Free-form surface optical system design method based on double-Zernike aberration

Abstract

The invention belongs to the technical field of optical design, and particularly relates to a free-form surface optical system design method based on double Zernike aberration. The method comprises the following steps: S1, rewriting an aberration contribution expression of a free-form surface optical system into a first double-Zernike polynomial based on a field-of-view Zernike polynomial and a pupil Zernike polynomial; s2, an offset vector is introduced into a view field vector of the rectangular Zernike polynomial; s3, carrying out the processing of the Zernike aberration of the full view field through employing a least square method, and carrying out the processing of the Zernike aberration of the full view field; and S4, constructing a performance evaluation model, analyzing and calculating the free-form surface component of the optical initial system by using the performance evaluation model, and substituting the free-form surface component into the optical initial system to complete the design of the free-form surface optical system. The free-form surface optical system obtained by the invention has relatively good imaging quality and relatively small free-form surface coefficient.

Description

Technical Field

[0001] The invention belongs to the technical field of optical design, and in particular relates to a free-form surface optical system design method based on double Zernike aberrations. Background Art

[0002] In recent years, the development and application of free-form surfaces have brought great advantages to the design of optical systems. Compared with spherical surfaces and quadratic surfaces, free-form surfaces have multiple degrees of freedom and strong aberration correction capabilities, and break the constraints of rotational symmetry. At the same time, free-form surface optical systems have great advantages in reducing system size, reducing the number of lenses, and reducing system weight, which makes free-form surfaces widely used in optical systems, especially in off-axis reflective optical systems.

[0003] At present, the parameters of free-form surface optical systems are mainly obtained by direct optimization through optical design software. This method uses the damped least squares method to optimize multiple free-form surface variables to meet the image quality requirements of the optical system. However, free-form surfaces have many degrees of freedom, and there are many variables to be optimized. There are aberration coupling problems between the variables, which will cause the optimized free-form surface to have a larger amount of removal than the fitting sphere, which will increase the processing difficulty and manufacturing cost of the free-form surface; it may also fall into a local extreme value during the optimization process and fail to obtain the best free-form surface component. Summary of the invention

[0004] In view of this, the invention aims to provide a free-form surface optical system design method based on double Zernike aberrations, so as to solve the problem that the prior art uses optical design software to design the free-form surface optical system, because the free-form surface has more degrees of freedom, there are many optimized variables, and there is aberration coupling between the variables, resulting in the optimized free-form surface having a larger removal amount relative to its fitting spherical surface, which increases the processing difficulty and manufacturing cost of the free-form surface, and falls into a local extreme value during the optimization process, and cannot obtain the best free-form surface component. The free-form surface optical system obtained by the present invention has better imaging quality and a smaller free-form surface coefficient.

[0005] To achieve the above object, the technical solution created by the present invention is implemented as follows: A free-form surface optical system design method based on double Zernike aberrations specifically comprises the following steps: S1: Based on the surface equation of the Zernike free-form surface, the aberration contribution expression of the free-form surface optical system is derived, and based on the field Zernike polynomial and the pupil Zernike polynomial, the aberration contribution expression of the free-form surface optical system is rewritten into the first double Zernike polynomial; S2: replacing the field of view Zernike polynomial in the first double Zernike polynomial with a rectangular Zernike polynomial, and introducing an offset vector into the field of view vector of the rectangular Zernike polynomial to obtain a second double Zernike polynomial; S3: Calculate the full-field Zernike aberration of the initial optical system using the ray tracing algorithm of the optical design software, and process the full-field Zernike aberration using the least square method to obtain the double Zernike aberration coefficient of the initial optical system; S4: A performance evaluation model is constructed based on the aberration coefficients of the second double Zernike polynomials and the double Zernike aberration coefficients of the optical initial system. The free-form surface components of the optical initial system are analytically calculated using the performance evaluation model. The free-form surface components are substituted into the optical initial system to complete the design of the free-form surface optical system.

