Design method of free-form surface optical system based on double Zernike aberration

Abstract

The present invention belongs to the field of optical design technology, and in particular relates to a free-form surface optical system design method based on double Zernike aberrations. S1: Based on the field Zernike polynomial and the pupil Zernike polynomial, the aberration contribution expression of the free-form surface optical system is rewritten as a first double Zernike polynomial; S2: An offset vector is introduced into the field vector of the rectangular Zernike polynomial; S3: The full-field Zernike aberration is processed using the least squares method; S4: A performance evaluation model is constructed, and the free-form surface components of the optical initial system are analytically calculated using the performance evaluation model, and the free-form surface components are substituted 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 present invention has good imaging quality and a small free-form surface coefficient.

Description

Technical Field

[0001] The present 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 has brought significant advantages to the design of optical systems. Compared to spherical and quadratic surfaces, free-form surfaces offer multiple degrees of freedom, strong aberration correction capabilities, and break the constraints of rotational symmetry. Free-form optical systems also offer significant advantages in reducing system size, lens count, and weight. This has led to their widespread application in optical systems, particularly in off-axis reflective optical systems.

[0003] Currently, the parameters of free-form optical systems are primarily optimized directly using optical design software. This method uses damped least squares to optimize multiple free-form surface variables to achieve the required image quality. However, free-form surfaces have many degrees of freedom, and there are many variables to optimize. This can lead to aberration coupling between these variables, which can cause the optimized free-form surface to have a larger amount of removal than the fitted sphere. This increases the difficulty and manufacturing cost of free-form surface processing. Furthermore, the optimization process may lead to local extrema, preventing the optimal free-form surface components from being obtained. Summary of the Invention

[0004] In view of this, the present invention aims to provide a free-form surface optical system design method based on double Zernike aberrations to solve the problem of using optical design software to design free-form surface optical systems in the prior art. Because free-form surfaces have many degrees of freedom and many variables to optimize, there is aberration coupling between the variables, resulting in the optimized free-form surface having a larger amount of removal relative to its fitting sphere, which increases the processing difficulty and manufacturing cost of the free-form surface. In addition, the optimization process may lead to falling into local extreme values ​​and making it impossible to obtain the optimal free-form surface components. 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:

[0006] A free-form surface optical system design method based on double Zernike aberrations specifically includes the following steps:

[0007] 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 as the first double Zernike polynomial based on the field Zernike polynomial and the pupil Zernike polynomial;

[0008] 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;

[0009] 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 squares method to obtain the double Zernike aberration coefficient of the initial optical system;

[0010] S4: Construct a performance evaluation model based on the aberration coefficients of the second double Zernike polynomial and the double Zernike aberration coefficients of the initial optical system. Use the performance evaluation model to analytically calculate the free-form surface components of the initial optical system. Substitute the free-form surface components into the initial optical system to complete the design of the free-form surface optical system.

[0011] Furthermore, step S1 specifically includes the following steps:

[0012] S11: Based on the surface equation of the Zernike free-form surface, the Zernike free-form surface components are obtained:

[0013] ;

[0014] in, is the surface of the Zernike free-form surface, c is the curvature radius 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;

[0015] 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:

[0016] ;

[0017] ;

[0018] 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 optical system, is the chief ray inclination angle 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;

[0019] S13: Set the incident angle of the principal ray of the free-form surface optical system at different fields of view to , then the aberration contribution of the free-form optical system to the off-axis field of view is for:

[0020] ;

[0021] S14: Calculate the incident angle of the principal ray of different fields of view on the primary mirror of the free-form optical system using the following formula:

[0022] ;

[0023] ;

[0024] ;

[0025] 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 ​​in 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;

[0026] S15: Based on the calculation result of step S14, the cosine value of the incident angle Perform Taylor expansion:

[0027] ;

[0028] ;

[0029] in, It is an intermediate parameter with no physical meaning. The value of A is different for different mirrors. pm is the mirror number of the free-form optical system.

