Initial Structural Design Method for Off-Axis Reflective Free-Form Optical System with Ultra-Large Field of View

Abstract

The present invention provides a method for designing an initial structure of an off-axis reflective free-form optical system with an ultra-large field of view, comprising the following steps: S1. According to the starting point S i,j and the target point T i,k calculate all the characteristic data points P of the first free-form surface Ω1 i,j,1 and fit them by the least squares method to obtain the first free-form surface Ω1; S2. Calculate all the characteristic data points P of the second free-form surface Ω2 according to the first free-form surface Ω1 i,j,2 , and fit them by the least squares method to obtain the second free-form surface Ω2, and construct the initial structure of the two-mirror free-form optical system; S3. Further iteratively optimize the initial structure by the optical path iteration method until the free-form surface ray system meets the imaging requirements. S4. Obtain the initial structure of the optimized free-form optical system when the number of reflectors N>2 by repeating steps S1, S2, and S3. The optical system designed by the present invention has the advantages of fast design speed, high stability, and good imaging quality.

Description

Technical Field

[0001] The present invention relates to the technical field of optical design, and particularly relates to a method for designing an initial structure of an off-axis reflective freeform optical system with an ultra-large field of view. Background Art

[0002] The off-axis reflective optical system with an ultra-large field of view has the advantages of a wide observation range, no chromatic aberration, no obscuration, light weight, high thermal stability, etc., and has important application value in the field of optical remote sensing. However, the ultra-large field of view and off-axis design of the system will cause complex aberrations. It is difficult to correct complex aberrations by using traditional spherical and aspherical optical elements with rotational symmetry, which limits the imaging quality of the system.

[0003] The freeform surface is a surface with non-rotational symmetry. Applying it to the design of an off-axis reflective optical system with an ultra-large field of view can greatly improve the design freedom of the system and optimize the imaging quality of the system. Generally speaking, in optical design, a good initial structure and subsequent optimization by optical design software are both very important steps. Among them, a reasonable initial structure is the key to designing an off-axis freeform surface system with an ultra-large field of view. If the initial structure is unreasonable, it will take a lot of time for optical designers to optimize the system.

[0004] Traditional methods for obtaining the initial structure of an off-axis freeform surface system with an ultra-large field of view include: 1. Search for similar optical structures in a lens library or patent as the initial system, and then use optical design software to change index parameters such as focal length or F-number to re-optimize the initial structure. 2. Obtain the solution of a coaxial spherical / quadratic surface system through paraxial aberration theory, and then use optical design software to gradually expand the field of view of the system and increase the off-axis amount through a progressive optimization method until the system meets the requirements of an ultra-large field of view and no longer has an obscuration amount. The above two methods usually have a large gap from the ideal system. Designers often need to spend a lot of time optimizing the system, and the design efficiency is low. Moreover, the optimization of the system has high experience requirements for designers. Otherwise, it is easy to fall into a local optimal solution and unable to obtain a reasonable system structure. Summary of the Invention

[0005] In view of the above problems, the purpose of the present invention is to propose a method for designing an initial structure of an off-axis reflective freeform optical system with an ultra-large field of view, which solves the problem of the lack of a direct solution method for the initial structure in the design and optimization process of the existing off-axis reflective freeform optical system with an ultra-large field of view, thereby improving the design efficiency of the optical system.

[0006] To achieve the above purpose, the present invention adopts the following specific technical solutions:

[0007] The present invention provides a method for designing an initial structure of an off-axis reflective freeform optical system with an ultra-large field of view, including the following steps:

[0008] Pretreatment step S0: Define system parameters:

[0009] The freeform optical system has K freeforms. Define the k-th freeform as Ω k , where k = 1, 2, …, K;

[0010] Divide the freeform optical system into M fields of view. Uniformly sample J characteristic rays for all full-aperture rays in each field of view using the grid method. Define the j-th characteristic ray in the i-th field of view as R i,j , where i = 1, 2, …, M; j = 1, 2, …, J;

[0011] Define the characteristic ray R i,j The intersection point with the entrance pupil is the starting point S i,j , and define the characteristic ray R i,j The intersection point with the k-th freeform Ω k is the characteristic data point P i,j,k ;

[0012] Define the characteristic ray R i,j After being reflected by k freeforms, it reaches the target point T i,k , when k = K, the point T i,k is the ideal image point I i ;

[0013] In the freeform optical system, the characteristic ray R i,j emitted from the starting point S i,j is reflected by the freeform Ω i,j,k at the characteristic data point P k and then reaches the target point T i,k After that, the characteristic ray R i,j continues to propagate and is reflected by the freeform Ω i,j,K at the characteristic data point P K to reach the ideal image point I i ;

[0014] S1. Calculate all the characteristic data points P i,j of the first freeform Ω i,k based on the starting point S 1 and the target point T i,j,1 and fit them by the least squares method to obtain the first freeform Ω 1 ;

[0015] S2. Calculate all the characteristic data points P 1 of the second freeform Ω 2 based on the first freeform Ω i,j,2 , and fit them by the least squares method to obtain the second freeform Ω 2, construct the initial structure of a two-mirror free-form optical system;

[0016] S3. Further iterate and optimize the initial structure by the optical path iteration method until the free-form ray system meets the imaging requirements.

