Aberration propagation calculation and aberration control method for free-form surface imaging

Abstract

The present invention discloses a method for calculating the propagation of aberrations and controlling aberrations in free-form surface imaging. Based on a given system optical path, the method calculates the object plane, image plane, entrance pupil, and exit pupil of each optical surface, and calculates the reference wavefront of the central field of view at each entrance pupil and exit pupil. The entrance pupil and field of view of the sampling system are used to generate a set of characteristic rays, and the optical path difference of the characteristic rays of each field of view from the entrance pupil of each surface to its exit pupil relative to the principal ray is calculated. The aberration field of each surface is obtained by fitting the optical path difference of the entire field of view; the contribution of each surface to the dominant aberration is determined based on the current system dominant aberration and the aberration field of each surface, thereby determining the surface to be optimized first; the aberration is reduced by optimizing the surface parameters corresponding to the current dominant aberration of the surface, and the process is repeated until the design meets the requirements. This method can effectively guide the optimization of the free-form surface imaging system, reduce the deviation of the free-form surface while ensuring imaging performance, and effectively reduce the difficulty of surface processing and detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical design, and in particular relates to a method for calculating and controlling aberration propagation of free-form surface imaging. Background Art

[0002] Optical imaging technology plays a vital role in modern life. Optical designers constantly strive for the most ideal imaging results. However, due to the presence of aberrations in imaging optical systems, achieving perfect imaging remains elusive. To improve imaging quality, optical designers typically rely on aberration calculation methods to optimize imaging optical systems by controlling aberrations.

[0003] Freeform optics, as an emerging technology, is leading a major revolution in the design of imaging optical systems. The geometric properties of freeform surfaces break the limitations of traditional optical surface shapes, enabling optical designers to design imaging optical systems that are more compact, lighter, and have superior optical performance. However, the high degree of freedom of freeform surfaces also brings many challenges to the design of imaging optical systems. Existing freeform surface imaging aberration calculation methods can only calculate the total aberration of the entire imaging optical system. However, in practical applications, the total aberration is the superposition of the aberrations of each optical surface, and each optical surface has a different aberration field distribution.

[0004] Free-form surface imaging optical systems can control specific aberrations by adjusting specific geometric parameters of the free-form surface. The control effect is closely related to the aberration field distribution of the free-form surface. However, existing free-form surface imaging aberration control methods have the following problems: (1) When the aberration to be controlled is determined, the aberration control effect of different free-form surfaces cannot be effectively evaluated due to the lack of accurate calculation of the aberration field distribution of each free-form surface. (2) If the geometric parameters of all free-form surfaces in the system are adjusted, the adjustments of different surfaces may cancel each other out, thereby reducing the efficiency of aberration control. In addition, the deviation of the free-form surface from the ideal sphere and its gradient are larger, which is not conducive to actual processing.

[0005] Therefore, to solve the aberration control problem in free-form surface imaging systems, it is crucial to accurately calculate the aberration field distribution of each free-form surface and determine its control effect on specific aberrations. This allows for targeted adjustment of the geometric parameters of the free-form surface with the best control effect, thereby improving aberration control efficiency, reducing the deviation and gradient of the free-form surface from the ideal sphere, and further optimizing the processing process. Summary of the Invention

[0006] In view of this, the present invention aims to provide a method for calculating and controlling aberration propagation in free-form surface imaging. This method can accurately calculate the aberration field distribution of each optical surface in a free-form surface imaging optical system and optimize the free-form surface design process to achieve improved imaging quality and facilitate processing.

[0007] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0008] The present invention provides a method for calculating aberration propagation and controlling aberration of free-form surface imaging, which specifically includes the following steps:

[0009] S1: Establish the initial structure of the free-form surface imaging optical system to be optimized;

[0010] S2: Calculate the object plane, image plane, entrance pupil, and exit pupil positions of each optical surface based on the position of the optical system aperture stop and the spatial posture of each optical surface, and calculate the reference wavefront of the central field of view at the entrance pupil and exit pupil of each optical surface;

[0011] S3: discretely sampling the entrance pupil and field of view of the optical system to generate a set of characteristic rays covering the entrance pupil and the entire field of view;

