Aspheric surface parameter fitting and surface deviation measurement method based on double model representation

Abstract

The application discloses a kind of based on double model representation's aspheric surface parameter fitting and surface shape deviation measurement method, comprising 1) collection aspheric surface optical element surface several points, processing obtains the three-dimensional data of each sampling point;2) establish initial optical path model and set its wavefront evaluation function;3) input aspheric element's design parameter in turn;4) by the coordinate data of measured XOY plane is fitted to obtain the coordinate of its center point, conversion to the coordinate system of with optical design software coaxial, carries out Zernike fitting and obtains Zernike coefficient;5) in aspheric surface optical path model, using Zernike coefficient in step 4 is represented to be measured aspheric surface, in the same optical design software, constructs aspheric surface using two kinds of representation mode;6) radius of curvature is set as variable, the rest aspheric surface parameters are unchanged, and optimization obtains actual radius of curvature;7) conic coefficient and high order coefficient are set as variable, and optimization obtains aspheric surface parameter and surface shape deviation.

Description

Technical Field

[0001] This invention belongs to the technical field of optical detection, specifically relating to a method for fitting aspherical parameters and measuring surface deviation based on dual-model characterization. Background Technology

[0002] In the design of modern optical systems, to improve image quality and simplify the system, the optical elements used are increasingly becoming aspherical. Fabricating such large aspherical optical elements requires matching high-precision processing techniques and inspection methods. However, the parameters of the actually manufactured optical elements deviate from the designed parameters. To obtain the aspherical parameters and surface shape deviations, surface shape fitting of the aspherical optical element is necessary. Comparing the fitting results with the design values ​​guides further processing, ensuring the optical element meets design requirements. Therefore, the accuracy of surface shape fitting directly affects the ability to evaluate and provide feedback on the actual manufacturing process.

[0003] A common method for surface fitting is to directly measure the contour curve of the aspherical optical element and then use a fitting program and algorithm to obtain the characteristic parameters of the element under test. However, this method can generally only handle simple surfaces with a few optical characteristic parameters, and it is not universally applicable to aspherical surfaces or even higher-order aspherical surfaces with more complex surface shapes, and the accuracy is not easy to guarantee. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of existing technologies. It proposes a method for fitting aspherical parameters and measuring surface deviation based on dual-model characterization, applicable to any surface shape that can be characterized by aspherical equations, exhibiting good applicability. Furthermore, the method utilizes optical design software for optimized fitting, eliminating the need for multiple iterations of data, thus making it more convenient and more accurate.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] The method of aspherical parameter fitting and surface deviation measurement based on dual-model characterization establishes a model through two characterization methods: aspherical equation and Zernike fitting. The model is then optimized by simulation using optical design software to obtain the parameters and surface deviation of the aspherical optical element under test.

[0007] Furthermore, the aspherical parameter fitting and surface deviation measurement method based on dual-model characterization is performed according to the following steps:

[0008] Step 1: Obtain the 3D topography of the aspherical optical element under test using a 3D coordinate sampling device such as a laser tracker or a coordinate measuring machine. Uniformly sample and mark the surface of the aspherical optical element under test. Measure each sampling point using a laser tracker. Process the collected data to obtain the 3D data at each sampling point. The data format is (x1, y1, z1), (x2, y2, z2), ..., (x... i ,y i , z i ), …(x n ,y n , z n The z-axis of the laser tracker coordinate system is opposite in direction to the z'-axis of the coordinate system defined in the optical design software.

[0009] Step 2: First, establish an initial optical path model in the optical design software, based on the design parameters of the aspherical optical element and its aspherical equation. An aspherical optical path model is created in optical design software, where... Let be the horizontal distance from the origin to a point on the surface of the aspherical optical element, z be the vertical height from the origin to the origin, R0 be the radius of curvature of the aspherical optical element, K be the quadratic coefficient, and a1, a2, a3, a4, and a5 be the higher-order coefficients. Setting all aspherical coefficients to 0 and the radius of curvature to infinity, we represent a plane mirror, denoted as S1. In the optical path model, parallel light is incident, reflected by S1, and returns. The wavefront evaluation function for this optical parameter is set in the optical system.

