High-performance optical imaging system and method based on all-optical link inverse diffraction calculation
The high-performance optical imaging system through all-optical link inverse diffraction calculation uses active lighting modules, single lenses and cameras, combined with phase recovery and angular spectrum diffraction algorithms, solves the problem of excessive volume and weight of traditional optical imaging systems, and realizes efficient information collection and object reconstruction.
Patent Information
- Application Number
- CN202211175168.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-26
- Publication Date
- 2025-07-25
- Estimated Expiration
- 2042-09-26
AI Technical Summary
Traditional optical imaging systems increase the volume, weight and complexity of the system in the process of correcting aberrations, making perfect imaging impossible.
A high-performance optical imaging system based on all-optical link inverse diffraction calculation is adopted, including an active lighting module, a single lens and a camera. The lens is designed through spatial bandwidth integration conservation, combined with a phase recovery algorithm and an angular spectrum diffraction algorithm to perform information reconstruction, and the object reconstruction is realized using the all-optical link inverse diffraction calculation method.
With fewer optical components, the same amount of information collection and reconstruction as in traditional imaging systems are achieved, significantly reducing the volume and weight of the optical imaging system and reducing costs.
Smart Images
Figure CN115437143B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of optical computational imaging, and particularly to a high-performance optical imaging system and method based on all-optical link inverse diffraction calculation. Background Art
[0002] Traditional optical imaging systems have the characteristic of "what you see is what you get". In order to directly obtain an object on a detector, traditional optical imaging systems focus more on the accurate propagation of object information. Therefore, aberration correction plays a very important role in traditional optical systems. However, aberration correction is essentially an overconstrained problem in mathematics. During the process of correcting aberration, the volume, weight, and complexity of the optical system will increase, and ultimately perfect imaging cannot be achieved.
[0003] Computational Imaging Technology (hereinafter referred to as CIT) is a new imaging mode different from the traditional imaging of "what you see is what you get". Different from traditional imaging that focuses on the accurate propagation of object information, computational imaging pays more attention to the process of obtaining object information. Starting from the process of information acquisition and loss in the entire imaging link, it analyzes the information acquisition and interpretation of the light field. In order to make the system more portable, the lens only serves as a medium for collecting, modulating, and transmitting object information. Different from the point-to-point light ray constraint criterion in traditional imaging, this system designs the lens based on the principle of conservation of spatial bandwidth product to determine the lens surface type parameters. In addition, using the essence of beam transmission, that is, the diffraction transmission of light through optical elements, an imaging method based on all-optical link diffraction calculation is proposed. This method transforms the diffraction transmission of light through the lens into the diffraction transmission calculation between surfaces, which can greatly reduce the complexity brought by measuring the transmission function of the lens. Combining the above two points, a high-performance optical imaging system and method based on all-optical link inverse diffraction calculation can achieve a good imaging effect on the premise of using fewer optical elements. Summary of the Invention
[0004] The present invention aims to provide a high-performance optical imaging system and method based on all-optical link inverse diffraction calculation, which can collect the same amount of information as a traditional imaging system with a simpler system and reconstruct the object through the method of all-optical link inverse diffraction calculation, which greatly reduces the volume and weight of the optical imaging system and reduces the cost of the optical imaging system.
[0005] In order to achieve the above object, the technical solution of the present invention is realized as follows:
[0006] In the first aspect, the present invention provides a high-performance optical imaging system based on all-optical link inverse diffraction calculation, and the system includes an active illumination module, a single lens, and a camera arranged in sequence along the optical axis direction:
[0007] The active illumination module is used to illuminate the object to be imaged;
[0008] The single lens is designed based on the principle of conservation of spatial bandwidth product. According to the required numerical aperture and field of view size, the size of the camera format and the pixel size are selected. According to the angular range of the outgoing light rays required by the pixel size, the surface type parameters of the single lens are determined, and are used to collect, convert and transmit the information of the object to be imaged;
[0009] The camera is used to record the light field intensity information at the target plane and multiple planes behind the target plane;
[0010] Combined with the surface type parameters of the single lens and the light field intensity information, the reconstruction of the object to be imaged is completed through the all-optical link inverse diffraction calculation method.