[0012] S4: calculating the propagation path and optical path information of each characteristic light by ray tracing, calculating the optical path difference of each field characteristic light from the entrance pupil reference wavefront of each optical surface to its exit pupil reference wavefront relative to the principal light according to the optical path information, and obtaining the aberration field distribution of each optical surface by fitting the full field optical path difference;

[0013] S5: determining the current dominant aberration of the system according to the aberration field distribution of the current optical system, and determining the contribution of each optical surface to the dominant aberration of the system according to the dominant aberration of the system and the aberration field distribution of each optical surface, thereby determining the optical surface to be optimized first;

[0014] S6: reducing the dominant aberration of the system by optimizing the surface parameters of the optical surface to be optimized first and corresponding to the dominant aberration of the system;

[0015] S7: Calculate the evaluation function value of the optimized optical system. If the evaluation function value of the optimized system no longer decreases or is less than the target threshold, output the optimized optical system. Otherwise, repeat steps S2-S6.

[0016] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0017] (1) The present invention creatively proposes a method for calculating the aberration propagation and controlling the aberration of free-form surface imaging. The method of the present invention can accurately control the aberration field distribution of each optical surface in the free-form surface imaging optical system and optimize the free-form surface design process to achieve the effect of improving imaging quality and facilitating processing.

[0018] (2) Based on the calculated aberration field propagation and distribution, the present invention can specifically adjust the surface coefficients of the free-form surface with better control effect, avoiding the mutual cancellation of the aberration control effects of each free-form surface; compared with the traditional aberration control method, the free-form surface imaging aberration control method created by the present invention can effectively guide the optimization of the free-form surface imaging system, reduce the deviation of the free-form surface while ensuring the imaging performance, and effectively reduce the difficulty of surface processing and detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A flowchart of the method for calculating the aberration propagation and controlling the aberration of free-form surface imaging according to an embodiment of the present invention;

[0020] Figure 2 Schematic diagram of the optical path structure of the free-form surface off-axis three-mirror system;

[0021] Figure 3 The aberration field distribution diagram of each optical surface of the free-form surface off-axis three-mirror system calculated using the free-form surface imaging aberration propagation calculation method of the present invention;

[0022] Figure 4 The system wavefront error diagram of the free-form surface off-axis three-mirror system obtained by using the free-form surface imaging aberration propagation calculation and aberration control method described in the present invention;

[0023] Figure 5 Deviation diagrams of the free-form surfaces of the free-form surface off-axis three-mirror system relative to the ideal spherical surface obtained using the free-form surface imaging aberration propagation calculation and aberration control method described in the present invention;

[0024] Figure 6 This is a graph showing the deviation of each free-form surface from the ideal spherical surface of an off-axis three-mirror system using traditional aberration control methods.

[0025] Figure 7 The gradient map of each free-form surface relative to the ideal spherical surface of the free-form surface off-axis three-mirror system obtained by using the free-form surface imaging aberration propagation calculation and aberration control method described in the present invention;

[0026] Figure 8 The gradient maps of each free-form surface of the off-axis three-mirror system relative to the ideal spherical surface are obtained using the traditional aberration control method;

[0027] Figure 9 Schematic diagram of the optical path structure of the free-form surface off-axis four-mirror system;

[0028] Figure 10 The aberration field distribution diagram of each optical surface of the free-form surface off-axis four-mirror system calculated using the free-form surface imaging aberration propagation calculation method of the present invention;

[0029] Figure 11 The system wavefront error diagram of the free-form surface off-axis quadruple mirror system obtained by using the free-form surface imaging aberration propagation calculation and aberration control method described in the present invention;

[0030] Figure 12 Deviation diagrams of the free-form surfaces of the free-form surface off-axis quadruple mirror system relative to the ideal spherical surface obtained using the free-form surface imaging aberration propagation calculation and aberration control method described in the present invention;

[0031] Figure 13 This is a graph showing the deviation of each free-form surface from the ideal spherical surface obtained using traditional aberration control methods.

[0032] Figure 14 The gradient map of each free-form surface relative to the ideal spherical surface of the free-form surface off-axis quadruple mirror system obtained by using the free-form surface imaging aberration propagation calculation and aberration control method of the present invention;

[0033] Figure 15 The gradient maps of each free-form surface of the off-axis quadruple mirror system relative to the ideal spherical surface are obtained using the traditional aberration control method. DETAILED DESCRIPTION

[0034] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. The present invention can be implemented in many different forms and should not be construed as being limited to the embodiments described below. Rather, this embodiment is provided to make this disclosure sufficient and complete and to fully convey the concept of the present invention to those skilled in the art.

