Method for acquiring light field information of freeform off-axis reflection system and optimization method

Abstract

The application provides a light field information acquisition method and an optimization method of a free-form surface off-axis reflection system, and the light field information acquisition method of the free-form surface off-axis reflection system comprises the following steps: obtaining light field information of the free-form surface off-axis reflection system according to light field information of free space and light field information at a free-form surface off-axis optical element; wherein the acquisition of the light field information at the free-form surface off-axis optical element comprises the following steps: decomposing input light field of the free-form surface off-axis optical element into superposition of Gaussian beams; equivalent propagations of the Gaussian beams through the free-form surface off-axis optical element by complex ray tracing; and combining the propagated Gaussian beams to obtain light field information of the output free-form surface off-axis optical element. The application considers the diffraction effect of light propagation when acquiring the light field information, can acquire more accurate light field information of the free-form surface off-axis reflection system, and can thus reasonably optimize the free-form surface off-axis reflection system.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of field tracing technology, in particular to a light field information acquisition method and an optimization method of a free-form surface off-axis reflection system. BACKGROUND

[0002] With the development and progress of science and technology, free-form surface optical elements are widely used in optical systems, providing more degrees of freedom for optical design and improving the performance of optical systems. The existing optical system modeling method is based on geometric ray tracing, which cannot simulate the physical effects such as diffraction existing in actual optical systems, and the method of designing optical systems only by geometric ray tracing principle has limitations. Physical optics uses complex functions to represent light waves, and describes the physical process of light propagation by establishing wave equations. The method of solving wave equations is called scalar diffraction theory. Under this framework, Kirchhoff formula, Rayleigh-Sommerfeld formula and angular spectrum formula of diffraction are developed to accurately represent the physical process of light propagation. According to these formulas, the spatial light field distribution before and after the known light field plane can be calculated. By combining matrix optics with scalar diffraction theory, a generalized theoretical formula for expressing the propagation of light field in paraxial optical systems, Collins formula, can be derived. However, the above formulas still cannot obtain the light field information propagating in the optical system containing free-form surface off-axis reflection optical elements, and further cannot reasonably optimize the free-form surface optical system. SUMMARY

[0003] The purpose of the present application is to solve the problem of obtaining more accurate light field information of a free-form surface off-axis reflection system, and to provide a light field information acquisition method and an optimization method of a free-form surface off-axis reflection system.

[0004] To achieve the above purpose, the present application adopts the following technical solutions:

[0005] The light field information acquisition method of the free-form surface off-axis reflection system comprises the following steps:

[0006] S1: obtaining the light field information of the free-form surface off-axis reflection system according to the light field information of the free space and the light field information at the free-form surface off-axis optical element;

[0007] Wherein, the acquisition of the light field information at the free-form surface off-axis optical element comprises the following steps:

[0008] S11: decomposing the input light field of the free-form surface off-axis optical element into a superposition of Gaussian beams;

[0009] S12: equivalent propagating the Gaussian beams through the free-form surface off-axis optical element by complex ray tracing;

[0010] S13: combining the propagated Gaussian beams to obtain the light field information of the output free-form surface off-axis optical element.

[0011] In some embodiments, the light field information in free space is obtained using an angular spectrum formula.

[0012] In some embodiments, the light field at a plane z in free space is represented by the following formula:

[0013]

[0014] where E l (x,y,z) represents the light field, k x ,k y ,k z are the components of the wave vector k in the x, y, z directions, respectively, the operator represents a two-dimensional inverse Fourier transform, represents the angular spectrum of the light field E l .

[0015] In some embodiments, in step S11, the Gaussian beams satisfy the following characteristics: a base ray corresponding to a single Gaussian beam is perpendicular to the local wavefront, the principal curvatures of the single Gaussian beam match the local principal curvatures of the arbitrary light field, the Gaussian beams have a proper ratio of beam diameter to separation of adjacent beams, and the density of the Gaussian beams is sufficient to adequately sample the aperture or wavefront in the relevant application.