[0010] Step 3: Input the design parameters of the aspherical element into the aspherical model in the optical design software, such as the radius of curvature, conic coefficient, and higher-order coefficients, to characterize the designed aspherical optical element.

[0011] Step 4: Using the measured coordinate data of the XOY plane (x1, y1, z1), (x2, y2, z2), ..., (x i y i ,z i ), …(x n y n ,z n The coordinates (x0, y0) of the center point projected onto the XOY plane are obtained by fitting the data, where... The difference between the original data and the center point coordinates is used to transform the data to a coordinate system coaxial with the optical design software: (x i -x0, y i -y0)|i=1,2,…n。Then Zernike fitting is performed to represent the actual surface shape as a linear combination of terms of Zernike polynomials: w(x,y)=c1Z1+c2Z2+…+c nZ n The Zernike coefficients c1, c2, ..., c are obtained by using the least squares method. n .

[0012] Step 5: Set its surface type to a surface that can be characterized by both Zernike coefficients and the aspherical equation, and substitute the negative Zernike coefficients calculated in Step 4 into (-c1, -c2, ..., -c n At this point, aspherical surfaces are constructed using two characterization methods in the same optical design software for comparison and optimization.

[0013] Step 6: Set the radius of curvature R0 as a variable, keeping the other aspherical parameters unchanged, and perform optimization. After optimization, the actual radius of curvature R0' that can characterize the aspherical optical element under test is obtained. The wavefront diagram automatically calculated by the optical design software can show the surface shape deviation W between the actual surface obtained by the process and the target aspherical surface.

[0014] Step 7: Set the conic coefficient and higher-order coefficients as variables for optimization. After optimization, the aspherical parameters R0', K', a1', a2', a3'... that are closest to the aspherical optical element on this surface are obtained. The wavefront diagram automatically calculated by the optical design software can be used to obtain the surface shape deviation W' between the fabricated aspherical optical element and the closest aspherical surface.

[0015] Compared with the prior art, the advantages of the present invention are:

[0016] The present invention provides a method for measuring the parameters and surface deviations of aspherical optical elements. This method establishes a model using both aspherical equations and Zernike fitting, and then performs simulation optimization using optical design software. This allows for the simple and rapid acquisition of the parameters and surface deviations of the aspherical optical element under test, thereby guiding the fabrication of the optical element. This method is applicable to any optical element that can be characterized by aspherical equations, exhibiting wide applicability and providing reliable and accurate feedback and evaluation for optical element fabrication, ensuring that the optical element meets design requirements. Attached Figure Description

[0017] Figure 1 Flowchart of the fitting process for the aspherical optical element of this invention;

[0018] Figure 2 : Schematic diagram of the designed parabolic surface;

[0019] Figure 3 Schematic diagram of parabolic sampling;

[0020] Figure 4 : Fitted surface deviation diagram;

[0021] The diagram is marked with: 1. Parabolic surface, 2. Laser tracker. Detailed Implementation

[0022] The present invention will now be described in further detail with reference to the accompanying drawings.

[0023] This invention utilizes two characterization methods—aspheric equations and Zernike fitting—and employs optical design software for simulation optimization, enabling convenient fitting of the parameters and surface deviations of aspheric optical elements. The method is as follows: Figure 1 As shown, it includes the following steps:

[0024] Step 1: Use a three-dimensional coordinate sampling device to collect several points on the surface of the fabricated aspherical optical element to be tested, and process them to obtain the three-dimensional data of each sampling point.

[0025] Specifically, the three-dimensional morphology of the aspherical optical element under test is obtained using three-dimensional coordinate sampling equipment such as a laser tracker or a coordinate measuring machine. Uniform sampling and marking are performed on the surface of the aspherical optical element under test. Each sampling point is measured using a laser tracker, and the collected data is processed to obtain the three-dimensional data at each sampling point. The data format is (x1, y1, z1), (x2, y2, z2), ..., (x... i ,y i , z i ), …(x n ,y n , z n The z-axis of the laser tracker coordinate system is opposite in direction to the z'-axis of the coordinate system defined in the optical design software.

[0026] Step 2: Establish an initial optical path model in the optical design software, that is, create the optical path that returns after parallel light is incident on the plane mirror S1, and set its wavefront evaluation function.