[0035] like Figure 1As shown, the free-form surface imaging aberration propagation calculation and aberration control method provided by the present invention is illustrated. The idea of ​​the method of the present invention is to calculate the object plane, image plane, entrance pupil and exit pupil of each optical surface on the basis of a given system optical path, and calculate the reference wavefront of the central field of view at each entrance pupil and exit pupil; sample the system entrance pupil and field of view to generate a set of characteristic rays, calculate the optical path difference of the characteristic ray of each field of view from the entrance pupil of each surface to its exit pupil relative to the main ray, and obtain the aberration field of each surface by fitting the optical path difference of the entire field of view; determine the contribution of each surface to the dominant aberration according to the current system dominant aberration and the aberration field of each surface, thereby determining the surface to be optimized first; reduce the aberration by optimizing the surface parameters corresponding to the current dominant aberration, and repeat the process until the design meets the requirements.

[0036] In a specific embodiment, the method of the present invention specifically comprises the following steps:

[0037] S1: Establish the initial structure of the free-form surface imaging optical system to be optimized;

[0038] In a specific embodiment of the present invention, the optical system in step S1 includes an aperture stop and a plurality of optical curved surfaces, wherein the surface shape of the optical curved surface is a spherical surface, an aspherical surface, or a free-form surface; wherein the free-form surface is characterized by a Zernike polynomial:

[0039] ;

[0040] Where z is the sag of the free-form surface, c is the curvature of the free-form surface at the vertex, k is the conic coefficient, ρ is the radial coordinate of the free-form surface diameter, and Z j is the jth Zernike polynomial, C j is the coefficient of the j-th Zernike polynomial, and M is the maximum number of terms in the preset Zernike polynomial.

[0041] It should be noted that in this embodiment, the freeform surface is defined using Zernike polynomials. This is primarily because each term in the Zernike polynomial has a clear correspondence with specific aberration types, facilitating more targeted control and adjustment during aberration analysis and optimization. Furthermore, this method is also applicable to freeform surface imaging optical systems defined using other types of polynomials (such as Legendre polynomials and XY polynomials), demonstrating its versatility and scalability.

[0042] S2: According to the position of the aperture stop of the optical system and the spatial posture of each optical surface, the object plane, image plane, entrance pupil and exit pupil positions of each optical surface are calculated, and the reference wavefront of the central field of view at the entrance pupil and exit pupil of each optical surface is calculated.

[0043] In a specific embodiment of the present invention, step S2 specifically includes the following steps:

[0044] The step S2 specifically includes the following steps:

[0045] S21: Calculate the object plane position of each optical surface using the following formula:

[0046] ;

[0047] Where n is the serial number of an optical surface in the optical system, do n is the distance from the object surface of the optical surface to the optical surface along the propagation direction of the main light of the central field of view, s n-1 is the distance from the previous optical surface to the optical surface along the propagation direction of the main light of the central field of view, di n-1 is the distance from the previous optical surface to its image plane along the propagation direction of the principal ray of the central field of view;

[0048] S22: Calculate the image plane position of each optical surface using the following formula:

[0049] ;

[0050] Wherein, di is the distance from the optical surface to the image plane of the optical surface along the propagation direction of the main light of the central field of view, h and h ’ are the incident height and exit height of the paraxial light on the optical surface, u and u respectively. ’ are the object-side aperture angle and image-side aperture angle of the paraxial ray respectively; the definition of do is the same as do n same;

[0051] S23: Calculate the entrance pupil position of each optical surface using the following formula:

[0052] ;

[0053] Wherein, ENP is the distance from the entrance pupil of the optical surface to the optical surface along the propagation direction of the main light of the central field of view;

[0054] S24: Calculate the exit pupil position of each optical surface using the following formula:

[0055] ;

[0056] Wherein, EXP is the distance from the optical surface to its exit pupil along the propagation direction of the principal ray of the central field of view;

[0057] S25: Calculate the reference wavefront radius RDY at the entrance pupil by the following formula i and the reference wavefront radius RDY at the exit pupil o :

[0058] ;

[0059] .

