Design method of square aperture free-form surface optical system added with manufacturable constraints

Abstract

The invention relates to a design method of an optical system, in particular to a design method of a square aperture free-form surface optical system added with manufacturable constraints, which is used for solving the defect of contradiction between the detection sensitivity of a satellite-borne space target detection system and the volume and weight of the system. According to the design method of the square aperture free-form surface optical system added with the manufacturable constraint, a square aperture diaphragm is used for replacing a traditional circular aperture diaphragm, an initial free-form surface optical system is generated through a free-form surface design method, orthogonal ChebyShev polynomials in a square area are used for representation, and the manufacturable constraint is added in the design optimization process; and higher detection sensitivity can be realized under a relatively smaller volume.

Description

Technical Field

[0001] The invention relates to an optical system design method, and in particular to a square aperture free-form surface optical system design method with added manufacturable constraints. Background Art

[0002] As the world continues to explore space, the number of spacecraft in orbit has increased significantly, and the amount of space debris generated by abandoned equipment and collisions has also continued to grow. These objects, collectively referred to as space targets, are diverse in type and complex in distribution, posing a serious threat to the safe operation of spacecraft in orbit.

[0003] To address this problem, countries are actively developing space target detection systems. In this field, satellite-borne detection systems have shown obvious advantages because they operate in a space environment and can avoid interference from the atmosphere and bad weather. Among them, off-axis three-mirror optical systems are widely used in satellite-borne detection missions due to their optical design features, such as efficient light collection capabilities and long focal lengths.

[0004] However, the detection capability of a satellite-borne space target detection system mainly depends on its detection sensitivity, which is directly related to the entrance pupil area of ​​the optical system. The traditional solution is to increase the detection sensitivity by increasing the entrance pupil area of ​​the optical system, but this method usually leads to a significant increase in the volume and mass of the optical system. In the space environment, satellite platforms have strict restrictions on the volume and weight of the optical system. Therefore, increasing the entrance pupil area without increasing the system volume has become a key technical bottleneck for improving the performance of satellite-borne space target detection systems.

[0005] In summary, the research on satellite-borne space target detection systems needs to resolve the contradiction between detection sensitivity and system volume and weight, and provide important technical guarantees for achieving long-term sustainable development of space activities. Summary of the invention

[0006] The purpose of the present invention is to solve the problem that there is a contradiction between the detection sensitivity of a satellite-borne space target detection system and the system volume and weight, and to provide a design method for a square aperture free-form surface optical system with added manufacturability constraints.

[0007] In order to solve the deficiencies of the above-mentioned prior art, the present invention provides the following technical solutions:

[0008] The design method of a square aperture free-form surface optical system with added manufacturability constraints is special in that it includes the following steps:

[0009] Step 1, according to the design index of the off-axis three-mirror optical system, the three-mirror optical system is selected as the initial model, and the initial model includes a primary mirror M1, a secondary mirror M2, and a third mirror M3; the off-axis optical path layout design is performed on the initial model, and the off-axis unobstructed transmission of the light beam is achieved by adjusting the relative positions of the secondary mirror M2 and the third mirror M3, so as to obtain the off-axis three-mirror optical system;

[0010] Step 2, using Zemax and Matlab to interact, and applying the point-by-point construction iteration method to optimize the primary mirror M1, secondary mirror M2, and third mirror M3 of the off-axis three-mirror optical system in step 1, to obtain the primary mirror M′1, secondary mirror M′2, and third mirror M′3, and then obtain the initial free-form surface optical system;

[0011] Step 3. In the initial free-form surface optical system obtained in step 2, ChebyShev polynomials are introduced to characterize the primary mirror M′1, the secondary mirror M′2, and the third mirror M′3, and optimization is performed by adding manufacturability constraints to obtain the primary mirror M″1, the secondary mirror M″2, and the third mirror M″3, thereby obtaining a square aperture free-form surface optical system.

[0012] Furthermore, the step 2 is specifically as follows:

[0013] Step 2.1, using Zemax and Matlab to interact, and applying the point-by-point construction iteration method to construct the initial free-form surface for the primary mirror M1, secondary mirror M2, and third mirror M3 of the off-axis three-mirror optical system in step 1;

[0014] Step 2.1.1, select the field of view, divide the square aperture, and obtain multiple characteristic rays;

[0015] Step 2.1.2, trace multiple characteristic rays in Zemax to obtain the starting point coordinates and direction vectors of the characteristic rays;

[0016] Step 2.1.3, in Matlab, according to the optical object-image relationship and the shortest ray algorithm, calculate the three-dimensional coordinates and normal vectors of the characteristic points of the characteristic ray on the initial free-form surface point by point;

[0017] Step 2.1.4, use the fitting algorithm to generate the initial free-form surface expression, and complete the initial free-form surface construction mirror by mirror;

[0018] Step 2.2, iteratively optimizing the initial free-form surface obtained in step 2.1 to obtain an initial free-form surface optical system;

[0019] Step 2.2.1, select the field of view, divide the square aperture, and obtain multiple characteristic rays;

[0020] Step 2.2.2: In Zemax, trace multiple characteristic rays to obtain the intersection points between the characteristic rays and the initial free-form surface;

[0021] Step 2.2.3, calculate the normal vector of each feature point in Matlab based on Fermat's principle and the object-image relationship;

[0022] Step 2.2.4, integrate the updated three-dimensional coordinates and normal vectors of the feature points, and re-fit to generate the initial free-form surface expression;

[0023] Step 2.2.5, iteratively optimize all initial free-form surfaces mirror by mirror to obtain the primary mirror M′1, the secondary mirror M′2, and the tertiary mirror M′3, and then obtain the initial free-form surface optical system.

