Splicing aspheric surface characterization method based on CGH lens zero position compensation detection light path

Abstract

The present application relates to the technical field of optical aspheric surface, especially refers to a kind of splicing aspheric surface characterization method based on CGH lens zero position compensation detection optical path, with the detection of aspheric surface as the guidance, based on zero position compensation detection principle, according to ray tracing method, Snell's law, diffraction principle and equal optical path principle, using the parameters required by the zero position compensation detection system of interferometer incident wave front as plane wave, compensator as single CGH lens and diffraction surface as binary optical surface 3 or binary optical surface 4 to characterize aspheric surface surface shape, and according to the aspheric surface type defined by the characterization method, it is called zero position splicing aspheric surface.According to the splicing aspheric surface characterization method, the measurement scheme can be determined in the design stage through the mathematical description of splicing aspheric surface, which avoids the influence of stray light and projection distortion of CGH detection, reduces the detection difficulty of splicing aspheric surface surface shape, and realizes the function of zero position splicing aspheric surface design.

Description

Technical Field

[0001] This invention relates to the field of optical aspherical technology, and in particular to a method for characterizing spliced ​​aspherical surfaces based on a CGH lens zero-position compensation detection optical path. Background Technology

[0002] Optical aspherical surfaces are an important type of optical surface shape. Compared to spherical lenses, aspherical lenses can more precisely control the direction and focusing effect of light, thereby achieving higher optical performance and less imaging distortion, and are therefore used in a wide range of fields.

[0003] However, for some special application scenarios, the optimization surface shape control capability of aspherical surfaces is limited, and the optimization efficiency is not high. Aspherical splicing, based on aspherical and toroidal surfaces, is composed of spliced ​​surface segments. A complete surface is divided into several sub-surfaces, and each sub-surface is described using existing optical surfaces. Simultaneously, adjacent sub-surfaces are controlled to maintain smooth connections, thus ensuring that the several sub-surfaces still mathematically constitute a complete surface.

[0004] In the process of stitching aspherical surfaces, computational holograms (CGHs) can flexibly diffract wavefronts of arbitrary shapes, acting as phase compensators to replace complex refracting lens combinations. The null-compensation testing method is currently the most accurate method for measuring the surface shape of optical elements. By introducing various compensators, gradient compensation is performed on the test piece to achieve null-position interferometry. CGH devices are binary optical diffraction elements that can generate free wavefronts of arbitrary shapes, making them highly suitable for null-position interferometry of optically stitched aspherical surfaces.

[0005] However, the CGH method is a one-to-one detection method, and the design of the compensator is closely related to the shape of the stitched aspherical surface. Since the stitched aspherical lens is a common part of the system optical path and the zero-position compensation detection optical path, and in actual production, the design of the system optical path and the design of the zero-position compensation detection optical path are carried out sequentially and unidirectionally, the design of the zero-position compensation detection optical path cannot provide feedback for the design of the system optical path, and it is impossible to effectively utilize the tolerance of the system optical path to optimize the zero-position compensation detection optical path. This means that even a very small deviation in the shape of the stitched aspherical surface can make the compensator structure very complex, rendering the zero-position compensation method infeasible. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the problem that in the prior art, since the design of spliced ​​aspherical surfaces precedes processing and testing, when using the zero-position compensation method for testing, the testing cannot provide feedback for the design, and the tolerance of the system optical path structure cannot be effectively utilized to fine-tune the testing scheme, resulting in a very complex testing scheme in some cases and reduced testing accuracy.

[0007] To address the aforementioned technical problems, this invention provides a method for characterizing spliced ​​aspherical surfaces based on a CGH lens null-compensation detection optical path, comprising:

[0008] In a zero-position compensation detection system where the incident wavefront of the interferometer is set to a plane wave and the compensator is a single CGH lens, the aperture of the interferometer standard mirror is D, the wavelength of the detection light is λ, the phase of the diffraction surface of the single CGH lens compensator is φ, the diffraction order is M, the radius of curvature of the refractive surface is r, the center thickness of the single CGH lens compensator is d, the refractive index of the material of the single CGH lens compensator is n, and the distance between the single CGH lens compensator and the aspherical surface is L.

[0009] Based on the aforementioned characterization parameters of the custom-defined zero-position spliced ​​aspherical surface, a zero-position compensation detection optical path is constructed. The detection light from the interferometer's standard mirror is incident parallel to the surface. Different heights and diffraction orders correspond to different points on the aspherical surface, and different diffraction plane directions correspond to different points on the zero-position spliced ​​aspherical surface. This optical path follows the principle of equal optical path, the principle of diffraction, and Snell's law. Therefore, after the light is reflected by the aspherical surface, it returns along the original optical path and, after passing through the single CGH lens compensator, re-forms a plane wave. Inside the interferometer, it interferes with the reference wave, thereby reflecting the surface information of the aspherical surface being measured.

[0010] In the zero-position compensation detection system model, the single CGH lens compensator takes the planar binary optical surface as the reference, and the phase function of the diffraction surface is the rotationally symmetric binary optical surface 3 or binary optical surface 4. When the phase function of the diffraction surface is the binary optical surface 3, it represents the zero-position splicing double aspherical surface; when the phase function of the diffraction surface is the binary optical surface 4, it represents the zero-position splicing multi-aspherical surface.

[0011] The detection light is incident as a plane wave, and the single CGH lens compensator and the aspherical surface form a zero spherical aberration system, which follows the principle of equal optical path length.

[0012] Based on the principle of equal optical path length, two detection rays are selected. One ray is the ray emitted from the center point of the diffraction surface, and the other ray is the parametric tracing ray, i.e., the off-axis ray. According to the parameters of the zero-position compensation detection system, the optical path length corresponding to the parametric tracing ray is determined, and the expressions of the two optical paths are combined to obtain the trajectory equation of the intersection point Q of the detection ray and the aspherical surface, i.e., the surface shape expression of the custom zero-position spliced ​​aspherical surface.

[0013] The zero-position splicing aspherical surface is a rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard mirror.

[0014] In one embodiment of the present invention, the binary optical surface 3 supports two concentric radial regions, each region having an independent radius, conic section, polynomial aspheric surface, and diffraction phase distribution; when the phase function of the diffraction surface is the binary optical surface 3, only the diffraction phases of the two concentric radial regions are considered, and the surface of the binary optical surface 3 is divided into two regions by two radial coordinates a1 and a2, wherein...

[0015] The phase expression of the internal radial region, extending from the surface center to radial coordinate a1, is as follows: Where N is the number of polynomial coefficients, ρ1 is the normalized radial aperture coordinate, and C 1i It is the coefficient of ρ1 raised to the power of 2i, and M1 is the diffraction order;

[0016] The outer radial region extends from radial coordinate a1 to radial coordinate a2. The phase expression of this outer region is: Phase shift N is the number of polynomial coefficients, ρ2 is the normalized radial aperture coordinate, and C 2i It is the coefficient of ρ² raised to the power of 2i, and M² is the diffraction order;

[0017] δ0 ensures phase continuity at the boundary between the inner and outer regions. Calculation At this time, the value of δ0 is temporarily set to 0, and the phase difference is an integer multiple of the wavelength, that is, δ0 = J2π, where J is any integer; in order to satisfy the continuity of the phase in the boundary region, the value of sinδ0 is calculated and set to 0.

