An adaptive design method for long focal length primary three-mirror integrated lightweight space camera

Abstract

The application provides a long-focus main three-mirror integrated lightweight space camera adaptive design method, and relates to the technical field of optical system design. The method designs an adaptive structure parameter search space, realizes adaptive acquisition of the structure parameter search space for different design requirements and optical path structure requirements, designs a main three-mirror distance discrimination model and a long-focus space camera size objective function, automatically judges the assembly and adjustment difficulty and the lightweight degree of the long-focus space camera, combines the main three-mirror distance discrimination model and the long-focus space camera size objective function with an off-axis degree function, an image quality evaluation function and an optical path intersection function, and designs a structure parameter objective function, obtains a long-focus space camera parameter combination most suitable for easy assembly and adjustment, lightweight and high imaging quality by searching the minimum value of the structure parameter objective function, and uses a free surface design method to obtain a free surface space camera.

Description

Technical Field

[0001] This invention relates to the field of optical system design technology, and in particular to an adaptive design method for a lightweight space camera integrating three primary lenses with a long focal length. Background Technology

[0002] Space cameras are core equipment in space remote sensing imaging technology, widely used to acquire images and data of the Earth's surface from satellites or spacecraft. To effectively monitor small-scale changes on the Earth's surface, space cameras need to be able to clearly capture surface details from a distance. Therefore, long-focal-length space cameras are commonly used imaging devices in space remote sensing. Since space cameras are generally off-axis multi-reflector freeform surface systems, the asymmetry of their surface shape and system structure increases the difficulty of assembly and adjustment. To address this, a primary three-mirror integration method is needed, integrating the primary mirror and the three mirrors onto the same substrate to reduce assembly and adjustment difficulty. Simultaneously, due to the limitations of space camera operating conditions, lightweight space cameras need to be designed to reduce launch costs and energy consumption, and improve the spacecraft's payload and operational efficiency. However, reducing the size of a space camera usually leads to a decrease in image quality. Current long-focal-length space camera design methods do not simultaneously balance the relationship between assembly and adjustment difficulty, lightweight design, and image quality during the design process; that is, there is no long-focal-length space camera design model that simultaneously guarantees ease of assembly and adjustment, lightweight design, and image quality. Currently, the design of structural parameters for space cameras often relies on the designer's experience, resulting in low levels of automation. Although some researchers have proposed using search algorithms to find the structural parameters that best meet the objective function within a certain range, this method is mainly applicable to non-long-focal-length space cameras and requires setting the search space for structural parameters based on empirical knowledge. If the structural parameters of long-focal-length space cameras are obtained directly using search methods, the search space needs to be expanded exponentially, which will significantly increase the time cost of the search and may even prevent the search from finding a usable solution. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide an adaptive design method for a lightweight space camera with integrated three main lenses for long focal length, which addresses the shortcomings of the prior art. This method adaptively designs a free-form long focal length space camera to meet the requirements of easy assembly and adjustment, lightweight design and high imaging quality.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: an adaptive design method for a lightweight space camera integrating three main lenses with a long focal length, comprising the following steps:

[0005] Step 1: Construct an adaptive mirror spacing search space;

[0006] The expression for the adaptive mirror spacing search space is:

[0007] |d max |=τ1ED (1)

[0008] d min |=τ2ED (2)

[0009] Where ED is the entrance pupil diameter, and τ1 and τ2 are the function weights of the upper and lower limits of the adaptive mirror spacing search space, respectively; d max and d min These are the upper and lower bounds of the adaptive mirror spacing search space, respectively;

[0010] The expressions for τ1 and τ2 are:

[0011]

[0012] Where f is the focal length of the long focal length space camera, F represents the F-number of the long focal length space camera, and xfov and yfov are the maximum field of view angles of the long focal length space camera in the x and y directions, respectively. and These are the focal length, F-number, and weights of the maximum field of view of the long focal length space camera in the x and y directions, respectively; and These are the focal length, F-number, and weights of the maximum field of view of the long focal length space camera in the x and y directions, respectively; and and Set according to actual needs;