[0060] It should be noted that although the above formula is used in this embodiment to calculate the object plane, image plane, entrance pupil and exit pupil positions of each optical surface, this method is not limited to this calculation method and is also applicable to other calculation methods that can accurately determine the above positional relationships.

[0061] S3: Discretely sample the entrance pupil and field of view of the optical system to generate a set of characteristic rays covering the entrance pupil and the entire field of view.

[0062] In a specific embodiment of the present invention, step S3 specifically includes the following steps:

[0063] With sampling density nrd p , sample the entrance pupil of the optical system and generate the entrance pupil sampling point p x,i 、p y,i ; With sampling density nrd H , sample the field of view of the optical system and generate the field of view sampling point H x,i 、H y,i , and according to the entrance pupil coordinates and field angle parameters of the sampling point, the i-th characteristic light is generated by the following formula:

[0064] ;

[0065] Among them, p x,i 、p y,i are the x and y coordinates of the i-th characteristic light on the entrance pupil plane, H x,i 、H y,i are the field of view angles of the i-th characteristic light in the x-direction and y-direction respectively.

[0066] It should be noted that, although the above formula samples light in this embodiment, the method is not limited to this sampling method, and is also applicable to other light sampling methods that can fully cover the entire entrance pupil and the entire field of view of the system.

[0067] S4: Calculate the propagation path and optical path information of each characteristic light ray by ray tracing, calculate the optical path difference of each field characteristic light ray from the entrance pupil reference wavefront of each optical surface to its exit pupil reference wavefront relative to the principal ray based on the optical path information, and obtain the aberration field distribution of each optical surface by fitting the full field optical path difference.

[0068] In a specific embodiment of the present invention, step S4 specifically includes the following steps:

[0069] S41: Calculate the optical path difference from the entrance pupil reference wavefront to the exit pupil reference wavefront using the following formula:

[0070] ;

[0071] Among them, OPD i OPL is the optical path difference of the i-th characteristic light from the entrance pupil reference wavefront to the exit pupil reference wavefront. i ray is the actual optical path of the characteristic light, δ i ray is the field of view offset of the characteristic light, OPL center is the optical path of the principal ray of the field of view corresponding to the i-th characteristic ray from the entrance pupil reference wavefront to the exit pupil reference wavefront, δ center is the field of view offset of the chief ray;

[0072] The field of view offset of the characteristic ray is calculated by the following formula:

[0073] ;

[0074] Wherein, x0 and y0 are respectively the x and y coordinates of the intersection of the characteristic light and the entrance pupil reference wavefront in the local coordinate system of the entrance pupil reference wavefront, and L0 and M0 are respectively the optical direction cosines of the characteristic light in the x direction and y direction in the local coordinate system of the entrance pupil reference wavefront;

[0075] S42: After calculating the optical path differences of all the characteristic rays, perform a least squares fitting of the Zernike polynomials on the optical path differences of the characteristic rays from the same field of view but different entrance pupil coordinates to obtain the fitted aberration coefficients corresponding to the field of view; further, analyze the aberration field distribution of each optical surface of the optical system using the aberration coefficients of the full field of view; the Zernike polynomials are expressed as follows:

[0076] ;

[0077] Among them, W(H xt ,H yt ) is the total aberration distribution of the optical surface in the tth field of view, Z j is the jth Zernike polynomial, C j is the corresponding aberration coefficient, and M is the maximum number of terms in the preset Zernike polynomial.

[0078] S5: Determine the current dominant aberration of the system according to the aberration field distribution of the current optical system, and determine the contribution of each optical surface to the dominant aberration of the system according to the dominant aberration of the system and the aberration field distribution of each optical surface, thereby determining the optical surface to be optimized first.

[0079] In a specific embodiment of the present invention, step S5 specifically includes the following steps:

[0080] S51: Confirm the dominant aberration component and type of the optical system by the following formula:

[0081] ;

[0082] Among them, W j,total represents the total aberration corresponding to the j-th Zernike polynomial of the optical system, W j,n (H xt ,H yt ) represents the aberration corresponding to the j-th Zernike polynomial on the n-th optical surface in the system at the t-th field of view, N is the total number of optical surfaces in the optical system, T is the total number of field sampling points, and the dominant aberration of the optical system refers to the aberration term with the largest value among the total system aberrations corresponding to the M-term Zernike polynomials;

[0083] S52: For the dominant aberration, the optical surface that is optimized first is selected using the following formula:

[0084] ;

[0085] ;

[0086] Among them, W dom,n It represents the contribution of the nth optical surface in the optical system to the dominant aberration term, η is the set weight factor, W dom,total represents the total system aberration corresponding to the dominant aberration term.

