Non-planar symmetric free-form surface off-axis three-reflector light number joint optimization method

Abstract

The invention relates to an optical system optimization method, in particular to a non-planar symmetric free-form surface off-axis three-mirror light number joint optimization method. According to the method, a secondary mirror and an image plane in a traditional plane symmetric off-axis three-mirror optical system are placed along the X axis, the volume limitation of the system in the Y-axis direction is relaxed, and the space in the X-axis direction in a cubic space is fully utilized; and then under the condition that the system index reaches the limit through optical design, the system index is further improved, the image quality is reduced at the moment, and the image is recovered through image processing subsequently. Finally, optical system parameters and neural network model parameters serve as optimization variables at the same time, joint optimization is carried out, and a better solution is obtained. The entrance pupil diameter and the focal length of the optical system can be greatly increased under the limitation of a limited cube volume.

Description

Technical Field

[0001] The present invention relates to an optical system optimization method, and particularly to a light-number joint optimization method for an off-axis three-reflection system with a non-planar symmetric free-form surface. Background Art

[0002] Optical systems are mainly divided into two categories: transmissive and reflective. Reflective optical systems are widely used in the field of space cameras due to their advantages such as achromatism, low energy loss, and insensitivity to temperature changes. Reflective optical systems can be further divided into coaxial and off-axis types in terms of structure. The off-axis system can avoid the problem of light blocking, but it will introduce high-order aberrations, and the free-form surface can well correct these aberrations with its powerful design freedom. A cube satellite is a small standardized satellite with a volume of only a few cubic decimeters. Due to the reduced cost, this type of satellite is becoming increasingly popular in scientific missions. However, it is a challenge to install a long-focus system in a small volume such as a cube satellite, especially for a reflective system. Most of the existing free-form surface off-axis reflective imaging optical systems are planar symmetric, that is, assuming that light is incident along the Z-axis, the system is only off-axis in the Y-axis direction and is symmetric about the YZ plane in the X-axis direction, which leads to a waste of space in the X-axis direction within the cube.

[0003] At the same time, the ability of the free-form surface is not infinite. How to further improve the system index when the traditional optical design reaches its limit is a difficult problem. In recent years, with the booming development of deep learning in the field of computer vision, image restoration technology based on neural networks has gradually become the focus of attention. Traditional image restoration only focuses on image processing and does not adjust the system itself. If geometric optical design and image restoration are combined for joint optimization, better solutions can be found, thereby obtaining higher-quality image output. In the design of a free-form surface optical system, if a convolutional neural network is introduced for image restoration, the advantages of free-form surface optics and image restoration neural networks can be fully integrated and utilized to further improve the system index while maintaining good image performance after image restoration. Summary of the Invention

[0004] The object of the present invention is to solve the technical problem that when installing a long-focus system in a cube satellite, it is easily restricted by the volume, resulting in a small focal length, and to provide a light-number joint optimization method for an off-axis three-reflection system with a non-planar symmetric free-form surface.

[0005] The technical concept of the present invention is as follows:

[0006] Based on a reference design of a structurally similar spherical off-axis three-mirror optical system, the system parameters are modified in the optical design software Zemax and free-form surface polynomials are added for optimization. During this process, parameters such as the maximum volume, field of view, and F-number of the system are kept unchanged, and the largest possible entrance pupil diameter and focal length are pursued on the premise that the imaging quality of the system reaches the diffraction limit. The powerful design freedom of the free-form surface can correct high-order off-axis aberrations. Assuming that the light incident direction is the Z-axis direction and the system is off-axis in the Y-axis direction, if the secondary mirror and the image plane in the off-axis three-mirror optical system are placed along the X-axis, the volume limitation of the system in the Y-axis direction can be relaxed, making full use of the space in the X-axis direction within the cubic space, thereby improving the system indicators. When the traditional optical design reaches its limit, if one wants to further increase the entrance pupil and focal length of the system, the imaging quality will inevitably decline, but subsequent image processing can be added to restore the image. Using a neural network alone to restore the blurred image formed by the optical system can improve the image quality within a limited range, but if the optical system parameters and the neural network model parameters are simultaneously used as optimization variables for joint optimization, a better solution can be obtained.