[0006] Furthermore, step S1 specifically includes the following steps: S11: Based on the surface equation of the Zernike free-form surface, the Zernike free-form surface components are obtained: ; in, is the surface of the Zernike free-form surface, c is the radius of curvature of the Zernike free-form surface, k is the conic surface coefficient of the Zernike free-form surface, r is the radial coordinate of the Zernike free-form surface, and is the Zernike free surface component composed of all Zernike coefficients and Zernike polynomials of the Zernike free surface; S12: Use optical design software to construct the initial optical structure, introduce the Zernike free-form surface component into the initial optical structure, and obtain the aberration contribution of the free-form surface component of the free-form surface optical system expression: ; ; in, is the normalized field of view vector, is the pupil vector, is the refractive index difference between the image and object sides of the free-form surface optical system, is the inclination angle of the chief ray at the edge of the field of view, is the height of the principal ray of the edge field of view on the free-form optical system, is the height of the intersection of the edge ray and the free-form optical system, t is the entrance pupil distance and the size of the primary mirror of the free-form optical system, is the displacement of the imaging aperture of the light of different fields of view on the free-form surface optical system; S13: Set the incident angle of the principal ray of different fields of view of the free-form surface optical system to , then the aberration contribution of the free-form surface optical system to the off-axis field of view is for: ; S14: The incident angle of the main ray of different fields of view on the primary mirror of the free-form surface optical system is calculated by the following formula: ; ; ; in, is the radius of curvature, is the normalized field of view, is the inclination angle of the main ray of the current field of view in the primary mirror, is the height of the chief ray of the current field of view on the primary mirror, is the vector of the field of view, is the scalar of the field of view. Different values ​​of h represent different fields of view. and are the values ​​of two different directions of the field of view, is the incident angle of the corresponding field of view on the primary mirror, pm is the mirror number of the free-form optical system; S15: Based on the calculation result of step S14, the cosine value of the incident angle Perform Taylor expansion: ; ; in, It is an intermediate parameter with no physical meaning. For different mirrors, the value of A is different. pm is the mirror number of the free-form surface optical system; S16: Replace the primary mirror with the next mirror, and repeat steps S14-S15 until the Taylor expansions of all mirrors are obtained; S17: Aberration contribution to the free-form surface optical system based on the calculation results of step S16 To update: ; S18: Based on the updated result of step S17, the aberration contribution expression of the free-form surface optical system is expressed as Rewritten as the first pair of Zernike polynomials , so that the aberration of the free-form optical system is orthogonal in the pupil domain and the field of view domain: ; in, is the total aberration contribution of the free-form surface component, is the field of view Zernike polynomial, is the pupil Zernike polynomial.

[0007] Further, in step S18, the aberration contribution of the free-form surface components of different mirrors is calculated based on the first double Zernike polynomials, and the aberration contribution of the free-form surface components of each mirror is added to obtain the total aberration contribution of the free-form surface components. The free-form surface component C of the first double Zernike polynomials is 5 -C 16 for: ; ; ; ; ; ; ; in, , x is a constant, is the refractive index difference between the image and object sides of the free-form surface optical system, is the height of the principal ray of the edge field of view on the free-form optical system, is the intersection height of the edge ray and the free-form optical system, Different kl correspond to different terms of the field of view Zernike polynomial, Different values ​​of nm correspond to different terms in the pupil Zernike polynomials.

[0008] Further, in step S2, the second double Zernike polynomial for: ; in, is the offset vector, is the field of view rectangle Zernike polynomial, is the pupil Zernike polynomial, To introduce the offset vector The aberration coefficient of the free-form surface component after .

[0009] Furthermore, in step S4, the performance evaluation model for: ; in, is the minimum value, is the double Zernike aberration coefficient of the initial optical system.

[0010] Furthermore, in step S4, the total aberration contribution of the free-form surface component is rewritten into a Zernike aberration coefficient in matrix form: ; in, is the structural parameter of the initial optical system, Free-form surface parameters introduced for different mirrors.