[0018] In one embodiment of the present invention, when the diffraction surface of the single CGH lens compensator faces the incident plane wave, the detection ray is emitted parallel to the interferometer standard mirror. Since the radial coordinates of the binary optical surface 3 are divided into an inner region of 0 to a1 and an outer region of a1 to a2, the parallel wave of the detection ray intersects the inner CGH surface at point A1. After the M1-order diffraction ray is emitted, it intersects the back refraction surface at point B1, and after refraction by the back surface, it intersects the aspherical surface at point Q1. The incident height of this detection ray at the interferometer standard mirror is h1. The parallel wave of the detection ray intersects the outer CGH surface at point A2. After the M2-order diffraction ray is emitted, it intersects the back refraction surface at point B2, and after refraction by the back surface, it intersects the aspherical surface at point Q2. The incident height of this detection ray at the interferometer standard mirror is h2. The variables inside are continuous variables;

[0019] ​When all parameters in the zero-position compensation detection optical path are fixed, the detection light rays are incident at heights h1 and h2, and the optical path lengths from points A1 and A2 to points Q1 and Q2 are the same. At this time, the trajectory function formed by points Q1 and Q2 is the zero-position splicing double aspherical formula characterized by the front surface of the single CGH lens compensator being a binary ray plane 3. The general form of the parameter expression can be expressed as:

[0020]

[0021]

[0022] Among them 0

[0023] According to the principle of equal optical path, when the radial coordinates of the diffraction surface are 0 to a1, two detection rays are selected. One of the rays is the ray emitted from the center point O1 of the diffraction surface of the single CGH lens compensator, and the path is: O1→O2→O; where O2 is the center vertex of the rear surface of the single CGH lens compensator, and O is the center vertex of the aspherical surface; the corresponding optical path is G0=n·d+L;

[0024] The other ray is the parametric tracing ray, i.e., the off-axis ray, with the path: A1→B1→Q1. Based on the parameters of the zero-position compensation detection system, the corresponding optical path of the parametric tracing ray is determined to be... in The distance between points A1 and B1 is... Let M1 be the intersection point of the refracted ray B1Q1 on the optical axis and point B1 be the distance between them. Let M1 be the distance between the intersection point M1 and Q1 of the refracted rays B1Q1 on the optical axis;

[0025] According to the principle of equal optical path length, we have G0 = G1, thus the distance between point M1 and point Q1 on the internal aspherical surface is:

[0026] With point O as the origin, and the front surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 3, the trajectory equation of any point Q1 within the aspherical region of the zero-position spliced ​​double aspherical surface is:

[0027]

[0028] Where u′1 is the angle between the refracted ray B1Q1 from the rear surface of the single CGH lens compensator and the optical axis. The distance from the intersection point M1 of the refracted ray B1Q1 on the rear surface of the single CGH lens compensator and the optical axis to the vertex O2 on the rear surface of the single CGH lens compensator;

[0029] ​Similarly, when the radial coordinates of the diffraction surface are a1 to a2, the distance between point M2 and point Q2 on the outer aspherical surface is... in The distance between points A2 and B2 is... Let M2 be the distance between the intersection point M2 and point B2 of the refracted ray B2Q2 on the optical axis. Let M2 be the distance between the intersection point M2 and Q2 of the refracted ray B2Q2 on the optical axis;

[0030] With point O as the origin, and the front surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 3, the trajectory equation of any point Q2 in the outer aspherical region of the zero-position splicing double aspherical surface is:

[0031]

[0032] Where u′2 is the angle between the refracted ray B2Q2 from the rear surface of the single CGH lens compensator and the optical axis. The distance from the point M2, the intersection of the refracted ray B2Q2 on the rear surface of the single CGH lens compensator and the optical axis, to the vertex O2 on the rear surface of the single CGH lens compensator;

[0033] The trajectory equations of points Q1 and Q2 are the surface shape expressions of the zero-position spliced ​​double aspherical surfaces when the front surface of the single CGH lens compensator in the zero-position compensation detection system is a binary optical surface 3; the zero-position spliced ​​double aspherical surface is a rotationally symmetric structure, and the maximum effective aperture is determined by the actual light transmission aperture of the interferometer's standard spherical mirror.

[0034] In one embodiment of the present invention, when the diffraction surface of the single CGH lens compensator faces the zero-position spliced ​​double aspherical surface, the detection light is emitted parallel to the interferometer standard mirror. Since the radial coordinates of the binary optical surface 3 are divided into an inner region 0~b1 and an outer region b1~b2, and the edge connecting the inner and outer regions is b1, which corresponds to point H1 on the refractive surface; the outgoing light after the detection light passes through the refractive surface intersects the inner region CGH surface at point B1, and the M1 order diffraction light, after exiting, intersects the aspherical surface at point Q1. The incident height of this detection light at the interferometer standard mirror is h1, and it intersects the front refractive surface at point A1; the outgoing light after the detection light passes through the refractive surface intersects the outer CGH surface at point B2, and the M2 order diffraction light, after exiting, intersects the aspherical surface at point Q2. The incident height of this detection light at the interferometer standard mirror is h2, and it intersects the front refractive surface at point A2; there are 0 The variables inside are continuous variables;

[0035] ​When all parameters in the zero-position compensation detection optical path are fixed, the detection light rays are incident at heights h1 and h2, and the optical path lengths from points A1 and A2 to points Q1 and Q2 are the same. At this time, the trajectory function formed by points Q1 and Q2 is the zero-position splicing double aspherical formula characterized by the rear surface of the single CGH lens compensator being a binary ray plane 3. The general form of the parameter expression can be expressed as:

[0036]

[0037]

[0038] Where 0 < ρ B1 <b1,b1<ρ B2 <b2;

[0039] According to the principle of equal optical path, when the radial coordinates of the diffraction surface are 0 to b1, two detection rays are selected. One of the rays is the ray emitted from the center point O1 of the refractive surface of the single CGH lens compensator, and the path is: O1→O2→O. Among them, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the aspherical surface. The corresponding optical path is G0=n·d+L.

[0040] The other ray is the parametric tracing ray, i.e., the off-axis ray, with the path: A1→B1→Q1. Based on the parameters of the zero-position compensation detection system, the corresponding optical path of the parametric tracing ray is determined to be... in The distance between points A1 and B1 is... Let M1 be the intersection point of the refracted ray B1Q1 on the optical axis and point B1 be the distance between them. Let M1 be the distance between the intersection point M1 and Q1 of the refracted rays B1Q1 on the optical axis;

[0041] According to the principle of equal optical path length, we have G0 = G1, thus the distance between point M1 and point Q1 on the internal aspherical surface is:

[0042] With point O as the origin, and the rear surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 3, the trajectory equation of any point Q1 in the aspherical region of the inner focal point of the zero-position splicing double aspherical surface is:

[0043]

[0044] in The angle between the refracted ray B1Q1 from the rear surface of the single CGH lens compensator and the optical axis. The distance from the intersection point M1 of the refracted ray B1Q1 on the rear surface of the single CGH lens compensator and the optical axis to the vertex O2 on the rear surface of the single CGH lens compensator;

[0045] Similarly, when the radial coordinates of the diffraction surface are a1 to a2, the distance between point M2 and point Q2 on the outer aspherical surface is... in The distance between points A2 and B2 is... Let M2 be the distance between the intersection point M2 and point B2 of the refracted ray B2Q2 on the optical axis. Let M2 be the distance between the intersection point M2 and Q2 of the refracted ray B2Q2 on the optical axis;

[0046] With point O as the origin, and the rear surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 3, the trajectory equation of any point Q2 in the aspherical region of the zero-position splicing double aspherical outer focal point is:

[0047]

[0048] in The angle between the refracted ray B2Q2 from the rear surface of the single CGH lens compensator and the optical axis. The distance from the point M2, the intersection of the refracted ray B2Q2 on the rear surface of the single CGH lens compensator and the optical axis, to the vertex O2 on the rear surface of the single CGH lens compensator;

[0049] The trajectory equations of points Q1 and Q2 are the surface shape expressions of the zero-position spliced ​​double aspherical surfaces when the rear surface of the single CGH lens compensator in the zero-position compensation detection system is a binary optical surface 3; the zero-position spliced ​​double aspherical surface is a rotationally symmetric structure, and the maximum effective aperture is determined by the actual light transmission aperture of the interferometer's standard spherical mirror.

[0050] In one embodiment of the present invention, the binary optical surface 4 supports multiple concentric radial regions, each region having an independent radius, conic section, polynomial aspheric surface, and diffraction phase distribution; when the phase function of the diffraction surface is the binary optical surface 4, only the diffraction phases of the multiple concentric radial regions are considered.