[0007] To achieve the above object and based on the above concept, the technical solution adopted by the present invention is as follows:

[0008] A method for jointly optimizing the F-number of a non-planar symmetric free-form surface optical system, which is characterized in that:

[0009] 1. Optimize a planar symmetric free-form surface off-axis three-mirror optical system based on the reference design, and represent its free-form surface using a fifth-order xy polynomial;

[0010] 2. Change the spatial structure of the optical system, set the secondary mirror and the image plane in the optical system along the X-axis, then set the tilting amounts of all the reflecting mirrors in the optical system with respect to their respective Y-axes as variables, set the tilting amount of the third mirror with respect to the X-axis to 0, and at the same time set all the polynomial coefficients in the fifth-order xy polynomial as variables; finally, optimize the optical system by modifying the variables until the optimization target is reached; the optimization target is: keep the maximum volume, field of view, and F-number of the optical system unchanged, and pursue the largest possible entrance pupil diameter and focal length on the premise that the imaging quality of the optical system reaches the diffraction limit;

[0011] 3. Further increase the entrance pupil diameter and focal length of the optical system and optimize. At this time, the spot diagram of the optical system deteriorates, and the subsequent blurred image restoration effect is related to the degree of deterioration of the spot diagram. In the present invention, the average RMS radius of the spot diagram in each field of view is about five times the pixel size;

[0012] 4. Select a set number of common data sets as training samples, simulate the blurred images formed after further increasing the entrance pupil diameter and focal length through the optical system based on the training samples, and use them as the input of a pre-set U-net neural network;

[0013] 5】Restore the blurred image using the U-net neural network, taking the variables of the optical system and the model parameters of the U-net neural network as optimization variables simultaneously, and performing joint optimization until the set training cycle is reached, thus completing the optical number joint optimization of the non-planar symmetric free-form surface optical system.

[0014] Further, step 4 is specifically as follows: 4.1】Export the optical system parameters after executing step 3 to Python; in the Pytorch library of Python, tensors therein will automatically create a computational graph during the calculation process, so that the gradients of the loss function with respect to each optimization variable can be easily obtained;

[0015] 4.2】Obtain the point spread function of each sub-region of the field of view of the optical system through ray tracing. Generally speaking, the PSF is different on different fields of view. Due to the limitations of computer memory and calculation time, we can approximately consider that the point spread function is spatially invariant within the sub-region of the entire field of view. To obtain the point spread function of a certain field point on the imaging plane, trace N rays with different pupil coordinates of this field point from the object space to the image plane. The intensity distribution of each ray on the image plane can be approximated as a Gaussian distribution. The intensity of all characteristic rays is superimposed to obtain the point spread function of this field point: Its expression is:

[0016]

[0017] where: PSF represents the point spread function, K represents the shape size of the PSF, and N represents the number of characteristic rays for ray tracing;

[0018] 4.3】Convolve each sub-region in the original image with the point spread function PSF of the corresponding sub-region, and then splice them to obtain a simulated blurred image, and use it as the input of the pre-set U-net neural network. Its expression is as follows:

[0019] IMG p,q =OBJ p,q *PSF p,q

[0020] where: IMG p,q represents the blurred image, OBJ p,q represents the original image, and p and q represent the numbers of the sub-regions.

[0021] Further, in step 4.2, taking the intersection point of the chief ray and the image plane during ray tracing as the grid center of the point spread function PSF, then the expression of the intensity distribution of one of the characteristic rays during ray tracing is as follows:

[0022]

[0023] Wherein: represents the intensity distribution of the characteristic light ray, r represents the distance from the intersection point of the characteristic light ray and the image plane to the intersection point of the chief ray and the image plane, is the physical size of each grid of the point spread function PSF, so the radius A circle within can obtain 98.89% of the energy.

