Method for constructing initial structure of off-axis multi-mirror free-form surface optical system

Abstract

The invention discloses a method for constructing an initial structure of an off-axis multi-mirror free-form surface optical system, belongs to the technical field of off-axis optical system design, and aims to solve the problems that in the construction process of a current SCE algorithm for imaging optical system design, initial point and ideal image point position selection is not clear, and the aperture, focal length and size of a solved system are not specifically limited. The method comprises the following steps: determining a characteristic light ray, and generating an initial structure which cannot be used as a subsequent optimization starting point; accurately solving the positions of an initial point and an ideal image point; solving all data points on the free-form surface through a seed curve expansion algorithm; calculating all sampling points of a plurality of free-form surfaces; polynomial fitting is carried out on the obtained data points; according to the method, the off-axis multi-mirror free-form surface initial structure which is close to the diffraction limit, free of shielding and capable of meeting the design required aperture, focal length and size can be directly generated, and the design method is simple, convenient and effective and can be applied to solving of various off-axis multi-mirror free-form surface initial structures.

Description

Technical Field

[0001] The invention relates to the technical field of off-axis optical system design, and in particular to a method for constructing an initial structure of an off-axis multi-reflective free-form surface optical system. Background Art

[0002] See the Journal of the European Optical Society-Rapid Publications, where Su Zhouping et al. published an article titled "Construct freeform surface directly in an initial layout of an off-axis reflective image system by seed curve extension and simulated annealing algorithm". In this paper, the SCE algorithm was used for the design of imaging optical systems for the first time. A seed curve was used to directly construct a three-dimensional free-form surface, completing the design of a single free-form surface in an off-axis two-mirror system. This scheme has the following problems: in the process of free-form surface construction, there is no specific method for selecting the initial point and the ideal image point position, which will result in the generation of low-precision invalid free-form surfaces; the aperture, focal length and size of the desired system cannot be specifically restricted, which will result in the system having good imaging quality after construction, but the other indicators are far from the design requirements and cannot be used as a starting point for subsequent optimization. Summary of the invention

[0003] The purpose of the present invention is to solve the problem that the initial structure generated cannot be used as the starting point for subsequent optimization, because the SCE algorithm currently used for the design of imaging optical systems has unclear selection of the initial point and the ideal image point position during the construction process, and has no specific restrictions on the aperture, focal length and size of the desired system. A method for constructing the initial structure of an off-axis multi-reflective free-form surface optical system is proposed.

[0004] The technical solution of the present invention to solve the technical problem is:

[0005] The method for constructing the initial structure of an off-axis multi-reflective free-form surface optical system comprises the following steps:

[0006] Step 1, determine the characteristic light;

[0007] First, on the starting plane S, m×n data points are sampled uniformly in a matrix manner. Each sampling point is used as the starting point of a ray, and a ray is emitted. The sampling rays are parallel to each other. The first starting point on the starting plane of the ray is set to S 11 , and S 11 The rays emitted from the same row are named S 1j, the starting point of the first line sent in the second line is set to S 21 , and S 21 The rays emitted from the same row are named S 2j , and so on;

[0008] Step 2, accurately determine the initial point and the ideal image point position;

[0009] When the number of off-axis reflection free-form surfaces N=1,

[0010] Surface initial point P 11 (x 11 ,y 11 ,z 11 ) and the surface center point P cc The coordinates are (0,0,z,α), P 11 is the first sampling ray r 11 A point on the propagation path, so x 11 ,y 11 The values ​​of are known; when the inclination angle of the plane is determined, point P cc The unit normal vector coordinates can be determined; by S 11 and S cc The sample ray emitted r 11 and r cc Passing point P 11 and point P cc After reflection, the ideal image point I is (0, y, z); according to Malus's law, the incident wavefront is a plane wave, and the parallel light emitted from the plane wave reaches the ideal image point after being reflected by the reflector. Each ray has the same optical path, so the coordinates of the ideal image point and the initial point can be determined;

[0011] When the number of off-axis reflective free-form surfaces N>1, usually N=3,