[0087] S6: reducing the dominant aberration of the system by optimizing the surface parameters corresponding to the optical surface to be optimized first and the dominant aberration of the system.

[0088] In a specific embodiment of the present invention, step S6 specifically includes the following steps:

[0089] For the optical surfaces that are optimized first, the surface parameters corresponding to the dominant aberrations are released, and an optimization objective function including distortion constraints, volume constraints, and relative spatial posture constraints of each surface is constructed in the optical design space. The variable parameter combination that minimizes the wavefront error of the optical system is solved through a constrained optimization algorithm.

[0090] S7: Calculate the evaluation function value of the optimized optical system. If the evaluation function value of the optimized system no longer decreases or is less than the target threshold, output the optimized optical system. Otherwise, repeat steps S2-S6.

[0091] Step S7 specifically includes the following steps:

[0092] The evaluation function value σ of the optimized optical system is calculated by the following formula merit :

[0093] ;

[0094] ;

[0095] ;

[0096] Among them, WFE avg Represents the average value of the optical system's wavefront error over the entire field of view, WFE std Indicates the standard deviation of the optical system wavefront error within the entire field of view, WFE t is the wavefront error value of the optical system corresponding to the t-th field of view, and T is the total number of field sampling points.

[0097] It should be noted that although the above steps are used to calculate the evaluation function value of the optical system in this embodiment, this method is not limited to the specific calculation form of the evaluation function, and is also applicable to other evaluation functions customized according to system performance requirements.

[0098] Free-form surfaces are often used in off-axis reflective optical systems. Therefore, the present invention selects a free-form surface off-axis three-mirror system and a free-form surface off-axis four-mirror optical system, and uses the free-form surface imaging aberration propagation calculation and aberration control method described in the present invention, as well as traditional aberration control methods to perform optimization designs respectively to verify the effect of the present invention.

[0099] The definition principles of the positive and negative signs of the optical system structural parameters given in the embodiments of the present invention are as follows:

[0100] The positive and negative signs of the radius of curvature are defined as follows: when the direction from the center of curvature of the lens surface to its vertex is in the same direction as the optical path, it is defined as negative, otherwise it is positive.

[0101] The principle for defining the positive and negative signs of the interval is: if the direction from the intersection of the current surface and the reference axis to the intersection of the next surface and the reference axis is the same as the direction of the optical path, it is positive; otherwise, it is negative.

[0102] The XYZ coordinate system is defined as follows: the Z axis is parallel to the reference axis and in the same direction as the optical path, the Y axis is perpendicular to the Z axis and upward, and the X axis is perpendicular to the plane formed by the Y axis and the Z axis.

[0103] The optical path structure diagram of the free-form surface off-axis three-mirror system selected in the present invention is as follows: Figure 2As shown, the system wavelength is 587nm, the aperture diameter is 200mm, the aperture is 3, the field of view is 4×4°, the volume is limited to within 60L, the distortion is limited to within 1%, and the target threshold of the optimized system evaluation function value is set to 0.07 wavelengths. Table 1 shows the specific structural parameters of each optical surface obtained using the free-form surface imaging aberration propagation calculation and aberration control method described in the present invention. Table 2 shows the Zernike polynomial coefficients of each optical surface. Table 3 shows the specific structural parameters of each optical surface obtained using traditional aberration control methods. Table 4 shows the Zernike polynomial coefficients of each optical surface.