[0030] S16: Replace the primary mirror with the next mirror and repeat steps S14-S15 until the Taylor expansions of all mirrors are obtained;

[0031] S17: Based on the calculation results of step S16, the aberration contribution to the free-form surface optical system To update:

[0032] ;

[0033] 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 aberrations of the free-form optical system are orthogonal in the pupil domain and the field of view domain:

[0034] ;

[0035] in, is the total aberration contribution of the free-form surface component, is the field of view Zernike polynomial, is the pupil Zernike polynomial.

[0036] Furthermore, 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 together to obtain the total aberration contribution of the free-form surface components. The free-form surface component C5-C 16 for:

[0037] ;

[0038] ;

[0039] ; ;

[0040] ;

[0041] ; ;

[0042] in, , x is a constant, is the refractive index difference between the image and object sides of the free-form 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 polynomials, Different values ​​of nm correspond to different terms in the pupil Zernike polynomials.

[0043] Furthermore, in step S2, the second double Zernike polynomial for:

[0044] ;

[0045] 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.

[0046] Furthermore, in step S4, the performance evaluation model for:

[0047] ;

[0048] in, is the minimum value, is the double Zernike aberration coefficient of the initial optical system.

[0049] Furthermore, in step S4, the total aberration contribution of the free-form surface component is rewritten into a Zernike aberration coefficient in matrix form:

[0050] ;

[0051] in, is the structural parameter of the initial optical system, Free-form surface parameters introduced for different mirrors.

[0052] Furthermore, in step S4, the free surface component of the optical initial system is solved based on the performance evaluation model. :

[0053] ;

[0054] ;

[0055] in, is the curvature radius 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.

[0056] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0057] The present invention creates a free-form surface optical system design method based on double Zernike aberrations, solving the problem of solving the free-form surface component of an optical system. The present invention uses double Zernike polynomials to achieve an analytical expression of the aberrations of the free-form surface optical system, uses the corresponding double Zernike aberration coefficients to calculate the full-field RMS of the optical system, establishes a system performance evaluation model, and finally solves the free-form surface component of the optical system using the least squares method. Compared with the built-in optimization algorithm of optical design software, the analytical calculation method of the present invention can obtain an optical system with a lower RMS and average MTF over the full field of view, better imaging quality, and a smaller free-form surface coefficient. Compared with the machining removal amount of the fitted sphere, it can reduce the difficulty and manufacturing cost of free-form surface optical components. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The accompanying drawings, which constitute part of the present invention, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0059] 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;

[0060] Figure 2 A schematic diagram of the imaging effect of the Zernike free-form surface in an optical system according to an embodiment of the present invention;

[0061] Figure 3 A schematic diagram of aberration contribution of a free-form surface considering the incident angle according to an embodiment of the present invention;

[0062] Figure 4 A schematic diagram of a rectangular field of view with a certain field of view deviation angle as described in an embodiment of the present invention;

[0063] Figure 5 A schematic structural diagram of an off-axis reflective optical system according to an embodiment of the present invention;

[0064] FIG6( a ) is a schematic diagram of the 0° MTF of each field of view of the initial off-axis reflective optical system according to an embodiment of the present invention;

[0065] 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;

[0066] FIG7( 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;

[0067] FIG7( 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;

[0068] 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;

[0069] 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;

[0070] FIG9( a ) is a histogram of the free-form surface component of the secondary mirror according to an embodiment of the present invention;

[0071] FIG9( b ) is a histogram of the free-form surface components of the three mirrors according to an embodiment of the present invention.

[0072] Description of reference numerals:

[0073] 1. Primary mirror; 2. Secondary mirror; 3. Tertiary mirror; 4. Aperture stop; 5. First plane mirror; 6. Second plane mirror. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0075] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0076] 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 orientations or positional relationships based on the orientations 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" and the like are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, features defined as "first", "second" and the like 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.

