Automatic design method of free-form surface off-axis multi-mirror system based on manufacturing constraints

Abstract

The application discloses an automatic design method of a free-form surface off-axis multi-reflection system based on manufacturing constraints and relates to the technical field of optical system design technology. A manufacturing constraint module is constructed; an optical excess amount judgment function is constructed; the convergence degree of light rays is measured by judging the distance between an imaging point and an ideal imaging point, and a light ray convergence degree function is constructed; a comprehensive target function is constructed based on the manufacturing constraint module, the optical excess amount judgment function and the light ray convergence degree function; parameters most suitable for design requirements are found through a search algorithm, and then a free-form surface off-axis multi-reflection system is obtained by using a surface design method. The application automatically judges whether the position parameters of the current system are reasonable through the manufacturing constraint module, and the generated off-axis multi-reflection system is more conducive to integrated processing and manufacturing; a unified evaluation index for automatically evaluating the system position parameters and imaging quality is designed through the comprehensive target function, the quantitative evaluation standard is increased, and the system more conforming to the manufacturing and design requirements is screened out.

Description

Technical Field

[0001] This invention belongs to the field of optical system design technology, specifically relating to an automatic design method for free-form surface off-axis multi-reflector systems based on manufacturing constraints. Background Technology

[0002] Off-axis multi-mirror systems, including two-mirror, three-mirror, and four-mirror systems, are important components of telescopes and imaging spectrometers, widely used in observation fields. The design and manufacturing of an off-axis multi-mirror system involves two stages: design and assembly. The design stage uses calculation and optical simulation software to generate a layout diagram of the off-axis multi-mirror system and the positional and optical parameters of each mirror. The assembly stage, based on the design, involves manufacturing mirrors that conform to the optical parameters and assembling them into their appropriate positions according to the positional parameters and layout diagram. In traditional separate assembly methods, precise alignment of the mechanical and optical axes of each mirror is difficult, requiring repeated optical alignment adjustments and making it challenging to achieve optimal assembly results. Recently emerging integrated manufacturing technology offers a new assembly method that allows for direct, ultra-precise machining of the optical system, eliminating the need for optical alignment operations and fundamentally reducing the difficulty of assembly. Integrated manufacturing technology imposes certain requirements on the mirror positions, i.e., manufacturing constraints, specifically requiring all mirrors to be placed on the same cylindrical profile. However, current design methods for freeform surface off-axis multi-mirror systems, such as the improved WW method, SMS method, and CI method, do not consider manufacturing constraints. In other words, there is no unified design model for off-axis multi-mirror systems based on manufacturing constraints, resulting in designs that do not meet the requirements of integrated manufacturing. Furthermore, current design methods for freeform surface off-axis multi-mirror systems rely on the optical designer's experience to set the mirror position parameters, which is not conducive to selecting the system that best meets the design requirements. Summary of the Invention

[0003] To address the problems existing in the prior art, this invention provides an automatic design method for free-form surface off-axis multi-reflection systems based on manufacturing constraints, aiming to automatically design free-form surface off-axis multi-reflection systems to meet the requirements of integrated machining and manufacturing constraints.

[0004] The technical solution of this invention is as follows:

[0005] Step 1: Construct a manufacturing constraint module based on the cocircularity function and the occlusion evaluation function; the cocircularity function is used to determine the degree of fit between each mirror and the cylindrical profile; the occlusion evaluation function is used to determine whether the edge of each mirror in the off-axis multi-mirror system blocks the light passing between other adjacent mirrors in the off-axis multi-mirror system;

[0006] Step 1.1: Construct a cocircularity function based on the distance between a point on the mirror and the center point of the cylindrical profile;

[0007] The expression for the degree of concircularity is:

[0008]

[0009] Among them, f M is the concircularity function; N is the number of uniform sampling points on each mirror; K is the total number of mirrors in the off-axis multi-mirror system; n is the mirror number; t is the sampling point number; rc is the radius of the cylindrical profile; This is the distance between a point on the mirror and the center point of the cylindrical profile.

[0010] Step 1.2: Construct the occlusion evaluation function.

[0011] Step 1.2.1: Draw perpendicular lines from the top and bottom edges of each mirror to the top and bottom edges of each pair of adjacent mirrors (excluding the mirror itself) to obtain a set of perpendicular lines, and calculate the minimum length of the perpendicular lines in the set; the edge rays refer to the two outermost rays of the light path between two mirrors; the image plane is treated as an optical surface, i.e., a mirror, during the calculation.