[0013] In equation (4), The expression is:

[0014]

[0015] Where N is the number of mirrors in the long focal length space camera;

[0016] To obtain an adaptive upper limit for inter-lens distance that is more suitable for long focal length space cameras, it is necessary to make It changes dynamically with the focal length f, and the expression is:

[0017]

[0018] The and The expression is:

[0019]

[0020] Where, τ c The parameter that varies with focal length f is shown in the following formula:

[0021]

[0022] Step 2: Construct the adaptive radius of curvature search space;

[0023] The optical relationship between adaptive inter-lens distance and optical power of a long-focal-length space camera is constructed using the ABCD matrix method, and the expression is:

[0024]

[0025] in, Let N be the optical power of the Nth reflecting mirror in the long focal length space camera; Let N be the optical power of the (N-1)th reflecting mirror in the long focal length space camera; d represents the optical power of the primary mirror in a long-focal-length space camera. N-1 Let be the distance between the (N-1)th and Nth mirrors in the long focal length space camera; A, B, C, and D are all functions of the optical power of the long focal length space camera and the adaptive mirror spacing.

[0026] Construct the objective function g of adaptive radius of curvature c The expression is:

[0027]

[0028] Among them, i N Let be the refractive index of the Nth mirror in the long-focal-length space camera, where n is the mirror number, 1 ≤ n ≤ N; r n Let be the adaptive radius of curvature of the nth mirror in the long focal length space camera;

[0029] The upper limit d of the adaptive mirror spacing search space max The lower bound d of the adaptive mirror spacing search space min Substituting d into equation (11) respectively N In the process, the corresponding adaptive curvature radius combinations {r} are obtained respectively. DMAX} and {r DMIN}, thus obtaining the adaptive radius of curvature search space for each mirror, expressed as:

[0030]

[0031] in, and These are the upper and lower bounds of the adaptive radius of curvature search space, respectively;

[0032] Step 3: Construct an adaptive tilt angle search space;

[0033] The tilt angle of clockwise tilt is defined as a positive number, and the tilt angle of counterclockwise tilt is defined as a negative number; the adaptive tilt angle search space of the primary mirror is represented in absolute value form as follows:

[0034] |α1|∈[0.5arcsin(ED / 2 / |d max |),0.5arcsin(ED / |d min |)] (14)

[0035] Where α1 represents the tilt angle of the primary mirror;

[0036] Construct the adaptive tilt angle search space for the secondary mirror; when α2 > 2α1, the rotation vector of the secondary mirror is -1; when α2 < 2α1, the rotation vector of the secondary mirror is 1; define the angle between the incident ray and the outgoing ray as an acute angle, and obtain the search space for the adaptive tilt angle of the secondary mirror, expressed as:

[0037]

[0038] Where α2 is the tilt angle of the secondary mirror, V s Let be the rotation vector of the secondary mirror;

[0039] Construct the adaptive tilt angle search space for the three mirrors; calculate that when the incident rays from the three mirrors coincide with the rays from the exiting three mirrors, the tilt angle of the three mirrors is 2(α2-α1), and derive the search space for the adaptive tilt angle of the three mirrors, expressed as:

[0040]

[0041] Among them, V T Let α be the rotation vector of the three mirrors, and α3 be the tilt angle of the three mirrors;

[0042] Step 4: Construct a distance discrimination model for the three main lenses of a long-focal-length space camera to evaluate the degree of integration of the three main lenses;

[0043] The distance between the primary three lenses of a long-focal-length space camera is the shortest distance between the primary lens and the other three lenses; the primary lens and the other three lenses are integrated onto a single substrate for manufacturing, ensuring that the distance between the primary lens and the other three lenses is less than a set threshold; a primary three-lens distance discrimination function g is defined. ft The expression is:

[0044]

[0045] Where, d ft It is the shortest distance between the primary mirror and the third mirror; Q is a set threshold, which is a constant;

[0046] For a long focal length space camera with a Z-shaped structure, the distance between the primary and secondary mirrors and the distance between the secondary three mirrors are set to be equal to increase the search speed of the search algorithm and enable the long focal length space camera to quickly converge to the target of the integrated primary and secondary mirrors. When the optical path structure of the long focal length space camera is designed to be Z-shaped, an additional mirror distance constraint condition needs to be added on the basis of equation (17), namely |d1|=|d2|, where d1 and d2 are the distance between the primary and secondary mirrors and the distance between the secondary three mirrors, respectively.

