2: Equivalent all non-imaging-order diffraction imaging systems to PSF n The FZP imaging model is established by initializing with a zero matrix and substituting the point spread function PSF1 and diffraction efficiency corresponding to the primary and secondary beams of the imaging into η1.

[0073]

[0074] In the formula, I represents the image acquired by the camera from the FZP imaging system, I0 represents the imaging target, and w represents the imaging noise. This represents convolution. For the above expression... Perform a Fourier transform, simplify, and then perform an inverse Fourier transform to obtain...

[0075]

[0076] Further modifications can yield the relevant imaging model.

[0077]

[0078] In the formula, FFT2 and IFFT2 are the two-dimensional Fourier transforms and inverse transforms, respectively. The FZP imaging system can acquire the actual image I, the principal-level spot spread function PSF1, and the corresponding diffraction efficiency η1. The PSF1 is iteratively optimized using the SPGD algorithm. n The correction value for the diffraction efficiency η1 is used below to optimize the equivalent point spread function and diffraction efficiency of multi-level diffraction using SPGD.

[0079] Step 3: Based on the corresponding imaging model parameters and SPGD, generate random disturbances Δη1 and ΔPSF. n Based on the generated random interference, positive and negative interference are further generated. The specific generation expressions and related processes are as follows:

[0080] Generate positive interference:

[0081] η1=η1+Δη1

[0082] PSF pos =η1×PSF0+(1-η1)×(PSF) n +ΔPSF n )

[0083] Generate negative interference:

[0084] η1=η1-Δη1

[0085] PSF neg =η1×PSF0+(1-η1)×(PSF) n -ΔPSF n )

[0086] Step 4: After determining the generation of positive and negative interference, obtain the image under positive interference through inverse filtering. and images under negative interference Further calculations yielded the positive performance index J. +and negative performance index J - The relevant calculations are as follows:

[0087] Positive performance metrics:

[0088]

[0089] Negative performance metrics:

[0090]

[0091] Step 5: After obtaining the positive and negative performance metrics, further iteratively update the PSF and η of the image to find the optimal path. The specific expressions for the relevant iterative updates are as follows.

[0092] PSF n (k+1) =PSF n (k) +γ1×(J +(k) -J -(k) )×ΔPSF n (k)

[0093] η1 (k+1) =η1 (k) +γ2×(J +(k) -J -(k) )×Δη1 (k)

[0094] In the above expression, It refers to the point spread function at time k+1 during the iteration process. This refers to the point spread function at time k during the iteration process, while This refers to the random perturbation at iteration k. Meanwhile, J in the above equation... +(k) With J -(k) They represent the passage at time k. and The evaluation metric for the recovered image after inverse filtering is defined as follows: The image evaluation metric J is defined as...

[0095]

[0096] In the formula, I(x,y) is the enhanced image gray level obtained by the first optimization, (x,y) is the image coordinate, and M and N are the resolutions of the image in the x and y directions.

[0097] Step 6: Calculate the fitness J for the random disturbance generated in Step 5, and find the optimal PSF. n And η1.

[0098] Step 7: Determine if the fitness J has reached the convergence condition. If it has not converged, repeat steps 4 to 6; if it has converged, obtain the PSF. n The optimal values ​​of η1 and η2.

[0099] Step 8: Replace the image with one of different details and grayscale distribution, and repeat steps 1 to 7 to obtain a new PSF. n The optimal values ​​of η1 and η1 are then calculated, and finally, the average of the obtained optimal values ​​is taken to obtain the result. as well as Substituting the obtained parameters into the following formula, we can obtain the equivalent PSF of the FZP imaging system.

[0100]

[0101] Step 9: Based on the imaging model in Step 1, obtain a method for rapid image enhancement.

[0102]

[0103] Finally, the FZP image can be quickly restored by using a two-dimensional inverse fast Fourier transform.

[0104] In summary, this invention implements a method for acquiring a diffraction imaging model and enhancing an image using SPGD. The beams emitted from a point light source 1 and a monochromatic extended light source 2 pass through an imaging target 3 and an equivalent far-field lens 4 before reaching a Fresnel lens 5, and then through a beam-contracting lens 6 before entering an imaging detection camera 7 for imaging. The experimental imaging system uses a point light source and an equivalent far-field lens to generate a parallel beam. After being converged and imaged by an FZP (Focus-Zip Diffusion Function), the camera acquires the spot image of its focal plane, i.e., the measured value of PSF1, as the initial value for SPGD. Through stochastic parallel gradient descent (SPGD), the optimal values ​​of the diffraction efficiency and point spread function of the FZP are obtained. Based on the model FZP imaging, a two-dimensional inverse Fourier transform is used to achieve rapid enhancement of the FZP image.

[0105] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

[0106] Many other changes and modifications can be made without departing from the concept and scope of this invention. It should be understood that this invention is not limited to the specific embodiments, and the scope of this invention is defined by the appended claims.

