A lens double curvature radius measurement method based on ray tracing simulation

Abstract

The application provides a lens double-side curvature radius measurement method based on ray tracing simulation, first, a ray tracing method based on measured ray deflection information is proposed according to the ray deflection measurement principle of the moire phase shift device, the method calculates the ray deflection matrix of the lens under the two-dimensional field of view based on the calculated transverse stripe and longitudinal stripe phase images through the four-step phase shift stripe images of the sample shot by the moire phase shift method, the gradient algorithm according to the pixels and the iteration approximation of the ray tracing simulation data and the experimental data to obtain the optimal curvature radius value, the measurement method can measure the double-side curvature radius of the lens sample with asymmetry under the transmission light path, and the high consistency of the measurement result with the nominal value and the white light interferometer proves the reliability of the measurement method.

Description

Technical Field This invention relates to the measurement of the radius of curvature of a lens, and more specifically, to a method for measuring the radius of curvature of both sides of a lens based on ray tracing simulation. This invention can be used to measure the radius of curvature of both sides of an asymmetric optical lens. Background Technology

[0001] Currently, the measurement of radius of curvature typically relies on surface measurement methods such as interferometers and profilometers. These methods usually utilize the physical characteristics of a single surface and require separate measurements of the radius of curvature of each of the two surfaces of the lens. While these methods can provide high-precision single-surface surface data, they generally suffer from disadvantages in the "double-sided radius of curvature measurement of double-sided asymmetric lenses," including complex procedures, alignment sensitivity, significant repeatability errors, strong dependence on surface reflection conditions, and insufficient correlation with actual transmission performance. These limitations make it difficult to meet the demand for rapid, stable, and widely applicable double-sided radius of curvature detection. Furthermore, measurement methods based on transmission optical paths are affected by the refractive properties of both surfaces of the lens, making it difficult to separate the curvature information of the two surfaces. Consequently, transmission optical path radius of curvature measurement methods are usually limited to highly specialized lens samples, such as biconvex or biconcave lenses, or lens samples with one flat surface. There is a lack of transmission optical path measurement methods capable of simultaneously measuring the radius of curvature of both surfaces of highly asymmetric lens samples.

[0002] US2010310130A1 introduces a phase-shifting schlieren experimental setup and algorithm for measuring the deflection angle of light transmitted through a sample. The phase-shifting schlieren method is a relatively novel deflection measurement technique. The phase-shifting schlieren method has a simple setup, eliminating the need for the complex and expensive experimental setup of traditional schlieren techniques. The measurement sensitivity and accuracy mainly depend on the optical path design, camera resolution, background noise, and related algorithms.

[0003] However, relying solely on deflection field data still presents the problem of inverse solution involving the coupling of two-sided parameters. To address this, this specification proposes a two-sided curvature inversion method that combines deflection information obtained from schlieren phase shift measurements with ray tracing simulation. This method involves establishing a lens optical model that includes parameters such as the curvature radii of the front and rear surfaces, using ray tracing to calculate and predict deflection imaging characteristics, and using measured data as constraints for parameter optimization. This allows for the simultaneous inversion of the curvature radii of both surfaces, making it particularly suitable for two-sided highly asymmetric lens samples.

[0004] This invention proposes a method for measuring the curvature radius of a lens based on ray tracing simulation, based on the experimental measurement of the schlieren phase shift method to measure the curvature radius of a lens sample with high asymmetry. This method solves the problem that existing transmission measurement methods cannot measure the curvature radius of a lens sample with high asymmetry. Summary of the Invention

[0005] To achieve the above objectives, the present invention adopts the following technical solution, the specific steps of which include: Two-dimensional refraction information of parallel light rays after passing through the lens under test is obtained, and the two-dimensional refraction information characterizes the change in the propagation direction of light rays at various positions within the field of view; A ray tracing model is established based on the curvature radius parameters of the lens. The propagation process of parallel light rays through the lens is simulated according to the curvature radius parameters to obtain the corresponding simulated deflection information. An objective function is constructed based on the difference between the two-dimensional deflection information and the simulated deflection information, and the radius of curvature parameter is iteratively optimized based on the objective function. The curvature radius parameter corresponding to the optimal objective function is determined as the measurement result of the front surface curvature radius and the rear surface curvature radius of the lens under test.