[0012] Step 1.2.2: Based on the coordinates of the foot of the perpendicular line, obtain the vector pointing from the top and bottom edges of the mirror to the coordinates of the foot of the perpendicular, and calculate the occlusion parameter of each mirror; the occlusion parameter indicates whether the mirror blocks the light rays passing through other mirrors in the off-axis multi-mirror system;

[0013] The expression for the occlusion parameter is:

[0014]

[0015] Where PO is the occlusion parameter of each mirror; JA is the vector angle discriminant, expressed as:

[0016]

[0017] Where β represents the angle between the vectors.

[0018] Step 1.2.3: Construct a set of system occlusion parameters based on the occlusion parameters of each mirror;

[0019] The set expression for the system occlusion parameters is:

[0020]

[0021] Wherein, {PO} is the set of system occlusion parameters; the superscript of PO is the serial number of the reflector, when the superscript is n, it represents the nth reflector; the subscript of PO represents the optical path, j(j+1) represents the optical path between the jth reflector and the (j+1)th reflector, when j=0, it is the optical path incident into the primary mirror.

[0022] Step 1.2.4: Construct an occlusion evaluation function based on the set of system occlusion parameters and the minimum value of the vertical length in the set of vertical lines.

[0023] The expression for the occlusion evaluation function is:

[0024]

[0025] Among them, f O For the occlusion evaluation function; This represents the minimum length of the set of perpendicular lines drawn from the edge point of the nth mirror to the edge rays between the jth and (j+1)th mirrors.

[0026] Step 2: Construct an optical margin judgment function; the optical margin judgment function is used to calculate the minimum distance between the reflector and the edge light rays passing through other reflectors when the reflector does not block the light.

[0027] The expression for the optical margin judgment function is:

[0028]

[0029] Among them, f OM This is the optical margin judgment function; It is the residual constant;

[0030] The expression for the residual constant is:

[0031]

[0032] in, is the margin constant; MR represents the minimum standard of optical margin, which is a constant.

[0033] Step 3: The degree of light convergence is measured by determining the distance between the imaging point and the ideal image point, thereby constructing a light convergence function; the light convergence function is used to determine the degree of dispersion of the intersection points of light rays and the image plane in each field of view;

[0034] The expression for the light convergence degree function is:

[0035]

[0036] Among them, f Cis the light convergence function; NC is the number of sampled rays; u is the sequence number of the sampled ray; (x u ,y u Let be the coordinates of the imaging point of the u-th sampling ray; HI is the equivalent image height of the field of view (0, ω) relative to the central field in the x and y directions; HI x and HI y Let HI be the components of HI in the x and y directions.

[0037] Step 4: Construct a comprehensive objective function based on the manufacturing constraint module, the optical margin judgment function, and the light convergence degree function;

[0038] The expression for the comprehensive objective function is:

[0039]

[0040] Among them, f S The objective function is denoted as s1; s1 to s4 are the weights of each function; d n The distance between the center points of the nth mirror and the next mirror is a position parameter; α n The tilt angle of the nth mirror is a position parameter; r n The radius of curvature at the vertex of the mirror is an optical parameter. It is the square of the eccentricity of the mirror, and is an optical parameter.

[0041] Step 5: Find the parameters that best meet the design requirements through a search algorithm, and then use the surface design method to obtain the free-form off-axis multi-reflector system; the parameters that best meet the design requirements are the parameters that minimize the comprehensive objective function; the parameters include position parameters and optical parameters.

[0042] Compared with the prior art, the technical solution proposed in this invention has the following beneficial effects:

[0043] 1. By setting a manufacturing constraint module, the system automatically determines whether the current system's position parameters are reasonable, ensuring the design of an off-axis multi-reflector system that meets manufacturing constraints. Compared with existing off-axis multi-reflector system design methods, the generated off-axis multi-reflector system is more conducive to integrated machining and manufacturing.

