Computer-generated hologram design method for convex aspheric surface
By constructing a dual-path optical model and using the Zernike polynomial fitting method, the problem of high-precision detection of convex aspherical optical elements was solved, enabling efficient design and manufacturing of computational holograms and improving the reliability and ease of operation of the detection system.
Patent Information
- Application Number
- CN202511927752.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-19
- Publication Date
- 2026-02-03
AI Technical Summary
Traditional methods are difficult to achieve high-precision, non-destructive measurement of convex aspherical optical elements, and existing computational hologram designs lack a systematic and engineering-oriented design process, especially in the areas of reverse path modeling, dual-pass verification, and Zernike phase optimization, where there are technical difficulties.
By constructing a dual-path optical model, using the Zernike polynomial fitting method for phase compensation, combining optical design software for stray light analysis, generating GDSII format engineering diagrams, and performing photolithography microfabrication, the computational hologram design of a convex aspherical surface is realized.
It enables high-precision inspection and engineering-feasible manufacturing of convex aspherical surfaces, improves the reliability and stability of the optical path integration of the inspection system, simplifies the operation process, and meets processing requirements.
Smart Images
Figure CN121454881A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of optical measurement technology, and in particular relates to a computational holographic design method for convex aspherical surfaces. Background Technology
[0002] In the field of modern precision optical manufacturing and inspection, aspherical optical elements are widely used in high-end optical systems, such as camera lenses, laser systems, astronomical telescopes, semiconductor lithography objectives, and freeform surface optical elements, due to their superior optical performance, such as reducing aberrations, improving light energy utilization, and reducing system size. However, because convex aspherical surfaces have complex surface structures, traditional contact inspection methods struggle to achieve high-precision, non-destructive measurements, while non-contact inspection methods such as interferometry face challenges such as difficulty in matching reference mirrors and complex optical path configurations.
[0003] Computer-generated holograms (CGHs) are high-precision, flexible, and customizable diffractive optical elements that can adjust the incident light wavefront to a specific target wavefront through phase modulation. They are often used as compensators or reference wavefront generators, and are especially suitable for curved surfaces that are difficult to detect directly, such as convex aspherical surfaces. When used with an interferometer, they can achieve detection accuracy close to the diffraction limit.
[0004] However, CGH design for convex aspherical surfaces faces numerous challenges: their surface shape exhibits large curvature and strong asymmetry, and traditional methods, mostly designed for concave or simple aspherical surfaces, are difficult to directly adapt. Furthermore, CGH design requires comprehensive consideration of wavefront error compensation, optical path configuration (such as backlight path and double-pass model), system aberration optimization, stray light suppression, and fabrication limitations. Technical difficulties exist, particularly in backlight path modeling, double-pass verification, Zernike phase optimization, and fringe parameter calculation. Existing methods are mostly focused on concave or planar surfaces, lacking a systematic and engineering-compliant design process for complex convex surfaces. Therefore, developing a CGH design method suitable for convex aspherical surfaces, capable of achieving high-precision wavefront compensation and engineering-feasible manufacturing, has become a technological necessity in the field of high-precision optical inspection and manufacturing. Summary of the Invention
[0005] The purpose of this invention is to solve the problems mentioned in the background art and to propose a computational holographic design method for convex aspherical surfaces.
[0006] A computational holographic design method for convex aspherical surfaces, the method comprising:
[0007] Step 1: Input the relevant parameters and perform a preliminary selection to choose the parameter combination that meets the processing capacity;
[0008] Step 2: Construct a dual-path optical model for the convex aspherical surface to be tested. Based on the surface shape expression of the convex aspherical surface (S3) and the principle of single-path ray tracing, iterative method, and equiphase surface method, calculate two preset coordinate points. Then, using the coordinates of the sampling points and the two preset coordinates, calculate the optical path difference and phase value that CGH (S2) needs to compensate, and complete the design of the computational hologram of the dual-path optical path.
