End-to-end automatic design method of free-form surface system

Abstract

The invention relates to an end-to-end automatic design method for a free-form surface system, and the method specifically comprises the steps: S1, providing an initial plane system, solving a first-order geometric structure which comprises a plurality of curved surfaces according to the initial plane system, and determining the focal power of each curved surface according to a field curvature equation and a focal length equation; s2, determining the focal power of each curved surface and adjusting the position of the curved surface by using a flat field condition and a linear astigmatism elimination equation; s3, determining a rapid automatic design strategy of the first-order geometric structure, the design strategy at least satisfying one of the following three conditions: the focal length of the system is equal to a given value, the sum psi of the focal powers of the curved surfaces is 0, and a parameter gamma related to astigmatism is 0; and S4, constructing a free-form surface system by using a surface normal correction method, further improving the image quality by using an iterative process of image surface correction and surface correction, and obtaining a final design result.

Description

Technical Field

[0001] The present invention relates to the field of optical design, and in particular to an end-to-end automated design method for a free-form surface system. Background Art

[0002] In the traditional optical design model, designers need to participate in solving the initial structure of the system and try various optimization strategies to improve the image quality step by step. The current automated design method for free-form surface systems still takes several minutes or even hours to calculate an automated design. Although a high-quality optical system can be obtained, if the result does not meet the design requirements in terms of volume, processing, and assembly, it is necessary to recalculate and wait for several minutes to hours again. Long waits can easily interrupt the designer's design ideas and work rhythm. If the speed of the automated design process can be increased several times, an optical system with high imaging quality can be directly obtained within the time of a single optimization of traditional optical design. Summary of the invention

[0003] In summary, it is indeed necessary to provide an end-to-end automated design method for free-form surface systems to overcome the above technical problems.

[0004] An end-to-end automated design method for a free-form surface system comprises the following steps:

[0005] S1, providing an initial plane system, solving a first-order geometric structure according to the initial plane system, the first-order geometric structure including a plurality of curved surfaces, and determining the optical focal length of each curved surface according to a field curvature equation and a focal length equation;

[0006] S2, using the flat field condition and the linear astigmatism elimination equation to determine the focal length of each curved surface and adjust the position of the curved surface;

[0007] S3, determining a fast automated design strategy for a first-order geometric structure, the design strategy satisfying at least one of the following three conditions, the three conditions being: the focal length of the system is equal to a given value, the sum of the focal powers of the surfaces ψ is 0, and the parameter γ related to astigmatism is 0; and

[0008] S4, use the surface normal correction method to construct the free-form surface system, use the iterative process of image plane correction and surface correction to further improve the image quality and obtain the final design result.

[0009] Compared with the prior art, the end-to-end automated design method for the free-form surface system provided by the present invention is a new optical design method, which changes the traditional optical design mode. The end-to-end design process provided by the present invention only requires simple input and does not require human participation, and can directly obtain an optical system with excellent imaging quality in the time of traditional single optimization. When the single end-to-end design result does not meet the design requirements or there is still room for performance improvement, the input parameters can be continuously changed to repeat the end-to-end design process until a system that meets the requirements is obtained. The single end-to-end design process is short, and the waiting process will not interrupt the designer's design ideas. In addition, the designer can also select a series of design results from a large number of high-quality optical systems according to actual needs to obtain the final design result. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 This is a schematic diagram of the initial three-reflection system structure provided by an embodiment of the present invention.

[0011] Figure 2 A schematic diagram of an astigmatism correction transformation vector provided in an embodiment of the present invention.

[0012] Figure 3 A flow chart of an end-to-end rapid automated design method provided by an embodiment of the present invention.

[0013] Main component symbols

[0014] First-order geometry of three-reflection system 100

[0015] Primary Mirror 102

[0016] Secondary mirror 104

[0017] Three Mirrors 106

[0018] Image plane 108

[0019] The following specific implementation manner will further illustrate the present invention in conjunction with the above-mentioned drawings. DETAILED DESCRIPTION

[0020] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and in combination with specific embodiments.