[0104] Table 1 - Structural parameters of the free-form surface off-axis three-mirror system obtained using the method of the present invention

[0105]

[0106] Table 2 - Zernike polynomial coefficients of the free-form surface off-axis three-mirror system obtained using the method of the present invention

[0107]

[0108] Table 3 - Structural parameters of free-form surface off-axis three-mirror system obtained using traditional aberration control method

[0109]

[0110] Table 4 - Zernike polynomial coefficients of free-form surface off-axis three-mirror system obtained using traditional aberration control method

[0111]

[0112] Figure 3 The aberration field distributions of each optical surface of the selected free-form surface off-axis three-mirror system are obtained using the free-form surface imaging aberration propagation calculation method described in the present invention. It should be noted that the aberration field distributions of each optical surface will change during the repetition of steps S2-S5. It can be seen that at the current stage, the dominant aberration of the system is the Z8 term. Setting η to 0.5 determines that the three surfaces of the free-form surface off-axis three-mirror system are the first optical surfaces to be optimized.

[0113] The system wavefront error of the free-form surface off-axis three-mirror system obtained by using the free-form surface imaging aberration propagation calculation and aberration control method of the present invention is as follows: Figure 4 As shown, it can be seen that the evaluation function value is less than the set target threshold at this time.

[0114] Figure 5 is the deviation value of each optical surface of the free-form surface off-axis three-mirror system relative to the ideal spherical surface obtained by the method of the present invention, Figure 6is the deviation value of each optical surface of the free-form surface off-axis three-mirror system relative to the ideal spherical surface obtained by using the traditional aberration control method. It can be seen that the free-form surface off-axis three-mirror system obtained by using the method of the present invention has a smaller total deviation of each optical surface.

[0115] Figure 7 is the gradient value of each optical surface of the free-form surface off-axis three-mirror system relative to the ideal spherical surface obtained by the method of the present invention, Figure 8 The gradient values ​​of each optical surface of the free-form surface off-axis three-mirror system relative to the ideal spherical surface are obtained using the traditional aberration control method. It can be seen that the free-form surface off-axis three-mirror system obtained using the method of the present invention has a smaller total gradient of each optical surface, which is more conducive to processing.

[0116] The optical path structure diagram of the free-form surface off-axis four-mirror system selected in the present invention is as follows: Figure 9 As shown, the system wavelength is 587nm, the aperture diameter is 8mm, the aperture is 10, the field of view is 10×8°, the volume is limited to within 0.15L, the distortion is limited to within 1%, and the target threshold of the optimized system evaluation function value is set to 0.02 wavelengths. Table 5 shows the specific structural parameters of each optical surface obtained using the method of the present invention, Table 6 shows the Zernike polynomial coefficients of each optical surface, Table 7 shows the specific structural parameters of each optical surface obtained using traditional aberration control methods, and Table 8 shows the Zernike polynomial coefficients of each optical surface.

[0117] Table 5 - Structural parameters of the free-form surface off-axis quadruple mirror system obtained using the method of the present invention

[0118]

[0119] Table 6 - Zernike polynomial coefficients of the free-form surface off-axis four-mirror system obtained using the method of the present invention

[0120]

[0121] Table 7 - Structural parameters of the free-form surface off-axis quadruple mirror system obtained using traditional aberration control methods

[0122]

[0123] Table 8 - Zernike polynomial coefficients of free-form surface off-axis quadruple mirror system obtained using traditional aberration control methods

[0124]

[0125] Figure 10 The aberration distribution of each optical surface is obtained using the method of the present invention for a selected free-form surface off-axis four-mirror system.

[0126] The system wavefront error of the free-form surface off-axis four-mirror system obtained by the method of the present invention is shown in FIG. Figure 11 As shown, it can be seen that the evaluation function value is less than the set target threshold at this time.

[0127] Figure 12 is the deviation value of each optical surface of the free-form surface off-axis four-mirror system relative to the ideal spherical surface obtained by the method of the present invention, Figure 13 is the deviation value of each optical surface of the free-form surface off-axis four-mirror system relative to the ideal spherical surface obtained by using the traditional aberration control method. It can be seen that the free-form surface off-axis four-mirror system obtained by using the method of the present invention has a smaller total deviation of each optical surface.

[0128] Figure 14 is the gradient value of each optical surface of the free-form surface off-axis four-mirror system relative to the ideal spherical surface obtained by the method of the present invention, Figure 15 The gradient values ​​of each optical surface of the free-form surface off-axis four-mirror system relative to the ideal spherical surface are obtained using the traditional aberration control method. It can be seen that the free-form surface off-axis four-mirror system obtained using the method of the present invention has a smaller total gradient of each optical surface, which is more conducive to processing.