[0009] Step 3: Use the Zernike polynomial fitting method to compensate for the phase value, and combine the compensated phase value with the phase value obtained from the discrete sampling points to form a continuous phase function distribution within a closed range; the phase distribution is characterized by various parameters of the polynomial.
[0010] Step 4: Perform stray light analysis on the computational hologram of the dual-path optical system. Use optical design software to view the position and size of the reflected light spot at different diffraction orders at the center of curvature of the standard spherical mirror; determine the maximum aperture radius required to completely remove interfering diffraction orders.
[0011] Step 5: Based on the continuous phase function represented by the coefficients of the Zernike polynomial, the minimum fringe width is obtained, and it is verified whether the minimum fringe width meets the processing requirements. Finally, the GDSII format engineering drawing required for processing is generated, and the physical object of the computational hologram is generated by photolithography micromachining of the chromium-plated quartz plate.
[0012] Further, in step 1, input the relevant parameters and perform a preliminary selection to choose a parameter combination that meets the processing capabilities; including:
[0013] Set the dimensions of the CGH, the size and curvature of the standard spherical mirror, and the corresponding parameters of the convex aspherical surface to be measured in the computer.
[0014] Step 2: Set the distance between the CGH and the standard spherical mirror as d, and the distance between the CGH and the convex aspherical mirror to be tested as s. Use a computer to calculate and optimize the Zernike coefficient of the CGH under different combinations of d and s to optimize the system aberration to the maximum spatial frequency of the CGH within the set range. Then generate a three-dimensional graph with d and s as the horizontal and vertical axes and the maximum spatial frequency of the CGH etching surface as the z-axis. Select a combination that meets the processing capabilities.
[0015] Further, in step 2, a dual-path optical model is constructed for the convex aspherical surface to be tested. Based on the surface shape expression of the convex aspherical surface (S3) and the principles of single-path ray tracing, iterative methods, and the equiphase surface method, two preset coordinate points are obtained. Then, using the coordinates of the sampling points and the two preset coordinates, the optical path difference and phase value that CGH(S2) needs to compensate are calculated, completing the design of the computational hologram for the dual-path optical path; including:
[0016] Step 21: Construct a dual-path optical model for the convex aspherical surface under test. Based on the surface shape expression of the convex aspherical surface (S3) and the principle of single-path ray tracing, point A on the diffraction surface of CGH (S2) at a preset position and perpendicular to the optical axis is compared with a sampling point (x) in the light-passing region of the convex aspherical surface. r ,y r ,z r Correspondingly, the points on the diffraction surface correspond one-to-one with the sampling points on the convex aspherical light-transmitting region, so that the coordinates (x, y) of point A on the diffraction surface are determined. a ,y a ,z a Perform calculations;
[0017] Step 22: Using an iterative calculation method, calculate the coordinates (x, y) of point B on the non-diffraction plane of the hologram at a preset position perpendicular to the optical axis. b ,y b ,z b The calculation is performed, where the coordinates (x, y) of point B on the non-diffraction surface are... b ,y b ,z b ) and the coordinates (x) of point A on the diffraction surface a ,y a ,z a Correspondingly, the points on the non-diffraction surfaces of CGH(S2) correspond one-to-one with the points on the diffraction surfaces;
[0018] Step 23: Using the equiphase surface method, the standard spherical mirror (S1) is considered as an equiphase surface. A geometric relationship is established, and the coordinates (x, y) of the point on the equiphase surface corresponding to point B on the non-diffraction surface of CGH (S2) are determined. t ,y t ,z t ), where the points on the equiphase surface correspond one-to-one with the points on the non-diffraction surface of CGH(S2);
[0019] Step 24, using the coordinates (x, y) of the sampling points in the light-transmitting region of the convex aspherical surface (S3) to be measured. r ,y r ,z r ), calculate the coordinates (x, y) of point A on the diffraction surface of the hologram (S5). a ,y a ,z a The coordinates (x) of point B on the non-diffraction surface of CGH(S2) b ,y b ,z b ) and the coordinates (x) of points on the equiphase surface. t ,y t ,z t ), calculate the optical path difference and phase value that need to be compensated for CGH(S2), and complete the design of the computational hologram for the dual-path optical path.