[0006] In some alternative implementations, the two-dimensional deflection information is obtained by an optical measurement method based on stripes or phase modulation, and calculated according to the correspondence between the optical phase information and the geometric parameters of the imaging system.

[0007] In some alternative implementations, the two-dimensional deflection information includes the distribution of deflection in two orthogonal directions.

[0008] In some alternative implementations, the objective function is the sum of squares or a weighted sum of squares of the differences between the two-dimensional deflection information and the simulated deflection information.

[0009] In some alternative implementations, the iterative optimization includes searching for multiple sets of parameter combinations in the radius of curvature parameter space to obtain the optimal solution of the objective function.

[0010] In some alternative implementations, the search process includes a combination of coarse-grained search and fine-grained search optimization.

[0011] In summary, compared with the prior art, the above technical solutions proposed by this invention can achieve the following beneficial effects: 1) The image acquisition process of this method utilizes the light deflection information of the lens under a large field of view, and can make full use of the refraction information of the lens under a large field of view; 2) The curvature radius measurement algorithm of this method utilizes the deflection information of transmitted light, which enables simultaneous measurement of the curvature radius of the front and rear surfaces of the lens; 3) The ray tracing simulation algorithm of this method utilizes the deflection information of light on two surfaces, and can separate the influence of the refractive properties of the front and rear surfaces on the deflection angle of light. Attached Figure Description

[0012] Figure 1This is a flowchart of a method for measuring the curvature radius of a lens based on ray tracing simulation, as proposed in an embodiment of the present invention.

[0013] Figure 2 These are four images of sinusoidal horizontal stripes provided in this embodiment of the invention.

[0014] Figure 3 These are four sinusoidal longitudinal stripe images provided in this embodiment of the invention.

[0015] Figure 4 This is a sinusoidal distributed circular stripe image provided in an embodiment of the present invention.

[0016] Figure 5 This is a diagram illustrating the calculation process of the longitudinal deflection angle tangent matrix of the lens provided in an embodiment of the present invention.

[0017] Figure 6 This is a diagram illustrating the calculation process of the tangent matrix of the lateral deflection angle of the lens provided in an embodiment of the present invention.

[0018] Figure 7 This is a calculation process diagram of the lens curvature radius coarse optimization process provided in the embodiment of the present invention.

[0019] Figure 8 This is a calculation process diagram of the lens curvature radius optimization process provided in the embodiment of the present invention.

[0020] Figure 9 This is a table of nominal production values ​​for lens sample parameters provided in this embodiment of the invention.

[0021] Figure 10 This is a comparison table of measurement results of lens curvature radius provided in the embodiments of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention, and this specification can be implemented in many ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this specification; therefore, this specification is not limited to the specific embodiments disclosed below.