[0129] In summary, the free-form surface imaging aberration propagation calculation and aberration control method of the present invention can accurately calculate the aberration distribution of each optical surface in the free-form surface imaging optical system, and based on the calculated aberration distribution, the geometric parameters of the free-form surface with better control effect can be adjusted in a targeted manner. Compared with traditional aberration control methods, the aberration control efficiency is higher, and it can ensure that the deviation and gradient of the free-form surface relative to the ideal spherical surface are smaller, which is more conducive to processing.

[0130] The above description is merely an embodiment of the present invention and does not limit the structure of the present invention in any form. Any simple modification, equivalent change and modification made to the above embodiment based on the technical essence of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A method for calculating and controlling aberration propagation of free-form surface imaging, characterized in that: The steps include: S1: Establish the initial structure of the free-form surface imaging optical system to be optimized; S2: Calculate the object plane, image plane, entrance pupil, and exit pupil positions of each optical surface based on the position of the optical system aperture stop and the spatial posture of each optical surface, and calculate the reference wavefront of the central field of view at the entrance pupil and exit pupil of each optical surface; S3: discretely sampling the entrance pupil and field of view of the optical system to generate a set of characteristic rays covering the entrance pupil and the entire field of view; S4: Calculate the propagation path and optical path information of each characteristic light by ray tracing, calculate the optical path difference of each field characteristic light from the entrance pupil reference wavefront of each optical surface to its exit pupil reference wavefront relative to the principal light based on the optical path information, and obtain the aberration field distribution of each optical surface by fitting the full field optical path difference; S5: determining the current dominant aberration of the system according to the aberration field distribution of the current optical system, and determining the contribution of each optical surface to the dominant aberration of the system according to the dominant aberration of the system and the aberration field distribution of each optical surface, thereby determining the optical surface that needs to be optimized first; The step S5 specifically includes the following steps: S51: Confirm the dominant aberration component and type of the optical system by the following formula: ； Among them, W j,total represents the total aberration corresponding to the j-th Zernike polynomial of the optical system, W j,n (H xt ,H yt ) represents the aberration corresponding to the j-th Zernike polynomial on the n-th optical surface in the system at the t-th field of view, N is the total number of optical surfaces in the optical system, T is the total number of field sampling points, and the dominant aberration of the optical system refers to the aberration term with the largest value in the total system aberrations corresponding to the M-term Zernike polynomials; S52: For the dominant aberration, the optical surface that is optimized first is selected using the following formula: ； ； Among them, W dom,n It represents the contribution of the nth optical surface in the optical system to the dominant aberration term, η is the set weight factor, W dom,total represents the total system aberration corresponding to the dominant aberration term; S6: reducing the dominant aberration of the system by optimizing the surface parameters of the optical surface to be optimized first and corresponding to the dominant aberration of the system; S7: Calculate the evaluation function value of the optimized optical system. If the evaluation function value of the optimized system no longer decreases or is less than the target threshold, output the optimized optical system. Otherwise, repeat steps S2-S6.

2. The method for calculating and controlling aberration propagation of free-form surface imaging according to claim 1, wherein: The optical system in step S1 includes an aperture stop and a plurality of optical curved surfaces, wherein the optical curved surfaces are spherical, aspherical, or free-form surfaces; wherein the free-form surfaces are characterized by Zernike polynomials: ； Where z is the sag of the free-form surface, c is the curvature of the free-form surface at the vertex, k is the conic coefficient, ρ is the radial coordinate of the free-form surface diameter, and Z j is the jth Zernike polynomial, C j is the coefficient of the j-th Zernike polynomial, and M is the maximum number of terms in the preset Zernike polynomial.