[0012] When the spacing D1, D2, L'3 and focal length f' are known, a mathematical method is used to calculate the initial structure of the coaxial three-mirror mirror and solve the radius of curvature of each mirror; the initial structure of the coaxial three-mirror mirror is processed off-axis to eliminate the obstruction of all field light; since the focal length of each mirror remains unchanged after the off-axis processing, the approximate position of the ideal image point of the free-form surface to be constructed can be obtained through each spherical surface during the construction process; the initial point P 11 That is the characteristic ray r 11 The coordinates of the intersection point with the sphere are used to obtain the specific ideal image point position. The method combining ray tracing and Fermat's principle is used to obtain the ideal image point position when the main light path is the extreme value in the normalized pupil range of (-1,1), (-1,-1), (1,-1), (1,1);

[0013] Step 3: Seed curve extension algorithm is used to obtain all data points on the free surface;

[0014] In step 2, when the P 11 The normal vector N of the point 11 It can be calculated that P 11 The tangent plane of point 2 takes the second characteristic ray r 12 With point P 11 The intersection point P of the tangent plane 12 As the second sampling point on the free surface, the normal vector N of the second data point can be obtained by the reflection law. 12 and its tangent plane, using characteristic ray r 13 The third sampling point is obtained by intersecting with the plane, and so on. Therefore, we can get the free surface P from P 11 ,P 12 ...to P 1j The first curve formed is called the seed curve; the data points on the next row of curves are the intersection points of the characteristic light rays and the tangent planes of all the data points on the previous curve, and so on, and the above process is repeated to obtain all the sampling points on the free surface P;

[0015] Step 4: Calculation of all sampling points of multiple free-form surfaces;

[0016] The above calculation process is only for the first free-form surface reflector P. The design of multiple free-form surfaces is as follows: use the spherical surface to obtain the free-form surface and construct the required initial point P. 11 and the ideal image point I1 corresponding to the system at this time, and then use the improved SCE algorithm to construct, replace the spherical surface 1 with the constructed free-form surface 1; use the free-form surface 1 and the spherical surface 2 to obtain the initial point P required for the construction of the free-form surface 2 11 The improved SCE algorithm is used to construct the ideal image point I2 corresponding to the system at this time, and the constructed free-form surface 2 replaces the spherical surface 2; and so on, the initial points and ideal image points required to construct the free-form surface are obtained by combining the free-form surface + the spherical surface, and then each free-form surface is constructed one by one until it is completed;

[0017] Step 5: Perform polynomial fitting on the obtained data points:

[0018] All data points are fitted into the form of XY polynomials by fitting the data point position coordinates and normal directions to characterize the free-form surface;

[0019] When the number of off-axis reflection free-form surfaces N=1 in step 2, the specific solution is as follows:

[0020] According to Malus's law, the incident wavefront is a plane wave. The parallel light emitted from the plane wave reaches the ideal image point after being reflected by the reflector, where each ray has the same optical path. We can get S 11and S cc The sample ray emitted r 11 and r cc Passing point P 11 and point P cc The optical path to the ideal image point I after reflection has the following relationship:

[0021] |S 11 P 11 |+|P 11 I|=|S cc P cc |+P cc I|

[0022] Surface center point P cc The normal direction of can be obtained from the reflection law vector form as follows

[0023]

[0024] in, are the unit direction vectors of the outgoing and incident light rays respectively;

[0025] The above two formulas can be used to determine the coordinates of the ideal image point and the initial point.

[0026] When the number of off-axis reflection free-form surfaces N>1 in step 2, N is usually 3, and the specific solution is as follows:

[0027] When the spacing D1, D2, L'3 and focal length f' are known, a mathematical method is used to calculate the initial structure of the coaxial three-mirror system and solve the radius of curvature of each mirror;

[0028] α1 is the blocking ratio of the secondary mirror to the primary mirror, α2 is the blocking ratio of the third mirror to the secondary mirror, β1 and β2 are the magnifications of the secondary mirror and the third mirror, D1 is the interval between the primary mirror and the secondary mirror, D2 is the interval between the secondary mirror and the third mirror, L'3 is the distance from the third mirror to the image plane, and R1, R2 and R3 are the curvature radii of the three mirrors respectively;

[0029] Then R1, R2 and R3 are the curvature radii of the three reflectors respectively:

[0030]

[0031] The distances between the three reflectors are:

[0032]

[0033] The image plane is required to be flat, that is, S IV =0

[0034]