[0021] An embodiment of the present invention provides an end-to-end automated design method for a free-form surface system, which specifically includes the following steps:

[0022] S1, providing an initial plane system, solving a first-order geometric structure according to the initial plane system, the first-order geometric structure including a plurality of curved surfaces, and determining the optical focal length of each curved surface according to a field curvature equation and a focal length equation;

[0023] S2, using the flat field condition and the linear astigmatism elimination equation to determine the focal length of each curved surface and adjust the position of the curved surface;

[0024] S3, determining a fast automated design strategy for a first-order geometric structure, the design strategy satisfying at least one of the following three conditions, the three conditions being: the focal length of the system is equal to a given value, the sum of the focal powers of the surfaces ψ is 0, and the parameter γ related to astigmatism is 0; and

[0025] S4, use the surface normal correction method to construct the free-form surface system, use the iterative process of image plane correction and surface correction to further improve the image quality and obtain the final design result.

[0026] Hereinafter, each step of the end-to-end automated design method for the free-form surface system provided by the present invention will be introduced in detail.

[0027] S1, providing an initial plane system, solving a first-order geometric structure based on the initial plane system, the first-order combined structure includes multiple curved surfaces, and determining the optical focal length of each curved surface based on the field curvature equation and the focal length equation.

[0028] In this step, the position of the surface is described by the distance d between the surfaces and the incident angle θ. If the principal ray of the central field of view is set as the central ray, the distance d between the surfaces is the distance between the corresponding points of the central ray on the adjacent surfaces, and the incident angle θ is the incident angle of the central ray on each surface. Figure 1 In this embodiment, the initial plane system is a three-mirror system, which includes a primary mirror 102, a secondary mirror 104, a third mirror 106, and an image plane 108. Wherein, d1 is the distance between the primary mirror 102 and the secondary mirror 104, d2 is the distance between the secondary mirror 104 and the third mirror 106, and d3 is the distance between the third mirror 106 and the image plane 108. θ1 is the incident angle of the central light on the primary mirror, θ2 is the incident angle of the central light on the secondary mirror, and θ3 is the incident angle of the central light on the third mirror.

[0029] Before determining the first-order geometric structure, the focal power of each surface is determined by the field curvature and astigmatism correction equations. In the off-axis case, the radius of curvature is not accurate enough to describe the focal power, so the distance between the central field of view and the image on each surface is used to express the focal power φ of the surface, where: n′ and n are the refractive indices of the front and back surfaces of a certain curved surface, respectively. i and l o When calculating the first-order geometric structure, the optical transfer matrix is ​​used to analyze the system. The transfer matrix of the kth surface is T k , the transfer matrix of the kth surface spacing is D k ,but where φ k is the focal length of the kth surface, dk and n k are the distance and refractive index between the kth surface and the (k+1)th surface respectively. If the imaging system has N surfaces, the optical transmission matrix of the system is In order to meet the given effective focal length (EFL), the spacing d and the focal power φ of each surface need to meet

[0030] Next, the optical focal length of the curved surface needs to be converted into specific surface parameters in order to obtain the first-order geometric structure. When a spherical surface, such as a rotationally symmetric surface, is used to establish the first-order geometric structure of an off-axis system, the same radius of curvature will correspond to different optical focal lengths on the meridian and sagittal planes. For high-performance systems with relatively large fields of view and apertures, in order to eliminate obstructions, the curved surface often has a larger off-axis angle. At this time, the optical focal length difference corresponding to the same radius of curvature on the meridian and sagittal planes will also be greater. Therefore, the embodiment of this method will use the bracelet surface for the first-order geometric structure. In an off-axis system, the bracelet surface can have different radii of curvature on the meridian and sagittal planes. The use of the bracelet surface can ensure that the optical focal length of each curved surface determined is consistent on the meridian and sagittal planes. It can be seen from the Coddington formula that the radius of the bracelet surface on the meridian and sagittal planes can be determined using the object-image distance of each curved surface, as shown in the following equation:

[0031]

[0032]

[0033] where θ′ and θ are the incident and exit angles, respectively, and R T and R S are the radii of curvature on the meridian plane and the sagittal plane, respectively.

[0034] S2, using the flat field condition and the linear astigmatism elimination equation to determine the optical power of each curved surface and adjust the position of the curved surface.

[0035] In this step, field curvature is an important aberration. In the absence of astigmatism, if you want to obtain a flat image surface, you need to make the Petzval curvature 0, that is, the sum of the focal lengths of each surface ψ is required to be 0, as shown in the formula The above is the flat field condition. Substitution The equation with the object-image distance of each surface as a variable can be obtained.