[0011] Further, the active illumination module includes a coherent light source and a collimating and beam expanding system;
[0012] The coherent light source is a laser light source or a narrowband monochromatic light source, and is used to irradiate the object to be imaged;
[0013] The collimating and beam expanding system is used to collimate and expand the outgoing light beam of the coherent light source, and the beam after collimation and beam expansion is then irradiated onto the object to be imaged.
[0014] Further, the single lens is a spherical lens, an aspherical lens or a free-form surface lens.
[0015] In a second aspect, the present invention provides an imaging method based on all-optical link inverse diffraction calculation, including:
[0016] Irradiate the object to be imaged with a coherent light source, collect, convert and transmit the information of the object to be imaged by a lens to a camera, use the camera to collect the light field intensity information at the target plane and multiple planes behind the target plane of the object to be imaged, and adopt a phase retrieval algorithm to obtain the target plane complex amplitude information;
[0017] Divide the surface type of the lens into multiple segmented curved surface elements, each curved surface element is equivalently replaced by two virtual plane elements located inside and outside the lens, the two virtual plane elements and the curved surface element satisfy the thin lens approximation condition, and the local curvature of the lens is characterized by phase compensation;
[0018] According to the obtained target plane complex amplitude information, perform inverse diffraction propagation from the target plane, and transmit and calculate through the virtual plane elements of the lens to the object plane to realize object reconstruction.
[0019] Further, the adopting a phase retrieval algorithm to obtain the target plane complex amplitude information specifically is:
[0020] Assign an arbitrary initial phase to the target plane Obtain the initial complex amplitude of the target surface where (x, y) represents the pixel coordinates on the target surface, I0(x, y) represents the light field amplitude information at the pixel point (x, y) on the measured target surface, and i represents the imaginary number;
[0021] According to the complex amplitude of the target surface, calculate the complex amplitude information U1(x, y), U2(x, y), and U3(x, y) at three planes d, 2d, and 3d behind the target surface through the angular spectrum diffraction transmission algorithm, and use the measured light field amplitude information to replace the calculated complex amplitude information |U1(x, y)|, |U2(x, y)|, |U3(x, y)|, and obtain the new complex amplitude information U update1 (x, y), U update2 (x, y), U update3 (x, y), and inverse diffractively transmit the updated complex amplitude information to the target surface and take the average to obtain the new complex amplitude of the target surface U update0 (x, y); where, respectively represent the light field amplitude information at the pixel point (x, y) on three planes d, 2d, and 3d behind the target surface;
[0022] Repeat the above process until the root mean square error between the updated target surface amplitude |U update0 (x, y)| and the measured light field amplitude information of the target surface is less than the set threshold ε. At this time, the complex amplitude of the target surface U update0 (x, y) is what is required.
[0023] Furthermore, divide the surface shape of the lens into multiple segmented curved surface elements, and each curved surface element is equivalently replaced by two virtual plane elements located inside and outside the lens. The two virtual plane elements and the curved surface element satisfy the thin lens approximation condition, specifically:
[0024] Divide the incident surface and the exit surface of the lens into N entrance 、N exit curved surface elements. The number of divided curved surface elements is determined by the curvature of the lens. Take the point where the axial distance is the largest z = d max and the smallest z = d min at each curved surface element and extend and construct a pair of equivalent outer plane elements P outer and equivalent inner plane elements P inner , as the equivalent plane group of the curved surface element. The equivalent inner plane element is located inside the lens, and the equivalent outer plane element is located outside the lens. The two satisfy the thin lens approximation condition; compensate for the local curvature of the curved surface element by loading the optical path parallel to the optical axis between the two virtual plane elements as the compensation phase.