[0035] Then, through the flat image condition, the equation is transformed into a quadratic equation about α1

[0036]

[0037] In the formula

[0038]

[0039] Considering the obstruction ratio, α1 is positive, and R1, R2 and R3 can be obtained by substituting α1 back; after the aperture is off-axis or the field of view is off-axis for the obtained coaxial three-mirror spherical system, appropriate constraints are imposed to control the eccentric tilt of each surface while ensuring that the surface curvature and the distance between the three reflectors remain unchanged, so that all field light rays are eliminated from obstruction; since the focal length of each reflector remains unchanged after the off-axis processing, the approximate position of the ideal image point of the free-form surface to be constructed can be obtained through each spherical surface during the construction process;

[0040] The initial structure of the coaxial three-mirror mirror is processed off-axis to eliminate the obstruction of all field light. Since the focal length of each mirror remains unchanged after the off-axis processing, the approximate position of the ideal image point of the free-form surface to be constructed can be obtained through each spherical surface during the construction process.

[0041] Initial point P 11 That is the characteristic ray r 11 The coordinates of the intersection point with the sphere are used to obtain the specific ideal image point position. The method of combining ray tracing with Fermat's principle is used to obtain the image point position when the optical path of the main light is the extreme value within the possible range. The normalized pupil is used to calibrate the range of possible ideal image point position coordinates on the image surface. The actual image point position Y and Z coordinates corresponding to the four specific pupil positions (-1,1), (-1,-1), (1,-1), and (1,1) are read by ray tracing to limit the possible range of the ideal image point of the free-form surface to be obtained; within this range, a suitable step size is selected, and the center point P of the free-form surface is used as the center point P of the free-form surface. cc The normal vector coordinates are used as restrictions, and the coordinates of the point that satisfies the extreme value of the optical path of the chief ray of the central field of view is the ideal image point.

[0042] Beneficial effects of the present invention:

[0043] The present invention proposes an initial point and ideal image point calibration algorithm that combines ray tracing with the Fermat principle to accurately obtain the initial point and ideal image point positions during the construction of the initial structure of the off-axis multi-reflector free-form surface; a single-view field off-axis multi-reflector free-form surface initial structure construction method under application-oriented and system parameter constraints is proposed. This method can directly generate an off-axis multi-reflector free-form surface initial structure that is close to the diffraction limit, unobstructed, and meets the design requirements for aperture, focal length and size, providing a good starting point for subsequent optimization. This design method is simple, convenient and effective, and can be applied to the solution of various off-axis multi-reflector free-form surface initial structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of off-axis imaging system for SCE algorithm solution.

[0045] Figure 2 Schematic diagram for solving the initial point and ideal image point of the off-axis SLR.

[0046] Figure 3 Schematic diagram of the coaxial three-mirror system.

[0047] Figure 4 Calibrate the coordinate range of the ideal image point position.

[0048] Figure 5a Schematic diagram of the process of constructing the first freeform surface for the off-axis multi-mirror system.

[0049] Figure 5b Schematic diagram of the process of constructing the second free-form surface for the off-axis multi-reflector system.

[0050] Figure 5c Schematic diagram of the process of constructing the third free-form surface for the off-axis multi-reflector system.

[0051] Figure 6a Schematic diagram of a single free-form surface reflector.

[0052] Figure 6b This is the MTF curve of the system constructed using the original SCE algorithm.

[0053] Figure 6c The MTF curve of the system is constructed using the improved SCE algorithm.

[0054] Figure 6d This is the point diagram of the system constructed using the original SCE algorithm.

[0055] Figure 6e Point diagram of the system constructed using the improved SCE algorithm.

[0056] Figure 7 The initial structural schematic diagram of the "Z"-shaped off-axis three-mirror free-form surface optical system has been completed.

[0057] Figure 8 The initial structural point diagram for the "Z"-shaped off-axis three-mirror free-form surface optical system is completed.

[0058] Fig. 9 The initial structural MTF curve of the "Z"-shaped off-axis three-mirror free-form surface optical system was completed. DETAILED DESCRIPTION

[0059] The present invention will be further described below in conjunction with the accompanying drawings.