[0016] In some embodiments, in step S12, the complex rays include base rays, secondary divergent rays, and secondary parallel waist rays; the base rays are rays that coincide with the optical axis of the Gaussian beam and propagate in the direction of the Gaussian beam; the secondary divergent rays are rays that start at the waist position and have an angle of θ with the optical axis; the secondary parallel waist rays are rays that are parallel to the base rays and have a distance w0 from the base rays; where θ represents the far-field divergence angle, and w0 represents the waist spot radius of the Gaussian beam.

[0017] In some embodiments, the Gaussian beams are propagated equivalently by tracing one base ray, four secondary divergent rays, and four secondary parallel waist rays.

[0018] In some embodiments, in step S13, the light field of the free-form off-axis optical element is represented by the following formula:

[0019] E out = P out BP in E in

[0020] where P in is an operator for propagating the light field from the input plane to the free-form surface, P out is an operator for propagating the light field from the surface to the output plane, E in is the light field of the input plane, and Eout for outputting a light field of a plane.

[0021] The application also provides an optimization method of the free-form surface off-axis reflection system, comprising the following steps:

[0022] A1: obtaining the light field information at the free-form surface off-axis optical element in the free-form surface off-axis reflection system according to the method, wherein the light field information comprises a wavefront phase of the light field;

[0023] A2: obtaining the aberration characteristics of the free-form surface off-axis reflection system according to the deviation of the wavefront phase of the light field from a spherical phase;

[0024] A3: superimposing a corresponding Zernike surface on the free-form surface according to the aberration characteristics of the free-form surface off-axis reflection system to correct the system aberration.

[0025] The application also provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer program is executed by a processor to realize the steps of the light field information acquisition method of the free-form surface off-axis reflection system.

[0026] The application also provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer program is executed by a processor to realize the steps of the optimization method of the free-form surface off-axis reflection system.

[0027] The application has the following beneficial effects:

[0028] The application can obtain more accurate light field information of the free-form surface off-axis reflection system by decomposing the input light field of the free-form surface off-axis optical element into superposition of Gaussian beams, equivalently propagating the Gaussian beams through the free-form surface off-axis optical element by complex ray tracing, and combining the propagated Gaussian beams to obtain the light field information of the output free-form surface off-axis optical element, considering the diffraction effect of light propagation during the acquisition of the light field information, thereby reasonably optimizing the free-form surface off-axis reflection system.

[0029] Other beneficial effects of the embodiments of the application will be further described below. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 The figure is a flowchart of the light field information acquisition method of the free-form surface off-axis reflection system in the embodiments of the application.

[0031] Figure 2 The figure is a schematic diagram of the light field of the free-form surface off-axis reflection system in the embodiments of the application.

[0032] Figure 3 The figure is a schematic diagram of the light field decomposition of the optical system in the embodiments of the application.

[0033] Figure 4 Figure 1 is a schematic diagram of a wavefront decomposition into Gaussian beamlets for any wavefront in embodiments of the present application;

[0034] Figure 5 Figure 2 is a schematic diagram of Gaussian beam propagation characteristics in embodiments of the present application;

[0035] Figure 6 Figure 3 is a schematic diagram of a general Gaussian beam represented by complex rays in embodiments of the present application;

[0036] Figure 7 Figure 4 is a schematic diagram of freeform optical field propagation in embodiments of the present application;

[0037] Figure 8 Figure 5 is a flowchart of an optical system optical field acquisition in embodiments of the present application;

[0038] Figure 9 Figure 6 is a flowchart of an optimization method for a freeform off-axis reflective system in embodiments of the present application;

[0039] Figure 10 Figure 7 is a layout of a freeform off-axis reflective system in embodiments of the present application;

[0040] Figure 11 Figure 8 is an image point diagram obtained by geometric ray tracing in embodiments of the present application;

[0041] Figure 12 Figure 9 is an image plane diffraction diagram in embodiments of the present application;

[0042] Figure 13 Figure 10 is a wavefront phase diagram of an input plane wave in embodiments of the present application;