[0025] Further, based on the obtained target plane complex amplitude information, inverse diffraction propagation is performed from the target plane, and the calculation is transmitted through the lens to the object plane to achieve object reconstruction. Specifically:
[0026] After obtaining the target plane complex amplitude U update0 (x,y), the angular spectrum inverse diffraction algorithm is used to calculate the complex amplitude distribution U exit,outer (x,y) of the equivalent outer plane element on each curved surface element of the lens exit surface. The complex amplitude distribution U exit,inner (x,y) on the equivalent inner plane element of each curved surface element of the lens exit surface is obtained through phase compensation. The calculation formula is:
[0027]
[0028] In the formula, z2(x,y) represents the axial coordinate of the point (x,y) on the curved surface element of the lens exit surface, d min,exit represents the axial coordinate of the equivalent inner plane element P inner of the curved surface element of the exit surface, d max,exit represents the axial coordinate of the equivalent outer plane element P outer of the curved surface element of the exit surface, n represents the refractive index of the lens, λ represents the central wavelength of the coherent light source, and i represents the imaginary number;
[0029] After obtaining the complex amplitude distribution U exit,inner (x,y) of the equivalent inner plane of each curved surface element of the lens exit surface, the angular spectrum inverse diffraction algorithm is also used to calculate the complex amplitude distribution U entrance,inner (x,y) on the equivalent inner plane of each curved surface element of the lens entrance surface. The complex amplitude distribution U entrance,outer (x,y) on the equivalent outer plane of each curved surface element of the lens entrance surface is obtained through phase compensation. The calculation formula is:
[0030]
[0031] In the formula, z1(x,y) represents the axial coordinate of the point (x,y) on the curved surface element of the lens entrance surface, d min,entrance represents the axial coordinate of the equivalent inner plane element P inner of the curved surface element of the entrance surface, d max,entrance represents the axial coordinate of the equivalent outer plane element P outer of the curved surface element of the entrance surface;
[0032] The complex amplitude distribution of the light field on the equivalent outer plane of each curved surface element of the lens incident surface is inversely diffracted and transmitted to the object plane, and the complex amplitude information of the light field diffracted by all curved surface elements to the object plane is superimposed to obtain the complex amplitude distribution of the object plane, thereby completing the object reconstruction. Preferably, the angular spectrum inverse diffraction algorithm is used for both the inverse diffraction from the equivalent inner plane of the lens exit curved surface element to the equivalent inner plane of the lens incident surface curved surface element and the inverse diffraction from the equivalent outer plane of the lens incident surface curved surface element to the object plane.
[0033] Compared with the prior art, the structure of the present invention is compact and simple. It allows collecting the same amount of information as a traditional imaging system with a simpler system and reconstructing the object through calculation, which greatly reduces the volume and weight of the optical imaging system and lowers the cost of the optical imaging system. BRIEF DESCRIPTION OF THE DRAWINGS
[0034] Figure 1 FIG. is a schematic structural diagram of a high-performance optical imaging system based on inverse diffraction calculation of an all-optical link provided by an embodiment of the present invention.
[0035] Figure 2 FIG. is a schematic design diagram of a lens in a high-performance imaging system based on inverse diffraction calculation of an all-optical link provided by an embodiment of the present invention.
[0036] Figure 3 FIG. is a schematic diagram of lens division in a high-performance imaging system based on inverse diffraction calculation of an all-optical link provided by an embodiment of the present invention.
[0037] Figure 4 FIG. is a target plane light field amplitude distribution and a high-fidelity object reconstruction diagram obtained by a method based on inverse diffraction calculation of an all-optical link provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0038] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.
[0039] An embodiment of the present invention provides a computational imaging system based on inverse diffraction of an all-optical link, as Figure 1 shown, which includes an active illumination module, a single lens, and a camera;
[0040] The active illumination module is used to illuminate the object to be imaged;
[0041] The single lens is designed based on the principle of conservation of spatial bandwidth product. According to the numerical aperture and field of view size of the required optical system, the appropriate camera format size and pixel size are selected. Then, based on the camera pixel size, the angular range of the outgoing light rays to be controlled is determined, and the lens surface profile is designed and optimized to determine the surface profile parameters of the lens, which are used to collect, modulate, and transmit object information to the target plane. The lens design process is as Figure 2 shown;
[0042] The camera is used to record the intensity information of the light field at the target plane and multiple planes behind the target plane;
[0043] Specifically, the active illumination module includes a coherent light source and a collimating and beam expanding system;
[0044] The coherent light source can be a laser light source or a monochromatic light source with a relatively narrow spectral bandwidth, which is used to irradiate the object to be imaged;
[0045] The collimating and beam expanding system collimates and expands the outgoing light beam of the light source, and the beam after collimation and beam expansion is then irradiated onto the object to be imaged.
[0046] The collimating and beam expanding system is used to shape the light beam emitted by the laser to improve the beam quality. By collimating and expanding it, the illumination area is increased and the illumination uniformity is improved. After the laser beam reaches the object plane, it loads the information of the object, which is collected, modulated, and transmitted to the target plane by the lens.