[0024] Furthermore, the step 3 is specifically as follows:

[0025] Step 3.1, perform ray tracing on the primary mirror M′1, the secondary mirror M′2, and the third mirror M′3 of the initial free-form surface optical system in step 2 in Zemax to obtain feature point data on the primary mirror M′1, the secondary mirror M′2, and the third mirror M′3, wherein the feature point data includes the three-dimensional coordinates and normal vectors of the feature points;

[0026] Step 3.2, the primary mirror M′1, the secondary mirror M′2, and the tertiary mirror M′3 are respectively characterized by 6th-order even-order Chebyshev polynomials, and each mirror surface is symmetrical about the YOZ plane; Matlab is used to fit the feature point data to generate the Chebyshev polynomial expression of each mirror surface;

[0027] Step 3.3, control the sum of the vector height differences of each mirror at the edge of the square area to be zero, and eliminate the piston term and tilt term caused by the polynomial itself;

[0028] Step 3.4, gradually improve the performance of the optical system through optimization cycles until the convergence condition is reached, and obtain the primary mirror M″1, the secondary mirror M″2, and the tertiary mirror M″3, and then obtain a square aperture free-form surface optical system; the convergence condition is that the change amplitude of the overall mirror vector height difference is less than or equal to the convergence threshold in multiple consecutive optimization cycles.

[0029] Furthermore, the step 3.3 is specifically as follows:

[0030] Step 3.3.1: Control the sum of the sag differences at the edges of the square aperture of each mirror sum is zero, and the constraint formula is:

[0031]

[0032] In the formula, a 0，2 、a 2，0 、a 2，2 It is a low-order component, reflecting the main curvature and asymmetry of the free-form surface in the xy direction; a 0，4 、a 4，0is the middle-order component, describing the fourth-order asymmetric distribution of the free-form surface; a 0，6 、a 6，0 is a high-order component; a 2，4 、a 4，2 is a mixed order term;

[0033] Step 3.3.2, eliminate the piston term caused by the polynomial itself:

[0034] piston=α 0，0 -α 2，0 -α 0，2 +α 4，0 +α 2，2 +α 0，4 -α 6，0 -α 4，2 -α 2，4 -α 0，6 =0

[0035] Step 3.3.3, eliminate the tilt term caused by the polynomial itself:

[0036] tilt=α 0，1 -3α 0,3 +5α 0,5 -α 2，1 +3α 2，3 +α 4，1 =0.

[0037] Furthermore, the step 3.4 is specifically as follows:

[0038] Step 3.4.1, in Zemax, take the image spot size as the optimization target, generate the system default operands, and optimize the mirror shape to minimize the image spot size;

[0039] Step 3.4.2, modify the optimization target, use the system contrast as the optimization index, and generate the system default operand;

[0040] Step 3.4.3, repeat steps 3.4.1 to 3.4.2 until the convergence condition is reached, and the primary mirror M″1, the secondary mirror M″2, and the tertiary mirror M″3 are obtained, and then a square aperture free-form surface optical system is obtained.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] The present invention provides a design method for a square aperture free-form surface optical system with added manufacturability constraints, replaces a traditional circular aperture diaphragm with a square aperture diaphragm, generates an initial free-form surface optical system using a free-form surface design method (point-by-point construction iteration method), characterizes the system with orthogonal Chebyshev polynomials in a square region, and adds manufacturability constraints during the design optimization process; compared with an off-axis three-mirror system of the same order characterized by an XY polynomial with added manufacturability constraints, the system entrance pupil area is increased by 27% under the premise of a relatively smaller system volume, thereby improving the system's detection sensitivity to space targets while reducing the detection difficulty of each mirror surface, and after defocusing, the detection system has excellent performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A three-dimensional diagram of the off-axis three-mirror optical system in step 2 of the embodiment of the square aperture free-form surface optical system design method with added manufacturability constraints of the present invention;

[0044] Figure 2 is a point diagram of each field of view of the off-axis three-mirror optical system in step 2 of the embodiment of the present invention;

[0045] Figure 3 A three-dimensional diagram of the initial free-form surface optical system in step 3 of the embodiment of the present invention;

[0046] Figure 4 is a point diagram of each field of view of the initial free-form surface optical system in step 3 of the embodiment of the present invention;

[0047] Figure 5 is the sum of the vector height differences zsag of the square aperture edge after adding constraints to the primary mirror M′1, the secondary mirror M′2, and the third mirror M′3 in step 4 of the embodiment of the present invention sum Graph of changes during the optimization cycle;