[0077] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art can understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0078] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0079] like Figure 1 As shown, a free-form surface optical system design method based on double Zernike aberrations specifically includes the following steps:

[0080] 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 of view Zernike polynomial and the pupil Zernike polynomial; S2: The field of view Zernike polynomial in the first double Zernike polynomial is replaced by a rectangular Zernike polynomial, and an offset vector is introduced into the field of view 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 performance evaluation model is used to analytically calculate the free-form surface component of the optical initial system, and the free-form surface component is substituted into the optical initial system to complete the design of the free-form surface optical system.

[0081] In some embodiments, step S1 specifically includes the following steps:

[0082] S11: Based on the surface equation of the Zernike free-form surface, the Zernike free-form surface components are obtained:

[0083] ;

[0084] in, is the surface of the Zernike free-form surface, c is the curvature radius 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;

[0085] 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:

[0086] ;

[0087] ;

[0088] 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 chief ray inclination angle 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;

[0089] 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 the imaging beams of different fields of view on the free-form surface are the same, so the aberration contributions of the off-axis field of view and the on-axis field of view are the same (ignoring the incident angle). When the free-form surface is located on the non-aperture surface, the footprints of the imaging beams of different fields of view on the free-form surface are different, because the imaging aperture of the light of different fields of view on the free-form surface will have different The offset, such as Figure 2 shown.

[0090] 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, it is necessary 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 with different fields of view is used. To express it. This way, we can use the optical axis ray equation to Perform tracing calculations face by face.

[0091] S13: Set the incident angle of the principal ray of the free-form surface optical system at different fields of view to , then the aberration contribution of the free-form surface optical system to the off-axis field of view is for:

[0092] ;

[0093] S14: Calculate the incident angle of the principal ray of different fields of view on the primary mirror of the free-form optical system using the following formula:

[0094] ;

[0095] ;

[0096] ;

[0097] 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 ​​in 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;

[0098] 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):

[0099] ;

[0100] ;

[0101] 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 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, we can set ,and The relevant term is the contribution of aberration introduced by taking into account the angle of incidence.

[0102] S16: Replace the primary mirror with the next mirror and repeat steps S14-S15 until the Taylor expansions of all mirrors are obtained;

[0103] S17: Based on the calculation results of step S16, the aberration contribution to the free-form surface optical system To update:

[0104] ;

[0105] S18: Based on the updated result of step S17, the aberration contribution expression of the free-form surface optical system is expressed as follows: Rewritten as the first pair of Zernike polynomials , so that the aberrations of the free-form optical system are orthogonal in the pupil domain and the field of view domain:

[0106] ;

[0107] in, is the total aberration contribution of the free-form surface component, is the field of view Zernike polynomial, is the pupil Zernike polynomial.

[0108] In some embodiments, there are many ways to order Zernike polynomials, and FringeZernike polynomials are used here.

[0109] 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 components C5-C 16 for:

[0110] ;

[0111] ;

[0112] ; ;

[0113] ;

[0114] ; ;

[0115] 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 polynomials, Different values ​​of nm correspond to different terms in the pupil Zernike polynomials.

[0116] In practical applications, such as Figure 4 As shown in the figure, the field of view of most initial optical systems is rectangular. To achieve the off-axis effect, there will be a certain field of view deviation angle. For such optical systems, using traditional circular Zernike polynomials to fit the field of view will result in inaccurate results, so rectangular Zernike polynomials are needed.

[0117] The Gram-Schmidt orthogonalization method can be used to convert circular Zernike polynomials to rectangular Zernike polynomials, that is, to convert the first double Zernike polynomials into the second double Zernike polynomials.

[0118] In some embodiments, the second bi-Zernike polynomial for:

[0119] ;

[0120] in, is the offset vector, is the Zernike polynomial of the field of view rectangle, is the pupil Zernike polynomial, To introduce the offset vector The aberration coefficient of the free-form surface component after the image is obtained. 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.

[0121] In some embodiments, the optical design software includes CODE V software.

[0122] In step S4, since the double Zernike polynomials achieve 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 to be optimal, the following formula must be satisfied:

[0123] ;

[0124] in, is the minimum value, is the double Zernike aberration coefficient of the initial optical system.