[0043] Figure 14 Figure 11 is a wavefront phase diagram at the system exit pupil in embodiments of the present application;

[0044] Figure 15 Figure 12 is a wavefront phase diagram at the system exit pupil after optimization in embodiments of the present application;

[0045] Figure 16 Figure 13 is an image plane diffraction diagram after optimization in embodiments of the present application;

[0046] BRIEF DESCRIPTION OF THE DRAWINGS

[0047] 41 - Gaussian beam, 42 - wavefront normal, 43 - arbitrary wavefront, 61 - secondary divergent ray, 62 - secondary sagittal ray, 63 - base ray, 71 - input plane, 72 - freeform surface, 73 - output plane. DETAILED DESCRIPTION

[0048] The following detailed description of the embodiments of the application. It should be emphasized that the following description is only exemplary, not intended to limit the scope of the application and its applications.

[0049] Example 1

[0050] As Figure 1 shown, the embodiment of the application provides a method for obtaining light field information of a free-form surface off-axis reflection system, comprising the following steps:

[0051] S1: obtaining light field information of a free-form surface off-axis reflection system according to light field information in free space and light field information at a free-form surface off-axis optical element;

[0052] Wherein, the light field information at the free-form surface off-axis optical element comprises the following steps:

[0053] S11: decomposing the input light field of the free-form surface off-axis optical element into a superposition of Gaussian beams;

[0054] S12: using complex ray tracing to simulate the propagation of the Gaussian beams through the free-form surface off-axis optical element;

[0055] S13: combining the propagated Gaussian beams to obtain the light field information of the output free-form surface off-axis optical element.

[0056] That is, it includes the following important parts:

[0057] 1) sub-regional acquisition of light field propagation in optical system;

[0058] 2) conversion of wavefront and Gaussian beam element;

[0059] 3) using complex ray tracing to realize the propagation of Gaussian beams at the free-form surface optical element;

[0060] Using the method of the embodiment, the light field information of the free-form surface off-axis reflection optical system can be obtained, the physical effects of the optical system can be simulated, and key parameters for free-form surface optical system design can be provided.

[0061] Specifically, the embodiment of the application comprises the following steps:

[0062] 1. Light field sub-regional acquisition method

[0063] The angular spectrum formula of diffraction can calculate the spatial light field distribution before and after the plane perpendicular to the known light field, which corresponds to the propagation of the light field along the optical axis direction in the optical system. As Figure 2 , Figure 3 shown, the free-form surface off-axis reflection system contains both the propagation of the light field along the optical axis direction in free space (in Figure 2(represented by gray areas), and also includes propagation under the constraint of freeform off-axis optical elements (in... Figure 2 (Represented by curves). To calculate the optical field of an optical system containing a freeform off-axis reflecting optical element, the complex amplitude E is used to uniformly represent the optical field at different planes. The propagation of the optical field in free space is calculated using the angular spectrum formula, and the propagation of the optical field under the constraint of the freeform off-axis optical element is calculated using the local basic interface method.

[0064] 1.1 Obtaining the light field propagating in free space

[0065] The propagation of a light field in free space can be calculated using the angular spectrum formula. Defined as light field E l angular spectrum, k x ,k y ,k z Let E be the component of the wave vector k in the x, y, and z directions, respectively. l (x,y,0), where l is the planar coordinate (x,y), angular spectrum It can be represented as:

[0066]

[0067] in, Operators represent two-dimensional Fourier transforms.

[0068] Using the angular spectrum operator, the light field E at plane z is... l (x,y,z) can be represented as:

[0069]

[0070] in, The operator represents the two-dimensional inverse Fourier transform, k z for

[0071]

[0072] The wave number k is expressed as k = n(2π / λ), where λ is the wavelength of light in a vacuum and n is the refractive index.

[0073] 1.2 Obtaining the optical field of a freeform off-axis optical element

[0074] The method of local basic interfaces can calculate the propagation of the light field at off-axis optical elements on freeform surfaces. This method is based on the following principle:

[0075] 1) Local basic interface approximation: The input light field can be decomposed into infinitesimal elements, which only interact with the local basic interface;

[0076] 2) Local independent response approximation: The response of the input light field to the interface can be decomposed into independent actions with local interface characteristics.