[0048] Figure 6 A curve diagram showing changes in the peak to valley value (PV) of the vector height difference in the optimization cycle after adding constraints to the primary mirror M′1, the secondary mirror M′2, and the tertiary mirror M′3 in step 4 of the embodiment of the present invention;

[0049] Figure 7 A three-dimensional diagram of the square aperture free-form surface optical system in step 4 of an embodiment of the present invention;

[0050] Figure 8 The light imprints of the primary mirror M″1, secondary mirror M″2, tertiary mirror M″3 and image plane of the square aperture free-form surface optical system in step 4 of the embodiment of the present invention; (b), (c), (d), and (e) correspond to the primary mirror M″1, secondary mirror M″2, tertiary mirror M″3 and image plane respectively;

[0051] Fig. 9A three-dimensional diagram of the circular aperture free-form surface optical system in step 5 of an embodiment of the present invention;

[0052] Fig.10 The light imprints of the primary mirror M01, the secondary mirror M02, the third mirror M03 and the image plane of the circular aperture free-form surface optical system in step 5 of the embodiment of the present invention; (b), (c), (d), and (e) correspond to the primary mirror M01, the secondary mirror M02, the third mirror M03 and the image plane respectively;

[0053] Fig.11 It is a point diagram of the square aperture free-form surface optical system in step 4 of the embodiment of the present invention;

[0054] Fig.12 It is a point diagram of the circular aperture free-form surface optical system in step 5 of the embodiment of the present invention;

[0055] Fig.13 The energy concentration curve of the square aperture free-form surface optical system before defocusing in step 6 of the embodiment of the present invention;

[0056] Fig.14 The energy concentration curve of the circular aperture free-form surface optical system before defocusing in step 6 of the embodiment of the present invention;

[0057] Fig.15 is a relative illumination curve of the square aperture free-form surface optical system before defocusing in step 6 of an embodiment of the present invention;

[0058] Fig.16 is a relative illumination curve of the circular aperture free-form surface optical system before defocusing in step 6 of the embodiment of the present invention;

[0059] Fig.17 The distortion grids of the square aperture free-form surface optical system before defocusing and the circular aperture free-form surface optical system before defocusing in step 6 of the embodiment of the present invention; (a) and (b) correspond to the square aperture free-form surface optical system and the circular aperture free-form surface optical system respectively;

[0060] Fig.18 The full-field wavefront aberration of the square aperture free-form surface optical system before defocusing in step 6 of the embodiment of the present invention;

[0061] Fig.19 The full-field wavefront aberration of the circular aperture free-form surface optical system before defocusing in step 6 of the embodiment of the present invention;

[0062] Fig. 20 It is a point diagram of the square aperture free-form surface optical system after defocusing and the circular aperture free-form surface optical system after defocusing in step 7 of the embodiment of the present invention; (a) and (b) correspond to the square aperture free-form surface optical system and the circular aperture free-form surface optical system respectively;

[0063] Fig.21 The energy concentration curve of the square aperture free-form surface optical system after defocusing in step 7 of the embodiment of the present invention;

[0064] Fig. 22 The energy concentration curve of the circular aperture free-form surface optical system after defocusing in step 7 of the embodiment of the present invention;

[0065] Fig.23 PV value distribution diagram of the vector height difference of each mirror surface minus the base spherical surface in the square aperture free-form surface optical system and the circular aperture free-form surface optical system in the embodiment of the present invention; (a), (b), (c) correspond to the primary mirror M″1, the secondary mirror M″2, and the tertiary mirror M″3 respectively; (d), (e), (f) correspond to the primary mirror M01, the secondary mirror M02, and the tertiary mirror M03 respectively;

[0066] Fig.24 is the result of 500 Monte Carlo simulations of tolerance analysis of the square aperture free-form surface optical system after defocusing in step 7 of the embodiment of the present invention;

[0067] Fig.25 It is the result of 500 Monte Carlo simulations of tolerance analysis of the circular aperture free-form surface optical system after defocusing in step 7 of the embodiment of the present invention. DETAILED DESCRIPTION

[0068] The present invention will be further described below in conjunction with the accompanying drawings and exemplary embodiments.

[0069] A design method for a square aperture free-form surface optical system with added manufacturability constraints. In an off-axis three-mirror optical system, a square aperture diaphragm is used to replace the traditional circular aperture diaphragm. Manufacturability constraints are added during the optimization process, and finally the design of a square aperture diaphragm detection system is completed.