[0011] Further, in step S4, the free surface component of the optical initial system is solved based on the performance evaluation model : ; ; in, is the radius of curvature of the mirror, is the normalized field of view, t is the entrance pupil distance and the size of the primary mirror of the free-form optical system.

[0012] Compared with the prior art, the invention can achieve the following beneficial effects: The present invention creates the free-form surface optical system design method based on double Zernike aberrations, solves the problem of solving the free-form surface component of the optical system, realizes the analytical expression of the aberration of the free-form surface optical system through double Zernike polynomials, calculates the full-field RMS of the optical system using the corresponding double Zernike aberration coefficients, establishes a system performance evaluation model, and finally solves the free-form surface component of the optical system through the least squares method. Compared with the built-in optimization algorithm of the optical design software, the analytical calculation method of the present invention obtains an optical system with smaller RMS and average MTF in the full field of view, better imaging quality, and a smaller free-form surface coefficient, and a smaller processing removal amount relative to the fitting sphere, which can reduce the difficulty of processing and manufacturing free-form surface optical elements and reduce manufacturing costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The drawings constituting part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation on the present invention. In the drawings: Figure 1 A schematic flow chart of a method for designing a free-form surface optical system based on double Zernike aberrations according to an embodiment of the present invention; Figure 2A schematic diagram of the imaging effect of the Zernike free-form surface in an optical system according to an embodiment of the present invention; Figure 3 A schematic diagram of aberration contribution of a free-form surface considering the incident angle described in an embodiment of the present invention; Figure 4 A schematic diagram of a rectangular field of view with a certain field of view deviation angle described in an embodiment of the present invention; Figure 5 A schematic diagram of the structure of an off-axis reflective optical system according to an embodiment of the present invention; FIG6 (a) is a schematic diagram of 0° MTF of each field of view of the initial off-axis reflective optical system according to an embodiment of the present invention; FIG6( b ) is a schematic diagram of the 90° MTF of each field of view of the initial off-axis reflective optical system according to an embodiment of the present invention; FIG. 7 (a) is a schematic diagram of the 0° MTF of each field of view of the optical system obtained by CODE V according to an embodiment of the present invention; FIG. 7 ( b ) is a schematic diagram of the 90° MTF of each field of view of the optical system obtained by CODE V according to an embodiment of the present invention; FIG8 (a) is a schematic diagram of the 0° MTF of each field of view of the optical system obtained by using the free-form surface optical system design method based on double Zernike aberrations according to an embodiment of the present invention; FIG8( b ) is a schematic diagram of the 90° MTF of each field of view of the optical system obtained by using the free-form surface optical system design method based on double Zernike aberrations according to an embodiment of the present invention; FIG9 (a) is a histogram of the free-form surface component of the secondary mirror according to an embodiment of the present invention; FIG9( b ) is a histogram of the free-form surface components of the three mirrors described in the embodiment of the invention.

[0014] Description of reference numerals: 1. Primary mirror; 2. Secondary mirror; 3. Third mirror; 4. Aperture; 5. First plane mirror; 6. Second plane mirror. DETAILED DESCRIPTION

[0015] In order to make the purpose, technical solution and advantages of the invention more clear, the invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the invention and do not constitute a limitation of the invention.

[0016] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0017] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0018] In the description of the invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the invention can be understood according to specific circumstances.