[0077] 1.2.1 Conversion of the input light field into a Gaussian beam element

[0078] like Figure 4 As shown, the local fundamental interface approximation decomposes the input light field into infinitesimal elements, and the response of the input light field to the freeform surface is decomposed into independent actions with local interface characteristics. Based on this method, the input light field can be decomposed into a Gaussian beam to calculate the propagation of the light field at the freeform surface. The Gaussian beam 41 has the following characteristics, making it the fundamental field in the decomposition process: (1) the Gaussian beam is easy to propagate in the optical system; (2) the Gaussian beam is the fundamental solution of the paraxial wave equation; (3) the Gaussian function is smooth and continuous (all derivatives are continuous); (4) the Gaussian beam is relatively compact and can be considered to have a finite width in actual calculations. Figure 4 In the Gaussian beam 41, the wavefront normal 42 is perpendicular to any wavefront 43.

[0079] To decompose any wavefront 43 into a Gaussian beam, the following principles must be followed:

[0080] 1) According to Malus's theorem in geometrical optics, the fundamental ray corresponding to a single Gaussian beam must be perpendicular to the local wavefront;

[0081] 2) The principal curvature of a single Gaussian beam must match the local principal curvature of any optical field;

[0082] 3) A Gaussian beam must have an appropriate beam diameter and a separation ratio with adjacent beams, which is called the overlap factor;

[0083] 4) The density of the Gaussian beam must be sufficient to adequately sample the aperture or wavefront in the relevant application.

[0084] 1.2.2 Complex ray representation of Gaussian beam

[0085] The field of a Gaussian beam propagating along the z-axis and satisfying the paraxial wave equation can be expressed as:

[0086]

[0087] Where c is a constant factor, the meanings of the other symbols are as follows:

[0088]

[0089] like Figure 5 As shown, w0 is the waist radius of the Gaussian beam; f is the confocal parameter of the Gaussian beam; R(z) is the radius of curvature of the isophase surface of the Gaussian beam intersecting the propagation axis at point z; and w(z) is the beam radius on the isophase surface of the Gaussian beam intersecting the propagation axis at point z.

[0090] The beam radius is minimum at the waist, the wavefront is flat R(z) = ∞, the Rayleigh range b (b = 2z R 、 ) refers to the distance that the beam area increases to twice the waist, i.e. In the Rayleigh range b, i.e. 2z R , the Gaussian beam can be approximated as parallel light, and the change of the beam radius is ignored. The divergence angle of the Gaussian beam near the waist is small, and for a Gaussian beam with a small waist size, the far-field divergence angle θ can be large

[0091]

[0092] In the far field (z >> z R )

[0093]

[0094] Since the existing diffraction calculation method cannot obtain the light field information propagating between the free-form optical elements, in order to solve this problem, with reference to Figure 6 , the general Gaussian beam is represented by a complex ray, which includes four secondary divergent rays 61, four secondary waist rays 62 (there are another two pairs of rays in the plane perpendicular to the paper) and a central base ray 63; the base ray is a ray coinciding with the optical axis of the Gaussian beam and propagating along the propagation direction of the Gaussian beam; the secondary divergent ray is a ray with an angle of θ with the optical axis and starting from the waist position; the secondary parallel waist ray is a ray with a distance w0 from the base ray and parallel to the base ray, wherein θ represents the far-field divergence angle, and w0 represents the waist spot radius of the Gaussian beam.

[0095] By analyzing the propagation characteristics of the Gaussian beam and extracting the key parameters, the general Gaussian beam propagating in an asymmetric optical system can be equivalently realized by complex ray tracing. The general divergent Gaussian beam can be equivalently propagated by tracing a base ray, four secondary divergent rays and four secondary parallel waist rays, and the base ray and two pairs of rays are as shown in Figure 6 , in this embodiment, each complex ray contains 9 rays.