[0020] Furthermore, in step 21, the convex aspherical surface detection device is arranged in sequence as follows: standard spherical mirror (S1), CGH (S2), and the convex aspherical surface to be tested (S3).
[0021] The standard spherical mirror (S1), CGH (S2), and the convex aspherical surface under test (S3) are coaxial;
[0022] Light rays emerge along the normal of the standard spherical mirror (S1) to form a spherical wave. When passing through CGH (S2), due to the phase compensation of CGH, an aspherical wave is formed and reflected at the convex aspherical mirror (S3) under test along the incident direction, passing through CGH (S2) again. After phase compensation by CGH (S2), a spherical wave is formed and propagates to the standard spherical mirror (S1), where it is incident along the normal of the standard spherical mirror (S1).
[0023] Furthermore, positional constraints are set based on the size of the interferometer's internal aperture, and the optimal distance is found by systematically scanning the distance parameters using a computer, thereby optimizing the performance of the computed hologram.
[0024] Furthermore, the standard spherical mirror has a focal length of 290 mm and a semi-diameter of 65.9 mm. The outer diameter of the main holographic region of the CGH is 65 mm and the inner diameter is 14 mm. The radius of curvature of the convex aspherical surface to be measured is 571.35 and the semi-diameter is 31.5 mm. The Zernike polynomial coefficients of the main holographic region of the hologram are shown in Table 1.
[0025] Table 1. Holographic Zernike polynomial coefficients of the main hologram designed based on the parameters of the convex aspherical surface under test.
[0026]
[0027] The unit for the coefficients of the Zernike polynomial is λ.
[0028] The significant advancement of this invention compared to existing technologies lies in:
[0029] (1) By setting position constraints according to the size of the aperture inside the interferometer, the present invention can achieve precise matching between the calculated hologram and the optical path of the interferometer, ensuring unobstructed transmission and effective diffraction of the beam, and effectively improving the reliability and stability of the optical path integration of the detection system.
[0030] (2) This invention uses a computer to systematically scan distance parameters and find the optimal distance combination, avoiding the need for preliminary steps such as... when designing a dual-path optical system. Figure 3 The backlight path design shown enables scientific optimization and automated configuration of hologram parameters, significantly improving the ease of operation of the detection scheme.
[0031] To more clearly illustrate the functional characteristics and structural parameters of the present invention, further explanation is provided below in conjunction with the accompanying drawings and specific embodiments. Attached Figure Description
[0032] Figure 1 This is a schematic diagram of a dual-channel optical path;
[0033] Figure 2 This is a schematic diagram of the dual-pass optical path in the embodiment;
[0034] Figure 3 This is a schematic diagram of a backlighting path;
[0035] Figure 4 This is a pseudo-color image of the wavefront aberration residuals of the optimized system in the embodiment;
[0036] Figure reference numerals and corresponding device names:
[0037] S1 - Standard spherical mirror, S2 - Computational holography, S3 - Convex aspherical surface to be measured. Detailed Implementation
[0038] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0039] In such Figure 1 In the dual-path optical detection device shown, light rays are emitted along the normal of the standard spherical mirror (S1) to form a spherical wave. When passing through CGH (S2), the phase compensation of CGH forms an aspherical wave, which is reflected at the convex aspherical mirror (S3) under test along the incident direction and passes through CGH (S2) again. After phase compensation by CGH (S2), it forms a spherical wave, which is then incident along the normal of the standard spherical mirror (S1) when it propagates to the standard spherical mirror (S1).
[0040] In the testing apparatus, the standard spherical mirror (S1), CGH (S2), and the convex aspherical surface to be tested (S3) share the same optical axis.
[0041] The precise matching between the aspherical wave and the light-transmitting region of the convex aspherical surface under test is generated by modulating the spherical wave with a CGH (S2) with a specific phase distribution.