[0017] S4. Obtain the initial structure of the optimized free-form optical system when the number of mirrors N > 2 by repeating steps S1, S2, and S3.

[0018] Preferably, the solution steps of the characteristic data point P i,j,1 in step S1 include:

[0019] S11. Calculate the optical path of the first characteristic ray R 1,1 in the first field of view after being reflected by the first free-form surface Ω 1 and reaching the first target point T 1,1 , and solve the characteristic data point P 1 of the first free-form surface Ω 1,j,1 in the first field of view;

[0020] S12. By calculating the ideal optical paths of the characteristic rays in the fields of view other than the first field of view after being reflected by the free-form surface Ω 1 and reaching the target points, further locate the coordinate positions of the characteristic data points in the other fields of view.

[0021] S13. Fit all the characteristic data points P 1 of the first free-form surface Ω i,j,1 by the least squares method to obtain the first free-form surface Ω 1 .

[0022] Preferably, step S11 includes:

[0023] The optical path 1,1 of the first characteristic ray R 1 in the first field of view after being reflected by the first free-form surface Ω 11 and reaching the first target point T is:

[0024]

[0025] where n 1 and n 2 are the refractive indices of the media where the incident ray and the outgoing ray of the first free-form surface Ω 1 are located;

[0026] The optical path 1,j of all the characteristic rays R 1 in the first field of view after being reflected by the first free-form surface Ω 1,1 and converging to the first target point T is:

[0027]

[0028] According to Malus' law, under ideal conditions:

[0029]

[0030] Solve for the characteristic data points P of the first freeform surface Ω in the first field of view according to formula (3) 1 of 1,j,1 .

[0031] Preferably, step S12 includes:

[0032] For the first freeform surface Ω 1 , given the incident direction of the characteristic ray R in the i-th field of view i,j , draw an auxiliary line parallel to the characteristic ray R i,j intersecting the first freeform surface Ω 1 at the surface vertex O 1 , draw a perpendicular line through the entrance pupil S i,j such that S i,j Sσ i,j is perpendicular to Sσ i,j O 1 ;

[0033] According to Malus' law, the optical paths of the light ray segments S i,j P i,j,1 T i,1 and S′ i,j O 1 T i,1 are equal, that is:

[0034]

[0035]

[0036]

[0037] wherein,

[0038] is the optical path of the light ray segment S i,j P i,j,1 T i,1 ;

[0039] is the optical path of the light ray segment S′ i,j O 1 T i,1 ;

[0040] Taking the point S i,jTaking the origin O′, a local coordinate system X′Y′Z′ is constructed. Given that the field of view angle of the i-th field of view is (ω X , ω Y ), then the angles between the projections of S ji,ji1, P (O′P i,j,1 ) on the X′OZ′ plane and the Y′OZ′ plane and the Z′ axis are ω X and ω Y respectively. Assuming that the projection length of the incident vector S i,j P i,j,1 on the Z′ axis is 1, according to the geometric relationship, the projection lengths of the incident vector S i,j P i,j,1 on the X′ axis and the Y′ axis are tanω X and tanω Y respectively. Then the unit incident vector S i,j P i,j,1 o exists:

[0041]

[0042] According to Equation (7), the straight-line equation where the light segment S″ i,j O 1 is located is constructed:

[0043]

[0044] And the plane equation of the tangent plane where the point S i,j and the point S″ i,j are located is:

[0045]

[0046] By combining Equations (7 - 9), the position coordinates of the point are solved, and thus all the characteristic data points P 1 of the first freeform surface Ω i,j,1 are obtained according to Equations (4 - 6);

[0047] Step S13 includes:

[0048] Fitting the calculated characteristic data points P i,j,1 of the first freeform surface to the expression of the XY polynomial to construct the first freeform surface Ω 1 ;

[0049] The expression of the XY polynomial is:

[0050]

[0051] where c is the curvature of the surface; l is the quadratic surface coefficient; is the freeform surface polynomial; Aq is the polynomial coefficient.

[0052] Preferably, step S2 includes the following sub-steps:

[0053] S21. Calculate the characteristic ray R i,j P i,j,1 T i,1 of the optical path from the entrance pupil S i,j to the ideal image point I i,j ; i of the optical path

[0054] S22. Solve all the characteristic data points P of the second free-form surface Ω 1 based on the optical path 2 and the first free-form surface Ω i,j,2 ;

[0055] S23. Fit all the characteristic data points P 2 of the second free-form surface Ω i,j,2 into a free-form surface characterized by an XY polynomial using the least squares method, obtaining the second free-form surface Ω 2 .

[0056] Preferably, step S21 includes:

[0057] The first characteristic ray R 1,1 propagates after passing through the first target point T 1,1 , reflects off the second free-form surface Ω 2 , and converges to the ideal image point I 1 . Then the optical path is:

[0058]

[0059] where n 3 is the refractive index of the medium in which the outgoing ray of the first free-form surface Ω 2 is located;

[0060] The characteristic ray R i,j emitted from the i-th field of view, after being reflected by the first free-form surface Ω 1 , converges to the target point T i,1 . The characteristic ray R i,j passes through the target point T i,1 , is incident on the second free-form surface Ω 2 at the point P i,j,2 , reflects, and converges to the ideal image point I i . The optical path is:

[0061]

[0062]

[0063] According to Malus' law, all characteristic rays converging from point T i,1 to the ideal image point I i have the same optical path;

[0064] Therefore, draw an auxiliary ray starting from point T i,1 that passes through the vertex O 2 of the second free-form surface Ω 2 and finally intersects at the image point I i . There is:

[0065]

[0066] Then the optical path i,j of the characteristic ray R i,j from the entrance pupil S i to the ideal image point I is:

[0067]

[0068] wherein, is the optical path of the ray segment T i,1 O 2 I i .