[0019] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0020] like Figure 1 As shown, a free-form surface optical system design method based on double Zernike aberrations specifically includes the following steps: S1: Based on the surface equation of the Zernike free-form surface, the aberration contribution expression of the free-form surface optical system is derived, and the aberration contribution expression of the free-form surface optical system is rewritten into the first double Zernike polynomial based on the field Zernike polynomial and the pupil Zernike polynomial; S2: The field Zernike polynomial in the first double Zernike polynomial is replaced by a rectangular Zernike polynomial, and an offset vector is introduced into the field vector of the rectangular Zernike polynomial to obtain the second double Zernike polynomial; S3: The full-field Zernike aberration of the optical initial system is calculated using the ray tracing algorithm of the optical design software, and the full-field Zernike aberration is processed using the least squares method to obtain the double Zernike aberration coefficient of the optical initial system; S4: A performance evaluation model is constructed based on the aberration coefficient of the second double Zernike polynomial and the double Zernike aberration coefficient of the optical initial system, and the free-form surface component of the optical initial system is analytically calculated using the performance evaluation model, and the free-form surface component is substituted into the optical initial system to complete the design of the free-form surface optical system.

[0021] In some embodiments, step S1 specifically includes the following steps: S11: Based on the surface equation of the Zernike free-form surface, the Zernike free-form surface components are obtained: ; in, is the surface of the Zernike free-form surface, c is the radius of curvature of the Zernike free-form surface, k is the conic surface coefficient of the Zernike free-form surface, r is the radial coordinate of the Zernike free-form surface, and is the Zernike free surface component composed of all Zernike coefficients and Zernike polynomials of the Zernike free surface; S12: Use optical design software to construct the initial optical structure, introduce the Zernike free-form surface component into the initial optical structure, and obtain the aberration contribution of the free-form surface component of the free-form surface optical system expression: ; ; in, is the normalized field of view vector, is the pupil vector, is the refractive index difference between the image and object sides of the free-form surface optical system, is the inclination angle of the chief ray at the edge of the field of view, is the height of the principal ray of the edge field of view on the free-form optical system, is the height of the intersection of the edge ray and the free-form optical system, t is the entrance pupil distance and the size of the primary mirror of the free-form optical system, is the displacement of the imaging aperture of the light of different fields of view on the free-form surface optical system; It should be noted that the introduced Zernike free-form surface component can be regarded as an additional non-rotationally symmetric surface shape change on the optical surface. When the free-form surface is at the aperture position, the footprints of imaging beams of different fields of view on the free-form surface are the same, so the aberration contribution of the off-axis field of view and the on-axis field of view is the same (ignoring the incident angle). When the free-form surface is located on the non-aperture surface, the footprints of imaging beams of different fields of view on the free-form surface are different, because the imaging aperture of light from different fields of view on the free-form surface will have The offset, such as Figure 2 shown.

[0022] Furthermore, since the contribution of free-form surface aberration is regarded as a change in the actual wavefront optical path, the above conclusion will no longer apply when the off-axis field of view is too large, such as Figure 3 As shown. At this time, we need to consider the incident angle of different off-axis fields of view on the free-form surface. The incident angle of light is related to the field of view of the light and the coordinates of the pupil. For wide-field free-form surface reflection systems, free-form surfaces are often used to correct off-axis aberrations. At this time, the change of the incident angle of light with the field of view is more significant. Therefore, the incident angle can be regarded as only related to the field of view H, and the incident angle of the main light of different fields of view is used In this way, the optical axis ray equation can be used to Perform tracing calculations face by face.

[0023] S13: Set the incident angle of the principal ray of different fields of view of the free-form surface optical system to , then the aberration contribution of the free-form surface optical system to the off-axis field of view is for: ; S14: The incident angle of the main ray of different fields of view on the primary mirror of the free-form surface optical system is calculated by the following formula: ; ; ; in, is the radius of curvature, is the normalized field of view, is the inclination angle of the main ray of the current field of view in the primary mirror, is the height of the chief ray of the current field of view on the primary mirror, is the vector of the field of view, is the scalar of the field of view. Different values ​​of h represent different fields of view. and are the values ​​of two different directions of the field of view, is the incident angle of the corresponding field of view on the primary mirror, pm is the mirror number of the free-form optical system; S15: Based on the calculation result of step S14, the cosine value of the incident angle Perform Taylor expansion (only the first two Taylor formulas are considered here): ; ; in, is an intermediate parameter with no physical meaning. For different mirrors, the value of A is different. pm is the mirror number of the free-form optical system. It should be noted that when the mirror is located at the aperture, t=0 can be used. For the convenience of calculation, ,and The relevant term is the aberration contribution introduced by taking into account the angle of incidence.