[0027] Specifically, an initial optical path model is first established in the optical design software, based on the design parameters of the aspherical optical element and its aspherical equation. An aspherical optical path model is created in optical design software, where... Let be the horizontal distance from the origin to a point on the surface of the aspherical optical element, z be the vertical height from the origin to the origin, R0 be the radius of curvature of the aspherical optical element, K be the quadratic coefficient, and a1, a2, a3, a4, and a5 be the higher-order coefficients. Setting all aspherical coefficients to 0 and the radius of curvature to infinity, we represent a plane mirror, denoted as S1. In the optical path model, parallel light is incident, reflected by S1, and returns. The wavefront evaluation function for this optical parameter is set in the optical system.

[0028] Step 3: Input the design parameters of the aspherical element into the aspherical model in the optical design software, such as the radius of curvature, conic coefficient, and higher-order coefficients, to characterize the designed aspherical optical element.

[0029] Step 4: Using the measured coordinate data of the XOY plane (x1, y1, z1), (x2, y2, z2), ..., (x i y i , z i ), …(x n y n ,z n The coordinates (x0, y0) of the center point projected onto the XOY plane are obtained by fitting the data, where... The difference between the original data and the center point coordinates is used to transform the data to a coordinate system coaxial with the optical design software: (x i -x0,y i -y0)|i=1,2,…n. Then perform Zernike fitting, representing the actual surface shape as a linear combination of Zernike polynomial terms: w(x,y)=c1Z1+c2Z2+…+c n Z n The Zernike coefficients c1, c2, ..., c are obtained by using the least squares method. n .

[0030] Step 5: Use the Zernike coefficients from Step 4 to characterize the aspheric surface under test in the aspheric optical path model. Construct the aspheric surface using two characterization methods in the same optical design software for comparison and optimization.

[0031] Specifically, its surface type is set to a surface that can be characterized by both Zernike coefficients and the aspherical equation, and the negative Zernike coefficients calculated in step 4 are substituted into (-c1, -c2, ..., -c n At this point, aspherical surfaces are constructed using two characterization methods in the same optical design software for comparison and optimization.

[0032] Step 6: Set the radius of curvature R0 as a variable, keep the other aspherical parameters unchanged, and perform optimization; after optimization, the actual radius of curvature R0' and the surface deviation W between the actual surface and the target aspherical surface are obtained.

[0033] Specifically, the radius of curvature R0 is set as a variable, while other aspherical parameters remain unchanged, and optimization is performed. After optimization, the actual radius of curvature R0' that can characterize the aspherical optical element under test is obtained. The wavefront diagram automatically calculated by the optical design software can show the surface shape deviation W between the actual surface obtained by the process and the target aspherical surface.

[0034] Step 7: Set the conic coefficient and higher-order coefficients as variables and optimize them; after optimization, the aspherical parameters R0', K', a1', a2', a3'... that are closest to the aspherical optical element on this surface are obtained, as well as the shape deviation W' after optimization.

[0035] Specifically, the conic coefficient and higher-order coefficients are set as variables for optimization. After optimization, the aspherical parameters R0', K', a1', a2', a3', ... of the surface closest to the aspherical optical element are obtained. The wavefront diagram automatically calculated by the optical design software can be used to determine the surface shape deviation W' between the fabricated aspherical optical element and the closest aspherical surface.

[0036] This embodiment uses a parabolic surface as an example.

[0037] Step 1 (e.g.) Figure 3 As shown): The parabolic optical element 1 is composed of 12 rotationally symmetric secondary mirrors. Samples are taken horizontally at 5cm intervals on the surface of each secondary mirror and marked with a marker. A laser tracker 2 measures the marked points. The collected data is processed to obtain the three-dimensional data at each sampling point. The format of the three-dimensional data is (x1, y1, z1), (x2, y2, z2), ..., (x...). i y i , z i Here, the z-axis of the laser tracker's coordinate system 2 is opposite in direction to the z'-axis of the coordinate system defined in the optical design software.