[0069] Preferably, step S22 includes:

[0070] Calculating the actual intersection point P i,j of the characteristic ray R i,j emitted from the entrance pupil S 1 and the fitted first free-form surface Ω i,j,1 a and the optical path length i,j of the ray segment S i,j,1 P a is:

[0071]

[0072] Obtaining the optical path length 2 of the second free-form surface Ω is:

[0073]

[0074] wherein, the characteristic data point P i,j,1 a is the characteristic ray R i,j emitted from the entrance pupil S i,jThe first free-form surface Ω 1 of the actual intersection point;

[0075] For the first free-form surface Ω after least squares fitting 1 , its surface equation is arranged into an equation expressed by F(x, y, z):

[0076]

[0077] Take the partial derivative of the first free-form surface equation F(x, y, z), and then substitute the coordinates of the characteristic data point P i,j,1 a to obtain the normal vector N 1 at each point on the first free-form surface Ω 1 as:

[0078]

[0079] According to the law of reflection / refraction:

[0080] n 1 (A 1 o ×N 1 o ) = n 2 (A 1 o′ ×N 1 o ) (20)

[0081] where

[0082]

[0083]

[0084] A 1 o , A 1 o′ are the unit vectors of the characteristic ray R i,j with respect to the first free-form surface Ω 1 for the incident ray and the reflected ray;

[0085] N 1 o is the unit normal vector at the point P i,j,1 a ;

[0086] According to formula (22), construct the equation of the line where the ray P i,j,1 a P i,j,2 is located, and combine formula (17) to find all the characteristic data points P 2 of the second free-form surface Ωi,j,2 .

[0087] Preferably, in the optical path iteration method of step S3, the current free-form surface system is used as a new initial structure, and then the optical paths for solving the characteristic data points of each free-form surface in the free-form surface system are continuously corrected. The specific process is as follows:

[0088] By setting an initial optical path correction amount ΔOPD 1 to correct the calculated optical path to obtain the optical path for recalculating the characteristic data points of the free-form surface

[0089]

[0090] where ε i,1 is the iteration coefficient for correction , and its expression is:

[0091]

[0092] where is the basic iteration coefficient,

[0093] Δε i,1 is the iteration amount of ε i,1 , and Δε i,1 ≥0;

[0094] When Δε i,1 = 0,

[0095] For the optical path its corrected optical path for each iteration is:

[0096]

[0097] where

[0098]

[0099] where

[0100] ε i,2 is the iteration coefficient for correction ;

[0101] is the basic iteration coefficient,

[0102] Δε i,2 is the iteration amount of ε i,2 , and Δε i,2 ≥0;

[0103] When Δε i,2 = 0,

[0104] ΔOPD 2 is the optical path correction amount of

[0105] Preferably, when the number of free-form surfaces is N, N>2, its design method is analogized in accordance with the free-form surface system of the off-axis mirror;

[0106] Set N-1 target points T i,k and N data points P 1,1,k ;

[0107] Repeat step S1 and step S2 to obtain all characteristic data points of N unknown free-form surfaces;

[0108] Fit all characteristic data points into a free-form surface, construct a free-form surface system, observe the system quality. If the imaging of some fields of view of the free-form surface system does not meet the imaging quality requirements; optimize and iterate the free-form surface system by the optical path iteration method of step S3 until the free-form surface system meets the imaging requirements, and output the free-form surface system.

[0109] Compared with the existing technology, the ultra-large field of view off-axis reflective free-form surface optical system obtained by the initial structure design method provided by the present invention has good imaging characteristics. After simple subsequent optimization, an optical system design result with high imaging quality and a reasonable opto-mechanical structure can be obtained. The optical system designed by the method provided by the present invention has the advantages of fast design speed, high stability, and good imaging quality. Brief Description of the Drawings

[0110] Figure 1 is a schematic flow chart of the initial structure design method of the ultra-large field of view off-axis reflective free-form surface optical system according to the embodiment of the present invention.

[0111] Figure 2 is an ideal imaging schematic diagram of the off-axis two-mirror optical system according to the embodiment of the present invention.

[0112] Figure 3 is a schematic diagram of constructing an auxiliary tangent plane according to the embodiment of the present invention.

[0113] Figure 4 is a schematic diagram of constructing auxiliary data points according to the embodiment of the present invention.

[0114] Figure 5 is a schematic diagram of constructing a local coordinate system according to the embodiment of the present invention.

[0115] Figure 6 It is a schematic diagram comparing the actual optical path length and the ideal optical path length of each field of view imaging provided by an embodiment of the present invention.

[0116] Figure 7 It is a schematic diagram of the optical structure of an off-axis two-mirror system in the XOZ plane designed by using the equal optical path surface expansion method provided by an embodiment of the present invention.