[0024] Furthermore, step 5 is specifically as follows: [5.1] Input the blurred image obtained in step 4 into the U-net neural network for restoration. The U-net neural network has relatively wide applications in the fields of image segmentation and image restoration;

[0025] [5.2] First, perform digital optimization in the optical-digital joint optimization. Calculate the structural similarity SSIM between the restored image of the U-net neural network and the clear image. The range of the structural similarity SSIM is between 0 and 1, and the larger the value, the more similar the two images are; and use 1 - SSIM as the loss function of the U-net neural network, perform backpropagation, and update and optimize the model parameters of the U-net neural network using the loss function;

[0026] [5.3] Then, perform optical optimization in the optical-digital joint optimization. Calculate the loss function 1 - SSIM of the restored image dimension and the gradients of the loss function of the optical system dimension with respect to each parameter of the optical system, so as to update and optimize the optical system parameters. The loss function of the optical system dimension includes: the volume, obscuration, focal length, and distortion of the optical system; It should be noted that although it is not required that the blur spots of each field of view of the optical system are very small during the optical-digital joint optimization process, it is still necessary to limit them, otherwise the optical-digital joint optimization will fail;

[0027] [5.4] Repeat steps 5.2 and 5.3 until the preset training cycle is reached, and complete the optical-digital joint optimization of the off-axis three-mirror with a non-planar symmetric free-form surface.

[0028] Furthermore, steps 1, 2, and 3 are all implemented using the optical design software Zemax.

[0029] Furthermore, in step 1, the free-form surface is represented by the following fifth-order xy polynomial:

[0030]

[0031] Wherein: z represents the surface sag, c represents the surface curvature, k represents the conic constant, a i,j represents the free-form surface polynomial coefficient; i and j both represent the powers; M represents the order of the fifth-order xy polynomial.

[0032] The beneficial effects of the present invention are:

[0033] 1. In view of the volume limitation of the cubic shape, the present invention places the secondary mirror and the image plane in the traditional off-axis three-mirror optical system with planar symmetry along the X-axis, greatly alleviating the volume constraint of the optical system in the Y-axis direction. At the same time, the powerful design freedom of the free-form surface is used to correct the high-order off-axis aberration, increasing the entrance pupil diameter and focal length of the optical system.

[0034] 2. The present invention breaks through the limit of traditional optical design by adding subsequent image processing, can restore the image when the imaging quality of the optical system is poor, and different from independent image restoration, takes both the optical system parameters and the model parameters of the neural network as optimization variables for joint optimization to obtain a better solution.

[0035] 3. The optical-number joint optimization method in the present invention is applicable to the design of any optical system. Through subsequent image restoration, it can make up for the problem of poor imaging quality of the optical system and can be widely applied to aspects such as simplification of optical systems and improvement of system indicators. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic structural diagram of a planar-symmetric free-form surface off-axis three-mirror optical system;

[0037] Figure 2 It is a spot diagram and MTF curve diagram of each field of view of a planar-symmetric free-form surface off-axis three-mirror optical system, where (a) is the spot diagram and (b) is the MTF curve diagram;

[0038] Figure 3 It is a schematic structural diagram of a non-planar-symmetric free-form surface off-axis three-mirror optical system;

[0039] Figure 4 It is a spot diagram and MTF curve diagram of each field of view of a non-planar-symmetric free-form surface off-axis three-mirror optical system, where (a) is the spot diagram and (b) is the MTF curve diagram;

[0040] Figure 5 It is a schematic structural diagram of a non-planar-symmetric free-form surface off-axis three-mirror optical system with deteriorated image quality after further increasing the entrance pupil diameter and focal length of the system;