Claims

1. A diffraction imaging system, characterized in that, The imaging system includes: a point light source and a monochromatic extended light source arranged sequentially along the optical axis of the point light source, an imaging target film, a far-field lens, a Fresnel lens (FZP), a beam-shrinking lens, and an imaging detection camera. The system also includes: a computer; the imaging detection camera is signal-connected to the computer.

2. The diffraction imaging system according to claim 1, characterized in that, The light beam emitted by the point light source or monochromatic extended light source passes through the imaging target film and the far-field lens to reach the Fresnel lens FZP, and then passes through the beam-shrinking lens to enter the imaging detection camera for imaging.

3. The diffraction imaging system according to claim 1, characterized in that, The computer is equipped with an image restoration processing unit, which is used to acquire the FZP diffraction efficiency measurement value η1 and the PSF1 corresponding to the principal order, and then optimize the equivalent point spread function PSF of other orders through SPGD iteration. n By combining the diffraction efficiency with the point spread function and diffraction efficiency at the optimal point, and then incorporating these into an inverse filter based on the imaging model with adjustable filter radius and frequency component thresholds, image restoration of the FZP imaging system can be achieved.

4. An image restoration method based on the SPGD algorithm, characterized in that, The method is applied to the system according to any one of claims 1-3, and the method comprises: Step 1: Switch the light source and imaging target film to point light source, and use the camera to acquire the focal plane image of the principal order diffraction light of FZP, i.e., FZP principal order PSF1; Step 2: Equivalent all non-imaging-order diffraction imaging systems to PSF n The FZP imaging model is established by initializing with a zero matrix and substituting the point spread function PSF1 and diffraction efficiency corresponding to the primary and secondary beams of the imaging into η1. In the formula, I represents the image acquired by the camera from the FZP imaging system, I0 represents the imaging target, and w represents the imaging noise. To represent convolution, the above expression... Perform a Fourier transform, simplify, and then perform an inverse Fourier transform to obtain: Further modifications yield the relevant imaging model: In the formula, FFT2 and IFFT2 are the two-dimensional Fourier transforms and inverse transforms, respectively. The FZP imaging system can acquire the actual image I, the principal-level spot spread function PSF1, and the corresponding diffraction efficiency η1. The PSF1 is iteratively optimized using the SPGD algorithm. n The correction value for the diffraction efficiency η1 is used below to optimize the equivalent point spread function and diffraction efficiency of multi-level diffraction using SPGD. Step 3: Based on the corresponding imaging model parameters and SPGD, generate random disturbances Δη1 and ΔPSF. n Based on the generated random interference, positive and negative interference are further generated. The specific generation expressions and related processes are as follows: Generate positive interference: η1=η1+Δη1 PSF pos =η1×PSF0+(1-η1)×(PSF n +ΔPSF n ) Generate negative interference: η1=η1-Δη1 PSF neg =η1×PSF0+(1-η1)×(PSF n -ΔPSF n ) Step 4: After determining the generation of positive and negative interference, obtain the image under positive interference through inverse filtering. and images under negative interference Further calculations yielded the positive performance index J. + and negative performance index J - The relevant calculations are as follows: Positive performance metrics: Negative performance metrics: Step 5: After obtaining the positive and negative performance metrics, further iteratively update the PSF and η of the image to find the optimal path. The specific expressions for the relevant iterative updates are as follows: PSF n (k+1) =PSF n (k) +γ1×(J +(k) -J -(k) )×ΔPSF n (k) η1 (k+1) =η1 (k) +γ2×(J +(k) -J -(k) )×Δη1 (k) In the above expression, It refers to the point spread function at time k+1 during the iteration process. This refers to the point spread function at time k during the iteration process, while This refers to the random perturbation at iteration k, and J in the above equation... +(k) With J -(k) They represent the passage at time k. and The evaluation metric for the recovered image after inverse filtering is defined as follows: The image evaluation metric J is defined as... In the formula, I(x,y) is the enhanced image gray level obtained by the first optimization, (x,y) is the image coordinate, and M and N are the resolutions of the image in the x and y directions; Step 6: Calculate the fitness J for the random disturbance generated in Step 5, and find the optimal PSF. n and η1; Step 7: Determine if the fitness J has reached the convergence condition. If it has not converged, repeat steps 4 to 6; if it has converged, obtain the PSF. n The optimal values ​​of η1; Step 8: Replace the image with one of different details and grayscale distribution, and repeat steps 1 to 7 to obtain a new PSF. n The optimal values ​​of η1 and η1 are then calculated, and finally, the average of the obtained optimal values ​​is taken to obtain the result. as well as Substituting the obtained parameters into the following formula, we obtain the equivalent PSF of the FZP imaging system: Step 9: Based on the imaging model from Step 1, obtain a method for rapid image enhancement; Finally, the FZP image can be quickly restored by using a two-dimensional inverse fast Fourier transform.

Images