[0096] 1.2.3 Free-form surface propagation

[0097] Figure 7 The schematic diagram for obtaining the light field propagating through the free-form surface 72 in this embodiment is shown in FIG. 1. The light field E in and the light field E out at the output plane 73 are defined on two parallel planes (non-parallel planes can also be calculated), and are connected by a free-form surface operator B. The transmission process can be written as

[0098] E out = P out BP in E in

[0099] where P in is the operator for propagating the light field from the input plane to the freeform surface, P out is the operator for propagating the light field from the surface to the output plane.

[0100] The freeform surface operator B contains three operators, two coordinate transformation operators and one boundary condition operator. The unit vectors corresponding to the coordinate axes of the global coordinate system are defined as The first coordinate transformation operator Q transforms the global coordinate system to the local coordinate system on the plane

[0101]

[0102] where T denotes the transpose of a matrix.

[0103] By the Q operator, all the waves from the input field are transformed to the local coordinate system on the freeform surface they are on

[0104]

[0105] where and denote the local Gaussian beams of the input field in the global coordinate system and the local coordinate system, respectively.

[0106] When the light field passes through the surface, the output local Gaussian beams are transformed back to the global coordinate system.

[0107]

[0108] Similarly, where and denote the local Gaussian beams on the output plane in the global coordinate system and the local coordinate system, respectively.

[0109] At the local position of the surface, the boundary condition C connects the input field and the output field,

[0110]

[0111] where C denotes the interaction of the local Gaussian beams with the local plane.

[0112] In summary, the freeform surface operator B can be expressed as

[0113] B = Q -1 CQ

[0114] As described above, the method based on local base interface in the embodiment calculates the propagation of the light field through the free-form off-axis optical element, and the acquisition of the light field information at the free-form off-axis optical element mainly includes the following steps:

[0115] 1) decomposing an arbitrary input light field into a superposition of Gaussian beams;

[0116] 2) implementing the propagation of the Gaussian beams through the free-form off-axis optical element by complex ray tracing;

[0117] 3) recombining the propagated Gaussian beams to obtain the total field, i.e. the light field information output from the free-form off-axis optical element (such recombination can be performed at any position in the entire optical system).

[0118] 2. Flowchart of the light field acquisition of the optical system

[0119] As shown in Figure 8 , for an optical system containing a free-form off-axis reflective optical element, the light field acquisition steps are as follows:

[0120] 1. Input light field

[0121] 2. Determine whether the input plane to the next optical element is free-space propagation, if yes, use the light field information acquisition method of free space to calculate, if not, use the light field information acquisition method at the free-form off-axis optical element to calculate;

[0122] 3. Calculate the output light field

[0123] The embodiment also provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the steps of the light field information acquisition method of the free-form off-axis reflective system.

[0124] Embodiment 2

[0125] Referring to Figure 9 , the embodiment of the application provides an optimization method of a free-form off-axis reflective system, which includes the following steps:

[0126] A1: acquiring the light field information at the free-form off-axis optical element in the free-form off-axis reflective system according to the method of embodiment 1, and the light field information includes the wavefront phase of the light field;

[0127] A2: obtaining the aberration characteristics of the free-form off-axis reflective system according to the deviation of the wavefront phase of the light field from the spherical phase;

[0128] A3: superimposing the corresponding Zernike surface shape on the free-form surface according to the aberration characteristics of the free-form off-axis reflective system to correct the system aberration.

[0129] The embodiment can optimize the free-form surface off-axis reflection system and improve the system performance by using the accurate free-form surface off-axis reflection system light field information obtained in embodiment 1.

[0130] The embodiment also provides a computer readable storage medium storing a computer program, and the computer program is executed by a processor to implement the steps of the optimization method of the free-form surface off-axis reflection system.