[0125] In some embodiments, the total aberration contribution of the freeform surface component is rewritten as a Zernike aberration coefficient in matrix form:

[0126] ;

[0127] in, is the structural parameter of the initial optical system, Free-form surface parameters introduced for different mirrors.

[0128] In some embodiments, the free-form surface component of the optical initial system is solved based on the performance evaluation model. :

[0129] ;

[0130] ;

[0131] in, is the curvature radius 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.

[0132] 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 free-form surfaces in the secondary mirror 2 and the tertiary 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. The free-form surface components obtained are shown in Table 1:

[0133] 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)

[0134]

[0135] The MTFs of the optical system obtained by the present invention and the damped least squares method at 0° and 90° at 50 lp / mm for each field of view are shown in Figures 7(a), 7(b), 8(a), and 8(b). Compared with the MTFs of the initial system in Figures 6(a) and 6(b), they are significantly improved. The larger the circle in the figure, the better the performance. The average RMS of the full-field aberrations and the average MTF of the full-field aberrations are compared in Table 2. The RMS of the full-field aberrations is the root mean square operation of the RMS of the aberrations in different fields of view, which is used to describe the overall performance of the optical system within the effective field of view. The calculation formula is as follows:

[0136] ;

[0137] Where N is the field number, is the RMS of the aberration of the Nth field of view.

[0138] Table 2. Comparison of full-field aberration RMS and average MTF

[0139]

[0140] Table 1 shows that the RMS values ​​of the free-form surface components of the secondary and tertiary mirrors, calculated analytically, are 3.43e-04mm and 0.002mm, respectively. These values ​​are orders of magnitude smaller than the 0.0136mm and 0.0145mm values ​​obtained using the damped least squares method in the optical design software. Figures 9(a) and 9(b) provide a more intuitive illustration of the difference between the two optimization methods. Table 2 shows that the full-field aberration RMS of the optical system optimized by the present invention is 0.0695 wavelengths, slightly better than the damped least squares method. This result is approximately 50% lower than the off-axis initial system. Furthermore, the average MTF of the optical system over the full field of view obtained by the analytical calculation is superior to that obtained by the damped least squares method. These results demonstrate that the analytically calculated optical system, while ensuring that the free-form surface components of the secondary and tertiary mirrors are small, also achieves superior imaging quality to that obtained using the damped least squares method. This, to a certain extent, can reduce the difficulty of fabricating free-form surfaces and lower production costs.

[0141] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present disclosure can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved. This is not limited herein.

[0142] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection 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 the aberration contribution expression of the free-form surface optical system is rewritten as the first double Zernike polynomial based on the field Zernike polynomial and the pupil 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 squares 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 polynomial 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 to complete the design of the free-form surface optical system.

2. The method for designing a free-form surface optical system based on double Zernike aberrations according to claim 1, wherein: 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 curvature radius 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 optical system, is the chief ray inclination angle 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 the free-form surface optical system at different fields of view to , then the aberration contribution of the free-form optical system to the off-axis field of view is for: ； S14: Calculate the incident angle of the principal ray of different fields of view on the primary mirror of the free-form optical system using 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 ​​in 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. The value of A is different for different mirrors. pm is the mirror number of the free-form 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: Based on the calculation results of step S16, the aberration contribution to the free-form surface optical system 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 aberrations of the free-form optical system are 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 method for designing a free-form surface optical system based on double Zernike aberrations according to claim 2, wherein: 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 component C5-C 16 for: ； ； ； ； ； ； ； in, , x is a constant, is the refractive index difference between the image and object sides of the free-form 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 polynomials, Different values ​​of nm correspond to different terms in the pupil Zernike polynomials.

4. The method for designing a free-form surface optical system based on double Zernike aberrations according to claim 1, wherein: 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 method for designing a free-form surface optical system based on double Zernike aberrations according to claim 4, wherein: 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, wherein: In step S4, the total aberration contribution of the free-form surface component is rewritten into the 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, wherein: In step S4, the free-form surface component of the optical initial system is solved based on the performance evaluation model : ； ； in, is the curvature radius 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.

Images