[0070] The specific steps include:

[0071] Step 1: Based on the optical radiation theory, establish a detection sensitivity model of the satellite-borne space target detection system for space targets, expressed by the equivalent apparent magnitude m of the target reflected light at the entrance pupil, which can be expressed as follows:

[0072]

[0073] In the formula, is the average wavelength, S d is the entrance pupil area (effective light transmission area) of the optical system, η is the average quantum efficiency of the detector, τ0 is the transmittance of the optical system, N B is the number of photoelectrons generated by background noise, N D is the number of photoelectrons generated by dark current, T snTo meet the signal-to-noise ratio threshold of a certain detection rate and false alarm rate, a is the size of a single pixel of the detector, d is the image spot diameter, h is Planck's constant, and c is the speed of light;

[0074] Qualitative analysis of the detection sensitivity model shows that, under the premise that the volume of the optical system remains unchanged, the detection sensitivity m varies with the entrance pupil area S of the optical system. d to increase and improve;

[0075] Step 2, according to the design index of the off-axis three-mirror optical system, select a three-mirror optical system with similar indexes as the initial model, the initial model includes a primary mirror M1, a secondary mirror M2, and a third mirror M3; perform off-axis optical path layout design on the initial model to ensure that the optical path leaves the optical center, and achieve off-axis unobstructed transmission of the light beam by adjusting the relative positions of the secondary mirror M2 and the third mirror M3, thereby obtaining an off-axis three-mirror optical system;

[0076] The design indicators of the off-axis three-mirror optical system include spectral range, focal length, field of view, aperture, image spot size, and distortion, as shown in Table 1:

[0077] Table 1

[0078]

[0079]

[0080] Figure 1 A three-dimensional diagram of the off-axis three-mirror optical system in step 2; Figure 2 is the spot diagram of each field of view of the off-axis three-mirror optical system in step 2; the average RMS size of the spot diagram is about 400 μm; the curvature radius, mirror spacing and mirror deflection angle of the primary mirror M1, secondary mirror M2 and third mirror M3 of the off-axis three-mirror optical system are shown in Table 2:

[0081] Table 2

[0082]

[0083]

[0084]

[0085] Step 3, using Zemax and Matlab to interact, apply the free-form surface optical system construction method - point-by-point construction iteration method, the primary mirror M1, secondary mirror M2, and third mirror M3 of the off-axis three-mirror optical system in step 2, obtain the primary mirror M′1, secondary mirror M′2, and third mirror M′3, and then obtain the initial free-form surface optical system, which is used as the starting point for the subsequent optimization of the square aperture free-form surface optical system characterized by the ChebyShev polynomial with manufacturable constraints;

[0086] Step 3.1, using Zemax and Matlab to interact, and applying the point-by-point construction iteration method to construct the initial free-form surface for the primary mirror M1, secondary mirror M2, and third mirror M3 of the off-axis three-mirror optical system in step 2;

[0087] Step 3.1.1, select the 11 fields of view, including (0°, -2°)(0°, 0°)(0°, 2°)(2°, -2°)(2°, 0°)(2°, 2°)(1.4°, -2°)(1.4°, -1.4°)(1.4°, 0°)(1.4°, 1.4°)(1.4°, 2°), divide the square aperture into 31 equal parts in the x and y directions, the number of sampling points = 31 × 31 = 961, the number of characteristic rays = 11 × 961 = 10571;

[0088] Step 3.1.2, in Zemax, perform ray tracing through the above field of view and aperture sampling to obtain the starting point coordinates and direction vector of the characteristic light;

[0089] Step 3.1.3, in Matlab, according to the optical object-image relationship and the shortest ray algorithm, calculate the three-dimensional coordinates and normal vectors of the feature points of the ray on the initial free-form surface point by point;

[0090] Step 3.1.4, using a fitting algorithm that simultaneously considers the three-dimensional coordinates of the feature points and the corresponding normal vectors, generating an initial free-form surface expression (XY polynomial representation) of the desired initial free-form surface;

[0091] Step 3.1.5, complete the above steps one by one for all initial free-form surfaces in the off-axis three-mirror optical system to complete the initial free-form surface construction;

[0092] Step 3.2, iteratively optimize the initial free-form surface obtained in step 3.1 to obtain the primary mirror M′1, the secondary mirror M′2, and the tertiary mirror M′3, and then obtain the initial free-form surface optical system;

[0093] Step 3.2.1, select the 11 fields of view described in step 3.1.1, and divide the square aperture into 51 equal parts in the x and y directions, for a total of 28611 characteristic rays;

[0094] Step 3.2.2, in Zemax, trace the characteristic ray to obtain the intersection point between the characteristic ray on the initial free-form surface and the initial free-form surface;

[0095] Step 3.2.3, write an algorithm based on Fermat's principle and the object-image relationship to solve the normal vector corresponding to each feature point;

[0096] Step 3.2.4, refitting the initial free-form surface expression (XY polynomial representation) using a fitting algorithm that simultaneously considers the three-dimensional coordinates and normal vectors of the updated feature points;

[0097] Step 3.2.5, iterate all the initial free-form surfaces one by one to complete the iterative optimization of the entire off-axis three-mirror optical system, and obtain the primary mirror M′1, the secondary mirror M′2, and the third mirror M′3, and then obtain the initial free-form surface optical system, which serves as the basic model for the subsequent design of the square aperture free-form surface optical system;

[0098] Figure 3 is a three-dimensional diagram of the initial free-form surface optical system in step 3; Figure 4 is the point diagram of each field of view of the initial free-form surface optical system in step 3;

[0099] Step 4, introducing ChebyShev polynomials into the initial free-form surface optical system obtained in step 3 to characterize the primary mirror M′1, the secondary mirror M′2, and the third mirror M′3, and optimizing by adding manufacturability constraints to obtain the primary mirror M″1, the secondary mirror M″2, and the third mirror M″3, and then obtaining a square aperture free-form surface optical system;