3. The method for calculating and controlling aberration propagation of free-form surface imaging according to claim 1, wherein: The step S2 specifically includes the following steps: S21: Calculate the object plane position of each optical surface using the following formula: ； Where n is the serial number of an optical surface in the optical system, do n is the distance from the object surface of the optical surface to the optical surface along the propagation direction of the main light of the central field of view, s n-1 is the distance from the previous optical surface to the optical surface along the propagation direction of the main light of the central field of view, di n-1 is the distance from the previous optical surface to its image plane along the propagation direction of the principal ray of the central field of view; S22: Calculate the image plane position of each optical surface using the following formula: ； Wherein, di is the distance from the optical surface to the image surface of the optical surface along the propagation direction of the main light of the central field of view, h and h ’ are the incident height and exit height of the paraxial light on the optical surface, u and u respectively. ’ are the object-side aperture angle and image-side aperture angle of the paraxial ray respectively; the definition of do is the same as do n same; S23: Calculate the entrance pupil position of each optical surface using the following formula: ； Wherein, ENP is the distance from the entrance pupil of the optical surface to the optical surface along the propagation direction of the main light of the central field of view; S24: Calculate the exit pupil position of each optical surface using the following formula: ； Wherein, EXP is the distance from the optical surface to its exit pupil along the propagation direction of the principal ray of the central field of view; S25: Calculate the reference wavefront radius RDY at the entrance pupil by the following formula i and the reference wavefront radius RDY at the exit pupil o : ； 。 4. The method for calculating and controlling aberration propagation of free-form surface imaging according to claim 1, wherein: The step S3 specifically includes the following steps: With sampling density nrd p , sample the entrance pupil of the optical system and generate the entrance pupil sampling point p x,i 、p y,i ; With sampling density nrd H , sample the field of view of the optical system and generate the field of view sampling point H x,i 、H y,i , and according to the entrance pupil coordinates and field angle parameters of the sampling point, the i-th characteristic light is generated by the following formula: ； Among them, p x,i 、p y,i are the x and y coordinates of the i-th characteristic light on the entrance pupil plane, H x,i 、H y,i are the field of view angles of the i-th characteristic light in the x-direction and y-direction respectively.

5. The method for calculating and controlling aberration propagation of free-form surface imaging according to claim 1, wherein: The step S4 specifically includes the following steps: S41: Calculate the optical path difference from the entrance pupil reference wavefront to the exit pupil reference wavefront using the following formula: ； Among them, OPD i OPL is the optical path difference of the i-th characteristic light from the entrance pupil reference wavefront to the exit pupil reference wavefront. i ray is the actual optical path of the characteristic light, δ i ray is the field of view offset of the characteristic light, OPL center is the optical path of the principal ray of the field of view corresponding to the i-th characteristic ray from the entrance pupil reference wavefront to the exit pupil reference wavefront, δ center is the field of view offset of the chief ray; The field of view offset of the characteristic ray is calculated by the following formula: ； Wherein, x0 and y0 are respectively the x and y coordinates of the intersection of the characteristic light and the entrance pupil reference wavefront in the local coordinate system of the entrance pupil reference wavefront, and L0 and M0 are respectively the optical direction cosines of the characteristic light in the x direction and y direction in the local coordinate system of the entrance pupil reference wavefront; S42: After calculating the optical path differences of all the characteristic rays, perform a least squares fitting of the Zernike polynomials on the optical path differences of the characteristic rays from the same field of view but different entrance pupil coordinates to obtain the fitted aberration coefficients corresponding to the field of view; further, analyze the aberration field distribution of each optical surface of the optical system using the aberration coefficients of the full field of view; the Zernike polynomials are expressed as follows: ； Among them, W(H xt ,H yt ) is the total aberration distribution of the optical surface in the tth field of view, Z j is the jth Zernike polynomial, C j is the corresponding aberration coefficient, and M is the maximum number of terms in the preset Zernike polynomial.

6. The method for calculating and controlling aberration propagation of free-form surface imaging according to claim 1, wherein: The step S6 specifically includes the following steps: For the optical surfaces that need to be optimized first, the surface parameters corresponding to the dominant aberrations are released, and an optimization objective function including distortion constraints, volume constraints, and relative spatial posture constraints of each surface is constructed in the optical design space. The variable parameter combination that minimizes the wavefront error of the optical system is solved through the constrained optimization algorithm.

7. The method for calculating and controlling aberration propagation of free-form surface imaging according to claim 1, wherein: The step S7 specifically includes the following steps: The evaluation function value σ of the optimized optical system is calculated by the following formula merit : ； ； ； Among them, WFE avg Represents the average value of the optical system's wavefront error over the entire field of view, WFE std Indicates the standard deviation of the optical system wavefront error within the entire field of view, WFE t is the wavefront error value of the optical system corresponding to the t-th field of view, and T is the total number of field sampling points.

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