[0060] The method for constructing the initial structure of the off-axis multi-reflective free-form surface optical system of the present invention comprises the following steps:

[0061] Step 1, determine the characteristic light:

[0062] like Figure 1 As shown, first, on the starting plane S, m×n data points are uniformly sampled in a matrix manner. Each sampling point is used as the starting point of a ray, and a ray is emitted. The sampling rays are parallel to each other. The first starting point on the starting plane of the ray is set to S 11 , and S 11 The rays emitted from the same row are named S 1j , the starting point of the first line sent in the second line is set to S 21 , and S 21 The rays emitted from the same row are named S 2j , and so on;

[0063] Step 2: When constructing the initial structure of the off-axis multi-reflection free-form surface, the initial point and the ideal image point position are accurately obtained:

[0064] When the number of off-axis reflection free-form surfaces to be constructed is N=1,

[0065] like Figure 2 As shown, the initial point P of the surface 11 (x 11 ,y 11 ,z 11 ) and the surface center point P cc The coordinates are (0,0,z,α), P 11 is the first sampling ray r 11 A point on the propagation path, so x 11 ,y 11 The values ​​of are known; when the inclination angle of the plane is determined, point P cc The unit normal vector coordinates can be determined. 11 and S cc The sample ray emitted r 11 and r cc Passing point P 11 and point P cc After reflection, the ideal image point I is (0, y, z).

[0066] According to Malus's law, the incident wavefront is a plane wave, and the parallel light emitted from the plane wave reaches the ideal image point after being reflected by the reflector, where each ray has the same optical path. 11 and S cc The sample ray emitted r 11 and r cc Passing point P 11 and point P ccThe optical path to the ideal image point I after reflection has the following relationship:

[0067] |S 11 P 11 |+|P 11 I|=|S cc P cc |+P cc I|

[0068] Surface center point P cc The normal direction of can be obtained from the reflection law vector form as follows

[0069]

[0070] in, are the unit direction vectors of the outgoing and incoming light rays respectively.

[0071] The above two formulas can be used to determine the coordinates of the ideal image point and the initial point.

[0072] When the number of off-axis reflective free-form surfaces N>1 needs to be constructed, usually N=3

[0073] like Figure 3 As shown, when the spacing D1, D2, L'3 and the focal length f' are known, a mathematical method is used to calculate the initial structure of the coaxial three-mirror system and solve the radius of curvature of each mirror.

[0074] α1 is the obstruction ratio of the secondary mirror to the primary mirror, α2 is the obstruction ratio of the three mirrors to the secondary mirror, β1 and β2 are the magnifications of the secondary and three mirrors, D1 is the interval between the primary and secondary mirrors, D2 is the interval between the secondary and three mirrors, L'3 is the distance from the three mirrors to the image plane, and R1, R2 and R3 are the curvature radii of the three mirrors respectively.

[0075] Then R1, R2 and R3 are the curvature radii of the three reflectors respectively:

[0076]

[0077] The distances between the three reflectors are:

[0078]

[0079] The image plane is required to be flat, that is, S IV =0

[0080]

[0081] Then, through the flat image condition, the equation is transformed into a quadratic equation about α1

[0082]

[0083] In the formula

[0084]

[0085] Considering the obstruction ratio, α1 is positive, and R1, R2 and R3 can be obtained by substituting α1 back. After the aperture is off-axis or the field of view is off-axis for the obtained coaxial three-mirror spherical system, appropriate constraints are imposed to control the eccentric tilt of each surface while ensuring that the surface curvature and the distance between the three reflectors remain unchanged, so that all field light rays are eliminated from obstruction. Since the focal length of each reflector remains unchanged after the off-axis processing, the approximate position of the ideal image point of the free-form surface to be constructed can be obtained through each spherical surface during the construction process.

[0086] The initial structure of the coaxial three-mirror is processed off-axis to eliminate the obstruction of all field light. Since the focal length of each mirror remains unchanged after the off-axis processing, the approximate position of the ideal image point of the free-form surface to be constructed can be obtained through each spherical surface during the construction process.