[0036] In off-axis systems, linear astigmatism that is asymmetric about the field of view is often the main component of the aberration. When calculating the first-order geometric structure, we choose to use the equation given by Chang to eliminate this linear astigmatism that is asymmetric about the field of view, as shown in the following equation:

[0037]

[0038] Among them, m k is the ratio of the image distance to the object distance of each surface, θ k is the incident angle of the central light on each curved surface. When γ is 0, the asymmetric linear astigmatism of the field of view is eliminated. Among them, if the object plane is not tilted, the image plane is perpendicular to the central light.

[0039] The above equation has the characteristic that it can be regarded as the scalar product of two vectors. Here, N=3 is taken as an example, as shown in the following equation:

[0040] γ=A·B=((1+m1)m2m3,(1+m2)m3,1+m3)·(tanθ1,tanθ2,tanθ3)

[0041] Among them, vector A is only related to the object-image distance of each curved surface, that is, it is closely related to the optical power of each curved surface; and vector B is only related to the incident angle. When vector A is orthogonal to vector B, the linear astigmatism of the asymmetric field of view is eliminated.

[0042] The following describes the formula based on The astigmatism correction transformation is used to correct the surface position in this method. The vector diagram of the astigmatism correction transformation is shown in Figure 2 As shown. When the focal power of each surface is determined, the A vector is also determined. At this time, the B vector can only make γ equal to 0 when it is located on the plane 100 perpendicular to the A vector. The angles of each surface in the given initial plane system usually cannot make the vector B located on the plane 100. Therefore, the vector B can be projected onto the plane 100 by projection transformation to obtain the vector B′, as shown in Figure 2 As shown. Figure 2 Through the projection transformation, vector B becomes vector B' which is orthogonal to vector A. When vector A remains unchanged, the scalar product γ of vector B' and A becomes 0, and vector B' can minimize |BB'|. To understand this projection transformation from the perspective of system structure, when the optical power is determined, this transformation eliminates the asymmetric linear astigmatism of the field of view on each curved surface under the minimum incident angle adjustment. This projection transformation can also be called astigmatism correction transformation.

[0043] S3, determining a fast automated design strategy for a first-order geometric structure, which design strategy satisfies at least one of the following three conditions: the focal length of the system is equal to a given value, the sum of the focal powers of each surface ψ is 0, and the parameter γ related to astigmatism is 0.

[0044] The input of this method is the system parameters such as focal length, field of view and F number, as well as a plane system according to the designer's initial conception. In order to prevent the final system from deviating too much from the initial plane system set by the designer, the spacing d of each surface in this method remains unchanged when determining the first-order geometric structure, and the incident angle θ of the central light on each surface will only change when using the astigmatism correction transformation. Assume that there are a total of N surfaces, with surface spacings d1, d2, ..., d N is determined according to a given plane system. Then the difference between the image distance of the kth surface and the object distance of the (k+1)th surface is known as d k If the image distances of the first (N-1) surfaces are known, the object distances of the second to Nth surfaces can be obtained. At the same time, the object distance of the first surface is a given object distance, usually infinite, and the image distance of the Nth surface is d N , so the object-image distance of each surface can be obtained. According to the formula The object-image distance of each surface can be used to solve the optical power of each surface. In summary, if the image distance of the first (N-1) surfaces is known, the optical power of each surface can be obtained. Therefore, the image distance of the first (N-1) surfaces will be set as a variable to solve the relevant equations.

[0045] The first-order geometric structure design strategy of this method is that the system satisfies the following three conditions as much as possible: the focal length of the system is equal to the given value, as shown in Formula As shown in the present invention, it is called the focal length equation; the sum of the focal powers of each surface ψ is 0, as shown in the formula As shown in the present invention, it is called the field curvature equation; the parameter γ related to astigmatism is 0, as shown in the formula As shown, the present invention calls it the astigmatism equation. The present invention will use the above three equations to solve the optical focal length and correct the incident angle of each surface. In the case of multiple solutions in the process of solving the equations, the present invention will calculate the corresponding first-order geometric structure respectively, and automatically select the system with the best image quality for the subsequent construction of the free-form surface system.

[0046] The end-to-end automated design method for the free-form surface system provided by the present invention selects different design strategies according to the number of reflectors, and is currently applicable to a four-mirror system at most. As described above, there are (N-1) variables in a system containing N reflectors. When N is greater than 3, the number of variables will not be less than the number of equations, and the design strategy is to solve the optical focal length of the first-order geometric structure by combining three equations. When N is not greater than 3, the number of variables will be less than the number of equations, and the design strategy is to combine the three conditions and the astigmatism correction transformation to determine the first-order geometric structure.