[0042] The aspherical wave, which matches the surface shape of the light-transmitting region of the convex aspherical surface (S3) and propagates along the normal direction of the light-transmitting region of the convex aspherical surface (S3), is compensated by holographic calculation (S2) to generate a spherical wave, which is then incident on the standard spherical mirror (S1) along the surface normal of the standard spherical mirror (S1).
[0043] This application provides a method for designing computational holograms for convex aspherical surfaces, the specific method of which is as follows:
[0044] Step 1: Set the dimensions of the CGH, the size and curvature of the standard spherical mirror, and the corresponding parameters of the convex aspherical surface to be measured in the computer.
[0045] Step 2: Define the distance between the CGH and the standard spherical mirror as 'd', and the distance between the CGH and the convex aspherical mirror under test as 's'. Use a computer to calculate and optimize the Zernike coefficients of the CGH under different combinations of 'd' and 's', optimizing the system aberrations to the maximum spatial frequency of the CGH within the set range. Then generate a 3D graph with 'd' and 's' as the horizontal and vertical axes, and the maximum spatial frequency of the CGH etching surface as the z-axis. Select a suitable combination within the processing capability.
[0046] Step 3: As Figure 2 As shown, a dual-path optical model is constructed for the convex aspherical surface under test. Based on the surface shape expression of the convex aspherical surface (S3) and the principle of single-path ray tracing, point A on the diffraction surface of CGH (S2) at a specified position and perpendicular to the optical axis is compared with a sampling point (x) in the light-passing region of the convex aspherical surface. r ,y r ,z r Correspondingly, the points on the diffraction surface correspond one-to-one with the sampling points on the convex aspherical light-transmitting region, so that the coordinates (x, y) of point A on the diffraction surface are determined. a ,y a ,z a Perform calculations;
[0047] Step 4: Use iterative calculation to calculate the coordinates (x, y) of point B on the non-diffraction plane of the hologram at a specified location perpendicular to the optical axis. b ,y b ,z b The calculation is performed, where the coordinates (x, y) of point B on the non-diffraction surface are... b ,y b ,z b ) and the coordinates (x) of point A on the diffraction surface a ,y a ,z a Correspondingly, the points on the non-diffraction surfaces of CGH(S2) correspond one-to-one with the points on the diffraction surfaces.
[0048] Step 5: Using the equiphase surface method, consider the standard spherical mirror (S1) as an equiphase surface, establish geometric relationships, and determine the coordinates (x, y) of the point on the equiphase surface corresponding to point B on the non-diffraction surface of CGH (S2). t ,y t ,z t The points on the equiphase surface correspond one-to-one with the points on the non-diffraction surface of CGH(S2).
[0049] Step 6: Use the coordinates (x, y) of the sampling points in the light-transmitting area of the convex aspherical surface (S3) to measure. r ,y r ,z r ), calculate the coordinates (x, y) of point A on the diffraction surface of the hologram (S5). a ,y a ,z a The coordinates (x) of point B on the non-diffraction surface of CGH(S2) b ,y b ,z b ) and the coordinates (x) of points on the equiphase surface. t ,y t ,z t ), calculate the optical path difference and phase value that need to be compensated for CGH(S2), and complete the design of the computational hologram for the dual-path optical path.
[0050] Step 7: Use the Zernike polynomial fitting method to compensate for the phase value, and combine the compensated phase value with the phase value obtained from the discrete sampling points to form a continuous phase function distribution within a closed range; the phase distribution is characterized by various parameters of the polynomial.
[0051] Step 8: Perform stray light analysis on the computational hologram of the dual-path optical system. By using optical design software, examine the position and size of the reflected light spots of different diffraction orders at the curvature center of the standard spherical mirror to determine the maximum aperture radius required to completely remove interfering diffraction orders.
[0052] Step 9: Based on the continuous phase function represented by the coefficients of the Zernike polynomial, the minimum fringe width is obtained, and it is verified whether the minimum fringe width meets the processing requirements. Finally, the GDSII format engineering drawing required for processing is generated, and the physical object of the computational hologram is generated by photolithography micromachining of the chromium-plated quartz plate.