[0041] Figure 6 It is a spot diagram and MTF curve diagram of each field of view of a non-planar-symmetric free-form surface off-axis three-mirror optical system with deteriorated image quality after further increasing the entrance pupil diameter and focal length of the system, where (a) is the spot diagram and (b) is the MTF curve diagram;

[0042] Figure 7 It is a schematic diagram of the optical-number joint optimization process of the embodiment of the present invention;

[0043] Figure 8Schematic diagram of the off-axis three-mirror optical system with a non-planar symmetric free-form surface after joint optimization of optics and numbers

[0044] Figure 9 Spot diagrams and MTF curves of each field of view of the off-axis three-mirror optical system with a non-planar symmetric free-form surface after joint optimization of optics and numbers, where (a) is the spot diagram and (b) is the MTF curve

[0045] Figure 10 Changes in the PSF of each field of view of the optical system before and after joint optimization of optics and numbers, where (a) is the PSF of each field of view before optimization and (b) is the PSF of each field of view after optimization

[0046] Figure 11 Output effects of a certain test image through different systems, where (a) is the clear image, (b) is the image formed by the D36 / f180 small aberration system, (c) is the image formed by the D44 / f220 system, (d) is the image output after joint optimization of optics and numbers, and (e) is the image output by the D44 / f220 system relying on an independent neural network to restore the image Specific implementation mode

[0047] To make the objectives, advantages and features of the present invention clearer, the following further details a joint optimization method of optics and numbers for an off-axis three-mirror with a non-planar symmetric free-form surface proposed by the present invention in combination with the accompanying drawings and specific embodiments. According to the following specific implementation mode, the advantages and features of the present invention will be clearer

[0048] This embodiment aims at a 1U cube satellite with a volume specification of 1dm 3 , and designs a long-focus free-form surface off-axis three-mirror optical system. The specific index requirements are as follows

[0049] Volume: < (80mm) 3 (The length, width and height are respectively < 80mm, leaving enough space for the mechanical structure);

[0050] Field of view: 4° × 4°

[0051] F number: 5

[0052] Aperture stop: Located 80mm in front of the primary mirror

[0053] Obscuration constraint: > 10mm

[0054] Maximum distortion: < 3%

[0055] Free-form surface: Fifth-order xy polynomial

[0056] The free-form surface is represented by the following fifth-order xy polynomial

[0057]

[0058] Among them: z represents the surface sag, c represents the surface curvature, k represents the quadratic constant, a i,j represents the coefficient of the free-form surface polynomial; i and j both represent powers; M represents the order of the fifth-order xy polynomial; x and y represent the coordinates on the free-form surface.

[0059] Optimization goal: Keep the maximum volume, field of view and F number of the optical system unchanged, and pursue the maximum entrance pupil diameter and focal length under the premise that the imaging quality of the optical system reaches the diffraction limit.

[0060] First, optimize the plane-symmetrical free-form off-axis three-mirror optical system, select a reference design with a similar structure, set the entrance pupil diameter and field of view in the system parameter column, and then use operands to control the volume of the optical system and the distance from the edge points of each surface to the surrounding light. Calculate the focal length based on the entrance pupil diameter and F number. The position of a certain field point on the image plane is equal to the focal length multiplied by the tangent of the field of view angle. In addition, it is necessary to control the maximum distortion, the main light passing through the center of the mirror, and the image plane inclination, etc. The free-form surface uses a fifth-order xy polynomial. Since the system is symmetrical about the YZ plane, the free-form surface polynomial only retains the even-order terms of x. Under the premise that the imaging quality reaches the diffraction limit, the plane-symmetrical free-form off-axis three-mirror optical system can be optimized to have a maximum entrance pupil diameter of 24mm and a focal length of 120mm. The optical system structure is as follows: Figure 1 The specific parameters are shown in Table 1:

[0061] Table 1 Surface parameters of the plane-symmetrical free-form surface off-axis three-mirror optical system