[0047] The first-order geometric structure design strategies for two reflectors (N=2), three reflectors (N=3) and four reflectors (N=4) are introduced below.

[0048] First-order geometric structure design strategy for three-mirror system:

[0049] According to the description of variables in the system in the previous article, there are two variables in the three-mirror system, which are the image distances of the first two mirrors. At this time, the number of variables will be less than the number of equations, and the first-order geometric structure design strategy of the three-mirror system is divided into two steps.

[0050] The first step is to first solve the optical power by combining the field curvature equation and the focal length equation, and then use the astigmatism correction transformation to correct the surface position while ensuring the solved optical power, so that the system can finally meet the three conditions at the same time. Solving the optical power by combining the field curvature equation and the focal length equation (there is an analytical solution at this time) can make the system meet the first two conditions. At this time, the surface position and optical power do not satisfy the astigmatism equation, that is, γ is not 0. Then, using the astigmatism correction transformation to adjust the incident angle at the current optical power can satisfy the astigmatism equation. In this way, the parameters of the first-order geometric structure that can meet the three conditions at the same time are determined.

[0051] Before the astigmatism correction transformation, if the absolute value of γ is relatively small, it means that the surface position at this time is relatively close to the position that satisfies the astigmatism equation. Therefore, the adjustment of the incident angle caused by the astigmatism correction transformation will also be relatively small, and the system will not be blocked due to the adjustment of the incident angle, and there is no need to enter the second step at this time. This situation corresponds to some geometric structures with relatively small astigmatism, such as the three-mirror anastigmat (TMA) structure. When the absolute value of γ is relatively large, the astigmatism correction change will cause the surface position to move more, and the use of the astigmatism correction transformation may cause the system to be blocked. This actually means that it may be difficult to find a solution that satisfies all three conditions around the initial plane system. Therefore, a fast and automated search process for optical power distribution is needed as the second step of the three-mirror system design strategy.

[0052] The second step is to first establish a number of first-order geometric structures with different focal power distributions, and then perform astigmatism correction transformations on these first-order geometric structures to obtain multiple systems with γ being 0. Finally, the system with the best imaging quality within the unobstructed range is selected as the final first-order geometric structure. Different focal power distributions are obtained by combining the focal length equation and the astigmatism equation with different γ, and an analytical solution exists at this time. Among them, γ is selected from 0 to the positive and negative directions in a certain step size. The astigmatism correction transformation is actually to find the next geometric structure with small aberration potential under the current focal power under the condition of minimum adjustment of the incident angle. Using the astigmatism equation with different γ values ​​to solve does not only consider the astigmatism aberration, but its essence is to obtain a variety of different focal power distributions. After that, a series of first-order geometric structures with small aberration potential can be obtained through astigmatism correction transformation. Searching for γ from 0 means that the surface position adjustment caused by astigmatism correction ranges from small to large. When surface obstruction occurs, the search process will stop. This method uses the average value of the RMS spot radius in each field of view to evaluate the imaging quality of a series of geometric structures. The best results will be combined with the direct design method to construct the free-form surface system.

[0053] First-order geometry design strategy for two-mirror system:

[0054] For a two-mirror system, if the previously mentioned rule for selecting variables is followed, there is only one variable, the primary mirror image distance, which will be unfavorable for solving the equation. When this method deals with the case of a two-mirror system, the distance between the secondary mirror and the image plane is also set as a variable, so that a strategy similar to that in a three-mirror system can be implemented in a two-mirror system.

[0055] First-order geometric structure design strategy for four-mirror system:

[0056] In a four-mirror system, after determining the surface spacing and incident angle according to a given initial plane system, there are three variables in the four-mirror system, which are the image distances of the first three mirrors. At this time, the number of variables is equal to the number of three equations. By directly combining the focal length equation, field curvature equation and astigmatism equation, the optical power of each surface can be obtained and the first-order geometric structure can be determined. The optimization algorithm can be used to calculate the numerical solution to this nonlinear system of equations. This method uses the general global optimization algorithm in the 1stopt software to solve this problem. This method can obtain the calculation results without relying on the selection of initial values. It is fast, stable and universal, and can obtain correct results in most cases.

[0057] S4, use the surface normal correction method to construct the free-form surface system, use the iterative process of image plane correction and surface correction to further improve the image quality and obtain the final design result.