[0044] 2. By setting a comprehensive objective function, a unified evaluation index is designed to simultaneously and automatically evaluate the system's position parameters and imaging quality. Compared with existing off-axis multi-lens reflex (MLR) system design methods, this approach adds quantitative evaluation criteria, enhancing the comparability of off-axis MLR systems and facilitating the selection of systems that better meet manufacturing and design requirements. Attached Figure Description

[0045] Figure 1This is a flowchart illustrating the automatic design method for a free-form surface off-axis multi-reflection system based on manufacturing constraints in this embodiment.

[0046] Figure 2 This is a schematic diagram of the obstruction judgment of the off-axis multi-reflector system in this embodiment;

[0047] Among them, (a) is unobstructed; (b) is partially obstructed by M3 between mirrors M1 and M2; and (c) is completely obstructed by M3 between mirrors M1 and M2.

[0048] Figure 3 This is a flowchart illustrating the process of obtaining a free-form off-axis multi-reflection system using a search algorithm and surface design method in this embodiment.

[0049] Figure 4 This is a layout diagram of the off-axis multi-reflector system in this embodiment. Detailed Implementation

[0050] To facilitate understanding of this application, a more complete description will be provided below with reference to the accompanying drawings. Preferred embodiments of this application are shown in the drawings. However, this application can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of this application.

[0051] This invention addresses the design problem of off-axis multi-mirror systems under integrated manufacturing constraints by proposing an automatic design scheme for free-form surface off-axis multi-mirror systems based on manufacturing constraints. Specifically, it refers to automatically generating a free-form surface off-axis multi-mirror system that meets manufacturing constraints and has good imaging quality to facilitate integrated manufacturing. In modeling the off-axis multi-mirror system based on manufacturing constraints, a manufacturing constraint module is designed. By constructing a cocircularity function and an occlusion evaluation function, the system's position parameters are automatically determined to be reasonable. Then, an optical margin judgment function and a light convergence function are designed, and combined with the manufacturing constraint module, a comprehensive objective function is designed. Finally, by searching for the minimum value of the comprehensive objective function, the most suitable off-axis structure for the design requirements is found, and the system is adjusted into a free-form surface off-axis multi-mirror structure using a free-form surface design method.

[0052] The automatic design method for off-axis multi-reflection systems with free-form surfaces based on manufacturing constraints in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0053] Step 1: Construct a manufacturing constraint module based on the cocircularity function and the occlusion evaluation function; the cocircularity function is used to determine the degree of fit between each mirror and the cylindrical profile; the occlusion evaluation function is used to determine whether the edge of each mirror in the off-axis multi-mirror system blocks the light passing between other adjacent mirrors in the off-axis multi-mirror system;

[0054] The degree of cocircularity refers to the degree of fit between each mirror and the cylindrical reference surface;

[0055] The occlusion assessment refers to determining whether the edge of each reflector in the system blocks light passing through other reflectors in the system;

[0056] Step 1.1: Construct a cocircularity function based on the distance between a point on the mirror and the center point of the cylindrical profile;

[0057] In this embodiment, the radius of the cylindrical profile is 150 mm.

[0058] Using the distance between a point on the mirror and the center point of the cylindrical profile, a function for the degree of concircularity is constructed, expressed as:

[0059]

[0060] Among them, f M is the concircularity function; N is the number of uniform sampling points on each mirror; K is the total number of mirrors in the off-axis multi-mirror system; n is the mirror number; t is the sampling point number; rc is the radius of the cylindrical profile; Let be the distance between a point on the mirror and the center point of the cylindrical profile, and its expression is:

[0061]

[0062] Among them, (x rc ,y rc () represents the coordinates of the center point of the cylindrical profile section; These are the coordinates of the sampling point on the reflector.

[0063] In this embodiment, the number of reflectors is 3, N=3, K=3.

[0064] Step 1.2: Construct the occlusion evaluation function;

[0065] Step 1.2.1: Draw perpendicular lines from the top and bottom edge points of each mirror to the top and bottom edge rays passing through each group of adjacent mirrors (excluding the mirror itself) to obtain a set of perpendicular lines, and calculate the minimum length of the perpendicular lines in the set; the edge rays refer to the two outermost rays of the light path between two mirrors; since the image plane has a certain height, it is treated as an optical surface, i.e., a mirror, during the calculation.

[0066] For example, to determine the occlusion of the primary mirror, perpendicular lines need to be drawn from the top and bottom edges of the primary mirror to the top and bottom edges of the light rays between the secondary and tertiary mirrors, and between the tertiary mirror and the image plane. Meanwhile, since the image plane has a certain height and may obstruct the light paths between other mirrors, it is treated as an optical surface, i.e., a mirror, and denoted as the (K+1)th mirror in the calculation.