[0131] Experimental example

[0132] Reference Figure 10 The implementation process of the embodiment is described by taking an off-axis single-lens reflex system as an example, and the following table 1 is the first-order Gaussian parameter of the system, and the following table 2 is the physical parameter of the system:

[0133] Table 1

[0134] Parameter Value Equivalent focal length -100 mm Entrance pupil diameter 20 mm

[0135] Table 2

[0136] Parameter Value [d1 / mm] -100 [alpha]1 / ° 5 Normalized radius (SCO NRADIUS | C69) 10 5th order Zernike coefficient (SCO ZP5 | C6) -0.125

[0137] Wherein, d i represents the interval between the i-th surface and the i+1-th surface, and the subscript number i of the remaining parameters represents the i-th optical surface parameter, and a represents the surface tilt angle.

[0138] Let the input light field E in of the system be a plane wave, and the propagation of the light field from the input plane to the free-form surface is free-space propagation, according to the flow chart, the light field of the input free-form surface can be calculated as

[0139]

[0140] The light field of the input free-form surface propagates to the system exit pupil through the action of the free-form surface, and the propagation of the light field at this point is the propagation at the free-form surface optical element, and through calculation, the light field at the system exit pupil can be obtained as

[0141]

[0142] By analyzing the deviation of the wavefront phase of the light field at the system exit pupil from the spherical phase, the aberration characteristics of the system can be obtained, and the corresponding Zernike surface shape is superimposed on the free-form surface according to the aberration of the system, so that the system aberration can be compensated and the system design can be optimized.

[0143] Figure 11 is a geometric ray tracing image point diagram, which can only reflect the spatial distribution of the light rays, Figure 12The light intensity distribution diagram of the image plane calculated for the embodiment takes into account the diffraction effect of light propagation and is more in line with the actual situation of the optical system. Figure 13 The wavefront phase diagram of the input plane wave is Figure 14 The wavefront phase diagram of the system exit pupil is obtained. By analyzing the deviation of the wavefront phase from the ideal spherical wave, the aberration distribution of the system is obtained, and the corresponding Zernike surface shape is superimposed on the freeform surface to correct the system aberration. The physical parameters of the optimized system are shown in Table 3.

[0144] Table 3

[0145] Parameter Value [d1 / mm] -100 [alpha]1 / ° 5 Normalized radius (SCO NRADIUS | C69) 10 4th order Zernike coefficient (SCO ZP4 | C5) -0.000947948 5th order Zernike coefficient (SCO ZP5 | C6) -0.124370891 6th order Zernike coefficient (SCO ZP6 | C7) 3.20E-12 8th order Zernike coefficient (SCO ZP8 | C9) -1.02E-10 9th order Zernike coefficient (SCO ZP9 | C10) 0.000358489

[0146] Figure 15 The wavefront phase diagram of the optimized system exit pupil can be seen that the PV value of the system wavefront distortion is reduced. As shown in Figure 16 , the diameter of the diffraction spot of the system image plane is reduced from 100 μm to 15 μm, and the performance of the system is improved.

[0147] Those skilled in the art will appreciate that embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage, etc.) containing computer usable program code.

[0148] The present application is described with reference to flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus produce a means for implementing the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in one or more flows and / or blocks in the flowcharts and / or block diagrams. Figure 1 The means for implementing the functions specified in one or more flows and / or blocks in the flowcharts and / or block diagrams.

[0149] These computer program instructions can also be stored in a computer-readable memory that can direct the computer or other programmable data processing apparatus to work in a specific manner, so that the instructions stored in the computer-readable memory produce a product including instruction means, which implements the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in one or more flows and / or blocks in the flowcharts and / or block diagrams. Figure 1the function specified in the one or more blocks.

[0150] These computer program instructions can also be loaded into computer or other programmable data processing devices, so that a series of operation steps are performed on the computer or other programmable data processing devices to generate computer-implemented processes, thus the instructions executed on the computer or other programmable data processing devices provide processes for implementing the flow Figure 1 the flow or flows and / or blocks Figure 1 the steps of the function specified in the one or more blocks.