[0058] The first is the construction of the free-form surface system. Since the first-order geometric structure has already performed optical focal length distribution and angle correction based on astigmatism and field curvature, and completed the correction of many low-order aberrations, the direct design method can be used to correct high-order aberrations at this time, and excellent imaging quality can be quickly obtained. The direct design method used in this method is the surface normal correction method, which can quickly realize the construction of the free-form surface imaging system.

[0059] In this direct design method, each surface needs to go through multiple fitting processes. By taking into account the fitting method of coordinates and normals at the same time, the original surface shape data points and the corrected normals of a surface are fitted to obtain a free-form surface. The original surface shape data points are obtained by ray tracing of characteristic rays of different apertures in multiple fields of view. The corrected normal is determined by the incident light and the outgoing light according to the law of reflection, where the incident light maintains its original direction and the outgoing light points to the ideal image point. The free-form surface system is established by fitting each surface in the system in turn. The process of fitting all free-form surfaces in the system needs to be performed multiple times until the imaging quality is no longer improved, and the construction of the free-form surface imaging system is completed.

[0060] The next step is to correct the free-form surface system. The determination of the image plane angle in the first-order geometric structure only considers the asymmetric linear astigmatism of the field of view. In order to further improve the imaging quality, an iterative process of image plane correction and surface normal correction is also required. In this iterative process, the image plane correction considers the aberration terms related to the image plane, and the surface correction also uses a direct design method such as surface normal correction. Since the system imaging quality is already excellent before the image plane correction, it can often be completed within a few iterations. When the imaging quality of the system meets the actual required standards, the final free-form surface system is obtained.

[0061] The entire design process of the end-to-end automated design method for the free-form surface system provided by the present invention is as follows: After the designer provides the system parameters and the initial plane system, the method first determines the surface position and optical focal length of each surface in the first-order geometric structure based on the flat field condition and the linear astigmatism elimination equation, and then uses the surface normal correction method to construct the free-form surface imaging system. Finally, the free-form surface imaging system is further corrected using the iterative process of image plane correction and surface correction to obtain the final design result. The flowchart of the end-to-end automated design method for the free-form surface system provided by the present invention is as follows: Figure 3 shown.

[0062] Furthermore, according to the free-form surface system finally obtained, a mirror surface meeting the parameters is manufactured, and after being installed, an optical lens element can be obtained.

[0063] The automated design method proposed in this paper realizes the end-to-end rapid design of free-form surface imaging systems, which may promote the change of optical design mode. This method is immediate and efficient. Designers can often obtain excellent design results after a few quick trials of the end-to-end design process. For designers who are familiar with the various structures of free-form surface systems, it is likely that one or two attempts will be enough to obtain an off-axis imaging system with excellent imaging quality. For beginners in optical design or practitioners in other fields of optics, the desired design results can usually be obtained after several trials.

[0064] The input of the end-to-end design method proposed by the present invention is an initial plane system. During the automatic design process, the position of the curved surface does not move or only moves in a small range. This feature ensures that the optical path structure of the system can be in accordance with the designer's general idea. As long as the designer reasonably places the plane position, the possibility of beam obstruction or lens interference is reduced. Even if these phenomena occur in the design result, the designer only needs to simply adjust the plane position during the trial and error process to avoid them.

[0065] If you need to design a compact optical system, you can give a loose initial plane system during the initial end-to-end design process. Based on the output system obtained in the initial end-to-end design process, the designer can predict the surface shape and size of the output system in the subsequent trial and error process. After that, the designer can continuously change the position of the plane to reduce the system volume to achieve a compact optical structure.

[0066] Please see the table below, which shows a comparison between the system designed by the end-to-end automated design method for the free-form surface system provided by the present invention and the prior art.

[0067]

[0068] The above table lists several representative free-form surface system design examples designed by the free-form surface system automatic design methods in the prior art. These design examples mainly include three-mirror systems and four-mirror systems. At the same time, the above table also gives the specific embodiments designed by the free-form surface system end-to-end automatic design method provided by the present invention. It can be seen from the above table that the free-form surface system end-to-end automatic design method proposed by the present invention is not only suitable for high-performance imaging systems, but also can realize end-to-end rapid automatic design.

[0069] In addition, those skilled in the art may also make other changes within the spirit of the present invention. Of course, these changes made according to the spirit of the present invention should be included in the scope of protection required by the present invention.