[0047] The embodiment of the present invention also provides an imaging method based on inverse diffraction calculation of an all-optical link. The method is as follows:
[0048] Step 1: Obtain the measured light field intensity distributions at the target plane and three planes at distances d, 2d, and 3d behind the target plane from the camera, and combine the phase retrieval algorithm to obtain the complex amplitude of the target plane;
[0049] Specifically, an arbitrary initial phase is assigned to the target plane to obtain the initial complex amplitude of the target plane where (x, y) represents the pixel coordinates on the target plane, represents the amplitude information at the pixel point (x, y) on the measured target plane, and i represents the imaginary number;
[0050] According to the complex amplitude of the target plane, the complex amplitude distributions U1(x, y), U2(x, y), and U3(x, y) of the light field at three planes behind the target plane can be calculated using the angular spectrum diffraction algorithm. The formula is:
[0051]
[0052]
[0053]
[0054] Among them, represents the Fourier transform, represents the inverse Fourier transform, λ represents the central wavelength of the coherent light source, i represents the imaginary number, U1(x, y) represents the complex amplitude distribution of the light field at the first plane d behind the target surface, U2(x, y) represents the complex amplitude distribution of the light field at the second plane 2d behind the target surface, and U3(x, y) represents the complex amplitude distribution of the light field at the third plane 3d behind the target surface.
[0055] Using the measured light field amplitude information at three planes to replace the calculated amplitude information |U1(x, y)|, |U2(x, y)|, |U3(x, y)|, and obtain the new complex amplitude information U update1 (x, y), U update2 (x, y), U update3 (x, y), and inversely diffractively transmit the updated complex amplitude information to the target surface and take the average to obtain the new target surface complex amplitude U update0 (x, y);
[0056] Repeat the above process until the root mean square error RMSE between the updated target surface amplitude |U update0 (x, y)| and the measured target surface amplitude information is less than the set threshold ε. At this time, the target surface complex amplitude U update0 (x, y) is what is required.
[0057]
[0058] In the formula, Number is the number of pixels of the camera.
[0059] Step 2: Divide the lens surface profile into multiple segmented surface elements, and each surface element is equivalently replaced by two virtual plane elements located inside and outside the lens. The two virtual plane elements and the surface element satisfy the thin lens approximation.
[0060] Specifically, as Figure 3 shown, divide the incident surface and the exit surface of the lens into N entrance , N exit surface elements. The number of divided surface elements can be determined by the curvature of the lens. The areas with larger curvature are divided more densely, and the areas with smaller curvature are divided more sparsely. Take the points where z = d max at the maximum axial distance and z = d min at the minimum axial distance of each surface element to extend and construct plane elements as the equivalent plane group of each surface element. The plane element located inside the lens and the plane element P inner , P outerSatisfy the thin lens approximation condition, and compensate for the local curvature of the curved surface element by loading the optical path parallel to the optical axis between two virtual plane elements as the compensation phase.
[0061] Step 3: According to the diffraction transmission theory between planes, select different diffraction calculation algorithms for different application scenarios. After obtaining the complex amplitude distribution of the target plane, perform inverse diffraction transmission from the target plane, and calculate the transmission through the lens to the object plane to realize object reconstruction.
[0062] Specifically, as Figure 4 (a) shows the light field intensity distribution of the target plane. After obtaining the complex amplitude U update0 (x,y) of the target plane by combining the phase retrieval algorithm in Step 2, use the angular spectrum inverse diffraction algorithm to calculate the complex amplitude distribution U exit,outer (x,y) on the equivalent outer plane of each curved surface element at the exit surface of the lens. The calculation formula is:
[0063]
[0064] In the formula, d max,exit is the axial coordinate of the equivalent outer plane element of the curved surface element at the exit surface of the lens, H is the axial coordinate of the target plane, f x , f y is the frequency domain coordinate system.
[0065] The complex amplitude distribution on the equivalent inner plane of each curved surface element at the exit surface of the lens is obtained through phase compensation calculation. The calculation formula is:
[0066]
[0067] In the formula, z2(x,y) represents the axial coordinate of the sampling point (x,y) on the curved surface element at the exit surface of the lens, d min,exit represents the axial coordinate of the equivalent inner plane P inner of the curved surface element at the exit surface, d max,exit represents the axial coordinate of the equivalent outer plane P outer of the curved surface element at the exit surface, n represents the refractive index of the lens, and λ represents the central wavelength of the coherent light source.