[0053] Example
[0054] This invention is a computational holographic design method for convex aspherical surfaces.
[0055] The expression for an ideal convex aspherical surface is:
[0056] ;
[0057] in Let R be the normalized radial coordinate, R be the vertex radius of curvature, k be the conic constant, and A be the radius of curvature. iLet be the i-th order aspherical coefficient. In this embodiment, R=571.351, k=9.75488, A1=0, A2=-5.9211239×10^(-14), A3=1.47798331×10^(-16), A4=-3.69302277×10^(-19), A5=-3.69302277×10^(-19), A6=4.377535326×10^(-22), A7=-3.0800478×10^(-25), A8=7.9477732×10^(-29).
[0058] In this embodiment, the distance t from the standard spherical mirror (S1) to the CGH (S2) is 120 mm, the thickness of the CGH (S2) is 6.35 mm, and the distance s from the CGH (S2) to the convex aspherical surface to be measured (S3) is 40 mm. The semi-diameter of the standard spherical mirror (S1) is 65.9 mm, and the focal length is 290 mm.
[0059] The Zernike polynomial coefficients of the main hologram designed based on the parameters of the convex aspherical surface to be measured are shown in Table 2.
[0060] Table 2 shows the calculated Zernike polynomial coefficients of the main hologram based on the parameters of the convex aspherical surface to be tested.
[0061]
[0062] The unit for the coefficients of the Zernike polynomial is λ.
[0063] like Figure 3 As shown, after optimization of the dual-path optical path using optical simulation software, the residual PV=0.0000λ and RMS=0.0000λ, where λ=632.8nm, meet the requirements.
[0064] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A computational holographic design method for convex aspherical surfaces, characterized in that, The method includes: Step 1: Input the relevant parameters and perform a preliminary selection to choose the parameter combination that meets the processing capacity; Step 2: Construct a dual-path optical model for the convex aspherical surface to be tested. Based on the surface shape expression of the convex aspherical surface (S3) and the principle of single-path ray tracing, iterative method, and equiphase surface method, calculate two preset coordinate points. Then, using the coordinates of the sampling points and the two preset coordinates, calculate the optical path difference and phase value that CGH (S2) needs to compensate, and complete the design of the computational hologram of the dual-path optical path. Step 3: Use the Zernike polynomial fitting method to compensate for the phase value, and combine the compensated phase value with the phase value obtained from the discrete sampling points to form a continuous phase function distribution within a closed range; the phase distribution is characterized by various parameters of the polynomial. Step 4: Perform stray light analysis on the computational hologram of the dual-path optical system. Use optical design software to view the position and size of the reflected light spot at different diffraction orders at the center of curvature of the standard spherical mirror; determine the maximum aperture radius required to completely remove interfering diffraction orders. Step 5: Based on the continuous phase function represented by the coefficients of the Zernike polynomial, the minimum fringe width is obtained, and it is verified whether the minimum fringe width meets the processing requirements. Finally, the GDSII format engineering drawing required for processing is generated, and the physical object of the computational hologram is generated by photolithography micromachining of the chromium-plated quartz plate.
2. The method according to claim 1, characterized in that, Step 1: Input the relevant parameters and perform a preliminary selection to choose the parameter combination that meets the processing capacity; include: Set the dimensions of the CGH, the size and curvature of the standard spherical mirror, and the corresponding parameters of the convex aspherical surface to be measured in the computer. Step 2: Set the distance between the CGH and the standard spherical mirror as d, and the distance between the CGH and the convex aspherical mirror to be tested as s. Use a computer to calculate and optimize the Zernike coefficient of the CGH under different combinations of d and s to optimize the system aberration to the maximum spatial frequency of the CGH within the set range. Then generate a three-dimensional graph with d and s as the horizontal and vertical axes and the maximum spatial frequency of the CGH etching surface as the z-axis. Select a combination that meets the processing capabilities.