[0087] Initial point P 11 That is the characteristic ray r 11 The coordinates of the intersection point with the sphere are used to obtain the specific ideal image point position. The method of combining ray tracing with Fermat's principle is used to obtain the image point position when the optical path of the main light is the extreme value within the possible range, such as Figure 4 As shown in the figure, the normalized pupil is used to calibrate the possible range of ideal image point position coordinates on the image plane. The Y and Z coordinates of the actual image point positions corresponding to the four specific pupil positions (-1,1), (-1,-1), (1,-1), and (1,1) are read by ray tracing to limit the possible range of ideal image points on the free-form surface to be determined. A suitable step size is selected within the range, and the center point P of the free-form surface is used as the starting point. cc The normal vector coordinates are used as restrictions, and the coordinates of the point that satisfies the extreme value of the optical path of the chief ray of the central field of view is the ideal image point.

[0088] Step 3: Seed curve extension algorithm obtains all data points on the free surface:

[0089] In step 2, if Figure 1 As shown, when the P 11 The normal vector N of the point 11 It can be calculated that P 11 The tangent plane of point 2 takes the second characteristic ray r 12 With point P 11 The intersection point P of the tangent plane 12 As the second sampling point on the free surface, the normal vector N of the second data point can be obtained by the reflection law. 12 and its tangent plane, using characteristic ray r 13 The third sampling point is obtained by intersecting with the plane, and so on. Therefore, we can get the free surface P from P 11 ,P 12...to P 1j The first curve formed is called the seed curve; the data points on the next row of curves are the intersection points of the characteristic light rays and the tangent planes of all the data points on the previous curve, and so on, and the above process is repeated to obtain all the sampling points on the free surface P;

[0090] Step 4, calculation of all sampling points of multiple free-form surfaces in the initial structure of off-axis multi-reflection free-form surfaces:

[0091] The above calculation process is only for the sampling points on the first free-form surface reflector P. The specific construction process for multiple free-form surfaces is as follows: Figure 5a As shown, the initial point P required for constructing a free-form surface is obtained by using a spherical surface. 11 and the ideal image point I1 corresponding to the system at this time, and then use the improved SCE algorithm to construct and replace the spherical surface with the constructed free surface I; Figure 5b As shown, the initial point P required for constructing the free-form surface 2 is obtained by using the free-form surface 1 and the spherical surface 2. 11 The ideal image point I2 corresponding to the system at this time is constructed using the improved SCE algorithm, and the constructed free surface 2 replaces the spherical surface 2. And so on, Figure 5c As shown, the initial points and ideal image points required for constructing each free-form surface are obtained by combining free-form surface + spherical surface, thereby completing the construction of all free-form surfaces.

[0092] Step 5: Perform polynomial fitting on the obtained data points:

[0093] The discrete data sampling points are fitted into the form of XY polynomials by the fitting method of the data point position coordinates and normal direction to characterize the free-form surface;

[0094]

[0095] Where c is the curvature of the free-form surface, k is the cone coefficient, and A i are the coefficients of the XY polynomial.

[0096] The construction of each free-form surface reflector in the initial structure of the off-axis multi-reflective free-form surface is based on an improved seed curve expansion method that combines ray tracing with the initial point and ideal image point calibration algorithm of the Fermat principle.

[0097] Each free-form surface reflector in the off-axis multi-reflector free-form surface initial structure is constructed by using the spherical initial structure and replacing the spherical reflectors one by one with the constructed free-form surface reflectors.

[0098] This design method is applicable to the initial structure solution of off-axis SLR free-form surface and various off-axis multi-reflector free-form surface optical systems.

[0099] like Figure 6a As shown in Figure 2, this method is used for the design of off-axis single free-form surface optical systems:

[0100] The off-axis single free-form surface reflector was designed using the original SCE and improved SCE algorithms. The criteria for evaluating the imaging quality of an optical system are the modulation transfer function curve MTF and the RMS size of the spot diagram. At the same spatial frequency, the larger the MTF, the better the imaging quality; the smaller the RMS of the spot diagram, the better the imaging quality. Figure 6b and Figure 6c As shown in Figure 2, the MTF curves of the original SCE and improved SCE algorithm construction systems are as follows: Figure 6d and Figure 6e As shown, the point diagram of the original SCE and improved SCE algorithm construction system is as follows. It can be seen that compared with the original SCE algorithm, the MTF at 20lp / mm of the improved SCE algorithm changes from 0.65 to 0.75, an increase of 15.3%. The spot radius of the improved SCE algorithm is smaller than the Airy disk, and the RMS changes from 0.0149 to 0.004, a decrease of 73.15%. The improved algorithm has a significant improvement in construction accuracy compared with the original SCE algorithm. From the above case, it can be seen that the construction accuracy of the improved SCE algorithm is significantly better than that of the original SCE algorithm.