[0068] After obtaining the complex amplitude distribution U exit,inner (x,y) on the equivalent inner plane of each curved surface element at the exit surface of the lens, use the angular spectrum inverse diffraction algorithm to calculate the complex amplitude distribution U entrance,inner (x,y) on the equivalent inner plane of each curved surface element at the entrance surface of the lens. The complex amplitude distribution U entrance,outer (x,y) on the equivalent outer plane of each curved surface element at the entrance surface of the lens can be obtained by the above phase compensation calculation.
[0069] The complex amplitude distribution of the equivalent external plane light field of each curved surface element on the incident surface of the lens is inversely diffracted and transmitted to the object plane. By superimposing the complex amplitude information of the light field diffracted by all curved surface elements to the object plane, the complex amplitude distribution of the light field on the object plane can be obtained, and the object reconstruction is completed. As Figure 4 (b) shows, this figure is the object reconstruction diagram after the inverse diffraction calculation of the full optical link for Figure 4 (a).
[0070] As mentioned above, it is only the preferred embodiment of the present invention and is not used to limit the protection scope of the present invention.
Claims
1. A high-performance optical imaging system based on all-optical link inverse diffraction calculation, the system comprising an active illumination module, a single lens, and a camera arranged in sequence along the optical axis direction, characterized in that: The active illumination module is used to illuminate the object to be imaged; The single lens is designed based on the principle of conservation of spatial bandwidth product. According to the required numerical aperture and field of view size, the size of the camera frame and the pixel size are selected. According to the angular range of the outgoing light rays required by the pixel size, the surface type parameters of the single lens are determined, and it is used to collect, convert, and transmit the information of the object to be imaged; The camera is used to record the light field intensity information at the target plane and multiple planes behind the target plane; Combined with the surface type parameters of the single lens and the light field intensity information, the reconstruction of the object to be imaged is completed through the all-optical link inverse diffraction calculation method.
2. The high-performance optical imaging system based on all-optical link inverse diffraction calculation according to claim 1, wherein The active illumination module includes a coherent light source and a collimation and beam expansion system; The coherent light source is a laser light source or a narrow-band monochromatic light source, and is used to irradiate the object to be imaged; The collimation and beam expansion system is used to collimate and expand the outgoing beam of the coherent light source, and the beam after collimation and beam expansion is then irradiated onto the object to be imaged.
3. The high-performance optical imaging system based on all-optical link inverse diffraction calculation according to claim 1, characterized in that, The single lens is a spherical, aspherical, or free-form surface lens.
4. An imaging method based on inverse diffraction calculation of an all-optical link, characterized in that, Including: Irradiate the object to be imaged with a coherent light source, collect, convert, and transmit the information of the object to be imaged by the lens to the camera, collect the light field intensity information at the target plane and multiple planes behind the target plane of the object to be imaged by the camera, and obtain the target plane complex amplitude information by using a phase retrieval algorithm; Divide the surface type of the lens into multiple segmented curved surface elements, and each curved surface element is equivalently replaced by two virtual plane elements located inside and outside the lens. The two virtual plane elements and the curved surface element satisfy the thin lens approximation condition, and the local curvature of the lens is characterized by phase compensation; According to the obtained target plane complex amplitude information, perform inverse diffraction propagation from the target plane, and calculate and transmit it to the object plane through the virtual plane element of the lens to realize object reconstruction.
5. The imaging method based on all-optical link inverse diffraction calculation according to claim 4, wherein The obtaining of the target plane complex amplitude information by using the phase retrieval algorithm is specifically: Assign an arbitrary initial phase to the target surface Obtain the initial complex amplitude of the target surface where (x, y) represents the pixel coordinates on the target surface, I0(x, y) represents the light field amplitude information at the pixel (x, y) on the measured target surface, and i represents the imaginary number; According to the complex amplitude of the target plane, calculate the complex amplitude information U1(x,y), U2(x,y), and U3(x,y) at three planes with distances d, 2d, and 3d behind the target plane through the angular spectrum diffraction transmission algorithm, and use the measured optical field amplitude information to replace the calculated complex amplitude information |U1(x,y)|, |U2(x,y)|, |U3(x,y)|, and obtain the new complex amplitude information U update1 (x,y), U update2 (x,y), U update3 (x,y). Inverse diffractively transmit the updated complex amplitude information to the target plane and take the average to obtain the new complex amplitude of the target plane U update0 (x,y); where respectively represent the optical field amplitude information at the pixel points (x,y) on the three planes with distances d, 2d, and 3d behind the target plane; Repeat the above process until the root mean square error between the updated target surface amplitude |U update0 (x, y)| and the measured target surface optical field amplitude information is less than the set threshold ε. At this time, the target surface complex amplitude U update0 (x, y) is what we want.