[0024] S16: Replace the primary mirror with the next mirror, and repeat steps S14-S15 until the Taylor expansions of all mirrors are obtained; S17: Aberration contribution to the free-form surface optical system based on the calculation results of step S16 To update: ; S18: Based on the updated result of step S17, the aberration contribution expression of the free-form surface optical system is expressed as Rewritten as the first pair of Zernike polynomials , so that the aberration of the free-form optical system is orthogonal in the pupil domain and the field of view domain: ; in, is the total aberration contribution of the free-form surface component, is the field of view Zernike polynomial, is the pupil Zernike polynomial.

[0025] In some embodiments, there are many ways to order Zernike polynomials, and FringeZernike polynomials are used here.

[0026] In some embodiments, in step S18, the aberration contribution of the free-form surface components of different mirrors is calculated based on the first double Zernike polynomial, and the aberration contribution of the free-form surface components of each mirror is added to obtain the total aberration contribution of the free-form surface components. The free-form surface component C of the first double Zernike polynomial is5 -C 16 for: ; ; ; ; ; ; ; in, , x is a constant, such as Can be used Instead, these definitions also apply below. is the refractive index difference between the image and object sides of the free-form surface optical system, is the height of the principal ray of the edge field of view on the free-form optical system, is the intersection height of the edge ray and the free-form optical system, Different kl correspond to different terms of the field of view Zernike polynomial, Different values ​​of nm correspond to different terms in the pupil Zernike polynomials.

[0027] In practical applications, such as Figure 4 As shown in the figure, the field of view of the initial optical system is mostly a rectangular field of view. In order to achieve the off-axis effect, there will be a certain field of view deviation angle. For such optical systems, using the traditional circular Zernike polynomial to fit the field of view will lead to inaccurate results, so it is necessary to use the rectangular Zernike polynomial.

[0028] The Gram-Schmidt orthogonalization method can be used to realize the conversion of circular Zernike to rectangular Zernike polynomials, that is, the first double Zernike polynomial is converted into the second double Zernike polynomial.

[0029] In some embodiments, the second bi-Zernike polynomial for: ; in, is the offset vector, is the field of view rectangle Zernike polynomial, is the pupil Zernike polynomial, To introduce the offset vector By calculating the coefficients of the second double Zernike polynomial, the full field of view RMS of the off-axis optical system with a rectangular field of view can be obtained.

[0030] In some embodiments, the optical design software includes CODE V software.

[0031] In step S4, since the double Zernike polynomials realize the orthogonality of aberrations in the field of view and pupil domains, the full-field RMS calculated corresponding to the double Zernike aberration coefficients can be used to evaluate the performance of the initial optical system in the full field of view. If the performance of the obtained free-form surface optical system is optimal, the following formula needs to be satisfied: ; in, is the minimum value, is the double Zernike aberration coefficient of the initial optical system.

[0032] In some embodiments, the total aberration contribution of the free-form surface component is rewritten as Zernike aberration coefficients in matrix form: ; in, is the structural parameter of the initial optical system, Free-form surface parameters introduced for different mirrors.

[0033] In some embodiments, the free-form surface component of the optical initial system is solved based on the performance evaluation model. : ; ; in, is the radius of curvature of the mirror, is the normalized field of view, t is the entrance pupil distance and the size of the primary mirror of the free-form optical system.