[0100] Step 4.1, perform ray tracing on the primary mirror M′1, secondary mirror M′2, and tertiary mirror M′3 of the initial free-form surface optical system obtained in step 3 in Zemax to obtain feature point data on the primary mirror M′1, secondary mirror M′2, and tertiary mirror M′3, including the three-dimensional coordinates and normal vectors of the feature points;

[0101] Step 4.2, the primary mirror M′1, the secondary mirror M′2, and the tertiary mirror M′3 are respectively characterized by 6th-order even-order Chebyshev polynomials, and only the even-order terms are retained to ensure that each mirror surface is symmetrical about the Y0Z plane; Matlab is used to fit the feature point data to generate the Chebyshev polynomial expression of each mirror surface;

[0102] The 6th-order even-order Chebyshev polynomial is as follows:

[0103]

[0104] Where c is the curvature at the vertex of the base surface (the inverse of the radius of curvature), k is the cone coefficient, and a i，j are the coefficients of the Chebyshev polynomial; x0 and y0 represent the normalized aperture values ​​in the x and y directions, respectively; T i (u) and T j (v) is a one-dimensional Chebyshev polynomial; i and j represent the order in the x and y directions respectively, i is an even number, i+j≤6;

[0105] The ChebyShev polynomial coefficients of the primary mirror M′1, secondary mirror M′2, and tertiary mirror M′3 are shown in Table 3:

[0106] Table 3

[0107]

[0108]

[0109] Step 4.3, add manufacturability constraints - control the sum of the height differences of each mirror at the edge of the square area to be zero, and eliminate the piston term and tilt term caused by the polynomial itself;

[0110] Step 4.3.1: Control the sum of the sag differences at the edges of the square aperture of each mirror sum is zero, and the constraint formula is:

[0111]

[0112] In the formula, a 0，2 、a 2，0 、a 2，2 It is a low-order component, reflecting the main curvature and asymmetry of the free-form surface in the xy direction; a 0，4 、a 4，0 is the middle-order component, describing the fourth-order asymmetric distribution of the free-form surface; a 0，6 、a 6，0 is a high-order component that captures more detailed free-form surface characteristics; a 2，4 、a 4，2 is a mixed order term, describing the complex interaction characteristics on the free-form surface;

[0113] The square aperture edge is the boundary area defined by the maximum or minimum values ​​of x and y;

[0114] Step 4.3.2, eliminate the piston term caused by the polynomial itself:

[0115] piston=α 0,0 -α 2,0 -α 0,2 +α 4,0 +α 2,2 +α 0,4 -α 6,0 -α 4,2 -α 2,4 -α 0,6 =0

[0116] Step 4.3.3, eliminate the tilt term caused by the polynomial itself:

[0117] tilt=α 0,1 -3α 0,3 +5α 0,5 -α 2,1 +3α 2,3 +α 4,1 =0

[0118] Step 4.4, gradually improve the performance of the optical system through optimization cycles until the convergence condition is reached, and obtain the primary mirror M″1, the secondary mirror M″2, and the tertiary mirror M″3, and then obtain a square aperture free-form surface optical system;

[0119] Step 4.4.1, in Zemax, take the image spot size as the optimization target, generate the system default operands, and optimize the mirror shape to minimize the image spot size;

[0120] Step 4.4.2, modify the optimization target, use the system contrast as the optimization index, and generate the system default operand;

[0121] Step 4.4.3, repeat steps 4.4.1 to 4.4.2, each execution of steps 4.4.1 to 4.4.2 is a cycle, until the convergence condition is reached, complete 9 cycles in total, gradually optimize the system performance, and finally obtain the primary mirror M″1, the secondary mirror M″2, the third mirror M″3, and then obtain a square aperture free-form surface optical system;

[0122] The convergence condition is that the change amplitude of the overall mirror elevation difference is less than or equal to the convergence threshold in multiple consecutive optimization cycles;

[0123] The optimization results are as follows:

[0124] Figures 5-6 The sum of the sag differences of the square aperture edges after adding constraints to the primary mirror M′1, the secondary mirror M′2, and the tertiary mirror M′3 in step 4 is zsag sum , the change curve of the vector height difference PV value in the optimization cycle;

[0125] The PV value of the sagittal difference of the primary mirror M′1 decreases from 1.38mm to 0.06mm, the PV value of the sagittal difference of the secondary mirror M′2 decreases from 1.62mm to 0.28mm, and the PV value of the sagittal difference of the third mirror M′3 decreases from 4.52mm to 0.24mm. It can be seen that by controlling the sum of the sagittal differences zsag sum It is zero, which greatly reduces the PV value of the overall mirror height difference, and the difficulty of free-form surface detection is greatly reduced;

[0126] After 9 rounds of optimization with manufacturability constraints and image spot size and contrast as optimization indicators, a square aperture free-form surface optical system with preset design indicators was successfully designed; the primary mirror is a 40mmx40mm square aperture stop, the base spherical curvature radii of the primary mirror M″1, secondary mirror M″2, and tertiary mirror M″3 are -341.964mm, -112.864mm, and -159.690mm respectively, the focal length is 150mm, and the field of view angle is 4°x4°;