6. The imaging method based on all-optical link inverse diffraction calculation according to claim 4, wherein The dividing the surface type of the lens into multiple segmented curved surface elements, and each curved surface element is equivalently replaced by two virtual plane elements located inside and outside the lens. The two virtual plane elements and the curved surface element satisfy the thin lens approximation condition, specifically: Divide the incident surface and the exit surface of the lens into N entrance , N exit curved surface elements. The number of divided curved surface elements is determined by the curvature of the lens. At the point where the axial distance of each curved surface element is the largest, z = d max and the point where it is the smallest, z = d min to extend and construct a pair of equivalent outer plane elements P outer and equivalent inner plane elements P inner . As the equivalent plane group of the curved surface element, the equivalent inner plane element is located inside the lens, and the equivalent outer plane element is located outside the lens. The two satisfy the thin lens approximation condition; compensate for the local curvature of the curved surface element by loading the optical path parallel to the optical axis between the two virtual plane elements as the compensation phase.
7. The imaging method based on all-optical link inverse diffraction calculation according to claim 4 or 5, characterized in that The performing inverse diffraction propagation from the target plane according to the obtained target plane complex amplitude information, and calculating and transmitting it to the object plane through the transmission of the lens to realize object reconstruction, specifically: After obtaining the complex amplitude U of the target plane update0 (x, y), the angular spectrum inverse diffraction algorithm is used to calculate the complex amplitude distribution U of the complex amplitude of the target plane transmitted to the equivalent outer plane elements of each curved surface element on the lens exit surface exit,outer (x, y), and the complex amplitude distribution U of the equivalent inner plane elements of each curved surface element on the lens exit surface exit,inner (x, y) is obtained by phase compensation, and the calculation formula is: where \(z_2(x,y)\) represents the axial coordinate of the point \((x,y)\) on the surface element of the lens exit surface, \(d\) min,exit represents the axial coordinate of the equivalent inner plane element \(P\) inner of the surface element of the exit surface, \(d\) max,exit represents the axial coordinate of the equivalent outer plane element \(P\) outer of the surface element of the exit surface, \(n\) represents the refractive index of the lens, \(\lambda\) represents the central wavelength of the coherent light source, and \(i\) represents the imaginary number; After obtaining the equivalent inner-plane complex amplitude distribution \(U(x,y)\) of each surface element on the exit surface of the lens, the angular spectrum inverse diffraction algorithm is also used to calculate the complex amplitude distribution \(U(x,y)\) on the equivalent inner plane of each surface element on the entrance surface of the lens. exit,inner The complex amplitude distribution \(U(x,y)\) on the equivalent outer plane of each surface element on the entrance surface of the lens is obtained by phase compensation, and the calculation formula is as follows: entrance,inner After obtaining the equivalent inner-plane complex amplitude distribution \(U(x,y)\) of each surface element on the exit surface of the lens, the angular spectrum inverse diffraction algorithm is also used to calculate the complex amplitude distribution \(U(x,y)\) on the equivalent inner plane of each surface element on the entrance surface of the lens. entrance,outer The complex amplitude distribution \(U(x,y)\) on the equivalent outer plane of each surface element on the entrance surface of the lens is obtained by phase compensation, and the calculation formula is as follows: where \(z_1(x,y)\) represents the axial coordinate of the point \((x,y)\) on the lens entrance surface element, \(d\) min,entrance represents the equivalent inner plane element \(P\) of the entrance surface element inner of the axial coordinate, \(d\) max,entrance represents the equivalent outer plane element \(P\) of the entrance surface element outer of the axial coordinate; Inverse diffraction transmit the light field complex amplitude distribution on the equivalent outer plane of each curved surface element of the lens incident surface to the object plane, and superimpose the light field complex amplitude information diffracted by all curved surface elements to the object plane to obtain the complex amplitude distribution of the object plane, and complete object reconstruction.