[0051] Number of regions a j Between 1 and 60, the number of phase terms is between 0 and 20; the surface of the diffraction plane is divided into regions, the first region extends from the vertex to the radial coordinate a1, the second region extends from a1 to a2, and so on, until the last region is passed, and the radial coordinate of the first region is greater than 0, and each subsequent region must be greater than the previous region.

[0052] All regions have independent diffraction phase distributions, and the phase expression for region j is: Where N is the number of polynomial coefficients, ρ j It is the normalized radial aperture, C ji It is ρ j The coefficient of the 2ith power, Mj is the diffraction order;

[0053] δ0 is the phase shift between the two regions, and the expression is: Calculate φ j When calculating φ, δ0 is temporarily set to 0. When the phase difference at the boundary between the two regions is an integer multiple of the wavelength, that is, δ0 = J2π, where J is any integer, the in-phase condition at the boundary between the two regions is satisfied, and the best imaging performance is obtained; to satisfy the problem of boundary continuity, calculate the sinδ0 of the boundary between every two regions and the sum of their squares, and set the sum of their squares to 0.

[0054] In an embodiment of the present invention, when the diffraction surface of the single CGH lens compensator faces the incident plane wave, the detection light exits parallel from the interferometer standard mirror. Since the radial coordinates on the surface of the binary optical surface 4 are divided into j regions, denoted as a j , the parallel wave of the detection light intersects the CGH surface at point A j point, after the light of the M j th diffraction order exits, it intersects the rear refraction surface at point B j point, and after being refracted by the rear surface, it intersects the aspheric surface at point Q j point; set the incident height of the light on the interferometer standard mirror as h j , due to the partition of the binary optical surface 4, the regions on the refraction surface are corresponding to the regions of the diffraction surface for sub-regions, and the incident heights are respectively expressed as h j , where 0 < h1 < h2... < h j < h; take h j as the parameter variable of the aspheric surface shape, h j is a continuous variable within the aperture range of the interferometer standard mirror ;

[0055] When the parameters in the null compensation detection optical path are fixed, the detection light enters with a height of h j , and the optical path from point A j to point Q j is the same; at this time, the trajectory function formed by point Q j is the null stitching multi-aspheric formula represented by the front surface of the single CGH lens compensator being the binary light surface 4, and the general form of the parameter expression can be expressed as:

[0056]

[0057] where 0 < h1 < a1 < h2 < a2 <... < h j < a j ;

[0058] According to the principle of equal optical path, when the radial coordinate of the diffraction surface is a j-1 ~a jAt that time, two detection rays are selected, one of which is the ray emitted from the center point O1 of the diffraction surface of the single CGH lens compensator, with the path: O1→O2→O; where point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the aspherical surface; the corresponding optical path is G0=n·d+L;

[0059] The other ray is a parametric tracing ray, i.e., an off-axis ray, with the path: A j →B j →Q j Based on the parameters of the zero-position compensation detection system, the optical path length corresponding to the parameter tracing ray is determined to be... in For A j Point and B j Distance between points For refracted ray B j Q j The intersection point M on the optical axis j Point and B j Distance between points For refracted ray B j Q j The intersection point M on the optical axis j Point and Q j Distance between points;

[0060] According to the principle of equal optical path length, G0 = G1, thus obtaining M. j Point and Q on the inner aspherical surface j The distance between the points is

[0061] With point O as the origin, and the front surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 4, any point Q within the aspherical region of the zero-position splicing multi-aspherical surface is considered. j The trajectory equation, that is, the surface shape expression of the zero-position spliced ​​multi-aspherical surface, is:

[0062]

[0063] Where u′ j B is the refracted light ray from the rear surface of the single CGH lens compensator. j Q j Angle with optical axis, B is the refracted light ray from the rear surface of the single CGH lens compensator. j Q j Intersection point M with the optical axis j The distance from the point to the vertex O2 of the rear surface of the single CGH lens compensator; the zero-position splicing aspherical surface is a rotationally symmetric structure, and the maximum effective aperture is determined by the actual light transmission aperture of the interferometer's standard spherical mirror.

[0064] In one embodiment of the present invention, when the diffraction surface of the single CGH lens compensator faces the zero-position stitching multi-asphere, the detection light is parallelly emitted from the interferometer standard mirror and intersects the front refraction surface at point A. j Since the radial coordinates of the surface of the binary optical surface 4 are divided into j regions, denoted as b j , the corresponding points on the outgoing light rays of its refraction surface are H j points. The outgoing light ray through the refraction surface intersects the CGH surface at point B j point, M j After the light ray of the diffraction order is emitted, it intersects the aspheric surface at point Q j point; set the incident height of the light ray on the interferometer standard mirror as h j . Due to the partitioning of the binary optical surface 4, the regions on the refraction surface are correspondingly divided into regions corresponding to the regions of the diffraction surface, and the incident heights are respectively represented as h j , where 0 < h1 < h2 … < h j < h; take h j as the parameter variable of the aspheric surface, h j is a continuous variable within the aperture range of the interferometer standard mirror ;

[0065] When the parameters in the zero-position compensation detection optical path are fixed, the detection light ray enters at a height of h j , and the optical path from point A j to point Q j is the same; at this time, the trajectory function formed by point Q j is the zero-position stitching multi-asphere formula characterized by the rear surface of the single CGH lens compensator being the binary light surface 4, and the general form of the parameter expression can be represented as:

[0066]

[0067] where

[0068] According to the principle of equal optical path, when the radial coordinate of the diffraction surface is b j-1 to b j , two detection light rays are selected. One light ray is the outgoing light ray from the center point O1 of the refraction surface of the single CGH lens compensator, and the path is: O1→O2→O; where, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the aspheric surface; the corresponding optical path is G0 = n·d + L;

[0069] The other light ray is a parameter tracing light ray, that is, an off-axis light ray, and the path is: A j →B j →Q j , and according to the parameter variables of the zero-position compensation detection system, the corresponding optical path of the parameter tracing light ray is determined to be in For A j Point and B j Distance between points For refracted ray B j q j The intersection point M on the optical axis j Point and B j Distance between points For refracted ray B j Q j The intersection point M on the optical axis j Point and Q j Distance between points;

[0070] According to the principle of equal optical path length, G0 = G1, thus obtaining M. j Point and Q on the inner aspherical surface j The distance between the points is

[0071] With point O as the origin, and the rear surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 4, any point Q within the aspherical region of the zero-position splicing multi-aspherical surface is considered. j The trajectory equation, that is, the surface shape expression of the zero-position spliced ​​multi-aspherical surface, is:

[0072]

[0073] in B is the refracted light ray from the rear surface of the single CGH lens compensator. j Q j Angle with optical axis, B is the refracted light ray from the rear surface of the single CGH lens compensator. j Q j Intersection point M with the optical axis j The distance from the point to the vertex O2 of the rear surface of the single CGH lens compensator; the zero-position splicing aspherical surface is a rotationally symmetric structure, and the maximum effective aperture is determined by the actual light transmission aperture of the interferometer's standard spherical mirror.

[0074] The technical solution of the present invention has the following advantages compared with the prior art:

[0075] This invention discloses a method for characterizing stitched aspherical surfaces based on a CGH lens null-compensation detection optical path. Guided by the detection method, and based on the principles of null-compensation detection and diffraction optics, it indirectly characterizes the surface shape of the stitched aspherical surface using various parameters required by a null-compensation detection system with an interferometer incident wavefront of a plane wave, a single CGH lens as the compensator, and a diffraction surface of either binary optical surface 3 or binary optical surface 4. A custom null-compensation stitched aspherical surface is proposed. Compared to general aspherical surfaces, this null-compensation stitched aspherical surface can increase the field of view and improve structural compactness, with each annular aspherical surface undertaking different imaging relationships.

[0076] The proposed method for characterizing spliced ​​aspherical surfaces based on the zero-position compensation detection optical path of CGH lenses allows for the determination of the measurement scheme during the design phase through the mathematical description of the spliced ​​aspherical surfaces. This effectively improves the feasibility of the zero-position compensation method, enhances the accuracy of surface shape detection and the accuracy of co-phase detection at the splicing points of the aspherical surfaces, avoids stray light effects and projection distortion encountered in CGH detection, reduces the difficulty of detecting the surface shape of the spliced ​​aspherical surfaces, and realizes the function of designing and detecting zero-position spliced ​​aspherical surfaces. Attached Figure Description

[0077] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein...