[0062] Surface Primary mirror Secondary mirror Tertiary mirror Image plane Radius of curvature (mm) -2.417580941176675E+002 -1.153892425790135E+002 -8.862869215291671E+001 - Central thickness (mm) <![CDATA[-5 . 937114701819261E+001]]> <![CDATA[5 . 261871820057819E+001]]> <![CDATA[-5 . 419780413893162E+001]]> - Rotation about X-axis (°) <![CDATA[2 . 089603234130396E+001]]> <![CDATA[-2 . 330517247539374E+001]]> <![CDATA[1 . 169141044827727E+001]]> <![CDATA[-1 . 500000006047827E+001]]> Rotation about Y-axis (°) 0 0 0 0 <![CDATA[a 01 > 3.406954259006000E-011 6.009499627512000E-011 -7.632212867316000E-011 - <![CDATA[a 20 > -6.170441876347000E-004 -3.037328741443000E-003 4.167455216156000E-004 - <![CDATA[a 02 > -4.737512139459000E-004 -4.136945962464000E-003 -1.009897603943000E-005 - <![CDATA[a 21 > -4.639995913529000E-006 -1.119376897454000E-005 3.887986746616000E-006 - <![CDATA[a 03 > -5.491708146524000E-006 -4.471150180480000E-005 -3.578349183157000E-006 - <![CDATA[a 40 > 1.490881965975000E-008 1.029470088125000E-007 3.531713203042000E-008 - <![CDATA[a 22 > 1.267645600740000E-008 -5.573593289524000E-007 1.265147824312000E-008 - <![CDATA[a 04 > -1.011024608316000E-009 -7.591463265940000E-007 -4.294839907065000E-008 - <![CDATA[a 41 > 9.064402783124999E-011 1.309569332345000E-008 1.073884481293000E-009 - <![CDATA[a 23 > -1.538210549984000E-011 1.079906477413000E-008 9.727178152306000E-010 - <![CDATA[a 05 > -5.140148352928000E-011 -3.530831297445000E-009 -1.329644415733000E-010 -

[0063] like Figure 2 The figure shows the point diagram and MTF curve of each field of view of the plane symmetrical free-form surface off-axis three-mirror optical system. Figure 2 (a) is the spot diagram, Figure 2 (b) is the MTF (transfer function) curve. From the point diagram, it can be seen that the mean square radius of the diffuse spot in each field of view is smaller than the Airy disk. From the MTF diagram, it can be seen that when the Nyquist frequency is 17lp / mm (pixel size 30μm), the optical system MTF is better than 0.9, close to the diffraction limit, and the surface system imaging quality is good.

[0064] Secondly, optimize the off-axis three-mirror optical system with a non-planar symmetric free-form surface. Based on the above planar symmetric system, set the secondary mirror and the image plane in the optical system along the X-axis, set all the tilting amounts of the three mirror reflectors with respect to their respective Y-axes as variables, set the tilting amount of the three mirrors with respect to the X-axis to 0, and set all the polynomial coefficients of the fifth-order XY polynomial of the free-form surface as variables. On the premise that the imaging quality reaches the diffraction limit, the maximum entrance pupil diameter that the non-planar symmetric system can optimize is 36 mm, and the focal length is 180 mm, which is a 50% improvement compared to the planar symmetric system. The system structure is as shown in Figure 3 shown, and the specific parameters are shown in Table 2:

[0065] Table 2 Parameters of each surface of the non-planar symmetric system

[0066]

[0067]

[0068] As shown in Figure 4 are the spot diagrams and MTF curves of each field of view of the off-axis three-mirror optical system with a non-planar symmetric free-form surface, where Figure 4 (a) is the spot diagram, Figure 4 (b) is the MTF curve. It can be seen from the spot diagram that the root mean square radius of the blur spots in each field of view is less than the Airy disk. It can be seen from the transfer function diagram that when the Nyquist frequency is 17 lp / mm (pixel size 30 μm), the system MTF is better than 0.9, approaching the diffraction limit, indicating that the imaging quality of the surface system is good.