[0047] Step 5: Construct the objective function g for the size of the long focal length space camera s Used to calculate the dimensions of a long focal length space camera;

[0048] Based on Snell's law and the inverse tracing method, the center and edge rays of the fields of view (0,0), (0,yfov / 2), (0,-yfov / 2), and (xfov / 2,0) are traced to obtain the coordinates of the intersection points of each ray with the mirror and the image plane, as well as the sets of x, y, and z coordinates of all intersection points {X}, {Y}, and {Z}. The objective function for the size of the space camera is g. s The expression is:

[0049] g s =|max{Y}-min{Y}|×|max{Z}-min{Z}|×2max{|X|} (18)

[0050] Step 6: Construct the objective function G for the structural parameters of the long focal length space camera;

[0051] The structural parameter objective function G of the long focal length space camera consists of the primary three-mirror distance discrimination model, the size objective function, the image quality evaluation function, the off-axis degree function, and the optical path intersection function, and its expression is:

[0052]

[0053] Where δ1, δ2, δ3, δ4, and δ5 are the weights of the objective function for each structural parameter of the long-focal-length space camera, and α n Let g be the tilt angle of the nth mirror in a long-focal-length space camera. q g oa and g p These are the image quality evaluation function, the off-axis degree function, and the optical path crossing function, respectively.

[0054] The image quality evaluation function g q Off-axis degree function g oa and optical path crossing function g p The expressions are as follows:

[0055]

[0056] Where K is the total number of sampling rays, i is the sequence number of the sampling ray, (x c ,y c ,z c (x) represents the coordinates of the ideal image point. i ,y i ,z i ) represents the coordinates of the imaging point of the i-th sampling ray; OA n OAM is the off-axis discrimination number. n Here, σ1 and σ2 are the discriminant numbers for the degree of off-axis deviation, respectively. n OAM function of residual discriminant n The weights; This represents the p-th optical path crossing vector of the long focal length space camera required by the design. This is the p-th optical path crossing vector of the current long-focal-length space camera;

[0057] Step 7: Use a search algorithm to find the minimum value of the objective function of the structural parameters of the long focal length space camera to obtain the most suitable structural parameters for the long focal length space camera; then, combine the obtained most suitable structural parameters of the long focal length space camera with the freeform surface design method to optimize the reflector into a freeform surface, and obtain a freeform surface long focal length space camera.

[0058] The beneficial effects of adopting the above technical solution are as follows: The adaptive design method for a lightweight space camera integrating three main lenses with a long focal length provided by the present invention has the following beneficial effects compared with the prior art:

[0059] 1. By setting up a search space model with adaptive structural parameters, a search space for mirror spacing, radius of curvature, and tilt angle that is applicable to different designs and optical path structure requirements is designed. Compared with existing long focal length space camera design methods, this further reduces the dependence on design experience, is more flexible, and improves search coverage and efficiency.

[0060] 2. By setting the distance discrimination module of the main three mirrors of the long focal length space camera and the size objective function of the long focal length space camera, the integration degree of the main three mirrors of the space camera is automatically improved and the size of the long focal length space camera is reduced. Compared with the existing long focal length space camera design methods, the generated long focal length space camera has lower assembly and adjustment difficulty and higher lightweight.