[0067] When determining the degree of occlusion of one mirror on the light path between two other mirrors, a total of four perpendicular lines need to be drawn, such as... Figure 2 As shown, the length of the perpendicular line is represented by l, the set of 4 perpendicular lines is {l}, and the minimum value min{l} in the set {l} can be calculated.

[0068] Step 1.2.2: Based on the coordinates of the foot of the perpendicular line, obtain the vector pointing from the top and bottom edges of the mirror to the coordinates of the foot of the perpendicular, and calculate the occlusion parameter of each mirror; the occlusion parameter indicates whether the mirror blocks the light rays passing through other mirrors in the off-axis multi-mirror system;

[0069] In this embodiment, since the coordinates of the four perpendicular points are known, four vectors pointing from the edge points of the mirror to the perpendicular coordinates can be obtained. By determining whether the angle between two vectors emanating from an edge point is greater than 90 degrees, it can be determined whether that point is obstructing the light path. That is, when the angle between two vectors emanating from an edge point is greater than 90 degrees, that point obstructs the light path. For the possibility that both the upper and lower edge points of the mirror may obstruct the light path, the determination method is to calculate the angle between any one of the two vectors emanating from one edge point and any one of the vectors emanating from the other edge point of the mirror. When the angle is greater than 90 degrees, obstruction exists.

[0070] Furthermore, the occlusion parameters of each mirror can be obtained, expressed as:

[0071]

[0072] Where PO is the occlusion parameter of each mirror; JA is the vector angle discriminant, expressed as:

[0073]

[0074] Where β represents the angle between the vectors.

[0075] Step 1.2.3: Construct a set of system occlusion parameters based on the occlusion parameters of each mirror;

[0076] In this embodiment, after calculating the occlusion parameters of all mirrors and the image plane, a set of system occlusion parameters can be constructed, expressed as:

[0077]

[0078] Wherein, {PO} is the set of system occlusion parameters; the superscript of PO is the serial number of the reflector, when the superscript is n, it represents the nth reflector; the subscript of PO represents the optical path, j(j+1) represents the optical path between the jth reflector and the (j+1)th reflector, when j=0, it is the optical path incident into the primary mirror.

[0079] Step 1.2.4: Construct an occlusion evaluation function based on the set of system occlusion parameters and the minimum value of the vertical length in the set of vertical lines;

[0080] In this embodiment, an occlusion evaluation function is constructed, with the expression:

[0081]

[0082] Among them, f O For the occlusion evaluation function; This represents the minimum length of the set of perpendicular lines drawn from the edge point of the nth mirror to the edge rays between the jth and (j+1)th mirrors.

[0083] At this point, the manufacturing constraint module based on the cocircularity function and the occlusion evaluation function has been completed.

[0084] Step 2: Construct an optical margin judgment function; the optical margin judgment function is used to calculate the minimum distance between the reflector and the edge light rays passing through other reflectors when the reflector does not block the light.

[0085] The optical margin refers to the minimum distance between the edge point of a reflector and the edge rays passing between other reflectors without obstructing light. In optical design, there are often requirements for optical margin, meaning that it is desirable for the reflector to maintain a certain distance from the light source without blocking it. Therefore, the margin constant is calculated using the following expression:

[0086]

[0087] in, is the margin constant; MR represents the minimum standard of optical margin, which is a constant.

[0088] In this implementation scheme, MR = 10.

[0089] Furthermore, an optical margin judgment function is constructed, with the following expression:

[0090]

[0091] Among them, f OM This is the optical margin judgment function.

[0092] Step 3: The degree of light convergence is measured by determining the distance between the imaging point and the ideal image point, thereby constructing a light convergence function; the light convergence function is used to determine the degree of dispersion of the intersection points of light rays and the image plane in each field of view;

[0093] The degree of light convergence refers to the degree of dispersion of the intersection points of light rays with the image plane in each field of view. The smaller the dispersion, the better the convergence.

[0094] Based on the object-image relationship, the position of the ideal image point corresponding to different field-of-view rays can be calculated, and the expression is:

[0095] HI=f·tan(ω-ω c (9)

[0096] Where f is the focal length of the system; HI is the equivalent image height of the field of view (0,ω) relative to the central field in the x and y directions; (0,ω c () is the central field of view.