Claims

1. An end-to-end automated design method for a free-form surface system, which specifically comprises the following steps: S1, providing an initial plane system, solving a first-order geometric structure according to the initial plane system, the first-order geometric structure including a plurality of curved surfaces, and determining the optical focal length of each curved surface according to a field curvature equation and a focal length equation; S2, using the flat field condition and the linear astigmatism elimination equation to determine the focal length of each curved surface and adjust the position of the curved surface; S3, determining a fast automated design strategy for a first-order geometric structure, the design strategy meeting at least one of the following three conditions, the three conditions being: the focal length of the system is equal to a given value, the sum of the focal powers of the surfaces ψ is 0, and the parameter γ related to astigmatism is 0; as well as S4, use the surface normal correction method to construct the free-form surface system, use the iterative process of image plane correction and surface correction to further improve the image quality and obtain the final design result.

2. The end-to-end automated design method for a free-form surface system according to claim 1, characterized in that: In step S1, the positions of the multiple surfaces are described using the spacing d and the incident angle θ of the surfaces, with the main ray of the central field of view being set as the central ray, the spacing d of the surfaces being the distance between the corresponding points of the central ray on adjacent surfaces, and the incident angle θ being the incident angle of the central ray on each surface.

3. The end-to-end automated design method for a free-form surface system according to claim 1, characterized in that: In step S1, before determining the first-order geometric structure, the optical power of each curved surface is determined by the field curvature and astigmatism correction equations. In the off-axis case, the optical power φ of the curved surface is expressed by the object-image distance of the central field of view on each curved surface, where: n′ and n are the refractive indices of the front and back surfaces of a certain curved surface, respectively. i and l o are the image distance and object distance of the surface respectively.

4. The end-to-end automated design method for a free-form surface system according to claim 1, characterized in that: In step S1, when calculating the first-order geometric structure, the optical transmission matrix is ​​used to analyze the system. The transmission matrix of the kth surface is T k , the transfer matrix of the kth surface spacing is D k ,but where φ k is the focal length of the kth surface, d k and n k are the distance and refractive index between the kth surface and the (k+1)th surface respectively.

5. The end-to-end automated design method for a free-form surface system according to claim 1, characterized in that: In step S2, in this step, in the absence of astigmatism, the sum ψ of the optical powers of the curved surfaces is 0.

6. The end-to-end automated design method for a free-form surface system according to claim 1, characterized in that: In step S3, the spacing d between the curved surfaces remains unchanged when determining the first-order geometric structure, and the incident angle θ of the central light on each curved surface will only change when using the astigmatism correction transformation.

7. The end-to-end automated design method for a free-form surface system according to claim 6, characterized in that: There are N surfaces with surface spacing d1, d2, …, d N It is determined according to a given plane system, and then the difference between the image distance of the kth surface and the object distance of the (k+1)th surface is known to be d k , the image distance of the first (N-1) surfaces is known, and the object distances of the second to Nth surfaces are obtained. At the same time, the object distance of the first surface is given. The object distance is infinite, and the image distance of the Nth surface is d N , thus obtaining the object-image distance of each surface.

8. The end-to-end automated design method for a free-form surface system according to claim 7, characterized in that: According to the formula The object-image distance of each surface is used to solve the optical power of each surface.

9. The end-to-end automated design method for a free-form surface system according to claim 1, characterized in that: In step S3, the first-order geometric structure design steps of the three-reflector system include: First, the field curvature equation and the focal length equation are combined to solve the optical power, and then the astigmatism correction transformation is used to correct the surface position while ensuring the solved optical power, so that the system can finally meet the three conditions at the same time; A plurality of first-order geometric structures with different optical power distributions are established, and then a plurality of systems with γ=0 are obtained by performing astigmatism correction transformation on these first-order geometric structures, and the final first-order geometric structure is selected within the unobstructed range.

10. The end-to-end automated design method for a free-form surface system according to claim 1, characterized in that: In step S4, the surface normal correction method includes: each surface undergoes multiple fitting processes, and the original surface data points of a surface and the corrected normal are fitted to obtain a free surface by a fitting method that simultaneously considers the coordinates and the normal; the original surface data points are obtained by ray tracing from characteristic rays of different apertures in multiple fields of view; the corrected normal is determined by the incident ray and the outgoing ray according to the law of reflection, wherein the incident ray keeps its direction unchanged and the outgoing ray points to the ideal image point.

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