[0034] like Figure 5 As shown, an off-axis optical system with a field of view is designed using optical design software. The focal length of the off-axis optical system is 5840 mm, the aperture 4 is located at the primary mirror 1, the aperture is 420 mm, the field of view is 1.15°×0.025°, and the field of view deviation angle is -1.025°. Now consider introducing a free-form surface in the secondary mirror 2 and the third mirror 3. The optical system is optimized according to the analytical calculation method of the present invention and the damped least squares method of CODE V, and the obtained free-form surface components are shown in Table 1: Table 1 Free-form surface components of secondary mirror 2 and tertiary mirror 3 (comparison between the present invention and the CODE V damped least squares method)

[0035] The MTF of the optical system obtained by the present invention and the damped least squares method at 0° and 90° in each field of view at 50lp / mm are shown in Figures 7(a), 7(b), 8(a) and 8(b), which are greatly improved compared with the MTF Figures 6(a) and 6(b) of the initial system. The larger the circle in the figure, the better the performance. The average RMS of the full-field aberration and the average MTF of the full-field are shown in Table 2. The RMS of the full-field aberration is the root mean square operation of the RMS of different field aberrations, which is used to describe the overall performance of the optical system within the effective field of view. The calculation formula is as follows: ; Where N is the field number, is the RMS of the aberration of the Nth field of view.

[0036] Table 2 Comparison of full field aberration RMS and average MTF

[0037] It can be found from Table 1 that the RMS of the free-form surface components of the secondary mirror 2 and the third mirror 3 obtained by analytical calculation of the present invention are 3.43e-04mm and 0.002mm respectively, which are smaller than 0.0136mm and 0.0145mm obtained by the damped least squares method of the optical design software. The difference between the two optimization methods can be more intuitively seen from Figures 9 (a) and 9 (b); it can be seen from Table 2 that the full-field aberration RMS of the optical system optimized by the present invention is 0.0695 wavelengths, which is slightly better than the optimization result of the damped least squares method. This result is reduced by about 50% compared with the off-axis initial system, and the average MTF of the optical system obtained by analytical calculation in the full field of view is better than the design result of the damped least squares method. According to the above results, it can be seen that the imaging quality of the optical system obtained by analytical calculation is better than the optimization result of the damped least squares method while ensuring that the free-form surface components of the secondary mirror and the third mirror are small. This can reduce the difficulty of processing and manufacturing free-form surfaces and reduce production costs to a certain extent.

[0038] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0039] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A free-form surface optical system design method based on double Zernike aberration, characterized by: The specific steps include: S1: Based on the surface equation of the Zernike free-form surface, the aberration contribution expression of the free-form surface optical system is derived, and based on the field Zernike polynomial and the pupil Zernike polynomial, the aberration contribution expression of the free-form surface optical system is rewritten into the first double Zernike polynomial; S2: replacing the field of view Zernike polynomial in the first double Zernike polynomial with a rectangular Zernike polynomial, and introducing an offset vector into the field of view vector of the rectangular Zernike polynomial to obtain a second double Zernike polynomial; S3: Calculate the full-field Zernike aberration of the initial optical system using the ray tracing algorithm of the optical design software, and process the full-field Zernike aberration using the least square method to obtain the double Zernike aberration coefficient of the initial optical system; S4: Construct a performance evaluation model based on the aberration coefficients of the second double Zernike polynomials and the double Zernike aberration coefficients of the optical initial system, and use the performance evaluation model to analytically calculate the free-form surface components of the optical initial system, substitute the free-form surface components into the optical initial system, and complete the design of the free-form surface optical system.