[0097] In this implementation scheme, f = 300mm, and the central field of view is (0°, 0°).

[0098] The degree of light convergence is measured by determining the distance between the imaging point and the ideal image point, thus constructing a light convergence function, the expression of which is:

[0099]

[0100] Among them, f C is the light convergence function; NC is the number of sampled rays; u is the sequence number of the sampled ray; (x u ,y u Let ) be the coordinates of the imaging point of the u-th sampling ray; HI x and HI y Let HI be the components of HI in the x and y directions.

[0101] Step 4: Construct a comprehensive objective function based on the manufacturing constraint module, the optical margin judgment function, and the light convergence degree function;

[0102] A comprehensive objective function is constructed based on the manufacturing constraint module, the optical margin judgment function, and the light convergence degree function, and its expression is:

[0103]

[0104] Among them, f S The objective function is denoted as s1; s1 to s4 are the weights of each function; d n The distance between the center points of the nth mirror and the next mirror is a position parameter; α n The tilt angle of the nth mirror is a position parameter; rn The radius of curvature at the vertex of the mirror is an optical parameter. It is the square of the eccentricity of the mirror, and is an optical parameter.

[0105] Step 5: Find the parameters that best meet the design requirements through a search algorithm, and then use the surface design method to obtain the free-form off-axis multi-reflector system; the parameters that best meet the design requirements are those that minimize the overall objective function; the parameters include position parameters and optical parameters;

[0106] The structure best suited to the design requirements is found by searching for the minimum value of the comprehensive objective function, such as... Figure 3 As shown, this process can be implemented using search algorithms (simulated annealing, ant colony optimization, genetic algorithm). Before using the search algorithm, the design requirements parameters input into the algorithm need to be determined, including the system's entrance pupil diameter ED, F-number, and maximum field of view. Then, the radius of curvature of the center point of the reflector, the square of the eccentricity, the tilt angle, and the distance between the reflectors are set as variables. Next, the maximum number of searches needs to be input, and random position parameters and optical parameters are generated as the initial values ​​for the search. After finding suitable position parameters and optical parameters, a surface design method (SMS method, CI method, improved WW method, etc.) is used to adjust the system into a freeform off-axis multi-reflector structure, thus obtaining a freeform off-axis multi-reflector system.