[0061] 3. By setting the objective function of the structural parameters of the long focal length space camera, a unified evaluation standard is designed to automatically evaluate the assembly and adjustment difficulty, lightweighting degree and imaging quality of the long focal length space camera. Compared with the existing design methods of long focal length space cameras, it more effectively balances the imaging requirements with the assembly and adjustment and lightweighting requirements, and makes it easier to select long focal length space cameras that simultaneously guarantee easy assembly and adjustment, lightweighting and high imaging quality. Attached Figure Description

[0062] Figure 1 A flowchart of an adaptive design method for a lightweight space camera integrating three main lenses with a long focal length is provided in an embodiment of the present invention;

[0063] Figure 2 The present invention provides a schematic diagram of the adaptive search space for the tilt angle of the secondary mirror, wherein (a) is the case where the incident ray and the outgoing ray on the secondary mirror coincide, (b) is the case where the rotation vector of the secondary mirror is -1, and (c) is the case where the rotation vector of the secondary mirror is 1.

[0064] Figure 3 A schematic diagram of the structure of a long focal length space camera provided in an embodiment of the present invention. Detailed Implementation

[0065] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0066] This embodiment presents an adaptive design method for a lightweight space camera integrating three main lenses with a long focal length. Figure 1 As shown, it includes the following steps:

[0067] Step 1: Construct an adaptive mirror spacing search space;

[0068] The expression for the adaptive mirror spacing search space is:

[0069] |d max |=τ1ED (1)

[0070] |d min |=τ2ED (2)

[0071] Where ED is the entrance pupil diameter, and τ1 and τ2 are the function weights of the upper and lower limits of the adaptive mirror spacing search space, respectively; d max and d min These are the upper and lower bounds of the adaptive mirror spacing search space, respectively;

[0072] The expressions for τ1 and τ2 are:

[0073]

[0074]

[0075] Where f is the focal length of the long focal length space camera, F represents the F-number of the long focal length space camera, and xfov and yfov are the maximum field of view angles of the long focal length space camera in the x and y directions, respectively. and These are the focal length, F-number, and weights of the maximum field of view of the long focal length space camera in the x and y directions, respectively; and These are the focal length, F-number, and weights of the maximum field of view of the long focal length space camera in the x and y directions, respectively; and and Set according to actual needs;

[0076] In this embodiment,

[0077] In equation (4), The expression is:

[0078]

[0079] Where N is the number of mirrors in the long focal length space camera;

[0080] To obtain an adaptive upper limit for inter-lens distance that is more suitable for long focal length space cameras, it is necessary to make It changes dynamically with the focal length f, and the expression is:

[0081]

[0082] The and The expression is:

[0083]

[0084] Where, τ c The parameter that varies with focal length f is shown in the following formula:

[0085]

[0086] Step 2: Construct the adaptive radius of curvature search space;

[0087] The optical relationship between adaptive inter-lens distance and optical power of a long-focal-length space camera is constructed using the ABCD matrix method, and the expression is:

[0088]

[0089] in, Let N be the optical power of the Nth reflecting mirror in the long focal length space camera; Let N be the optical power of the (N-1)th reflecting mirror in the long focal length space camera; d represents the optical power of the primary mirror in a long-focal-length space camera. N-1Let be the distance between the (N-1)th and Nth mirrors in the long focal length space camera; A, B, C, and D are all functions of the optical power of the long focal length space camera and the adaptive mirror spacing.

[0090] Construct the objective function g of adaptive radius of curvature c The expression is:

[0091]

[0092] Among them, i N Let be the refractive index of the Nth mirror in the long-focal-length space camera, where n is the mirror number, 1 ≤ n ≤ N; r n Let be the adaptive radius of curvature of the nth mirror in the long focal length space camera;

[0093] The upper limit d of the adaptive mirror spacing search space max The lower bound d of the adaptive mirror spacing search space min Substituting d into equation (11) respectively N In the process, the corresponding adaptive curvature radius combinations {r} are obtained respectively. DMAX} and {r DMIN}, thus obtaining the adaptive radius of curvature search space for each mirror, expressed as:

[0094]

[0095] in, and These are the upper and lower bounds of the adaptive radius of curvature search space, respectively;

[0096] In equation (12), the upper limit d of the adaptive mirror spacing search space is given by... max Substituting d into equation (11) N The adaptive curvature radius combination {r} obtained in DMAX The N adaptive curvature radii contained in} are not necessarily exactly the upper limit of the adaptive curvature radius search space. Therefore, it is necessary to use the maximum value operation to obtain the upper limit of the adaptive curvature radius search space. Equation (13) is similar.