[0078] Figure 1 This invention provides a meridional cross-section optical path diagram of the zero-position compensation detection system when the incident wavefront of the interferometer is a plane wave and the front surface of the single CGH lens compensator is a binary optical surface 3.

[0079] Figure 2 This invention provides a meridional cross-section optical path diagram of the zero-position compensation detection system when the incident wavefront of the interferometer is a plane wave and the rear surface of the single CGH lens compensator is a binary optical surface 3.

[0080] Figure 3 This invention provides a meridional cross-section optical path diagram of the zero-position compensation detection system when the incident wavefront of the interferometer is a plane wave and the front surface of the single CGH lens compensator is a binary optical surface 4.

[0081] Figure 4 The present invention provides a meridional cross-sectional optical path diagram of a zero-position compensation detection system when the incident wavefront of the interferometer is a plane wave and the rear surface of the single CGH lens compensator is a binary optical surface 4. Detailed Implementation

[0082] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0083] This invention, guided by detection methods, provides a spliced ​​aspherical characterization method based on a plane wave and a single CGH lens zero-position compensation detection optical path with a binary optical surface 3 or a binary optical surface 4 as the diffraction surface. It also defines a type of aspherical surface, which is called zero-position spliced ​​aspherical surface.

[0084] In a zero-position compensation detection system where the incident wave in the interferometer is a plane wave and the compensator is a single CGH lens, the aperture of the interferometer standard mirror is set to D, the wavelength of the detection light is λ, the phase of the diffraction surface of the single CGH lens compensator is φ, the diffraction order is M, the radius of curvature of the refractive surface is r, the center thickness of the single CGH lens compensator is d, the refractive index of the material of the single CGH lens compensator is n, and the distance between the single CGH lens compensator and the aspherical surface is L.

[0085] Based on the aforementioned characterization parameters of the custom-defined zero-position spliced ​​aspherical surface, a zero-position compensation detection optical path is constructed. The detection light from the interferometer's standard mirror is incident parallel to the surface. Different heights and diffraction orders correspond to different points on the aspherical surface, and different diffraction plane directions correspond to different points on the zero-position spliced ​​aspherical surface. This optical path follows the principle of equal optical path, the principle of diffraction, and Snell's law. Therefore, after the light is reflected by the aspherical surface, it returns along the original optical path and, after passing through a single CGH lens compensator, re-forms a plane wave. Inside the interferometer, it interferes with the reference wave, thereby reflecting the surface information of the aspherical surface being measured.

[0086] In the zero-position compensation detection system model, the single CGH lens compensator takes the planar binary optical surface as the reference, and the phase function of the diffraction surface is either the rotationally symmetric binary optical surface 3 or the binary optical surface 4. When the phase function of the diffraction surface is the binary optical surface 3, it represents the zero-position splicing double aspherical surface. When the phase function of the diffraction surface is the binary optical surface 4, it represents the zero-position splicing multi-aspherical surface.

[0087] When the phase function of the diffraction surface is the binary optical surface 3 in the rotationally symmetric formula, the derivation process of the surface shape characterization of the zero-position spliced ​​double aspherical surface is as follows.

[0088] The binary optical surface 3 supports two concentric radial regions, each with an independent radius, conic section, polynomial aspheric surface, and diffraction phase distribution. When the phase function of the diffraction surface is the binary optical surface 3, only the diffraction phases of the two concentric radial regions are considered. The surface of the binary optical surface 3 is divided into two regions by two radial coordinates a1 and a2, wherein...

[0089] The phase expression of the internal radial region, extending from the surface center to radial coordinate a1, is as follows: Where N is the number of polynomial coefficients, ρ1 is the normalized radial aperture coordinate, and C 1i ρ1 raised to the power of 2i is the coefficient, and M1 is the diffraction order.

[0090] The outer radial region extends from radial coordinate a1 to radial coordinate a2. The phase expression of this outer region is: Phase shift N is the number of polynomial coefficients, ρ2 is the normalized radial aperture coordinate, and C 2i It is the coefficient of ρ² raised to the power of 2i, and M² is the diffraction order.

[0091] δ0 ensures phase continuity at the boundary between the inner and outer regions. Calculation At this time, the value of δ0 is temporarily set to 0, and the phase difference is an integer multiple of the wavelength, that is, δ0 = J2π, where J is any integer; in order to satisfy the continuity of the phase in the boundary region, the value of sinδ0 is calculated and set to 0.

[0092] The binary optical surface 3 is not limited to two steps, but can be made into 2n steps, and the diffraction efficiency is related to the number of steps; the more steps, the higher the efficiency. For example, a binary optical surface 2 with two steps has a first-order diffraction efficiency of 40.5%, while a binary optical surface 2 with four steps has a first-order diffraction efficiency of 81.1%. However, as the number of steps increases, the manufacturing process becomes more complex, so the number of steps in the design can be determined according to specific requirements.

[0093] The following section derives and calculates the aspherical surface shape for two cases: one where the diffraction surface of the single CGH lens compensator faces the incident plane wave, and the other where the diffraction surface of the single CGH lens compensator faces the zero-position spliced ​​aspherical surface.

[0094] Reference Figure 1 As shown, when the diffraction surface of the single CGH lens compensator faces the incident plane wave, the detection ray is emitted parallel to the interferometer standard mirror. Since the radial coordinates of the binary optical surface 3 are divided into an inner region of 0 to a1 and an outer region of a1 to a2, the parallel wave of the detection ray intersects the inner CGH surface at point A1. After the M1-order diffraction ray is emitted, it intersects the back refraction surface at point B1, and after refraction by the back surface, it intersects the aspherical surface at point Q1. The incident height of this detection ray at the interferometer standard mirror is h1. The parallel wave of the detection ray intersects the outer CGH surface at point A2. After the M2-order diffraction ray is emitted, it intersects the back refraction surface at point B2, and after refraction by the back surface, it intersects the aspherical surface at point Q2. The incident height of this detection ray at the interferometer standard mirror is h2. The variables inside are continuous variables.

[0095] ​When all parameters in the zero-position compensation detection optical path are fixed, the detection light rays are incident at heights h1 and h2, and the optical path lengths from points A1 and A2 to points Q1 and Q2 are the same. At this time, the trajectory function formed by points Q1 and Q2 is the zero-position splicing double aspherical formula characterized by the front surface of the single CGH lens compensator being a binary ray plane 3. The general form of the parameter expression can be expressed as:

[0096]

[0097]

[0098] Among them 0

[0099] According to the principle of equal optical path, when the radial coordinates of the diffraction surface are 0 to a1, two detection rays are selected. One of the rays is the ray emitted from the center point O1 of the diffraction surface of the single CGH lens compensator, and the path is: O1→O2→O. Among them, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the aspherical surface. The corresponding optical path is G0=n·d+L.

[0100] The other ray is the parametric tracing ray, i.e., the off-axis ray, with the path: A1→B1→Q1. Based on the parameters of the zero-position compensation detection system, the optical path of the parametric tracing ray is determined to be G1=n· in The distance between points A1 and B1 is... Let M1 be the intersection point of the refracted ray B1Q1 on the optical axis and point B1 be the distance between them. Let M1 be the distance between the intersection point M1 and Q1 of the refracted ray B1Q1 on the optical axis.

[0101] According to the principle of equal optical path length, we have G0 = G1, thus the distance between point M1 and point Q1 on the internal aspherical surface is:

[0102] With point O as the origin, and the front surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 3, the trajectory equation of any point Q1 within the aspherical region of the zero-position spliced ​​double aspherical surface is:

[0103]

[0104] Where u′1 is the angle between the refracted ray B1Q1 from the rear surface of the single CGH lens compensator and the optical axis. The distance from the intersection point M1 of the refracted ray B1Q1 on the rear surface of the single CGH lens compensator and the optical axis to the vertex O2 on the rear surface of the single CGH lens compensator.