[0117] Figure 8 It is a schematic diagram of the optical structure of an off-axis two-mirror system in the YOZ plane designed by using the equal optical path surface expansion method provided by an embodiment of the present invention. Specific implementation manners

[0118] In the following, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same modules are denoted by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, their detailed descriptions will not be repeated.

[0119] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

[0120] Figure 1 It shows a schematic flow chart of an initial structure design method for an ultra-wide field of view off-axis reflective free-form optical system provided by an embodiment of the present invention.

[0121] As Figure 1 shown, the initial structure design method for an ultra-wide field of view off-axis reflective free-form optical system provided by an embodiment of the present invention includes the following steps:

[0122] Pretreatment step S0: Define system parameters according to the design requirements of the ultra-wide field of view off-axis reflective free-form optical system:

[0123] Assume that the free-form optical system has K free-form surfaces, and define the kth free-form surface as Ω k (k = 1, 2,... K).

[0124] Divide the free-form optical system into M fields of view, and uniformly sample J characteristic rays for each full-aperture ray in each field of view by the grid method. Define the jth characteristic ray in the ith field of view as R i,j (i = 1, 2,... M; j = 1, 2,... J).

[0125] Define the characteristic ray R i,j The intersection point with the entrance pupil is the starting point S i,j , define the characteristic ray R i,j And the kth free-form surface Ωk The intersection point is the characteristic data point P i,j,k ;

[0126] Define the characteristic ray R i,j After being reflected by k free-form surfaces, it reaches the target point T i,k , when k = K, the point T i,k is the ideal image point I i .

[0127] In a free-form surface optical system, the characteristic ray R i,j emitted from the entrance pupil S i,j is reflected by the free-form surface Ω i,j,k at the characteristic data point P k and then reaches the target point T i,k .

[0128] The ray continues to propagate. Ideally, it is reflected by the free-form surface Ω i,j,K at the characteristic data point P K and reaches the ideal image point I i .

[0129] Figure 2 Shows the ideal imaging schematic diagram of an off-axis two-mirror optical system provided according to an embodiment of the present invention.

[0130] As Figure 2 shown, the first characteristic ray R 1,1 emitted from the starting point S 1,1 of the first field of view of the optical system at the entrance pupil 1 is incident on the first free-form surface Ω 1 , and after being reflected by the first free-form surface Ω 1,1 it reaches the first target point T 2 on the spatial target surface and then reaches the ideal image point I i after being reflected by the second free-form surface Ω

[0131] The first characteristic ray R 1,1 intersects the first free-form surface Ω 1 at the first characteristic data point P 1,1,1 ;

[0132] The first characteristic ray R 1,1 intersects the second free-form surface Ω 2 at the second characteristic data point P 1,1,2 ;

[0133] S1. Calculate all the characteristic data points P i,j of the first free-form surface Ω i,k based on the starting point S 1 and the target point T i,j,1 and fit them by the least squares method to obtain the first free-form surface Ω1 ;

[0134] Step S1 includes the following sub-steps:

[0135] S11. Solve for the characteristic data point P 1,j from the starting point S 1,1,1 , the first characteristic data point P 1,1 and the first target point T 1,j,1 .

[0136] The position coordinates of the starting point S 1,1 , the first characteristic data point P 1,1,1 and the first target point T 1,1 of the first field of view of the optical system are known;

[0137] The optical path 1,1 of the first characteristic ray R 1 in the first field of view after reflection by the first free-form surface Ω 11 and reaching the first target point T is:

[0138]

[0139] where n 1 and n 2 are the refractive indices of the media at the spatial positions where the incident ray and the outgoing ray of the first free-form surface Ω 1 are located;

[0140] According to Malus' law, the condition for the optical system to form a perfect image is that the optical path between corresponding points on the incident wavefront and the outgoing wavefront is a constant value.

[0141] Figure 3 Fig. shows a schematic diagram of constructing an auxiliary tangent plane according to an embodiment of the present invention.

[0142] As Figure 3 shown, an auxiliary tangent plane Ω 1,1 is made through the point S 1,1 for the characteristic ray R S1 . The characteristic ray R 1,j intersects the tangent plane Ω S1 at the point Sσ 1,j . At this time, the tangent plane Ω S1 can be regarded as the incident plane wave where the point S 1,1 is located, and the point Sσ 1,j and the point S 1,1 are located in the same incident plane wave.

[0143] All the characteristic rays R 1,j in the first field of view start from the point S' 1,j and pass through the first free-form surface Ω 1After reflection, it converges to the first target point T 11 The optical path is:

[0144]

[0145] According to Malus' law, under ideal conditions:

[0146]

[0147] Solve for the characteristic data points P of the first freeform surface Ω of the first field of view according to formula (3) 1 of 1,j,1 .

[0148] S12. By calculating the ideal optical paths of the characteristic rays in the fields of view other than the first field of view, the coordinates of the characteristic data points in the other fields of view are then located.

[0149] The specific steps are as follows:

[0150] Figure 4 Fig. shows a schematic diagram of the construction of the auxiliary data points provided by an embodiment of the present invention.