[0097] Step 3: Construct an adaptive tilt angle search space;

[0098] The tilt angle of clockwise rotation is defined as positive, and the tilt angle of counterclockwise rotation is defined as negative. The main purpose of tilting the primary mirror is to eliminate the obstruction of incident light by the secondary mirror. The sign of its tilt angle does not affect the optical path structure. Therefore, the adaptive tilt angle search space of the primary mirror can be expressed in absolute value form as follows:

[0099] |α1|∈[0.5arcsin(ED / 2 / |d max|),0.5arcsin(ED / |d min |)] (14)

[0100] Where α1 represents the tilt angle of the primary mirror;

[0101] The tilt angle of the secondary mirror affects the optical path structure. According to the definition of optical path structure, when the extension of the incident ray from the secondary mirror rotates counterclockwise and can coincide with the outgoing ray at an angle less than 180 degrees, the rotation vector of the secondary mirror is -1; otherwise, it is 1. Therefore, an adaptive tilt angle search space for the secondary mirror can be constructed based on the optical path structure requirements, such as... Figure 2 As shown. It can be deduced that when α2 > 2α1, the rotation vector of the secondary mirror is -1; when α2 < 2α1, the rotation vector of the secondary mirror is 1. Simultaneously, to ensure the compactness of the structure, the angle between the incident and outgoing rays is defined as an acute angle. Therefore, the search space for the adaptive tilt angle of the secondary mirror is derived, expressed as:

[0102]

[0103] Where α2 is the tilt angle of the secondary mirror, V s Let be the rotation vector of the secondary mirror;

[0104] Construct the adaptive tilt angle search space for the three mirrors; calculate that when the incident rays from the three mirrors coincide with the rays from the exiting three mirrors, the tilt angle of the three mirrors is 2(α2-α1), and derive the search space for the adaptive tilt angle of the three mirrors, expressed as:

[0105]

[0106] Among them, V T Let α be the rotation vector of the three mirrors, and α3 be the tilt angle of the three mirrors;

[0107] Step 4: Construct a distance discrimination model for the three main lenses of a long-focal-length space camera to evaluate the degree of integration of the three main lenses;

[0108] The distance between the primary three lenses of the long focal length space camera is the shortest distance between the primary lens and the other three lenses. To achieve easy assembly and adjustment, the primary lens and the other three lenses need to be integrated onto a single substrate for manufacturing, ensuring that the distance between the primary lens and the other three lenses is less than a set threshold. A primary three-lens distance discrimination function g is defined. ft The expression is:

[0109]

[0110] Where, d ft It is the shortest distance between the primary mirror and the third mirror; Q is a set threshold, which is a constant, and Q < 150;

[0111] In this embodiment, Q = 100;

[0112] For a long focal length space camera with a Z-shaped structure, the distance between the primary and secondary mirrors and the distance between the secondary three mirrors are set to be equal to increase the search speed of the search algorithm and enable the long focal length space camera to quickly converge to the target of the integrated primary and secondary mirrors. When the optical path structure of the long focal length space camera is designed to be Z-shaped, an additional mirror distance constraint condition needs to be added on the basis of equation (17), namely |d1|=|d2|, where d1 and d2 are the distance between the primary and secondary mirrors and the distance between the secondary three mirrors, respectively.