2. The free-form surface optical system design method based on double Zernike aberration according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11: Based on the surface equation of the Zernike free-form surface, the Zernike free-form surface components are obtained: ； in, is the surface of the Zernike free-form surface, c is the radius of curvature of the Zernike free-form surface, k is the conic surface coefficient of the Zernike free-form surface, r is the radial coordinate of the Zernike free-form surface, and is the Zernike free surface component composed of all Zernike coefficients and Zernike polynomials of the Zernike free surface; S12: Use optical design software to construct the initial optical structure, introduce the Zernike free-form surface component into the initial optical structure, and obtain the aberration contribution of the free-form surface component of the free-form surface optical system expression: ； ； in, is the normalized field of view vector, is the pupil vector, is the refractive index difference between the image and object sides of the free-form surface optical system, is the inclination angle of the chief ray at the edge of the field of view, is the height of the principal ray of the edge field of view on the free-form optical system, is the height of the intersection of the edge ray and the free-form optical system, t is the entrance pupil distance and the size of the primary mirror of the free-form optical system, is the displacement of the imaging aperture of the light of different fields of view on the free-form surface optical system; S13: Set the incident angle of the principal ray of different fields of view of the free-form surface optical system to , then the aberration contribution of the free-form surface optical system to the off-axis field of view is for: ； S14: The incident angle of the main ray of different fields of view on the primary mirror of the free-form surface optical system is calculated by the following formula: ； ； ； in, is the radius of curvature, is the normalized field of view, is the inclination angle of the main ray of the current field of view in the primary mirror, is the height of the chief ray of the current field of view on the primary mirror, is the vector of the field of view, is the scalar of the field of view. Different values ​​of h represent different fields of view. and are the values ​​of two different directions of the field of view, is the incident angle of the corresponding field of view on the primary mirror, pm is the mirror number of the free-form optical system; S15: Based on the calculation result of step S14, the cosine value of the incident angle Perform Taylor expansion: ； ； in, It is an intermediate parameter with no physical meaning. For different mirrors, the value of A is different. pm is the mirror number of the free-form surface optical system; S16: Replace the primary mirror with the next mirror, and repeat steps S14-S15 until the Taylor expansions of all mirrors are obtained; S17: Aberration contribution to the free-form surface optical system based on the calculation results of step S16 To update: ； S18: Based on the updated result of step S17, the aberration contribution expression of the free-form surface optical system is expressed as Rewritten as the first pair of Zernike polynomials , so that the aberration of the free-form optical system is orthogonal in the pupil domain and the field of view domain: ； in, is the total aberration contribution of the free-form surface component, is the field of view Zernike polynomial, is the pupil Zernike polynomial.

3. The free-form surface optical system design method based on double Zernike aberration according to claim 2, characterized in that: In step S17, the aberration contribution of the free-form surface components of different mirrors is calculated based on the first double Zernike polynomials, and the aberration contribution of the free-form surface components of each mirror is added to obtain the total aberration contribution of the free-form surface components. The free-form surface components C5-C 16 for: ； ； ； ； ； ； ； in, , x is a constant, is the refractive index difference between the image and object sides of the free-form surface optical system, is the height of the principal ray of the edge field of view on the free-form optical system, is the intersection height of the edge ray and the free-form optical system, Different kl correspond to different terms of the field of view Zernike polynomial, Different values ​​of nm correspond to different terms in the pupil Zernike polynomials.

4. The free-form surface optical system design method based on double Zernike aberration according to claim 1, characterized in that: In step S2, the second double Zernike polynomial for: ； in, is the offset vector, is the field of view rectangle Zernike polynomial, is the pupil Zernike polynomial, To introduce the offset vector The aberration coefficient of the free-form surface component after the image is obtained.

5. The free-form surface optical system design method based on double Zernike aberration according to claim 4, characterized in that: In step S4, the performance evaluation model for: ； in, is the minimum value, is the double Zernike aberration coefficient of the initial optical system.

6. The method for designing a free-form surface optical system based on double Zernike aberrations according to claim 5, characterized in that: In step S4, the total aberration contribution of the free-form surface component is rewritten into a Zernike aberration coefficient in matrix form: ； in, is the structural parameter of the initial optical system, Free-form surface parameters introduced for different mirrors.

7. The method for designing a free-form surface optical system based on double Zernike aberrations according to claim 6, characterized in that: In step S4, the free surface component of the optical initial system is solved based on the performance evaluation model : ； ； in, is the radius of curvature of the mirror, is the normalized field of view, t is the entrance pupil distance and the size of the primary mirror of the free-form optical system.

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