[0151] As Figure 4 shown, for the first freeform surface Ω 1 , given the incident direction of R i,j , draw an auxiliary ray parallel to R i,j that intersects the first freeform surface Ω 1 at the surface vertex O 1 . Draw a perpendicular line through the entrance pupil S i,j such that S i,j S″ i,j is perpendicular to S′ i,j O 1 .

[0152] At this time, S i,j P i,j,1 T i,1 and S″ i,j O 1 T i,1 can be regarded as two light ray segments of a plane wave emitted and converging to the T 1 point after reflection by the first freeform surface Ω i,1 . According to Malus' law, the optical paths of the light ray segments S i,j P i,j,1 T i,1 and S″ i,j O 1 T i,1 are equal, that is:

[0153]

[0154]

[0155]

[0156] Among them, is the optical path of the light ray segment S i,j P i,j,1 T i,1 of. is the optical path of the light ray segment S″ i,j O 1 T i,1 of.

[0157] Figure 5 shows a schematic diagram of the construction of the local coordinate system provided according to an embodiment of the present invention.

[0158] As Figure 5 shown, taking the point S i,j as the origin O′, a local coordinate system X′Y′Z′ is constructed.

[0159] It is known that the field of view angle of the i-th field of view is (ω X , ω Y ), then the projections of S i,j P i,j,1 (O′P i,j,1 ) on the X′OZ′ plane and the Y′OZ′ plane and the angles with the Z′ axis are ω X and ω Y , respectively.

[0160] Assume that the projection length of the incident vector S i,j P i,j,1 on the Z′ axis is 1. According to the geometric relationship, the projection lengths of the incident vector S i, j P i,j,1 on the X′ axis and the Y′ axis are tanω X and tanω Y , respectively. Then the unit incident vector S i,j P i,j,1 o exists:

[0161]

[0162] According to Equation (7), the straight line equation where the light ray segment S″ i,j O 1 is located is:

[0163]

[0164] And the plane equation of the tangent plane where the point S ij and the point S″ ij are located is:

[0165]

[0166] Solve the simultaneous equations (7 - 9) to find the position coordinates of the point so as to obtain all the characteristic data points P of the first free - form surface Ω according to equations (4 - 6) 1 i,j,1 .

[0167] S13. Perform least - squares fitting on all the characteristic data points P of the first free - form surface Ω 1 to obtain the first free - form surface Ω i,j,1 . 1 .

[0168] The free - form surface expression for free - form surface fitting in the present invention is an XY polynomial, and its equation is:

[0169]

[0170] where c is the curvature of the surface vertex, l is the quadratic surface coefficient, is the free - form surface polynomial, and A q are the coefficients of each term.

[0171] S2. Calculate all the characteristic data points P of the second free - form surface Ω 1 based on the first free - form surface Ω 2 , and perform least - squares fitting on them to obtain the second free - form surface Ω i,j,2 . 2 .

[0172] Step S2 includes the following sub - steps:

[0173] S21. Calculate the characteristic ray R of the optical path of the light ray segment S i,j P i,j,1 T i,1 from the entrance pupil S i,j to the ideal image point I i . The optical path i

[0174] The first characteristic ray R 1,1 propagates through the first target point T 1,1 and then continues to propagate. After being reflected by the second free - form surface Ω 2 , it converges to the ideal image point I 1 . Then the optical path is:

[0175]

[0176] where n 3 is the first free - form surface Ω 2 ​The refractive index of the medium at the spatial position where the outgoing light ray is located. The characteristic ray R emitted from the i-th field of view i,j , after being reflected by the first free-form surface Ω 1 , converges to the target point T i,1 . Under ideal conditions, the characteristic ray R i,j passes through the point T i,1 , and is reflected by the second free-form surface Ω 2 at the point P ij 2 and converges to the ideal image point I i , and there is the following relationship between the optical paths :

[0177]

[0178]

[0179] According to Malus's law, all the characteristic rays between the target point T i,1 and the ideal image point I i have the same optical path;

[0180] Therefore, draw an auxiliary ray starting from the target point T i,1 that passes through the vertex O 2 of the second free-form surface Ω 2 and finally intersects at the ideal image point I i , and there is:

[0181]

[0182] Then the optical path i,j of the characteristic ray R i,j from the starting point S i to the ideal image point I can be expressed as:

[0183]

[0184] where is the optical path of the ray segment T i,1 O 2 I i .

[0185] In an actual optical system, characteristic rays with different fields of view and different apertures may be reflected and imaged at the same point on the free-form surface. However, for a super-large field-of-view system, the free-form surface cannot converge the rays with different fields of view and different apertures to the ideal image point. Therefore, the optical path of the fitted surface from the entrance pupil S ij to the target point T i1 is different from the ideal optical path

[0186] S22. Solve for all the characteristic data points P of the second free-form surface Ω based on the optical path. and the first free-form surface Ω 1 ; 2 Calculate the actual intersection point P of the characteristic ray R emitted from the starting point S i,j,2 ;

[0187] and the optical path length of the ray segment SP i,j is: i,j with the first free-form surface Ω after fitting 1 i,j,1 a i,j i,j,1 a P i,j,1 a

[0188]

[0189]

[0190] 2

[0191]

[0192]

[0193] i,j,1 a where P i,j i,j is the actual intersection point of the characteristic ray R emitted from the starting point S i,j 1 with the first free-form surface Ω;