[0127] Figure 7This is a 3D diagram of the square aperture freeform surface optical system after adding constraints in step 4; Figure 8 It is the light imprint of the primary mirror M″1, secondary mirror M″2, tertiary mirror M″3 and image plane in step 4; (b), (c), (d), (e) correspond to the primary mirror M″1, secondary mirror M″2, tertiary mirror M″3 and image plane respectively; the light distribution of the primary mirror M″1 is constrained by the aperture stop and presents a square feature; the light distribution of the secondary mirror M″2 and tertiary mirror M″3 is more complicated, reflecting the role of free-form surface in aberration correction;

[0128] Step 5: Use the initial model in step 2 as the starting point for adding constrained circular aperture stop design optimization, sample the sagitta of data points at different polar angles at the maximum aperture, and then use the sagitta difference of adjacent data points to be zero as a manufacturable constraint, and finally optimize to obtain a circular aperture free-form surface optical system;

[0129] Step 5.1: For the initial model in step 2, set the aperture stop to a circular aperture stop with a radius of 20 mm, and keep other parameters unchanged;

[0130] Step 5.2, during the optimization process, add the image spot size as a system index generation operand, and after one optimization, add the contrast as a system index generation operand;

[0131] Step 5.2.1, add the image spot size as an optimization index to the objective function of the system, optimize the focusing performance of the light, and minimize the image spot size;

[0132] Set the low-order terms of the mirror's XY polynomial to variable parameters;

[0133] Use Zemax to add RMS Spot Radius as an optimization target, generate system default operands, and run the optimization to adjust the initial free-form surface shape of the mirror.

[0134] Step 5.2.2, add contrast as an optimization index to improve the imaging quality by optimizing the MTF (modulation transfer function) of the system;

[0135] After the initial optimization, the middle-order terms of the XY polynomial of the mirror are further added as variables;

[0136] Add contrast as the optimization target, generate the system default operands, and gradually optimize the contrast within the target wavelength range of each field of view point of the system;

[0137] Step 5.3, sample the vector height of data points at different polar angles at the maximum aperture, then set the vector height difference of adjacent data points to zero as a manufacturability constraint, gradually set the high-order terms of the XY polynomial as variables, and finally optimize to obtain a 6th-order even-order XY polynomial;

[0138] At different polar angle positions at the maximum aperture of the mirror (radius 20mm), the sag data points on the mirror are sampled;

[0139] The difference in the vector height of adjacent data points is set to zero, and the vector height difference constraint is added to the objective function to control the edge error of the mirror shape within the manufacturable range; in the later stage of optimization, the high-order terms of the XY polynomial are gradually released as variables, and the mirror shape is further adjusted to improve the system performance, and a circular aperture free-form surface optical system is obtained, and the parameters are as follows:

[0140] The primary mirror M01 is a circular aperture stop with a radius of 20 mm. The base spherical curvature radii of the primary mirror M01, secondary mirror M02, and tertiary mirror M03 are -333.962 mm, -143.829 mm, and -162.889 mm, respectively. The focal length is 150 mm, and the field of view angle is 4°x4°.

[0141] Fig. 9 is a three-dimensional diagram of the circular aperture free-form surface optical system in step 5;

[0142] Fig.10 The light imprints of the primary mirror M01, secondary mirror M02, tertiary mirror M03 and image plane of the circular aperture free-form surface optical system in step 5; (b), (c), (d), and (e) correspond to the primary mirror M01, secondary mirror M02, tertiary mirror M03 and image plane respectively;

[0143] The XY polynomial coefficients of the primary mirror M01, secondary mirror M02, and tertiary mirror M03 are shown in Table 4:

[0144] Table 4

[0145]

[0146]

[0147] Step 6. Comparing the square aperture free-form surface optical system of step 4 with the circular aperture free-form surface optical system of step 5, it can be found that compared with the circular aperture free-form surface optical system, under the premise of a relatively smaller system volume (0.78 cubic decimeters vs. 0.96 cubic decimeters), the entrance pupil area of ​​the square aperture free-form surface optical system is increased by 27%, which improves the detection sensitivity of the system to space targets while reducing the detection difficulty of each mirror surface. After defocusing, the detection system has excellent performance. The specific comparison is as follows:

[0148] The point diagram, energy concentration, relative illumination, distortion grid and full-field wave aberration of the square aperture free-form surface optical system and the circular aperture free-form surface optical system are shown in Figure 2. Figure 6 , Figure 7 , Figure 8 , Fig. 9 and Fig.10 As shown;

[0149] like Figures 11-12 As shown in the figure, the average RMS image spot diameter of the square aperture free-form surface optical system is 0.56 μm, which is much smaller than the Airy disk diameter of 5.4 μm; the average RMS image spot diameter of the circular aperture free-form surface optical system is 0.52 μm, which is much smaller than the Airy disk diameter of 6 μm.