[0113] Step 5: Construct the objective function g for the size of the long focal length space camera s Used to calculate the dimensions of a long focal length space camera;

[0114] Based on Snell's law and the inverse tracing method, the center and edge rays of the fields of view (0,0), (0,yfov / 2), (0,-yfov / 2), and (xfov / 2,0) are traced to obtain the coordinates of the intersection points of each ray with the mirror and the image plane, as well as the sets of x, y, and z coordinates of all intersection points {X}, {Y}, and {Z}. The objective function for the size of the space camera is g. s The expression is:

[0115] g s =|max{Y}-min{Y}|×|max{Z}-min{Z}|×2max{|X|} (18)

[0116] Step 6: Construct the objective function G for the structural parameters of the long focal length space camera;

[0117] The structural parameter objective function G of the long focal length space camera is composed of the primary three-mirror distance discrimination model, the size objective function, the image quality evaluation function, the off-axis degree function, and the optical path intersection function, and its expression is:

[0118]

[0119] Where δ1, δ2, δ3, δ4, and δ5 are the weights of the objective function for each structural parameter of the long-focal-length space camera, and α n Let g be the tilt angle of the nth mirror in a long-focal-length space camera. q g oa and g p These are the image quality evaluation function, the off-axis degree function, and the optical path crossing function, respectively.

[0120] The image quality evaluation function g q Off-axis degree function g oa and optical path crossing function g p The expressions are as follows:

[0121]

[0122] Where K is the total number of sampling rays, i is the sequence number of the sampling ray, (x c ,y c ,z c (x) represents the coordinates of the ideal image point. i ,y i ,z i ) represents the coordinates of the imaging point of the i-th sampling ray; OA n Let OA be the off-axis discrimination number, where OA is the number of mirrors that do not block any light. n =0, otherwise OA n The value is the shortest distance from the mirror to the blocked light ray; when n = N + 1, it represents the image plane; OAM n OAM is the margin discrimination number, which is defined as follows: when the shortest distance between the nth mirror and any ray in the system is greater than 10mm. n =0, otherwise OAM n The value is the absolute value of the difference between the shortest distance from the reflector to the blocked light ray and 10 mm; σ1 and σ2 are the off-axis discrimination numbers OA, respectively. n OAM function of residual discriminant n The weights; This represents the p-th optical path crossing vector of the long focal length space camera required by the design. This is the p-th optical path crossing vector of the current long-focal-length space camera;

[0123] In this embodiment, δ1 = 1 × 10 -8 , δ2=δ3=50, δ4=δ5=1, σ1=5, σ2=1, Q=100;

[0124] In terms of volume, with the same design requirements, but using an empirical method, the volume of the long focal length space camera is 4.36m. 3 In comparison, the space camera obtained using this method is smaller in size, achieving the goal of weight reduction;

[0125] Step 7: Use a search algorithm to find the minimum value of the objective function of the structural parameters of the long focal length space camera to obtain the most suitable structural parameters for the long focal length space camera; then, combine the obtained most suitable structural parameters of the long focal length space camera with the freeform surface design method to optimize the reflector into a freeform surface, and obtain a freeform surface long focal length space camera.

[0126] Before using the search algorithm in this embodiment, it is necessary to determine the design requirements parameters input into the algorithm, including the system's focal length, F-number, maximum field of view, and optical path structure requirements. Then, the radius of curvature, tilt angle, and mirror spacing of the reflector are set as variables. Next, the maximum number of searches is input, and random structure parameters are generated within the search space as initial values ​​for the search. After finding suitable structure parameters, a freeform surface design method (such as the SMS method, CI method, or the improved WW method) is used to optimize the reflector into a freeform surface, thus obtaining a freeform surface long focal length space camera.