[0038] Step 2: In the optical design software, first establish an initial optical path model, setting all aspherical coefficients to 0 and the radius of curvature to infinity, representing a plane mirror, denoted as S1. Parallel light is incident in the optical path model, reflected by S1, and then returns. The wavefront evaluation function for this optical parameter is then set.

[0039] Step 3 (e.g.) Figure 2 As shown): The designed parabolic surface has a height of 625 mm, a diameter of 3 m, a radius of curvature of 2048 mm, a thickness of 1024 mm, a conic coefficient of -1, and the equation for the aspherical surface is: The expression for this parabola is: z = 2.44 × 10⁻⁶ 4 r 2 ,in Let be the horizontal distance from the origin to a point on parabolic surface 1, z be the sag within the aperture of parabolic surface 1, R0 be the radius of curvature of parabolic surface 1, K be the quadratic coefficient, and a1, a2, a3, a4, and a5 be the higher-order coefficients. The design parameters of parabolic surface 1, such as the radius of curvature, conic coefficient, and higher-order coefficients, are sequentially input into the initial optical path model to characterize the designed parabolic surface 1, thus obtaining the parabolic optical path model.

[0040] Step 4: Fit the coordinates of the center point (x0, y0) from the measured coordinate data of the XOY plane, transform the original data and the center point coordinates to a coordinate system coaxial with the optical design software, and then perform Zernike fitting to obtain the Zernike coefficients.

[0041] Specifically, the coordinates (x0, y0) of the center point projected onto the XOY plane are obtained by fitting the measured coordinate data of the XOY plane. The difference between the original data and the center point coordinates is used to transform the data to a coordinate system coaxial with the optical design software: (x i -x0,y i -y0)|i=1,2,…n. Then perform Zernike fitting, representing the actual surface shape as a linear combination of Zernike polynomial terms: w(x,y)=c1Z1+c2Z2+…+c n Z n The Zernike coefficients c1, c2, ..., c are obtained by using the least squares method. 66 .

[0042] Step 5: Set its surface type to a surface that can be characterized by both Zernike coefficients and the aspherical equation, and substitute the negative Zernike coefficients calculated in Step 4 into (-c1, -c2, ..., -c n At this point, aspherical surfaces are constructed using two characterization methods within the same optical design software for comparison and optimization.

[0043] Step 6 (e.g.) Figure 4 As shown): The radius of curvature R0 is set as a variable, while other aspherical parameters remain unchanged, for optimization. After optimization, the actual radius of curvature R0' that can characterize the parabolic optical element is obtained as 2347.13 mm. The wavefront diagram automatically calculated by the optical design software shows the surface shape deviation W between the processed actual surface and the target parabolic surface, with RMS of 1.19745 mm and PV of 15.0151 mm. Figure 4 As shown. This guides the further processing of parabolic surface 1.

[0044] The contents not described in detail in this specification are common knowledge to those skilled in the art.

[0045] In summary, the aspherical parameter fitting and surface deviation calculation method based on dual-model characterization of the present invention can conveniently and accurately fit the parameters and surface deviation of aspherical optical elements, providing accurate and reliable parameter indicators for subsequent processing and focus confirmation.

[0046] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for fitting aspherical parameters and measuring surface deviation based on dual-model characterization, characterized in that, A model is established using two characterization methods: aspherical equations and Zernike fitting. Simulation optimization is then performed using optical design software to obtain the parameters and surface deviations of the aspherical optical element under test. The method is carried out according to the following steps: Step 1: Use a three-dimensional coordinate sampling device to collect several points on the surface of the fabricated aspherical optical element to be tested, and process them to obtain the three-dimensional data of each sampling point; Step 2: Establish an initial optical path model in the optical design software, that is, create the optical path that returns after parallel light is incident on the plane mirror S1, and set its wavefront evaluation function; Step 3: Input the design parameters of the aspherical element into the aspherical model in the optical design software in sequence to characterize the designed aspherical optical element; Step 4: Fit the coordinates of the center point from the measured coordinate data of the XOY plane. , The difference between the original data and the center point coordinates is transformed to a coordinate system coaxial with the optical design software, and then Zernike fitting is performed to obtain the Zernike coefficients. Step 5: Use the Zernike coefficients from Step 4 to characterize the aspheric surface under test in the aspheric optical path model. Construct the aspheric surface using two characterization methods in the same optical design software for comparison and optimization. Step 6: Set the radius of curvature R0 as a variable, keep the other aspherical parameters unchanged, and perform optimization; after optimization, the actual radius of curvature R0' and the surface deviation W between the actual surface and the target aspherical surface are obtained; Step 7: Set the conic coefficient and higher-order coefficients as variables and optimize them; after optimization, the aspherical parameters that are closest to the aspherical optical element are obtained: radius of curvature R0', conic coefficient K', higher-order coefficients a1', a2', a3'... and the optimized shape deviation W'.