[0101] The method described above is used to solve a "Z"-shaped off-axis three-reflection initial structure, such as Figure 7 As shown in the figure, it is the initial structure layout diagram after the solution is completed. It can be seen that each free-form surface reflector is of appropriate size and its location is reasonably arranged. Figure 8 As shown in the figure, it is the spot diagram of the initial structure after the solution is completed. It can be seen that the size of the diffuse spot is similar to the size of the Airy disk; Fig. 9 As shown in Figure 1, this is the MTF curve of the initial structure after the solution is completed. It can be seen that the MTF reaches the diffraction limit.

Claims

1. A method for constructing an initial structure of an off-axis multi-reflective free-form surface optical system, characterized in that: The method comprises the following steps: Step 1, determine the characteristic light; First, on the starting plane S, m×n data points are sampled uniformly in a matrix manner. Each sampling point is used as the starting point of a ray, and a ray is emitted. The sampling rays are parallel to each other. The first starting point on the starting plane of the ray is set to S 11 , and S 11 The rays emitted from the same row are named S 1j , the starting point of the first line sent in the second line is set to S 21 , and S 21 The rays emitted from the same row are named S 2j , and so on; Step 2, accurately determine the initial point and the ideal image point position; When the number of off-axis reflection free-form surfaces N = 1, Surface initial point P 11 (x 11 ,y 11 ,z 11 ) and the surface center point P cc The coordinates are (0,0,z,α), P 11 is the first sampling ray r 11 A point on the propagation path, so x 11 ,y 11 The values ​​of are known; when the inclination angle of the plane is determined, point P cc The unit normal vector coordinates can be determined; by S 11 and S cc The sample ray emitted r 11 and r cc Passing point P 11 and point P cc After reflection, the ideal image point I is (0, y, z); according to Malus's law, the incident wavefront is a plane wave, and the parallel light emitted from the plane wave reaches the ideal image point after being reflected by the reflector. Each ray has the same optical path, so the coordinates of the ideal image point and the initial point can be determined; When the number of off-axis reflective free-form surfaces N>1, usually N=3, When the spacing D1, D2, L'3 and focal length f' are known, a mathematical method is used to calculate the initial structure of the coaxial three-mirror mirror and solve the radius of curvature of each mirror; the initial structure of the coaxial three-mirror mirror is processed off-axis to eliminate the obstruction of all field light; since the focal length of each mirror remains unchanged after the off-axis processing, the approximate position of the ideal image point of the free-form surface to be constructed can be obtained through each spherical surface during the construction process; the initial point P 11 That is the characteristic ray r 11 The coordinates of the intersection point with the sphere are used to obtain the specific ideal image point position. The method combining ray tracing and Fermat's principle is used to obtain the ideal image point position when the main light path is the extreme value in the normalized pupil range of (-1,1), (-1,-1), (1,-1), (1,1); Step 3: Seed curve extension algorithm is used to obtain all data points on the free surface; In step 2, when the P 11 The normal vector N of the point 11 It can be calculated that P 11 The tangent plane of point 2 takes the second characteristic ray r 12 With point P 11 The intersection point P of the tangent plane 12 As the second sampling point on the free surface, the normal vector N of the second data point can be obtained by the reflection law. 12 and its tangent plane, using characteristic ray r 13 The third sampling point is obtained by intersecting with the plane, and so on. Therefore, we can get the free surface P from P 11 ,P 12 ...to P 1j The first curve formed is called the seed curve; the data points on the next row of curves are the intersection points of the characteristic light rays and the tangent planes of all the data points on the previous curve, and so on, and the above process is repeated to obtain all the sampling points on the free surface P; Step 4: Calculation of all sampling points of multiple free-form surfaces; The above calculation process is only for the first free-form surface reflector P. The design of multiple free-form surfaces is as follows: use the spherical surface to obtain the free-form surface and construct the required initial point P. 11 and the ideal image point I1 corresponding to the system at this time, and then use the improved SCE algorithm to construct, replace the spherical surface 1 with the constructed free-form surface 1; use the free-form surface 1 and the spherical surface 2 to obtain the initial point P required for the construction of the free-form surface 2 11 The improved SCE algorithm is used to construct the ideal image point I2 corresponding to the system at this time, and the constructed free-form surface 2 replaces the spherical surface 2; and so on, the initial points and ideal image points required to construct the free-form surface are obtained by combining the free-form surface + the spherical surface, and then each free-form surface is constructed one by one until it is completed; Step 5, performing polynomial fitting on the obtained data points; The free-form surface is characterized by fitting all data points into an XY polynomial by fitting the data point position coordinates and normal.