[0192] For the first free-form surface Ω after least squares fitting 1 , rearrange its surface equation into an equation expressed as F(x, y, z):

[0193]

[0194] Take the partial derivatives of the first free-form surface equation F(x, y, z), and then substitute the coordinates of the characteristic data point P i,j,1 a to obtain the normal vector N 1 at each point on the first free-form surface Ω 1 as:

[0195]

[0196] According to the law of refraction / reflection:

[0197] n 1 (A 1 o ×N 1 o ) = n 2 (A1 o′ ×N 1 o ) (20)

[0198] Wherein,

[0199]

[0200]

[0201] A 1 o , A 1 o′ are respectively the unit vectors of the characteristic ray R i,j with respect to the first free-form surface Ω 1 for the incident ray and the reflected ray;

[0202] N 1 o is the unit normal vector at point P i,j,1 a .

[0203] Construct the equation of the straight line where the ray segment P i,j,1 a P i,j,2 is located according to formula (22). Combining with formula (17), all the characteristic data points P 2 of the second free-form surface Ω i,j,2 can be obtained.

[0204] S23. Fit all the characteristic data points P 2 of the second free-form surface Ω i,j,2 into a free-form surface characterized by an XY polynomial using the least squares method, and obtain the second free-form surface Ω 2 .

[0205] The equation of the XY polynomial is:

[0206]

[0207] Wherein, c is the curvature of the surface vertex, l is the conic coefficient, is the free-form surface polynomial, and A q are the coefficients of each term.

[0208] S3. Further iteratively optimize the initial structure by the optical path iteration method until the free-form surface optical system meets the imaging requirements. Figure 6 shows a comparison schematic diagram of the actual optical path length and the ideal optical path length of each field of view imaging provided by the embodiment of the present invention.

[0209] As Figure 6As shown, an ideal optical system actually extends the imaging characteristics of an optical system in the paraxial region to an arbitrarily large space. Therefore, for an actual optical system, there is a deviation between the actual optical path length and the ideal optical path length of the imaging in each field of view. The free-form surface system constructed according to Step S1 and Step S2 can initially meet the system optical power requirements, but the imaging quality of the edge field of view is poor and needs to be further iteratively optimized.

[0210] In the optical path iteration method proposed by the present invention, the current free-form surface system is used as a new initial structure, and then the optical paths for solving the characteristic data points of each free-form surface in the system are continuously corrected in sequence. The specific process is as follows:

[0211] First, by setting an initial optical path correction amount ΔOPD 1 correct the calculated optical path to obtain the optical path for recalculating the characteristic data points of the free-form surface

[0212]

[0213] where ε i,1 is the iteration coefficient for correction and its expression is:

[0214]

[0215] where is the basic iteration coefficient, Δε i,1 (Δε i,1 ≥0) is the iteration amount of ε i,1 and when Δε i,1 = 0,

[0216] For the optical path its corrected optical path for each iteration can be expressed as:

[0217]

[0218] where

[0219]

[0220] where

[0221] ε i,2 is the iteration coefficient for correction ;

[0222] is the basic iteration coefficient;

[0223] Δε i,2(Δε i,2 ≥0) is the iteration amount of ε i,2 ;

[0224] When Δε i,2 = 0,

[0225] ΔOPD 2 is the optical path correction amount of Figure 7 FIG. shows the optical structure in the XOZ plane of an off-axis two-mirror system designed by using the equal optical path surface expansion method according to an embodiment of the present invention.

[0226] Figure 8 FIG. shows the optical structure in the YOZ plane of an off-axis two-mirror system designed by using the equal optical path surface expansion method according to an embodiment of the present invention.

[0227] As Figures 7-8 shown, the ultra-large field of view off-axis reflective free-form optical system obtained by the design method provided by the present invention has good imaging characteristics. After simple subsequent optimization, an optical system design result with high imaging quality and a reasonable opto-mechanical structure can be obtained.

[0228] S4. Obtain the initial structure of the optimized free-form optical system when the number of mirrors N > 2 by repeating steps S1, S2, and S3.

[0229] For an off-axis multi-mirror free-form system (the number of mirrors is N, N > 2), its design method is analogized in the same way as the above off-axis two-mirror free-form system.

[0230] Set N - 1 target points T i,k and N data points P 1,1,k in the preprocessing step S0. Further repeating steps S1 and S2 can obtain all the characteristic data points of N unknown free-form surfaces. Fit the characteristic data points into a free-form surface, construct a free-form surface system, observe the system quality. If the imaging of some fields of view of the free-form surface system does not meet the imaging quality requirements, use the optical path iteration method in step S3 to optimize and iterate the free-form surface system until the free-form surface system meets the imaging requirements, and output the free-form surface system.