[0107] In this implementation scheme, ED = 100mm, F-number is 3, maximum field of view is 4°×4°, simulated annealing is used as the search algorithm, the initial temperature is 1500 degrees, and when the number of searches reaches more than 40, a stable minimum value of the comprehensive objective function is obtained, which is 18.15. In this implementation scheme, the surface design method used is a modified WW method. The layout diagram of the obtained off-axis multi-reflector system is shown below. Figure 4 As shown, the three mirrors of the off-axis three-mirror system are all close to cylindrical profiles, meaning they meet manufacturing constraints. Furthermore, the light rays from each field of view converge at the ideal image plane, indicating good image quality. In conclusion, the automatic design method for off-axis multi-mirror systems based on manufacturing constraints proposed in this invention can automatically generate off-axis multi-mirror freeform surface systems that meet manufacturing constraints and have good image quality. The manufacturing constraint module ensures that the generated off-axis multi-mirror system meets manufacturing requirements, and the comprehensive objective function can balance manufacturing constraints with image quality, meeting the characteristics of integrated manufacturing.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not 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; therefore, these 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 automatic design method for off-axis multi-reflection systems of freeform surfaces based on manufacturing constraints, characterized in that, Includes the following steps: Step 1: Construct a manufacturing constraint module based on the cocircularity function and the occlusion evaluation function; the cocircularity function is used to determine the degree of fit between each mirror and the cylindrical profile; the occlusion evaluation function is used to determine whether the edge of each mirror in the off-axis multi-mirror system blocks the light passing between other adjacent mirrors in the off-axis multi-mirror system; The expression for the degree of concircularity is: (1) Among them, f M is the concircularity function; N is the number of uniform sampling points on each mirror; K is the total number of mirrors in the off-axis multi-mirror system; n is the mirror number; t is the sampling point number; rc is the radius of the cylindrical profile; This is the distance between a point on the reflector and the center point of the cylindrical profile. The expression for the occlusion evaluation function is: (6) In this context, the superscript of PO indicates the number of the reflector. When the superscript is n, it represents the nth reflector. The subscript of PO indicates the light path. j(j+1) represents the light path between the jth and (j+1)th reflectors. When j=0, it represents the light path incident into the primary mirror. For the occlusion evaluation function; This represents the minimum length of the set of perpendicular lines drawn from the edge point of the nth mirror to the edge rays between the jth and (j+1)th mirrors. Step 2: Construct an optical margin judgment function; the optical margin judgment function is used to calculate the minimum distance between the reflector and the edge light rays passing through other reflectors when the reflector does not block the light. The expression for the optical margin judgment function is: (8) Among them, f OM This is the optical margin judgment function; It is the residual constant; The expression for the residual constant is: (7) in, is the margin constant; MR represents the minimum standard of optical margin, which is a constant. Step 3: The degree of light convergence is measured by determining the distance between the imaging point and the ideal image point, thereby constructing a light convergence function; the light convergence function is used to determine the degree of dispersion of the intersection points of light rays and the image plane in each field of view; The expression for the light convergence degree function is: (10) in, is the light convergence function; NC is the number of sampled rays; u is the sequence number of the sampled ray; (x u , y u Let be the coordinates of the imaging point of the u-th sampling ray; HI is the equivalent image height of the field of view (0, ω) relative to the central field in the x and y directions; HI x and HI y Let HI be the components of HI in the x and y directions; Step 4: Construct a comprehensive objective function based on the manufacturing constraint module, the optical margin judgment function, and the light convergence degree function; The expression for the comprehensive objective function is: (11) in, The objective function is denoted as s1; s1 to s4 are the weights of each function; d n The distance between the center points of the nth mirror and the next mirror is a position parameter; α n The tilt angle of the nth mirror is a position parameter; r n The radius of curvature at the vertex of the mirror is an optical parameter. It is the square of the eccentricity of the mirror, and belongs to optical parameters; Step 5: Find the parameters that best meet the design requirements through a search algorithm, and then use the surface design method to obtain the free-form off-axis multi-reflector system; the parameters that best meet the design requirements are the parameters that minimize the comprehensive objective function; the parameters include position parameters and optical parameters.

2. The automatic design method for off-axis multi-reflection systems of freeform surfaces based on manufacturing constraints according to claim 1, characterized in that, Step 1 includes the following specific steps: Step 1.1: Construct a cocircularity function based on the distance between a point on the mirror and the center point of the cylindrical profile; Step 1.2: Construct the occlusion evaluation function.

3. The automatic design method for off-axis multi-reflection systems of freeform surfaces based on manufacturing constraints according to claim 2, characterized in that, Step 1.2 includes the following specific steps: Step 1.2.1: Draw perpendicular lines from the top and bottom edges of each mirror to the top and bottom edges of each pair of adjacent mirrors (excluding the mirror itself) to obtain a set of perpendicular lines, and calculate the minimum length of the perpendicular lines in the set; the edge rays refer to the two outermost rays of the light path between two mirrors; the image plane is treated as an optical surface, i.e., a mirror, during the calculation. Step 1.2.2: Based on the coordinates of the foot of the perpendicular line, obtain the vector pointing from the top and bottom edges of the mirror to the coordinates of the foot of the perpendicular, and calculate the occlusion parameter of each mirror; the occlusion parameter indicates whether the mirror blocks the light rays passing through other mirrors in the off-axis multi-mirror system; Step 1.2.3: Construct a set of system occlusion parameters based on the occlusion parameters of each mirror; Step 1.2.4: Construct an occlusion evaluation function based on the set of system occlusion parameters and the minimum value of the vertical length in the set of vertical lines.

4. The automatic design method for off-axis multi-reflection systems of freeform surfaces based on manufacturing constraints according to claim 3, characterized in that, The expression for the occlusion parameter is: (3) Where PO is the occlusion parameter of each mirror; JA is the vector angle discriminant, expressed as: (4) Where β represents the angle between the vectors.

5. The automatic design method for off-axis multi-reflection systems of freeform surfaces based on manufacturing constraints according to claim 3, characterized in that, The set expression for the system occlusion parameters is: (5) Where {PO} is the set of system occlusion parameters.

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