[0105] Similarly, when the radial coordinates of the diffraction surface are a1 to a2, the distance between point M2 and point Q2 on the outer aspherical surface is...​ in The distance between points A2 and B2 is... Let M2 be the distance between the intersection point M2 and point B2 of the refracted ray B2Q2 on the optical axis. Let M2 be the distance between the intersection point M2 and Q2 of the refracted ray B2Q2 on the optical axis.

[0106] With point O as the origin, and the front surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 3, the trajectory equation of any point Q2 in the outer aspherical region of the zero-position splicing double aspherical surface is:

[0107]

[0108] Where u′2 is the angle between the refracted ray B2Q2 from the rear surface of the single CGH lens compensator and the optical axis. The distance from the point M2, where the refracted ray B2Q2 intersects the optical axis at the rear surface of the single CGH lens compensator, to the vertex O2 of the rear surface of the single CGH lens compensator.

[0109] The trajectory equations of points Q1 and Q2 are the surface shape expressions of the zero-position spliced ​​double aspherical surfaces when the front surface of the single CGH lens compensator in the zero-position compensation detection system is a binary optical surface 3; the zero-position spliced ​​double aspherical surface is a rotationally symmetric structure, and the maximum effective aperture is determined by the actual light transmission aperture of the interferometer's standard spherical mirror.

[0110] Reference Figure 2 As shown, when the diffraction surface of the single CGH lens compensator faces the zero-position spliced ​​double aspherical surface, the detection light is emitted parallel to the interferometer standard mirror. Since the radial coordinates of the binary optical surface 3 are divided into an internal region 0~b1 and an external region b1~b2, and the edge connecting the internal and external regions is b1, which corresponds to point H1 on the refractive surface; the outgoing light after the detection light passes through the refractive surface intersects the internal region CGH surface at point B1. After the M1 order diffraction light is emitted, it intersects the aspherical surface at point Q1. The incident height of this detection light at the interferometer standard mirror is h1, and it intersects the front refractive surface at point A1; the outgoing light after the detection light passes through the refractive surface intersects the external CGH surface at point B2. After the M2 order diffraction light is emitted, it intersects the aspherical surface at point Q2. The incident height of this detection light at the interferometer standard mirror is h2, and it intersects the front refractive surface at point A2; there are 0 The variables inside are continuous variables.

[0111] ​When all parameters in the zero-position compensation detection optical path are fixed, the detection light rays are incident at heights h1 and h2, and the optical path lengths from points A1 and A2 to points Q1 and Q2 are the same. At this time, the trajectory function formed by points Q1 and Q2 is the zero-position splicing double aspherical formula characterized by the rear surface of the single CGH lens compensator being a binary ray plane 3. The general form of the parameter expression can be expressed as:

[0112]

[0113]

[0114] Where 0 < ρ B1 <b1,b1<ρ B2 <b2。

[0115] According to the principle of equal optical path, when the radial coordinates of the diffraction surface are 0 to b1, two detection rays are selected. One of the rays is the ray emitted from the center point O1 of the refractive surface of the single CGH lens compensator, and the path is: O1→O2→O. Among them, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the aspherical surface. The corresponding optical path is G0=n·d+L.

[0116] The other ray is the parametric tracing ray, i.e., the off-axis ray, with the path: A1→B1→Q1. Based on the parameters of the zero-position compensation detection system, the corresponding optical path of the parametric tracing ray is determined to be... in The distance between points A1 and B1 is... Let M1 be the intersection point of the refracted ray B1Q1 on the optical axis and point B1 be the distance between them. Let M1 be the distance between the intersection point M1 and Q1 of the refracted ray B1Q1 on the optical axis.

[0117] According to the principle of equal optical path length, we have G0 = G1, thus the distance between point M1 and point Q1 on the internal aspherical surface is:

[0118] With point O as the origin, and the rear surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 3, the trajectory equation of any point Q1 in the aspherical region of the inner focal point of the zero-position splicing double aspherical surface is:

[0119]

[0120] in The angle between the refracted ray B1Q1 from the rear surface of the single CGH lens compensator and the optical axis. The distance from the intersection point M1 of the refracted ray B1Q1 on the rear surface of the single CGH lens compensator and the optical axis to the vertex O2 on the rear surface of the single CGH lens compensator.

[0121] Similarly, when the radial coordinates of the diffraction surface are a1 to a2, the distance between point M2 and point Q2 on the outer aspherical surface is... in The distance between points A2 and B2 is... Let M2 be the distance between the intersection point M2 and point B2 of the refracted ray B2Q2 on the optical axis. Let M2 be the distance between the intersection point M2 and Q2 of the refracted ray B2Q2 on the optical axis.

[0122] With point O as the origin, and the rear surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 3, the trajectory equation of any point Q2 in the aspherical region of the zero-position splicing double aspherical outer focal point is:

[0123]

[0124] in The angle between the refracted ray B2Q2 from the rear surface of the single CGH lens compensator and the optical axis. The distance from the point M2, where the refracted ray B2Q2 intersects the optical axis at the rear surface of the single CGH lens compensator, to the vertex O2 of the rear surface of the single CGH lens compensator.

[0125] The trajectory equations of points Q1 and Q2 are the surface shape expressions of the zero-position spliced ​​double aspherical surfaces when the rear surface of the single CGH lens compensator in the zero-position compensation detection system is a binary optical surface 3; the zero-position spliced ​​double aspherical surface is a rotationally symmetric structure, and the maximum effective aperture is determined by the actual light transmission aperture of the interferometer's standard spherical mirror.

[0126] When the phase function of the diffraction surface is the binary optical surface 3 in the rotationally symmetric formula, the derivation process of the surface shape characterization of the zero-position spliced ​​double aspherical surface is as follows.

[0127] The binary optical surface 4 supports multiple concentric radial regions, each region having an independent radius, conic section, polynomial aspheric surface, and diffraction phase distribution; when the phase function of the diffraction surface is the binary optical surface 4, only the diffraction phases of multiple concentric radial regions are considered.

[0128] Number of regions a j Between 1 and 60, the number of phase terms is between 0 and 20; the diffraction surface is divided into regions, the first region extends from the vertex to the radial coordinate a1, the second region extends from a1 to a2, and so on, until the last region is passed, and the radial coordinate of the first region is greater than 0, and each subsequent region must be greater than the previous region.

[0129] All regions have independent diffraction phase distributions, and the phase expression for region j is: Where N is the number of polynomial coefficients, ρj is the normalized radial aperture, C ji is ρ j the coefficient of the 2i-th power of, M j is the diffraction order.

[0130] δ0 is the phase shift between the two regions, and the expression is: Calculate φ j When calculating φ, δ0 is temporarily set to 0. When the phase difference at the boundary between the two regions is an integer multiple of the wavelength, that is, δ0 = J2π, where J is any integer, the condition of the same phase at the boundary between the two regions is satisfied, and the best imaging performance is obtained; to satisfy the problem of boundary continuity, calculate the sinδ0 of the boundary between every two regions and the sum of its squares, and set the sum of its squares to 0.

[0131] The aspheric surface shape is derived and calculated in the following two cases: the diffraction surface of the single CGH lens compensator faces the incident plane wave and the diffraction surface of the single CGH lens compensator faces the null stitching aspheric surface.

[0132] Refer to Figure 3 As shown, when the diffraction surface of the single CGH lens compensator faces the incident plane wave, the detection light is parallelly emitted from the interferometer standard mirror. Since the radial coordinates on the surface of the binary optical surface 4 are divided into j regions, denoted as a j , the parallel wave of the detection light intersects the CGH surface at point A j , and after the light of the M j -order diffraction order is emitted, it intersects the rear refracting surface at point B j , and after being refracted by the rear surface, it intersects the aspheric surface at point Q j ; set the incident height of the light on the interferometer standard mirror as h j , due to the partition of the binary optical surface 4, the regions on the refracting surface are correspondingly divided into regions corresponding to the regions of the diffraction surface, and the incident heights are respectively expressed as h j , where 0 < h1 < h2… < h j < h; take h j as the parameter variable of the aspheric surface shape, and h j is a continuous variable within the interferometer standard mirror aperture range .