[0231] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

[0232] The specific embodiments of the present invention described above do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and deformations made according to the technical concept of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A method for designing the initial structure of an off-axis reflective freeform optical system with an ultra-large field of view, characterized in that, it includes the following steps: Preprocessing step S0, defining system parameters: The number of freeform surfaces of the freeform optical system is K, and the k-th freeform surface is defined as Ω k , where k = 1, 2, …, K; Divide the freeform optical system into M fields of view, and uniformly sample J characteristic rays for all-aperture rays in each field of view by the grid method. Define the j-th characteristic ray in the i-th field of view as R i,j , where i = 1, 2, …, M; j = 1, 2, …, J; Define the characteristic ray R i,j The intersection point with the entrance pupil is the starting point S i,j , and define the characteristic ray R i,j The intersection point with the k-th free-form surface Ω k is the characteristic data point P i,j,k ; Define the characteristic ray R i,j After being reflected by k free-form surfaces, it reaches the target point T i,k , when k = K, the point T i,k is the ideal image point I i ; In the freeform optical system, a characteristic ray R i,j emitted from a starting point S i,j is reflected by a freeform surface Ω i,j,k at a characteristic data point P k and then reaches a target point T i,k After that, the characteristic ray R i,j continues to propagate and is reflected by the freeform surface Ω i,j,K at the characteristic data point P K to reach an ideal image point I i ; S1. Calculate all the characteristic data points P of the first free-form surface Ω according to the starting point S i,j and the target point T i,k and fit them by the least squares method to obtain the first free-form surface Ω 1 ; i,j,1 1 ;​ The solution steps for the feature data point P in the step S1 i,j,1 include: S11. Calculate the first characteristic ray R in the first field of view 1,1 After being reflected by the first freeform surface Ω 1 It reaches the first target point T 1,1 The optical path of, and solve the characteristic data point P of the first freeform surface Ω in the first field of view 1 ; 1,j,1 ; S12. By calculating the ideal optical path of the characteristic light rays in the remaining fields of view except the first field of view after being reflected by the free-form surface Ω 1 to reach the target point, and further locating the coordinate positions of the characteristic data points in the remaining fields of view; S13. Fit all the characteristic data points P of the first free-form surface Ω 1 to obtain the first free-form surface Ω i,j,1 by the least squares method 1 ; The step S12 includes: For the first free-form surface Ω 1 , given the incident direction of the characteristic ray R i,j of the i-th field of view, draw an auxiliary line parallel to the characteristic ray R i,j that intersects the first free-form surface Ω 1 at the surface vertex O 1 . Draw a perpendicular line through the entrance pupil S i,j such that S i,j S′ i,j is perpendicular to S′ i,j O 1 ; According to Malus' law, the optical path lengths of the light segments S i,j P i,j,1 T i,1 and S′ i,j O 1 T i,1 are equal, that is: Wherein, is the optical path of the light segment S i,j P i,j,1 T i,1 ; is the optical path of the light segment S′ i,j O 1 T i,1 ; Taking point S i,j as the origin O′, a local coordinate system X′Y′Z′ is constructed; Given that the field of view angle of the i-th field of view is (ω X , ω Y ), then the angles between the projections of S i,j P i,j,1 (O′P i,j,1 ) on the X′OZ′ plane and the Y′OZ′ plane and the Z′ axis are ω X and ω Y respectively; Assuming that the projection length of the incident vector S i,j P i,j,1 on the Z′ axis is 1, according to geometric relations, the projection lengths of the incident vector S i,j P i,j,1 on the X′ axis and the Y′ axis are tanω X and tanω Y respectively, then the unit incident vector S i,j P i,j,1 o exists: Construct the light ray segment S″ according to Equation (7). i,j O 1 The equation of the straight line where it is located: and point S i,j and point S″ i,j The plane equation of the tangent plane where they are located: Solve the simultaneous equations (7-9) to obtain the position coordinates of point , and then calculate all the characteristic data points P 1 of the first free-form surface Ω i,j,1 according to equations (4-6); The step S13 includes: Fit the calculated characteristic data points P of the first free-form surface i,j,1 to the expression of the XY polynomial to construct the first free-form surface Ω 1 ; The expression of the XY polynomial is: Among them, c is the curvature of the surface; l is the quadratic surface coefficient; is the free-form surface polynomial; A q is the polynomial coefficient; S2. According to the first free-form surface Ω 1 calculate all the characteristic data points P 2 of the second free-form surface Ω i,j,2 , and obtain the second free-form surface Ω 2 by fitting them with the least squares method, and construct the initial structure of the two-mirror free-form surface optical system; S3. Further iteratively optimize the initial structure by the optical path iteration method until the freeform surface ray system meets the imaging requirements; S4. Obtain the optimized initial structure of the freeform optical system when the number of reflectors N > 2 by repeating the steps S1, S2, and S3.

2. The method for designing the initial structure of an off-axis reflective freeform optical system with an ultra-large field of view according to claim 1, characterized in that, The step S11 includes: The first characteristic ray R under the first field of view 1,1 After passing through the first freeform surface Ω 1 Is reflected and reaches the first target point T 1,1 Of the optical path Is: where n 1 and n 2 are the refractive indices of the media in which the incident light ray and the outgoing light ray of the first free-form surface Ω 1 are located; All characteristic rays R in the first field of view 1,j After being reflected by the first free-form surface Ω 1 Converge to the first target point T 1,1 The optical path of Is: According to Malus' law, under ideal conditions: Solve for the characteristic data points \(P\) of the first free-form surface \(\Omega\) in the first field of view according to Equation (3). 1 of the first free-form surface \(\Omega\) in the first field of view 1,j,1 .