[0150] like Figures 13-14 As shown, both the square aperture free-form surface optical system and the circular aperture free-form surface optical system have 80% of the energy concentrated within the diameter of 4.6 μm, and 90% of the energy concentrated within the diameter of 9.2 μm;

[0151] like Figures 15-16 As shown, on the image plane, the illumination uniformity of the square aperture free-form surface optical system and the circular aperture free-form surface optical system on the image plane is 98% and 97% respectively;

[0152] like Fig.17 As shown, the maximum grid distortion of the square aperture free-form surface optical system and the circular aperture free-form surface optical system are 0.39% and 0.34% respectively, which meet the design specifications;

[0153] like Figures 18-19 As shown, the full-field RMS wave aberration of the square aperture free-form surface optical system and the circular aperture free-form surface optical system is 0.039λ and 0.017λ respectively;

[0154] Since the image spot of the system on the image plane is much smaller than the size of a single pixel of the detector, in order to improve the position interpolation accuracy, the system is defocused so that the image spot is distributed in 2×2 pixels; after the two systems are defocused by 0.07mm, the geometric image spot diameters of the two systems are close to 2 times the pixel size, meeting the application requirements of the spaceborne detection system, such as Fig. 20 As shown;

[0155] At this time, the energy concentration curve of the image spot is as follows: Figures 21-22 As shown, 85% of the energy of both systems is concentrated within the diameter of 18.4 μm;

[0156] The PV values ​​of the elevation differences after subtracting the base spherical surface of the primary mirror M″1, secondary mirror M″2, and tertiary mirror M″3 are 0.06mm, 0.28mm, and 0.24mm respectively. Fig.23 As shown in (a), (b), and (c), the PV values ​​of the elevation differences of the primary mirror M01, secondary mirror M02, and tertiary mirror M03 after subtracting the base spherical surface are 0.24 mm, 0.43 mm, and 0.38 mm, respectively. Fig.23 As shown in (d), (e), and (f), by adding manufacturability constraints, the PV values ​​of the sagittal height difference between the curved surface of the mirror and the base spherical surface are reduced by 75%, 35%, and 37%, respectively, and the difficulty of curved surface detection is greatly reduced;

[0157] To summarize the above comparison results, the square aperture free-form surface optical system is smaller than the circular aperture free-form surface optical system (0.78dm 3 vs 0.96dm 3 ), the entrance pupil area increased by 27% (1600mm 2 vs1257mm 2 ), and the PV value of the vector height difference is reduced by at least 35%, while the other system indicators, such as field of view, focal length, image spot size, and energy concentration, are similar; according to the detection sensitivity model obtained in step 1, it can be seen that the system can detect the equivalent magnitude of the weakest space target at the entrance pupil of the system is increased by 0.24, that is, it can detect the light reflected by weaker space targets, thus improving the system's detection capability for weak space targets;

[0158] Step 7, performing tolerance analysis on the square aperture free-form surface optical system in step 4 after defocusing and the circular aperture free-form surface optical system in step 5 after defocusing;

[0159] The energy concentration of the system after defocusing within the image plane diameter of 18.4μm (i.e., twice the pixel size) is used as the index of tolerance analysis; under the conventional processing and adjustment level, the tolerance allocation results of each lens are shown in Table 5, and both systems use this tolerance allocation table;

[0160] Table 5

[0161]

[0162]

[0163] Under the above tolerance constraints, 500 Monte Carlo simulations were performed on the feasibility of the system energy concentration at different wavelengths and fields of view. Figures 24-25 As shown in the figure, for the square aperture free-form surface optical system, there is a 90% probability that the energy concentration value within 18.4μm on the image plane is greater than 87.0%; for the circular aperture free-form surface optical system, there is a 90% probability that the energy concentration value within 18.4μm on the image plane is greater than 85.2%; the tolerance analysis results show that both systems meet the requirements of visible light space target detection;

[0164] Therefore, the free-form surface design method-construction iteration method is used to optimize the initial structure, and then the orthogonal ChebyShev polynomial free-form surfaces in the square area are used to characterize the mirror surface. And the manufacturability constraints are added in the optimization process to optimize the off-axis three-mirror system with a square aperture stop. The entrance pupil area can be increased while the volume is relatively smaller, thereby realizing the improvement of the optical system's ability to detect space targets.

Claims

1. A design method for a square aperture free-form surface optical system with added manufacturability constraints, characterized in that: The steps include: Step 1, according to the design index of the off-axis three-mirror optical system, the three-mirror optical system is selected as the initial model, and the initial model includes a primary mirror M1, a secondary mirror M2, and a third mirror M3; the off-axis optical path layout design is performed on the initial model, and the off-axis unobstructed transmission of the light beam is achieved by adjusting the relative positions of the secondary mirror M2 and the third mirror M3, so as to obtain the off-axis three-mirror optical system; Step 2, using Zemax and Matlab to interact, and applying the point-by-point construction iteration method to optimize the primary mirror M1, secondary mirror M2, and third mirror M3 of the off-axis three-mirror optical system in step 1, to obtain the primary mirror M′1, secondary mirror M′2, and third mirror M′3, and then obtain the initial free-form surface optical system; Step 3. In the initial free-form surface optical system obtained in step 2, ChebyShev polynomials are introduced to characterize the primary mirror M′1, the secondary mirror M′2, and the third mirror M′3, and optimization is performed by adding manufacturability constraints to obtain the primary mirror M″1, the secondary mirror M″2, and the third mirror M″3, thereby obtaining a square aperture free-form surface optical system.