[0133] When the parameters in the null compensation detection optical path are fixed, the detection light is incident with a height of h j , and the optical path from point A j to point Q j is the same; at this time, the trajectory function formed by point Q j is the null stitching multi-aspheric formula characterized by the front surface of the single CGH lens compensator being the binary light surface 4, and the general form of the parameter expression can be expressed as:

[0134]

[0135] Among them 0 j j .

[0136] According to the principle of equal optical path length, when the radial coordinate of the diffraction plane is a j-1 ~a j At that time, two detection rays are selected, one of which is the ray emitted from the center point O1 of the diffraction surface of the single CGH lens compensator, with the path: O1→O2→O; where point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the aspherical surface; the corresponding optical path is G0=n·d+L.

[0137] The other ray is a parametric tracing ray, i.e., an off-axis ray, with the path: A j →B j →Q j Based on the parameters of the zero-position compensation detection system, the optical path length corresponding to the parameter tracing ray is determined to be... in For A j Point and B j Distance between points For refracted ray B j Q j The intersection point M on the optical axis j Point and B j Distance between points For refracted ray B j Q j The intersection point M on the optical axis j Point and Q j Distance between points.

[0138] According to the principle of equal optical path length, G0 = G1, thus obtaining M. j Point and Q on the inner aspherical surface j The distance between the points is

[0139] With point O as the origin, and the front surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 4, any point Q within the aspherical region of the zero-position splicing multi-aspherical surface is considered. j The trajectory equation, that is, the surface shape expression of the zero-position spliced ​​multi-aspherical surface, is:

[0140]

[0141] Where u′ j B is the refracted light ray from the rear surface of the single CGH lens compensator. j Q j Angle with optical axis, ​​For the refracted light ray B on the rear surface of the single CGH lens compensator j Q j The intersection point M with the optical axis j The distance from the point to the vertex O2 of the rear surface of the single CGH lens compensator; The zero-position stitching multi-asphere is a rotationally symmetric structure, and the maximum effective aperture is determined by the actual light passing aperture of the interferometer standard spherical mirror

[0142] Refer to Figure 4 As shown, when the diffraction surface of the single CGH lens compensator faces the zero-position stitching multi-asphere, the detection light ray is parallelly emitted from the interferometer standard mirror and intersects the front refraction surface at point A j Point, since the radial coordinates on the surface of the binary optical surface 4 are divided into j regions, denoted as b j And the corresponding points on the outgoing light rays of its refraction surface are H j Points, the outgoing light ray through the refraction surface intersects the CGH surface at point B j Point, after the light ray of the M j th diffraction order is emitted, it intersects the aspheric surface at point Q j Point; Set the incident height of the light ray on the interferometer standard mirror as h j Due to the partition of the binary optical surface 4, the regions on the refraction surface are correspondingly divided into regions on the diffraction surface, and the incident heights are respectively expressed as h j Where 0 < h1 < h2… < h j < h; Take h j As the parameter variable of the aspheric surface, h j Is a continuous variable within the interferometer standard mirror aperture range

[0143] When the parameters in the zero-position compensation detection optical path are fixed, the detection light ray enters at a height of h j From point A j To point Q j The optical path of the point is the same; At this time, the trajectory function formed by point Q j Is the zero-position stitching multi-asphere formula characterized by the rear surface of the single CGH lens compensator being the binary light surface 4, and the general form of the parameter expression can be expressed as:

[0144]

[0145] Where

[0146] According to the principle of equal optical path, when the radial coordinate of the diffraction surface is b j-1 ~b j ​At that time, two detection rays are selected. One ray is the ray emitted from the center point O1 of the refractive surface of the single CGH lens compensator. The path is: O1→O2→O. Among them, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the aspherical surface. The corresponding optical path is G0=n·d+L.

[0147] The other ray is a parametric tracing ray, i.e., an off-axis ray, with the path: A j →B j →Q j Based on the parameters of the zero-position compensation detection system, the optical path length corresponding to the parameter tracing ray is determined to be... in For A j Point and B j Distance between points For refracted ray B j Q j The intersection point M on the optical axis j Point and B j Distance between points For refracted ray B j Q j The intersection point M on the optical axis j Point and Q j Distance between points.

[0148] According to the principle of equal optical path length, G0 = G1, thus obtaining M. j Point and Q on the inner aspherical surface j The distance between the points is

[0149] With point O as the origin, and the rear surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 4, any point Q within the aspherical region of the zero-position splicing multi-aspherical surface is considered. j The trajectory equation, that is, the surface shape expression of the zero-position spliced ​​multi-aspherical surface, is:

[0150]

[0151] in B is the refracted light ray from the rear surface of the single CGH lens compensator. j Q j Angle with optical axis, B is the refracted light ray from the rear surface of the single CGH lens compensator. j Q j Intersection point M with the optical axis j The distance from the point to the vertex O2 of the rear surface of the single CGH lens compensator; the zero-position splicing aspherical surface is a rotationally symmetric structure, and the maximum effective aperture is determined by the actual light transmission aperture of the interferometer's standard spherical mirror.

[0152] Compared to ordinary aspherical surfaces, the zero-position splicing aspherical surface can increase the field of view and improve the structural compactness, and each annular aspherical surface undertakes different imaging relationships.

[0153] The above-mentioned method for characterizing spliced ​​aspherical surfaces based on the zero-position compensation detection optical path of a CGH lens is guided by the detection method. Based on the zero-position compensation detection principle and the principle of diffraction optics, it indirectly characterizes the surface shape of the spliced ​​aspherical surface by utilizing the parameters required for a zero-position compensation detection system with an interferometer incident wavefront of a plane wave, a single CGH lens as the compensator, and a diffraction surface of a binary optical surface 3 or a binary optical surface 4. Through the mathematical description of the spliced ​​aspherical surface, its measurement scheme can be determined in the design stage, which can effectively improve the feasibility of the zero-position compensation method, improve the accuracy of surface shape detection and the accuracy of co-phase at the splicing point of the spliced ​​aspherical surface, avoid the stray light influence and projection distortion faced by CGH detection, reduce the detection difficulty of the spliced ​​aspherical surface shape, and realize the function of zero-position spliced ​​aspherical surface design for detection.

[0154] The aforementioned method for characterizing spliced ​​aspherical surfaces based on the zero-position compensation detection optical path of a CGH lens can improve production efficiency. By meeting detection requirements, it can reduce the time spent on repeated trials and adjustments, avoid ineffective designs, reduce production difficulty, and thus improve production efficiency.