[0151] The above is further detailed description of the present application in conjunction with specific / preferred embodiments, and cannot be deemed as limiting the specific implementation of the present application to these descriptions. For those skilled in the art to which the present application belongs, without departing from the concept of the present application, they can make several substitutions or variations to the described embodiments, and these substitutions or variations shall be deemed as falling within the protection scope of the present application. In the description of the present specification, the description of the terms "an embodiment", "some embodiments", "preferred embodiment", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are contained in at least one embodiment or example of the present application. The illustrative description of the above terms in the present specification does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any suitable manner in any one or more embodiments or examples. Those skilled in the art can combine and combine the different embodiments or examples described in the present specification and the features of the different embodiments or examples, without mutual contradiction. Although the embodiments of the present application and their advantages have been described in detail, it should be understood that various changes, substitutions and modifications can be made herein without departing from the scope of the patent application.

Claims

1. A method for obtaining light field information of a freeform off-axis reflective system, characterized in that, The method comprises the following steps: S1: obtaining the light field information of the free-form off-axis reflective system according to the light field information in free space and the light field information at the free-form off-axis optical element; Wherein, the light field information at the free-form off-axis optical element comprises the following steps: S11: decomposing the input light field of the free-form off-axis optical element into superposition of Gaussian beams; S12: equivalent propagation of the Gaussian beams through the free-form off-axis optical element by complex ray tracing; wherein, the complex ray comprises a base ray, four secondary divergent rays and four secondary parallel waist rays, and the Gaussian beams are equivalent to propagate by tracking the base ray, the four secondary divergent rays and the four secondary parallel waist rays; the base ray is a ray coinciding with the optical axis of the Gaussian beam and along the propagation direction of the Gaussian beam; the secondary divergent ray is a ray with the optical axis angle θ as the starting point at the beam waist position; the secondary parallel waist ray is a ray with a distance w0 from the base ray and parallel to the base ray; wherein θ represents the far-field divergence angle, and w0 represents the waist spot radius of the Gaussian beam; S13: combining the propagated Gaussian beams to obtain the light field information of the output free-form off-axis optical element.

2. The method of claim 1, wherein, In step S1, the light field information in free space is obtained using the angular spectrum formula.

3. The method of claim 2, wherein, The light field at the plane z in free space is represented by the following formula: where E l (x, y, z) represents the light field, k x , k y , k z are the components of the wave vector k in the x, y, z directions, F -1 is the Fourier transform operator, and represents the angular spectrum of the light field E l .

4. The method of claim 1, wherein, In step S11, the Gaussian beams satisfy the following characteristics: The base ray corresponding to a single Gaussian beam is perpendicular to the local wavefront, the principal curvature of the single Gaussian beam matches the local principal curvature of the arbitrary light field, the Gaussian beams have appropriate beam diameter and separation ratio of adjacent beams, and the density of the Gaussian beams is sufficient to fully sample the aperture or wavefront in the relevant application.

5. The method of claim 1, wherein, In step S13, the light field of the output free-form off-axis optical element is represented by the following formula: E out = P out BP in E in where P in is an operator for propagating a light field from an input plane to a freeform surface, P out is an operator for propagating a light field from a curved surface to an output plane, E in is a light field of the input plane, E out is a light field of the output plane.

6. A method of optimizing a freeform off-axis reflecting system, characterized in that, The method comprises the following steps: A1: obtaining the light field information at the free-form off-axis optical element in the free-form off-axis reflective system according to the method of any one of claims 1-5, wherein the light field information comprises the wavefront phase of the light field; A2: obtaining the aberration characteristics of the free-form off-axis reflective system according to the deviation of the wavefront phase of the light field from the spherical phase; A3: superimposing the corresponding Zernike surface shape on the free-form surface according to the aberration characteristics of the free-form off-axis reflective system to correct the system aberration.

7. A computer-readable storage medium storing a computer program, wherein the computer program comprises the following steps of: The computer program is executed by the processor to realize the steps of the method of any one of claims 1-5.

8. A computer-readable storage medium storing a computer program, the computer-readable storage medium comprising: The computer program is executed by the processor to realize the steps of the method of claim 6.

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