2. The method for constructing the initial structure of the off-axis multi-reflective free-form surface optical system according to claim 1, characterized in that: When the number of off-axis reflection free-form surfaces N=1 in step 2, the specific solution is as follows: According to Malus's law, the incident wavefront is a plane wave. The parallel light emitted from the plane wave reaches the ideal image point after being reflected by the reflector, where each ray has the same optical path. We can get S 11 and S cc The sample ray emitted r 11 and r cc Passing point P 11 and point P cc The optical path to the ideal image point I after reflection has the following relationship: |S 11 P 11 |+|P 11 I|=|S cc P cc |+|P cc I| Surface center point P cc The normal direction of can be obtained from the reflection law vector form as follows in, are the unit direction vectors of the outgoing and incident light rays respectively; The above two formulas can be used to determine the coordinates of the ideal image point and the initial point.

3. The method for constructing the initial structure of the off-axis multi-reflective free-form surface optical system according to claim 1, characterized in that: When the number of off-axis reflection free-form surfaces N>1 in step 2 is usually N=3, the specific solution is as follows: When the spacing D1, D2, L'3 and focal length f' are known, a mathematical method is used to calculate the initial structure of the coaxial three-mirror system and solve the radius of curvature of each mirror; α1 is the blocking ratio of the secondary mirror to the primary mirror, α2 is the blocking ratio of the third mirror to the secondary mirror, β1 and β2 are the magnifications of the secondary mirror and the third mirror, D1 is the interval between the primary mirror and the secondary mirror, D2 is the interval between the secondary mirror and the third mirror, L'3 is the distance from the third mirror to the image plane, and R1, R2 and R3 are the curvature radii of the three mirrors respectively; Then R1, R2 and R3 are the curvature radii of the three reflectors respectively: The distances between the three reflectors are: The image plane is required to be flat, that is, S IV =0 Then, through the flat image condition, the equation is reorganized into a quadratic equation about α1 Aα1 2 +Bα1+C=0 In the formula Considering the obstruction ratio, α1 is positive, and R1, R2 and R3 can be obtained by substituting α1 back; after the aperture is off-axis or the field of view is off-axis for the obtained coaxial three-mirror spherical system, appropriate constraints are imposed to control the eccentric tilt of each surface while ensuring that the surface curvature and the distance between the three reflectors remain unchanged, so that all field light rays are eliminated from obstruction; since the focal length of each reflector remains unchanged after the off-axis processing, the approximate position of the ideal image point of the free-form surface to be constructed can be obtained through each spherical surface during the construction process; The initial structure of the coaxial three-mirror mirror is processed off-axis to eliminate the obstruction of all field light. Since the focal length of each mirror remains unchanged after the off-axis processing, the approximate position of the ideal image point of the free-form surface to be constructed can be obtained through each spherical surface during the construction process. Initial point P 11 That is the characteristic ray r 11 The coordinates of the intersection point with the sphere are used to obtain the specific ideal image point position. The method of combining ray tracing with Fermat's principle is used to obtain the image point position when the optical path of the main light is the extreme value within the possible range. The normalized pupil is used to calibrate the range of possible ideal image point position coordinates on the image surface. The actual image point position Y and Z coordinates corresponding to the four specific pupil positions (-1,1), (-1,-1), (1,-1), and (1,1) are read by ray tracing to limit the possible range of the ideal image point of the free-form surface to be obtained; within this range, a suitable step size is selected, and the center point P of the free-form surface is used as the center point P of the free-form surface. cc The normal vector coordinates are used as restrictions, and the coordinates of the point that satisfies the extreme value of the optical path of the chief ray of the central field of view is the ideal image point.

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