2. The method for fitting aspherical parameters and measuring surface deviation based on dual-model characterization according to claim 1, characterized in that, In step 1, a laser tracker or a coordinate measuring machine (CMM) is used to obtain the three-dimensional morphology of the aspherical optical element under test. Uniform sampling and marking are performed on the surface of the aspherical optical element. The laser tracker measures each sampling point, and the collected data is processed to obtain the three-dimensional data at each sampling point. The data format is as follows: , where i is the i-th data point and n is the total number of three-dimensional data points; the z-axis of the laser tracker coordinate system is opposite in direction to the z'-axis of the coordinate system defined in the optical design software.

3. The method for fitting aspherical parameters and measuring surface deviation based on dual-model characterization according to claim 1, characterized in that, In step 2, an initial optical path model is first established in the optical design software, based on the design parameters of the aspherical optical element and its aspherical equation. An aspherical optical path model is established in optical design software, in which... Let z be the horizontal distance from the origin to a point on the surface of the aspherical optical element, and z be the vertical height from the origin to a point on the surface of the aspherical optical element. Let be the radius of curvature of the aspherical optical element, and K be the coefficient of the quadratic term. , , , , The coefficients are higher-order terms; all aspherical coefficients are set to 0, and the radius of curvature is infinite, representing a plane mirror, denoted as S1; in the optical path model, parallel light is incident, reflected by S1 and returns; the wavefront evaluation function of this optical parameter is set in the optical system.

4. The method for fitting aspherical parameters and measuring surface deviation based on dual-model characterization according to claim 1, characterized in that, In step 3, the design parameters of the aspherical element include radius of curvature, conic coefficient, and higher-order coefficient.

5. The method for fitting aspherical parameters and measuring surface deviation based on dual-model characterization according to claim 1, characterized in that, In step 4, the coordinate data of the measured XOY plane are used. The coordinates of its center point projected onto the XOY plane were obtained by fitting. , ),in The difference between the original data and the center point coordinates is used to transform the data to a coordinate system coaxial with the optical design software. Then, Zernike fitting is performed to represent the actual surface shape as a linear combination of the terms of a Zernike polynomial: Z i Let i be a Zernike polynomial, where i = 1, 2, 3, 4, ..., n. The Zernike coefficients are obtained by solving the least squares method. .

6. The method for fitting aspherical parameters and measuring surface deviation based on dual-model characterization according to claim 1, characterized in that, In step 5, the surface type is set to a surface that can be characterized by both the Zernike coefficient and the aspherical equation, and the negative Zernike coefficient calculated in step 4 is substituted into the equation. At this point, aspherical surfaces are constructed using two characterization methods in the same optical design software for comparison and optimization.

7. The method for fitting aspherical parameters and measuring surface deviation based on dual-model characterization according to claim 1, characterized in that, In step 6, the radius of curvature R0 is set as a variable, while the other aspherical parameters remain unchanged, and optimization is performed. After optimization, the actual radius of curvature R0' that can characterize the aspherical optical element under test is obtained. The wavefront diagram automatically calculated by the optical design software can show the surface shape deviation W between the actual surface processed and the target aspherical surface.

8. The method for fitting aspherical parameters and measuring surface deviation based on dual-model characterization according to claim 1, characterized in that, In step 7, the conic coefficient and higher-order coefficients are set as variables for optimization; after optimization, the aspherical parameters R0', K', a1', a2', a3'... closest to the aspherical optical element are obtained; the wavefront diagram automatically calculated by the optical design software can be used to obtain the surface shape deviation W' between the processed aspherical optical element and the closest aspherical surface.

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