[0127] In this embodiment, the focal length f is 5000mm, the F-number is 12, the maximum field of view is 10°×1°, and the optical path structure is required to be [-1,1,0,0,0] (i.e., a Z-shaped structure). Simulated annealing is used as the search algorithm, with an initial temperature of 1500 degrees Celsius. When the number of searches reaches more than 90, a stable minimum value of the comprehensive objective function is obtained, which is 17.28. The layout diagram of the obtained long focal length space camera is shown below. Figure 3 As shown;

[0128] In this embodiment, the surface design method used is a modified WW method; the results show that the generated space camera's three main mirrors have good integration, and the light rays from each field of view converge at the ideal image plane; and the space camera's volume is 1.28m. 3 This demonstrates a compact structure. In conclusion, the adaptive design method for a lightweight, long-focal-length space camera integrating three primary mirrors proposed in this invention can adaptively generate a long-focal-length space camera that meets the requirements of easy assembly and adjustment, lightweight design, and good imaging quality. Specifically, the adaptive design method for the search space of mirror spacing, radius of curvature, and tilt angle can generate a targeted search space for the structural parameters of the long-focal-length space camera based on design requirements. The primary three-mirror distance discrimination model ensures that the generated long-focal-length space camera has the advantage of easy assembly and adjustment. The size objective function ensures that the long-focal-length space camera meets the requirements of lightweight design. The structural parameter objective function simultaneously ensures that the long-focal-length space camera has the characteristics of easy assembly and adjustment, lightweight design, and high imaging quality.