2. The method for designing a square aperture free-form surface optical system with added manufacturability constraints according to claim 1, characterized in that: The step 2 is specifically as follows: Step 2.1, using Zemax and Matlab to interact, and applying the point-by-point construction iteration method to construct the initial free-form surface for the primary mirror M1, secondary mirror M2, and third mirror M3 of the off-axis three-mirror optical system in step 1; Step 2.1.1, select the field of view, divide the square aperture, and obtain multiple characteristic rays; Step 2.1.2, trace multiple characteristic rays in Zemax to obtain the starting point coordinates and direction vectors of the characteristic rays; Step 2.1.3, in Matlab, according to the optical object-image relationship and the shortest ray algorithm, calculate the three-dimensional coordinates and normal vectors of the characteristic points of the characteristic ray on the initial free-form surface point by point; Step 2.1.4, use the fitting algorithm to generate the initial free-form surface expression, and complete the initial free-form surface construction mirror by mirror; Step 2.2, iteratively optimizing the initial free-form surface obtained in step 2.1 to obtain an initial free-form surface optical system; Step 2.2.1, select the field of view, divide the square aperture, and obtain multiple characteristic rays; Step 2.2.2: In Zemax, trace multiple characteristic rays to obtain the intersection points between the characteristic rays and the initial free-form surface; Step 2.2.3, calculate the normal vector of each feature point in Matlab based on Fermat's principle and the object-image relationship; Step 2.2.4, integrate the updated three-dimensional coordinates and normal vectors of the feature points, and re-fit to generate the initial free-form surface expression; Step 2.2.5, iteratively optimize all initial free-form surfaces mirror by mirror to obtain the primary mirror M′1, the secondary mirror M′2, and the tertiary mirror M′3, and then obtain the initial free-form surface optical system.

3. The method for designing a square aperture free-form surface optical system with added manufacturability constraints according to claim 1 or 2, characterized in that: The step 3 is specifically as follows: Step 3.1, perform ray tracing on the primary mirror M′1, the secondary mirror M′2, and the third mirror M′3 of the initial free-form surface optical system in step 2 in Zemax to obtain feature point data on the primary mirror M′1, the secondary mirror M′2, and the third mirror M′3, wherein the feature point data includes the three-dimensional coordinates and normal vectors of the feature points; Step 3.2, the primary mirror M′1, the secondary mirror M′2, and the tertiary mirror M′3 are respectively characterized by 6th-order even-order Chebyshev polynomials, and each mirror surface is symmetrical about the YOZ plane; Matlab is used to fit the feature point data to generate the Chebyshev polynomial expression of each mirror surface; Step 3.3, control the sum of the vector height differences of each mirror at the edge of the square area to be zero, and eliminate the piston term and tilt term caused by the polynomial itself; Step 3.4, gradually improve the performance of the optical system through optimization cycles until the convergence condition is reached, and obtain the primary mirror M″1, the secondary mirror M″2, and the tertiary mirror M″3, and then obtain a square aperture free-form surface optical system; the convergence condition is that the change amplitude of the overall mirror vector height difference is less than or equal to the convergence threshold in multiple consecutive optimization cycles.

4. The method for designing a square aperture free-form surface optical system with added manufacturability constraints according to claim 3, characterized in that: The step 3.3 is specifically as follows: Step 3.3.1: Control the sum of the sag differences at the edges of the square aperture of each mirror sum is zero, and the constraint formula is: In the formula, a 0，2 、a 2，0 、a 2，2 It is a low-order component, reflecting the main curvature and asymmetry of the free-form surface in the xy direction; a 0，4 、a 4，0 is the middle-order component, describing the fourth-order asymmetric distribution of the free-form surface; a 0，6 、a 6，0 is a high-order component; a 2，4 、a 4，2 is a mixed order term; Step 3.3.2, eliminate the piston term caused by the polynomial itself: piston = a 0，0 -a 2，0 -a 0，2 +a 4，0 +a 2，2 +a 0，4 -a 6，0 -a 4，2 -a 2，4 -a 0，6 =0 Step 3.3.3, eliminate the tilt term caused by the polynomial itself: tilt = a 0，1 -3a 0，3 +5a 0，5 -a 2，1 +3a 2，3 +a 4，1 =0.

5. The method for designing a square aperture free-form surface optical system with added manufacturability constraints according to claim 4, characterized in that: The step 3.4 is specifically as follows: Step 3.4.1, in Zemax, take the image spot size as the optimization target, generate the system default operands, and optimize the mirror shape to minimize the image spot size; Step 3.4.2, modify the optimization target, use the system contrast as the optimization index, and generate the system default operand; Step 3.4.3, repeat steps 3.4.1 to 3.4.2 until the convergence condition is reached, and the primary mirror M″1, the secondary mirror M″2, and the tertiary mirror M″3 are obtained, and then a square aperture free-form surface optical system is obtained.

Images