[0069] Further increase the system entrance pupil diameter to 44 mm and the focal length to 220 mm and optimize. At this time, the imaging quality deteriorates. The structure of the optimized optical system is as shown in Figure 5 shown, and the specific parameters are shown in Table 3:

[0070] Table 3 Parameters of each surface of the non-planar symmetric system with deteriorated image quality

[0071]

[0072]

[0073] As shown in Figure 6 are the spot diagrams and MTF curves of each field of view of the off-axis three-mirror optical system with a non-planar symmetric free-form surface and deteriorated image quality, where Figure 6 (a) is the spot diagram, Figure 6 (b) is the MTF curve. It can be seen from the spot diagram that the average root mean square radius of the blur spots in each field of view is about 147 μm, and the maximum geometric radius is about 629 μm. At the same time, the system MTF is also very poor.

[0074] Subsequently, the image is restored through a neural network, and optical-digital joint optimization is performed. In this embodiment, 400 images are selected from the public dataset DIV2K as the training set, with a batch size of 8. A total of 50 batches are trained completely once as one cycle. First, the optical system parameters after executing step 3 are exported to Python; then, the point spread function of each sub-region of the field of view of the optical system is obtained through ray tracing, and its expression is:

[0075]

[0076] where: PSF represents the point spread function, K represents the shape and size of the PSF, and N represents the number of characteristic rays for ray tracing;

[0077] Taking the intersection point of the chief ray and the image plane during ray tracing as the grid center of the point spread function PSF, the intensity distribution expression of one of the characteristic rays during ray tracing is as follows:

[0078]

[0079] where, represents the intensity distribution of the characteristic ray, r represents the distance from the intersection point of the characteristic ray and the image plane to the intersection point of the chief ray and the image plane, is the physical size of each grid of the point spread function PSF.

[0080] Finally, each sub-region in the original image is convolved with the point spread function PSF of the corresponding sub-region, and then stitched to obtain a simulated blurred image, and its expression is as follows:

[0081] IMG p,q =OBJ p,q *PSF p,q 。

[0082] where: IMG p,q represents the blurred image, OBJ p,q represents the original image, and p and q represent the sub-region numbers.

[0083] In this embodiment, 7×7 fields of view are sampled, with 900 characteristic rays in each field of view. The PSFs of these 49 fields of view are obtained through ray tracing, and then the PSFs of 13×13, a total of 169 fields of view, are obtained through interpolation, and then convolved with the corresponding parts of the clear image to obtain the blurred image formed by the simulated optical system.

[0084] The blurred image is restored by using the U-net neural network, and the variables of the optical system and the model parameters of the U-net neural network are jointly optimized as optimization variables at the same time. The digital optimization and optical optimization in the optical-numerical joint optimization are completed for the same batch of images respectively. Specifically, the digital optimization in the optical-numerical joint optimization is firstly performed to obtain the structural similarity SSIM between the restored image of the U-net neural network and the clear image, and the range of the structural similarity SSIM is between 0 and 1. 1-SSIM is used as the loss function of the U-net neural network, and the model parameters of the U-net neural network are updated and optimized by using the loss function. Then, the optical optimization in the optical-numerical joint optimization is performed to obtain the loss function 1-SSIM of the restored image dimension and the gradient of the loss function of the optical system dimension for each parameter of the optical system, so as to update and optimize the optical system parameters, wherein the loss function of the optical system dimension includes: the volume, occlusion, focal length and distortion of the optical system.

[0085] The learning rate of the neural network model parameters is set to 1e-4, the learning rate of the surface curvature radius, center thickness, rotation angle around the X axis, and rotation angle around the Y axis in the optical system is set to 1e-4, and the learning rate of the free-form surface polynomial coefficient is set to the absolute value of the original value × 1e-8. In order to prevent the gradient from being too large at certain moments and causing instability in training, a gradient clipping operation is added to the gradient of the optical system parameters to limit it. The entire training process includes 100 cycles. After 80 cycles, the learning rate of each parameter decays exponentially with a decay factor of 0.9.