[0155] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0156] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations 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, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0157] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0158] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0159] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for characterizing spliced ​​aspherical surfaces based on a CGH lens zero-position compensation detection optical path, characterized in that, include: In a zero-position compensation detection system where the incident wavefront of the interferometer is set to a plane wave and the compensator is a single CGH lens compensator, the aperture of the standard mirror of the interferometer is [missing information]. The detection wavelength is The phase of the diffraction surface of the single CGH lens compensator is Diffraction order is The radius of curvature of the refractive surface is The center thickness of the single CGH lens compensator is The refractive index of the material of the single CGH lens compensator is The distance between the single CGH lens compensator and the aspherical surface is ; Based on the aforementioned characterization parameters of the custom-defined zero-position spliced ​​aspherical surface, a zero-position compensation detection system is constructed. The detection light rays of the interferometer's standard mirror are incident parallel to each other. Different heights and different diffraction orders correspond to different points on the aspherical surface, and different diffraction plane directions correspond to different points on the zero-position spliced ​​aspherical surface. This optical path follows the principle of equal optical path, the principle of diffraction, and Snell's law. Therefore, after the light rays are reflected by the aspherical surface, they return along the original optical path and are re-formed into a plane wave after passing through a single CGH lens compensator. Inside the interferometer, the plane wave interferes with the reference wave, thereby reflecting the surface information of the aspherical surface being measured. In the zero-position compensation detection system, the single CGH lens compensator takes the planar binary optical surface as the reference, and the phase function of the diffraction surface is either binary optical surface 3 or binary optical surface 4 in the rotational symmetry formula. When the phase function of the diffraction surface is binary optical surface 3, it represents zero-position splicing double aspherical surface; when the phase function of the diffraction surface is binary optical surface 4, it represents zero-position splicing multi-aspherical surface. The detection light is incident as a plane wave, and the single CGH lens compensator and the aspherical surface form a zero spherical aberration system, which follows the principle of equal optical path length. Based on the principle of equal optical path length, two detection rays are selected. One ray is the ray emitted from the center point of the diffraction surface, and the other ray is the parametric tracing ray, i.e., the off-axis ray. According to the parameters of the zero-position compensation detection system, the optical path length corresponding to the parametric tracing ray is determined. Then, by combining the expressions for the two optical path lengths, the intersection point between the detection ray and the aspherical surface is obtained. The trajectory equation of a point, i.e., the surface shape expression of a custom zero-position spliced ​​aspherical surface; The zero-position splicing aspherical surface is a rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard mirror. The binary optical surface 3 supports two concentric radial regions, each with an independent radius, conic section, polynomial aspheric surface, and diffraction phase distribution. When the phase function of the diffraction surface is the binary optical surface 3, only the diffraction phases of the two concentric radial regions are considered. The surface of the binary optical surface 3 is defined by two radial coordinates. and Divided into two areas, among which ; The internal radial region extends from the surface center to the radial coordinate. The phase expression for this internal region is: ,in The number of polynomial coefficients. These are normalized radial aperture coordinates. yes of The coefficient of a power. It is the diffraction order; External radial region from radial coordinates To radial coordinates The phase expression for this outer region is: Phase shift , The number of polynomial coefficients. These are normalized radial aperture coordinates. yes of The coefficient of a power. It is the diffraction order; To ensure phase continuity at the boundary between the inner and outer regions, calculate... hour, The value is temporarily set to 0, and the phase difference is an integer multiple of the wavelength, i.e. ,in Let be any integer; to satisfy the continuity of the phase in the boundary region, calculate... The value is set to 0.

2. The method for characterizing spliced ​​aspherical surfaces based on a CGH lens null-compensation detection optical path according to claim 1, characterized in that, When the diffraction surface of the single CGH lens compensator faces the incident plane wave, the detection light is emitted parallel to the standard mirror of the interferometer. Since the radial coordinates of the binary optical surface 3 are divided into internal... and external The region where the parallel wave of the detected light intersects with the internal CGH surface. point, After the first diffraction order light rays are emitted, they intersect with the back refraction surface. The point, after refraction by the back surface, intersects the aspherical surface at... The point is where the incident height of the detection ray at the standard mirror of the interferometer is... The parallel wave of the detection light intersects with the external CGH surface. point, After the first diffraction order light rays are emitted, they intersect with the back refraction surface. The point, after refraction by the back surface, intersects the aspherical surface at... The point is where the incident height of the detection ray at the standard mirror of the interferometer is... ;have ,Will and As a parameter of the aspherical surface shape, Within the range of the standard mirror aperture of the interferometer [- , The variable inside is a continuous variable. Within the range of the standard mirror aperture of the interferometer The variables inside are continuous variables; When all parameters in the zero-position compensation detection system are fixed, the height of the detection light is as follows: , Incident, by , Click , The optical path lengths at all points are the same; at this time , The trajectory function formed by the points is the zero-position splicing double aspherical formula characterized by the front surface of a single CGH lens compensator being a binary optical surface 3. The general form of the parametric expression can be expressed as: ； ； in , ; According to the principle of equal optical path length, when the radial coordinate of the diffraction plane is... At that time, two detection rays are selected, one of which is the center point of the diffraction surface of the single CGH lens compensator. The path of the emitted ray is: ;in, The point is the center vertex of the rear surface of the single CGH lens compensator. The point is the center vertex of the aspherical surface; the corresponding optical path is ; The other ray is a parametric tracing ray, i.e., an off-axis ray, with the following path: Based on the parameters of the zero-position compensation detection system, the optical path length corresponding to the parameter tracing ray is determined to be... ,in for Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points; According to the principle of equal optical path length, we have ,get Points and the interior aspherical surface The distance between the points is ; by Point 3 is the origin of the coordinate system. When the front surface of the single CGH lens compensator in the zero-position compensation detection system is a binary optical surface 3, any point in the aspherical region inside the zero-position splicing double aspherical surface is considered. The trajectory equation is: ； in For the refracted light rays at the rear surface of a single CGH lens compensator Angle with optical axis, For the refracted light rays at the rear surface of a single CGH lens compensator Intersection with optical axis Point to the vertex of the surface of the single CGH lens compensator The distance; Similarly, when the radial coordinates of the diffraction plane are... hour, Point and external aspherical surface The distance between the points is ,in for Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points; by Point 3 is the origin of the coordinate system. When the front surface of the single CGH lens compensator in the zero-position compensation detection system is a binary optical surface 3, any point in the outer aspherical region of the zero-position splicing double aspherical surface is considered. The trajectory equation is: ； in For the refracted light rays at the rear surface of a single CGH lens compensator Angle with optical axis, For the refracted light rays at the rear surface of a single CGH lens compensator Intersection with optical axis Point to the vertex of the surface of the single CGH lens compensator The distance; The Point and The trajectory equation of the point is the surface shape expression of the zero-position splicing double aspherical surface when the front surface of the single CGH lens compensator in the zero-position compensation detection system is a binary optical surface 3; the zero-position splicing double aspherical surface is a rotationally symmetric structure, and the maximum effective aperture is determined by the actual light transmission aperture of the interferometer standard mirror.

3. The method for characterizing spliced ​​aspherical surfaces based on a CGH lens null-compensation detection optical path according to claim 1, characterized in that... When the diffraction surface of the single CGH lens compensator faces the zero-position spliced ​​double aspherical surface, the detection light is emitted parallel to the interferometer standard mirror. Since the radial coordinates of the binary optical surface 3 are divided into internal... and external The area, and the edges connecting the interior and exterior. In the reflection of the face should be Point; the emitted ray after the detection light passes through the refracting surface intersects with the surface of the internal region CGH at... point, After the first diffraction order light rays are emitted, they intersect the aspherical surface at... The point is where the incident height of the detection ray at the standard mirror of the interferometer is... Intersecting with the front refraction surface Point; the emitted ray after the detection light passes through the refracting surface intersects with the external CGH surface. point, After the first diffraction order light rays are emitted, they intersect the aspherical surface at... The point is where the incident height of the detection ray at the standard mirror of the interferometer is... Intersecting with the front refraction surface Point; have ,Will and As a parameter of the aspherical surface shape, Within the range of the standard mirror aperture of the interferometer [- , The variable inside is a continuous variable. Within the range of the standard mirror aperture of the interferometer The variables inside are continuous variables; When all parameters in the zero-position compensation detection system are fixed, the height of the detection light is as follows: , Incident, by , Click , The optical path lengths at all points are the same; at this time , The trajectory function formed by the points is the zero-position splicing double aspherical formula characterized when the rear surface of the single CGH lens compensator is a binary optical surface 3. The general form of the parametric expression can be expressed as: ； ； in , ; According to the principle of equal optical path length, when the radial coordinate of the diffraction plane is... At that time, two detection rays are selected, one of which is the center point of the refractive surface of the single CGH lens compensator. The path of the emitted ray is: ;in, The point is the center vertex of the rear surface of the single CGH lens compensator. The point is the center vertex of the aspherical surface; the corresponding optical path is ; The other ray is a parametric tracing ray, i.e., an off-axis ray, with the following path: Based on the parameters of the zero-position compensation detection system, the optical path length corresponding to the parameter tracing ray is determined to be... ,in for Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points; According to the principle of equal optical path length, we have ,get Points and the interior aspherical surface The distance between the points is ; by Point 3 is the origin of the coordinate system. When the rear surface of the single CGH lens compensator in the zero-position compensation detection system is a binary optical surface 3, any point in the aspherical region of the focal point of the zero-position splicing double aspherical surface is considered. The trajectory equation is: ； in For the refracted light rays at the rear surface of a single CGH lens compensator Angle with optical axis, For the refracted light rays at the rear surface of a single CGH lens compensator Intersection with optical axis Point to the vertex of the surface of the single CGH lens compensator The distance; Similarly, when the radial coordinates of the diffraction plane are... hour, Point and external aspherical surface The distance between the points is ,in for Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points; by Point 3 is the origin of the coordinate system. When the rear surface of the single CGH lens compensator in the zero-position compensation detection system is a binary optical surface 3, any point in the aspherical region of the zero-position splicing double aspherical outer focal point is considered. The trajectory equation is: ； in For the refracted light rays at the rear surface of a single CGH lens compensator Angle with optical axis, For the refracted light rays at the rear surface of a single CGH lens compensator Intersection with optical axis Point to the vertex of the surface of the single CGH lens compensator The distance; The Point and The trajectory equation of the point is the surface shape expression of the zero-position spliced ​​double aspherical surface when the rear surface of the single CGH lens compensator in the zero-position compensation detection system is a binary optical surface 3; the zero-position spliced ​​double aspherical surface is a rotationally symmetric structure, and the maximum effective aperture is determined by the actual light transmission aperture of the interferometer standard mirror.