[0023] This embodiment provides a method for measuring the radius of curvature of a lens on both sides based on ray tracing simulation. The method specifically includes the following steps: Step S1: Based on the schlieren phase-shift experimental setup, measure the two-dimensional deflection angle of parallel light rays passing through the sample; Step S2: Based on the ray tracing simulation algorithm, calculate the two-dimensional deflection angle of parallel light rays passing through the simulated sample. Based on the experimental and simulated two-dimensional deflection angles, perform residual calculation and iterative optimization to obtain the simulated sample parameters that minimize the residuals, which are used as the measured value of the radius of curvature. Step S1 includes: Step S1.1: Place the lens to be tested on the sample holder of the schlieren phase shift measurement device, and take a four-step phase shift fringe image of the sample under a large field of view using the camera in the device; Step S1.2: Based on the four-step phase-shifted fringe image captured in step S1.1, calculate the phase value of each pixel in the fringe image under the two-dimensional measurement field of view using the phase-shifting algorithm; Step S1.3: Based on the phase value calculated in step S1.2, the phase value is solved from the phase periodic value domain to the continuous phase value domain using the phase unwrapping algorithm; Step S1.4: Based on the continuous phase values ​​obtained in step S1.3, and according to the spatial relationship between the phase values ​​of each pixel in the two-dimensional measurement field of view and the corresponding light rays, calculate the experimental deflection tangent value of the corresponding light rays after passing through the sample; Step S1.5: Based on the experimental deflection tangent value of the light after passing through the sample calculated in step S1.4, calculate the spherical diopter of the sample in the entire two-dimensional field of view using a pixel-by-pixel gradient algorithm; Step S2 includes: Step S2.1: Based on the average value of the spherical refractive power in the central region obtained in step S1.5, calculate the initial value of the radius of curvature according to the lens maker's formula to obtain the initial value of the radius of curvature measurement; Step S2.2: Based on the initial value of the radius of curvature obtained in step S2.1, the simulated deflection angle tangent value under the combination of coarse step size radius of curvature is iteratively calculated using the ray tracing simulation iterative algorithm with coarse step size iteration method. Step S2.3: Calculate the residual value of the simulated deflection angle tangent under the coarse step curvature radius combination calculated in step S2.2 and the experimental deflection angle tangent value of the light after passing through the sample obtained in step S1.4, and obtain the coarse step residual value matrix. Step S2.4: Based on the coarse step size residual value matrix obtained in step S2.3, the minimum residual position under the coarse step size is obtained. The simulated deflection angle tangent value under the combination of curvature radius under the fine step size is calculated iteratively near the minimum residual position using the ray tracing simulation iterative algorithm and the fine step size iterative method. Step S2.5: Calculate the residual value by comparing the simulated deflection angle tangent value under the combination of fine step curvature radius calculated in step S2.4 with the experimental deflection angle tangent value of the light after passing through the sample obtained in step S1.4, and obtain the fine step residual value matrix. Step S2.6: Based on the fine step size residual value matrix obtained in step S2.5, obtain the position of the minimum residual under the fine step size, and use it as the measurement value of the double-sided curvature radius of the lens.

[0024] The four-step phase-shifting fringe image described in step S1.1 includes four sinusoidal horizontal fringe images, four sinusoidal vertical fringe images, and one sinusoidal circular fringe image.

[0025] The image consists of four sinusoidal horizontal stripe images. The phase change direction of the stripes is perpendicular to the optical platform of the instrument. The first image is a zero-phase sine function, and the phase value of each of the other three images is increased by one-quarter of a period based on the previous image.

[0026] The image consists of four sinusoidal longitudinal stripe images. The phase change direction of the stripes is parallel to the optical platform of the instrument. The first image is a zero-phase sinusoidal function, and the phase value of each of the other three images is increased by one-quarter of a period based on the previous image.

[0027] The image is a sinusoidal circular stripe image, with the center of the stripes coinciding with the center of the camera's field of view.

[0028] The phase shift algorithm described in step S1.2 includes the following steps: Step S1.2.1: Based on the measured sinusoidal distribution transverse fringe images, calculate the difference between the first and third images to obtain the sinusoidal intensity value sin(Φ) of the transverse fringe image. h )matrix; Step S1.2.2: Based on the measured sinusoidal distribution transverse fringe images, calculate the difference between the second and fourth images to obtain the cosine intensity value cos(Φ) of the transverse fringe image. h )matrix; Step S1.2.3: The sinusoidal intensity value of the horizontal stripe image from step S1.2.1, sin(Φ... h The matrix is ​​divided element by element by the cosine intensity value of the horizontal stripe image in step S1.2.2, cos(Φ). h The matrix is ​​used to obtain the tangent intensity value tan(Φ) of the horizontal stripe image. h )matrix; Step S1.2.4: Calculate the tangent intensity value tan(Φ) of the horizontal stripe image from step S1.2.3. h Taking the arctangent function of the matrix yields the phase value Φ of the horizontal stripe image. h matrix; Step S1.2.5: Based on the measured sinusoidal longitudinal fringe images, calculate the difference between the first and third images to obtain the sinusoidal intensity value sin(Φ) of the longitudinal fringe image. v )matrix; Step S1.2.6: Based on the measured sinusoidal longitudinal fringe images, calculate the difference between the second and fourth images to obtain the cosine intensity value cos(Φ) of the longitudinal fringe image. v )matrix; Step S1.2.7: The sinusoidal intensity value of the longitudinal stripe image from step S1.2.5, sin(Φ... v The matrix is ​​divided element by element by the cosine intensity value of the vertical stripe image in step S1.2.6, cos(Φ). v The matrix is ​​used to obtain the tangent intensity value tan(Φ) of the longitudinal stripe image. v )matrix; Step S1.2.8: Calculate the tangent intensity value tan(Φ) of the longitudinal stripe image from step S1.2.7. v Taking the arctangent function of the matrix yields the phase value Φ of the vertical stripe image. v matrix.