[0086] The optical-digital joint optimization process is as follows: Figure 7 As shown in Figure 2, the optimized optical system structure is as follows: Figure 8 The specific parameters are shown in Table 4:

[0087] Table 4 Surface parameters of non-planar symmetric system after optical-numerical joint optimization

[0088]

[0089]

[0090] like Figure 9 The figure shows the point diagram and MTF curve of each field of view of a non-planar symmetrical free-form surface off-axis three-mirror optical system with deteriorated image quality. Figure 9 (a) is the spot diagram, Figure 9 (b) is the MTF curve. From the point diagram, it can be seen that the average mean square radius of the diffuse spot in each field of view has increased compared to before the joint optimization of the number of light, but the shape of the diffuse spot in each field of view is more similar, which is conducive to the neural network to extract the features of the blurred image. Similarly, the MTF curves of each field of view are also more similar. Figure 10Shown is the change in the PSF of each field of view of the optical system before and after the joint optimization of the optical and numerical apertures. Among them, Figure 10 (a) is the PSF of each field of view before optimization, Figure 10 (b) is the PSF of each field of view after optimization. It can be more intuitively seen from this that the PSF of each field of view before and after optimization tends to be consistent.

[0091] Another 100 images were selected from the public dataset DIV2K as the test set. First, the image formed by a non-planar symmetric optical system with an entrance pupil diameter of 36 mm was simulated, and its PSNR and SSIM with the clear image were calculated. Secondly, the image formed by a non-planar symmetric optical system with an entrance pupil diameter of 44 mm was simulated and the PSNR and SSIM were calculated. Finally, the PSNR and SSIM of the restored image after the joint optimization of the optical and numerical apertures were calculated, including two steps: simulating the image formed by the jointly optimized optical system and the neural network restored image. In addition, in order to show the advantage of the joint optimization of the optical and numerical apertures compared with simply relying on the neural network to restore the image, a comparative experiment was also conducted in this embodiment. Except for not changing the optical system parameters, the rest of the training process was the same as that of the joint optimization training process of the optical and numerical apertures, and the PSNR and SSIM of its output image and the clear image were calculated. The results are shown in Table 5:

[0092] Table 5 Quantitative evaluation of the average PSNR and SSIM of the test dataset

[0093]

[0094] It can be seen from the table that the output image of the system after the joint optimization of the optical and numerical apertures has only a slight quality degradation compared with the small aberration system, which is within an acceptable range. At the same time, the entrance pupil diameter and focal length of the system are effectively increased. Compared with simply relying on the independent neural network to restore the image, the joint optimization of the optical and numerical apertures shows obvious advantages.

[0095] As Figure 11 shown is the output effect of a certain test image through different systems. Among them, Figure 11 (a) is the clear image, Figure 11 (b) is the image formed by the D36 / f180 small aberration system, Figure 11 (c) is the image formed by the D44 / f220 system, Figure 11 (d) is the image output after the joint optimization of the optical and numerical apertures, Figure 11 (e) is the image output by the D44 / f220 system relying on the independent neural network to restore the image.

Claims

1. A method for jointly optimizing the optical numbers of an off-axis three-mirror system with a non-planar symmetric free-form surface, characterized in that It includes the following steps:

1. Optimize a planar symmetric free-form off-axis three-mirror optical system based on a reference design, and represent its free-form surface by a fifth-order xy polynomial; 2. Place the secondary mirror and the image plane in the optical system along the X-axis. Then, set the tilting amounts of all the reflecting mirrors in the optical system with respect to their respective Y-axes as variables, set the tilting amount of the tertiary mirror with respect to the X-axis to 0, and at the same time set all the polynomial coefficients in the fifth-order xy polynomial as variables. Finally, optimize the optical system by modifying the variables until the optimization goal is achieved. The optimization goal is: while keeping the maximum volume, field of view, and F-number of the optical system unchanged, pursue the maximum entrance pupil diameter and focal length on the premise that the imaging quality of the optical system reaches the diffraction limit; 3. Further increase the entrance pupil diameter and focal length of the optical system; 4. Select a set number of public data sets as training samples. Based on the training samples, simulate the blurred images formed after further increasing the entrance pupil diameter and focal length through the optical system, and use them as the input to a pre-set U-net neural network; 5. Use the U-net neural network to restore the blurred images. Take the variables of the optical system and the model parameters of the U-net neural network as optimization variables simultaneously, and perform joint optimization until the set training cycle is reached, completing the optical number joint optimization of the non-planar symmetric free-form off-axis three-mirror system.

2. The optical number joint optimization method for an off-axis three-mirror anastigmat with a non-planar symmetric freeform surface according to claim 1, wherein Step 4 is specifically as follows: 4.1 Export the optical system parameters after executing Step 3 to Python; 4.2 Obtain the point spread function of each sub-region of the field of view of the optical system through ray tracing. Its expression is: where: PSF represents the point spread function, K represents the shape size of the PSF, and N represents the number of characteristic rays for ray tracing; 4.3 Convolve each sub-region in the original image with the point spread function PSF of the corresponding sub-region, and then splice them to obtain the simulated blurred image, which is used as the input to a pre-set U-net neural network. Its expression is as follows: IMG p,q = OBJ p,q *PSF p,q Where: IMG p,q represents a blurred image, OBJ p,q represents the original image, and p and q represent the numbers of sub-regions.

3. A method for joint optimization of optical number of a non-planar symmetric free-form off-axis three-mirror system according to claim 2, characterized in that: In Step 4.2, take the intersection point of the chief ray and the image plane during ray tracing as the grid center of the point spread function PSF. Then, the intensity distribution expression of one of the characteristic rays during ray tracing is as follows: Wherein: represents the intensity distribution of the characteristic ray, and r represents the distance from the intersection point of the characteristic ray and the image plane to the intersection point of the chief ray and the image plane, Δx×Δy is the physical size of each grid of the point spread function PSF.

4. A method for jointly optimizing the optical numbers of an off-axis three-mirror anastigmat with a non-planar symmetric free-form surface according to any one of claims 1 to 3, characterized in that Step 5 is specifically as follows: 5.1 Input the blurred images obtained in Step 4 into the U-net neural network for restoration; 5.2 First, perform digital optimization in the optical number joint optimization, calculate the structural similarity SSIM between the restored image of the U-net neural network and the clear image. The range of the structural similarity SSIM is between 0 and 1; and use 1 - SSIM as the loss function of the U-net neural network, and update and optimize the model parameters of the U-net neural network using the loss function; 【5.3】 Then perform the optical optimization in the joint optical and numerical optimization, calculate the gradient of the loss function 1-SSIM for the restored image dimension and the loss function for the optical system dimension with respect to each parameter of the optical system, so as to update and optimize the parameters of the optical system. The loss function for the optical system dimension includes: The volume, obscuration, focal length, and distortion of the optical system; 5.4 Repeat Steps 5.2 and 5.3 until the pre-set training cycle is reached, completing the optical number joint optimization of the non-planar symmetric free-form off-axis three-mirror system.

5. A method for joint optimization of optical numbers of an off-axis three-mirror system with a non-planar symmetric free-form surface according to claim 1, characterized in that: Steps 1, 2, and 3 are all implemented using the optical design software Zemax.

6. A method for joint optimization of optical numbers of an off-axis three-mirror system with a non-planar symmetric free-form surface according to claim 5, characterized in that: In step 1, the free-form surface is represented by the following fifth-order xy polynomial: Where: z represents the surface sag, and c represents the surface curvature. k represents the conic constant, a i,j represents the free-form surface polynomial coefficient; both i and j represent the power; M represents the order of the fifth-order xy polynomial.

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