4. The method for characterizing spliced ​​aspherical surfaces based on a CGH lens null-compensation detection optical path according to claim 1, characterized in that... The binary optical surface 4 supports multiple concentric radial regions, each region having an independent radius, conic section, polynomial aspherical surface, and diffraction phase distribution; when the phase function of the diffraction surface is the binary optical surface 4, only the diffraction phases of multiple concentric radial regions are considered. Number of regions The number of phase terms is between 1 and 60, and the number of phase terms is between 0 and 20; the diffraction surface is divided into regions, with the first region extending from the vertex to the radial coordinate. The second area from Extending to This continues until the last region is passed, and the radial coordinate of the first region is greater than 0. After that, each region must be greater than the previous region. All regions have independent diffraction phase distributions, and the regions The phase expression is: ,in It is the number of polynomial coefficients. It is the normalized radial aperture. yes of The coefficient of a power. It is a diffraction order; The phase shift between the two regions is expressed as: ,calculate hour, Let's set it to 0 for now. When the phase difference between the two regions at the boundary is an integer multiple of the wavelength, that is... At that time, among them If the integer is any integer, then the in-phase condition of the two region boundaries is satisfied, resulting in optimal imaging performance; to ensure boundary continuity, the boundary value between every two regions is calculated. It and its sum of squares, and set the sum of squares to 0.

5. The method for characterizing spliced ​​aspherical surfaces based on a CGH lens null-compensation detection optical path according to claim 4, characterized in that, When the diffraction surface of the single CGH lens compensator faces the incident plane wave, the detection light is emitted parallel to the interferometer standard mirror. Since the radial coordinates of the binary optical surface 4 are divided into... Each region is denoted as [number]. The parallel wave of the detected light intersects with the CGH surface. point, After the first diffraction order light rays are emitted, they intersect with the back refraction surface. The point, after refraction by the back surface, intersects the aspherical surface at... Point; set the incident height of the light ray at the standard mirror of the interferometer as... Due to the partitioning of the binary optical surface 4, the regions on the refractive surface are divided into regions corresponding to the regions on the diffraction surface, and the incident heights are respectively represented as... ,in ;Will As a parameter of the aspherical surface shape, Within the range of the standard mirror aperture of the interferometer [ , The variables inside are continuous. When all parameters in the zero-position compensation detection system are fixed, the height of the detection light is as follows: Incident, by Click The optical path lengths at all points are the same; at this time The trajectory function formed by the points is the zero-position splicing multi-aspheric surface formula characterized when the front surface of the single CGH lens compensator is a binary optical surface 4. The general form of the parametric expression can be expressed as: ； in ; According to the principle of equal optical path length, when the radial coordinate of the diffraction plane is... At that time, two detection rays are selected, one of which is the center point of the diffraction surface of the single CGH lens compensator. The path of the emitted ray is: ;in, The point is the center vertex of the rear surface of the single CGH lens compensator. The point is the center vertex of the aspherical surface; the corresponding optical path is ; The other ray is a parametric tracing ray, i.e., an off-axis ray, with the following path: Based on the parameters of the zero-position compensation detection system, the optical path length corresponding to the parameter tracing ray is determined to be... ,in for Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points; According to the principle of equal optical path length, we have ,get Points and the interior aspherical surface The distance between the points is ; by Point 4 is the origin of the coordinate system. When the front surface of the single CGH lens compensator in the zero-position compensation detection system is a binary optical surface 4, any point in the aspherical region inside the multiple aspherical surfaces is used for zero-position splicing. The trajectory equation, that is, the surface shape expression of the zero-position spliced ​​multi-aspherical surface, is: ； in For the refracted light rays at the rear surface of a single CGH lens compensator Angle with optical axis, For the refracted light rays at the rear surface of a single CGH lens compensator Intersection with optical axis Point to the vertex of the surface of the single CGH lens compensator The distance; the zero-position splicing aspherical surface is a rotationally symmetric structure, and the maximum effective aperture is determined by the actual light transmission aperture of the interferometer standard mirror.

6. The method for characterizing spliced ​​aspherical surfaces based on a CGH lens null-compensation detection optical path according to claim 4, characterized in that, When the diffraction surface of the single CGH lens compensator faces the zero-position spliced ​​aspherical surface, the detection light is emitted parallel to the interferometer standard mirror and intersects with the front refractive surface. Point, because the radial coordinates of the 4th surface of the binary optical surface are divided into Each region is denoted as [number]. The refracting surface corresponds to the outgoing ray as follows: The point, the light rays emitted through the refracting surface intersect the CGH surface at... point, After the first diffraction order light rays are emitted, they intersect the aspherical surface at... Point; set the incident height of the light ray at the standard mirror of the interferometer as... Due to the partitioning of the binary optical surface 4, the regions on the refractive surface are divided into regions corresponding to the regions on the diffraction surface, and the incident heights are respectively represented as... ,in ;Will As a parameter of aspherical surfaces, Within the range of the standard mirror aperture of the interferometer [ , The variables inside are continuous. When all parameters in the zero-position compensation detection system are fixed, the height of the detection light is as follows: Incident, by Click The optical path lengths at all points are the same; at this time The trajectory function formed by the points is the zero-position splicing multi-aspheric surface formula characterized when the rear surface of a single CGH lens compensator is a binary optical surface 4. The general form of the parametric expression can be expressed as: ； in ; According to the principle of equal optical path length, when the radial coordinate of the diffraction plane is... At that time, two detection rays are selected, one of which is the center point of the refractive surface of the single CGH lens compensator. The path of the emitted ray is: ;in, The point is the center vertex of the rear surface of the single CGH lens compensator. The point is the center vertex of the aspherical surface; the corresponding optical path is ; The other ray is a parametric tracing ray, i.e., an off-axis ray, with the following path: Based on the parameters of the zero-position compensation detection system, the optical path length corresponding to the parameter tracing ray is determined to be... ,in for Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points; According to the principle of equal optical path length, we have ,get Points and the interior aspherical surface The distance between the points is ; by Point 4 is the origin of the coordinate system. When the rear surface of the single CGH lens compensator in the zero-position compensation detection system is a binary optical surface 4, any point in the aspherical region inside the multiple aspherical surfaces is used for zero-position splicing. The trajectory equation, that is, the surface shape expression of the zero-position spliced ​​multi-aspherical surface, is: ； in For the refracted light rays at the rear surface of a single CGH lens compensator Angle with optical axis, For the refracted light rays at the rear surface of a single CGH lens compensator Intersection with optical axis Point to the vertex of the surface of the single CGH lens compensator The distance; the zero-position splicing aspherical surface is a rotationally symmetric structure, and the maximum effective aperture is determined by the actual light transmission aperture of the interferometer standard mirror.

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