[0029] The phase unwrapping algorithm described in step S1.3 includes the following steps: Step S1.3.1: Calculate the phase value Φ of the horizontal stripe image obtained in step S1.2.4. h The matrix is ​​used to calculate the phase difference between each pixel and its vertically adjacent pixels, thus obtaining the phase gradient ΔΦ of the horizontal stripe image. h matrix; Step S1.3.2: Calculate the phase gradient ΔΦ of the horizontal stripe image obtained in step S1.3.1. h The matrix is ​​obtained by subtracting the period value from the positive gradient values ​​that are greater than the positive threshold and adding the period value to the negative gradient values ​​that are less than the negative threshold. Step S1.3.3: Taking the center position of the circular stripe image as the zero-phase point, add the value of the corrected phase gradient matrix of the horizontal stripe image at the corresponding pixel to the phase value of each pixel, and use this as the corrected phase value of the corresponding vertical adjacent pixel to obtain the unwrapped phase Φ of the horizontal stripe image. hu matrix; Step S1.3.4: Calculate the phase value Φ of the longitudinal stripe image obtained in step S1.2.8. v The matrix is ​​used to calculate the phase difference between each pixel and its horizontally adjacent pixels, thus obtaining the phase gradient ΔΦ of the vertical stripe image. v matrix; Step S1.3.5: Calculate the phase gradient ΔΦ of the longitudinal stripe image obtained in step S1.3.4. v The matrix is ​​obtained by subtracting the period value from the positive gradient values ​​greater than the positive threshold and adding the period value to the negative gradient values ​​less than the negative threshold. Step S1.3.6: Taking the center position of the circular stripe image as the zero-phase point, add the value of the corrected phase gradient matrix of the vertical stripe image at the corresponding pixel to the phase value of each pixel, and use this as the corrected phase value of the corresponding horizontally adjacent pixel to obtain the unwrapped phase Φ of the vertical stripe image. vu matrix.

[0030] The algorithm for calculating the experimental deflection tangent of the light after passing through the sample, as described in step S1.4, includes the following steps: Step S1.4.1: Determine the unwrapped phase Φ of the horizontal stripe image obtained in step S1.3.3. hu The matrix is ​​obtained by dividing the phase value of each pixel by the tangent period π to obtain the matrix of the number of horizontal stripe periods of the light rays corresponding to the pixel on the image screen. Step S1.4.2: Based on the matrix of horizontal fringe period counts of the corresponding light rays on the image screen obtained in step S1.4.1, multiply the horizontal fringe period value of each pixel by the physical length s of the horizontal fringe period of the image screen. h We obtain the y-matrix representing the vertical distance ray from the center of the camera's field of view to the image screen corresponding to each pixel. Step S1.4.3: Based on the longitudinal distance matrix y between the ray corresponding to each pixel on the image screen and the center of the camera's field of view obtained in step S1.4.2, divide the longitudinal distance value of each pixel by the effective focal length f1 of the objective lens of the schlieren phase shift measurement device to obtain the tangent value of the longitudinal deflection angle tan(α) of the ray corresponding to each pixel after passing through the sample. v )matrix; Step S1.4.4: Determine the unwrapping phase Φ of the longitudinal stripe image obtained in step S1.3.6. vu The matrix is ​​obtained by dividing the phase value of each pixel by the tangent period π to obtain the matrix of the number of vertical stripe periods of the light rays corresponding to the pixel on the image screen. Step S1.4.5: Based on the matrix of vertical fringe period counts of the corresponding light rays on the image screen obtained in step S1.4.4, multiply the vertical fringe period value of each pixel by the physical length s of the vertical fringe period of the image screen. v We obtain the x matrix representing the horizontal distance x of the light rays corresponding to each pixel from the center of the camera's field of view on the image screen. Step S1.4.6: Based on the lateral distance matrix x between the light rays corresponding to each pixel on the image screen and the center of the camera's field of view obtained in step S1.4.5, divide the lateral distance value of each pixel by the effective focal length f1 of the objective lens of the schlieren phase shift measurement device to obtain the tangent value of the lateral deflection angle tan(α) of the light rays corresponding to each pixel after passing through the sample. h )matrix.