3. The method according to claim 1, characterized in that, Step 2: Build a dual-path optical model for the convex aspherical surface to be tested, and calculate two preset coordinate points based on the surface shape expression of the convex aspherical surface (S3) and the single-path ray tracing principle, iterative method, and equiphase surface method. Using the sampling point coordinates and two preset coordinates, the optical path difference and phase value that need to be compensated for in CGH(S2) are calculated, and the design of the computational hologram for the dual-path optical path is completed. include: Step 21: Construct a dual-path optical model for the convex aspherical surface under test. Based on the surface shape expression of the convex aspherical surface (S3) and the principle of single-path ray tracing, point A on the diffraction surface of CGH (S2) at a preset position and perpendicular to the optical axis is compared with a sampling point (x) in the light-passing region of the convex aspherical surface. r ,y r ,z r Correspondingly, the points on the diffraction surface correspond one-to-one with the sampling points on the convex aspherical light-transmitting region, so that the coordinates (x, y) of point A on the diffraction surface are determined. a ,y a ,z a Perform calculations; Step 22: Using an iterative calculation method, calculate the coordinates (x, y) of point B on the non-diffraction plane of the hologram at a preset position perpendicular to the optical axis. b ,y b ,z b The calculation is performed, where the coordinates (x, y) of point B on the non-diffraction surface are... b ,y b ,z b ) and the coordinates (x) of point A on the diffraction surface a ,y a ,z a Correspondingly, the points on the non-diffraction surfaces of CGH(S2) correspond one-to-one with the points on the diffraction surfaces; Step 23: Using the equiphase surface method, the standard spherical mirror (S1) is considered as an equiphase surface. A geometric relationship is established, and the coordinates (x, y) of the point on the equiphase surface corresponding to point B on the non-diffraction surface of CGH (S2) are determined. t ,y t ,z t ), where the points on the equiphase surface correspond one-to-one with the points on the non-diffraction surface of CGH(S2); Step 24, using the coordinates (x, y) of the sampling points in the light-transmitting region of the convex aspherical surface (S3) to be measured. r ,y r ,z r ), calculate the coordinates (x, y) of point A on the diffraction surface of the hologram (S5). a ,y a ,z a The coordinates (x) of point B on the non-diffraction surface of CGH(S2) b ,y b ,z b ) and the coordinates (x) of points on the equiphase surface. t ,y t ,z t ), calculate the optical path difference and phase value that need to be compensated for CGH(S2), and complete the design of the computational hologram for the dual-path optical path.
4. The method according to claim 1, characterized in that, In step 21, the standard spherical mirror (S1), CGH (S2), and the convex aspherical surface to be tested (S3) are set up in sequence in the convex aspherical surface testing device. The standard spherical mirror (S1), CGH (S2), and the convex aspherical surface under test (S3) share the same optical axis; Light rays emerge along the normal of the standard spherical mirror (S1) to form a spherical wave. When passing through CGH (S2), due to the phase compensation of CGH, an aspherical wave is formed and reflected at the convex aspherical mirror (S3) under test along the incident direction, passing through CGH (S2) again. After phase compensation by CGH (S2), a spherical wave is formed and propagates to the standard spherical mirror (S1), where it is incident along the normal of the standard spherical mirror (S1).
5. A computational hologram for a convex aspherical surface according to claim 1, characterized in that: The standard spherical mirror has a focal length of 290 mm and a semi-diameter of 65.9 mm. The outer diameter of the main holographic region of the CGH is 65 mm and the inner diameter is 14 mm. The radius of curvature of the convex aspherical surface to be measured is 571.35 and the semi-diameter is 31.5 mm. The Zernike polynomial coefficients of the main holographic region of the hologram are shown in Table 1. Table 1. Holographic Zernike polynomial coefficients of the main hologram designed based on the parameters of the convex aspherical surface to be tested. ； The unit for the coefficients of the Zernike polynomial is λ.