3. The method for designing the initial structure of an off-axis reflective freeform optical system with an ultra-large field of view according to claim 1, characterized in that, Step S2 includes the following sub-steps: S21. Calculate the optical path of the characteristic ray R from the entrance pupil S to the ideal image point I according to the optical path of the light ray segment S i,j P i,j,1 T i,1 i,j i,j i ​​​​​ S22. Solve for all the characteristic data points P of the second freeform surface Ω according to the optical path and the first freeform surface Ω 1 ; 2 i,j,2 ​​ S23. Fit all the characteristic data points P of the second free-form surface Ω 2 into a free-form surface characterized by an XY polynomial using the least squares method to obtain the second free-form surface Ω i,j,2 . 2 .

4. The method for designing the initial structure of an off-axis reflective freeform optical system with an ultra-large field of view according to claim 3, characterized in that, The step S21 includes: The first characteristic ray R 1,1 passes through the first target point T 1,1 and then continues to propagate, passes through the second free-form surface Ω 2 and after reflection, converges to the ideal image point I 1 , then the optical path is: where n 3 is the refractive index of the medium in which the outgoing light ray of the first free-form surface Ω 2 is located; The characteristic ray R emitted from the i-th field of view i,j , after being reflected by the first free-form surface Ω 1 , converges to the target point T i,1 , the characteristic ray R i,j passes through the target point T i,1 , and is incident on the second free-form surface Ω 2 at the point P i,j,2 , and after being reflected, converges to the ideal image point I i . The optical path is as follows: According to Malus' law, all characteristic rays starting from point T i,1 and converging to the ideal image point I i have the same optical path; Therefore, starting from point T i,1 a secondary ray is drawn through the second freeform surface Ω 2 and the vertex O of the surface 2 and finally intersects at the image point I i , and there is: Then the characteristic ray R i,j from the entrance pupil S i,j to the ideal image point I i has an optical path as follows: Among them, is the optical path of the light segment T i,1 O 2 I i .

5. The method for designing the initial structure of an off-axis reflective freeform optical system with an ultra-large field of view according to claim 4, characterized in that, The step S22 includes: Calculate the characteristic ray R i,j emitted from the entrance pupil S i,j and the actual intersection point P 1 with the first freeform surface Ω after fitting i,j,1 a and the optical path length of the ray segment S i,j P i,j,1 a is as follows as follows: Obtain the second free-form surface Ω 2 The optical path length is as follows: Among them, the characteristic data point P i,j,1 a is the characteristic ray R i,j emitted from the entrance pupil S i,j and the actual intersection point with the first free-form surface Ω 1 ; For the first freeform surface Ω after least squares fitting 1 , rearrange its surface equation into an equation expressed as F(x, y, z): Take the partial derivatives of the first free-form surface equation F(x, y, z), and then substitute the coordinates of the characteristic data point P i,j,1 a to obtain the normal vector N of each point on the first free-form surface Ω 1 as follows: 1 For: According to the law of refraction / reflection: n 1 (A 1 o ×N 1 o ) = n 2 (A 1 o ′ × N 1 o ) (20) Wherein, A 1 o , A 1 o′ are respectively the characteristic ray R i,j with respect to the first free-form surface Ω 1 unit vectors of the incident ray and the reflected ray; N 1 o is the unit normal vector at the point P i,j,1 a ; Construct the straight line equation where the light ray is located according to formula (22), and combine formula (17) to find all the characteristic data points P of the second free-form surface Ω 2 . i,j,2 .

6. The method for designing the initial structure of an off-axis reflective freeform optical system with an ultra-large field of view according to claim 5, characterized in that, In the optical path iteration method of step S3, take the current freeform surface system as a new initial structure, and then continuously correct the optical paths of the characteristic data points used to solve each freeform surface in the freeform surface system in turn. The specific process is as follows: By setting an initial optical path correction amount ΔOPD 1 for the already calculated optical path perform correction to obtain the optical path for recalculating the free-form surface characteristic data points where ε i,1 is the iteration coefficient for correction , and its expression is: Among them, is the basic iteration coefficient, Δε i,1 is ε i,1 the iteration amount of, Δε i,1 ≥ 0; When Δη i,1 = 0, For the optical path The corrected optical path for each iteration is as follows: Wherein, Wherein, ε i,2 is the iteration coefficient for correction ; as the basic iteration coefficient, Δε i,2 is ε i,2 the iteration amount of, Δε i,2 ≥ 0; When Δη i,2 = 0, ΔOPD 2 is the optical path correction amount of 7. The method for designing the initial structure of an off-axis reflective freeform optical system with an ultra-large field of view according to claim 6, characterized in that, When the number of freeform surfaces is N, N > 2, its design method is analogized in the same way as the off-axis reflector freeform surface system in claim 1; Set N - 1 target points T in the preprocessing step S0 i,k and N data points P 1,1,k ; Repeat steps S1 and S2 to obtain all the characteristic data points of N unknown freeform surfaces; Fit all the characteristic data points into freeform surfaces, construct a freeform surface system, observe the system quality. If the imaging of some fields of view of the freeform surface system does not meet the imaging quality requirements, optimize and iterate the freeform surface system by the optical path iteration method of step S3 until the freeform surface system meets the imaging requirements, and output the freeform surface system.

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