[0129] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. An adaptive design method for a lightweight space camera integrating three main lenses with a long focal length, characterized in that: Includes the following steps: Step 1: Construct an adaptive mirror spacing search space; The expression for the adaptive mirror spacing search space is: (1)； (2)； Where ED is the entrance pupil diameter. and These are the function weights for the upper and lower bounds of the adaptive mirror spacing search space, respectively; and These are the upper and lower bounds of the adaptive mirror spacing search space, respectively; The and The expression is: (3)； (4)； in, The focal length of a long-focal-length space camera. The F-number indicates the focal length of a space camera. and These are the maximum field of view angles of the long-focal-length space camera in the x and y directions, respectively. , , and They are respectively The focal length, F-number of a medium-to-long focal length space camera, and the weights of the maximum field of view in the x and y directions for a long focal length space camera; , , and They are respectively The focal length, F-number of a medium-to-long focal length space camera, and the weights of the maximum field of view in the x and y directions for a long focal length space camera; In equation (4), The expression is: (5)； in, The number of mirrors in a long-focal-length space camera; To obtain an adaptive upper limit for inter-lens distance that is more suitable for long focal length space cameras, it is necessary to make It changes dynamically with the focal length f, and the expression is: (6)； The and The expression is: (7)； (8)； in, The parameter that varies with focal length f is shown in the following formula: (9) ； Step 2: Construct the adaptive radius of curvature search space; The optical relationship between adaptive inter-lens distance and optical power of a long-focal-length space camera is constructed using the ABCD matrix method, and the expression is: (10)； in, Let N be the optical power of the Nth reflecting mirror in the long focal length space camera; Let N be the optical power of the (N-1)th reflecting mirror in the long focal length space camera; The optical power of the primary mirror in a long-focal-length space camera; Let be the distance between the (N-1)th and Nth mirrors in the long focal length space camera; A, B, C, and D are all functions of the optical power of the long focal length space camera and the adaptive mirror spacing. Constructing an objective function for adaptive radius of curvature The expression is: (11)； in, Let n be the refractive index of the Nth mirror in the long focal length space camera, where n is the mirror number, and 1≤n≤N; Let be the adaptive radius of curvature of the nth mirror in the long focal length space camera; Upper limit of the adaptive mirror spacing search space Lower bound of the adaptive mirror spacing search space Substituting into equation (11) respectively In the process, the corresponding adaptive curvature radius combinations are obtained respectively. }and{ }, thus obtaining the adaptive radius of curvature search space for each mirror, expressed as: (12)； (13)； in, and These are the upper and lower bounds of the adaptive radius of curvature search space, respectively; Step 3: Construct an adaptive tilt angle search space; The tilt angle of clockwise tilt is defined as a positive number, and the tilt angle of counterclockwise tilt is defined as a negative number; the adaptive tilt angle search space of the primary mirror is represented in absolute value form as follows: (14)； in, Indicates the tilt angle of the primary mirror; Construct an adaptive tilt angle search space for the secondary mirror; when When, the rotation vector of the secondary mirror is -1; when At this time, the rotation vector of the secondary mirror is 1; defining the angle between the incident and outgoing rays as an acute angle, the search space for the adaptive tilt angle of the secondary mirror is obtained, expressed as: (15)； in, The tilt angle of the secondary mirror. Let be the rotation vector of the secondary mirror; Construct an adaptive tilt angle search space for the three mirrors; calculate the tilt angle of the three mirrors when the incident rays from the three mirrors coincide with the rays from the exiting three mirrors. The search space for the adaptive tilt angle of the three mirrors is obtained, and its expression is: (16)； in, Let be the rotation vector of the three mirrors. The tilt angle of the three mirrors; Step 4: Construct a distance discrimination model for the three main lenses of a long-focal-length space camera to evaluate the degree of integration of the three main lenses; The distance between the primary three lenses of a long-focal-length space camera is the shortest distance between the primary lens and the other three lenses; the primary lens and the other three lenses are integrated onto a single substrate for manufacturing, ensuring that the distance between the primary lens and the other three lenses is less than a set threshold; a primary three-lens distance discrimination function is defined. The expression is: (17)； in, It is the shortest distance between the primary mirror and the third mirror; The set threshold is a constant; For a long focal length space camera with a Z-shaped structure, the distance between the primary and secondary mirrors and the distance between the secondary three mirrors are set to be equal to increase the search speed of the search algorithm and enable the long focal length space camera to quickly converge to the target of the integrated primary and secondary mirrors. When the optical path structure of the long focal length space camera is designed to be Z-shaped, an additional mirror distance constraint condition needs to be added on the basis of equation (17), namely |d1|=|d2|, where d1 and d2 are the distance between the primary and secondary mirrors and the distance between the secondary three mirrors, respectively. Step 5: Construct the objective function for the size of the long focal length space camera to calculate the size of the long focal length space camera; Based on Snell's law and the inverse tracing method, the center and edge rays of the fields of view (0,0), (0,yfov / 2), (0,-yfov / 2), and (xfov / 2,0) are traced to obtain the coordinates of the intersection points of each ray with the mirror and the image plane, as well as the sets {X}, {Y}, and {Z} of the x, y, and z coordinates of all intersection points. The objective function for the size of the space camera is... The expression is: (18) ； Step 6: Construct the objective function for the structural parameters of the long focal length space camera ; The objective function of the structural parameters of the long focal length space camera It consists of a primary three-mirror distance discrimination model, a size objective function, an image quality evaluation function, an off-axis degree function, and an optical path crossing function, and its expression is: (19)； in, , , , and These are the weights of the objective function for each structural parameter of the long-focal-length space camera. Let be the tilt angle of the nth mirror in the long focal length space camera. , and These are the image quality evaluation function, the off-axis degree function, and the optical path crossing function, respectively. Step 7: Use a search algorithm to find the minimum value of the objective function of the structural parameters of the long focal length space camera to obtain the most suitable structural parameters for the long focal length space camera; then, combine the obtained most suitable structural parameters of the long focal length space camera with the freeform surface design method to optimize the reflector into a freeform surface, and obtain a freeform surface long focal length space camera.

2. The adaptive design method for a lightweight space camera integrating three main lenses with a long focal length as described in claim 1, characterized in that: The image quality evaluation function Off-axis degree function and optical path intersection function The expressions are as follows: (20)； (21)； (22)； Where K is the total number of sampling rays, and i is the sequence number of the sampling ray. , , ) represents the coordinates of the ideal image point, ( , , () represents the coordinates of the imaging point of the i-th sampling ray; The off-axis discrimination number, The remainder discriminant number, and These are the discriminant numbers for the degree of off-axis. Functions of residual discriminant The weights; This represents the p-th optical path crossing vector of the long focal length space camera required by the design. This is the p-th optical path crossing vector of the current long focal length space camera.

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