[0031] The pixel-wise gradient algorithm described in step S1.5 includes the following steps: Step S1.5.1: Based on the longitudinal deflection angle tangent value tan(α) obtained in step S1.4.3 v The matrix is ​​used to calculate the difference between the tangent of the deflection angle of each pixel and its vertically adjacent pixels, thus obtaining the vertical gradient Δtan(α) of the vertical deflection angle tangent. v )matrix; Step S1.5.2: Based on the longitudinal gradient Δtan(α) of the longitudinal deflection angle tangent value in step S1.5.1. v The matrix is ​​used to divide the longitudinal gradient value of the longitudinal deflection tangent of each pixel by the distance s between the centers of adjacent pixels on the camera and the sample surface. y The longitudinal principal refractive power D of the sample was obtained throughout the two-dimensional vision. y matrix; Step S1.5.3: Based on the tangent value of the lateral deflection angle tan(α) obtained in step S1.4.6 h The matrix is ​​used to calculate the difference between the tangent of the deflection angle of each pixel and its horizontally adjacent pixel, thus obtaining the horizontal gradient Δtan(α) of the horizontal deflection angle tangent. h )matrix; Step S1.5.4: Based on the lateral gradient Δtan(α) of the lateral deflection angle tangent value in step S1.5.3. h The matrix is ​​used to divide the longitudinal gradient value of the longitudinal deflection tangent of each pixel by the distance s between the centers of adjacent pixels on the camera and the sample surface. x The longitudinal principal refractive power D of the sample was obtained throughout the two-dimensional vision. x matrix.

[0032] The spherical refractive power of the sample in the entire two-dimensional field of view is gradually reduced by the longitudinal principal refractive power D. y The elements of the matrix and the lateral principal diopter D x The matrix is ​​obtained by averaging its elements.

[0033] The lens maker's formula described in step S2.1, without the thin lens approximation, is as follows: D=(1-n) / {1 / R1-1 / R2+d*(n-1) / (n*R1*R2)} Where D is the central refractive power of the sample, R1 is the radius of curvature of the front surface of the sample, R2 is the radius of curvature of the rear surface of the sample, d is the central thickness of the sample, and n is the refractive index of the sample. According to the mirror maker's formula, in the initial case of symmetry, the formula for estimating the initial value of the radius of curvature is: R0=[(n-1) / D]*[1+(1-d*D / n)^0.5] Where R0 is the initial value of the radius of curvature. The ray tracing simulation iterative algorithm described in step S2.2 includes the following steps: Step S2.2.1: Based on the rough value of the radius of curvature obtained in step S2.1, calculate the two-dimensional sag matrix of the two surfaces of the lens using the standard sag formula; Step S2.2.2: Based on the two-dimensional vector height matrix of the two surfaces of the lens obtained in step S2.2.1, the two-dimensional vector height matrix is ​​converted into a two-dimensional normal vector matrix through the normal vector transformation formula of the lens surface; Step S2.2.3: Based on the two-dimensional normal vector matrix of the front surface of the lens obtained in step S2.2.2, calculate the refraction of the two-dimensional parallel ray matrix and the two-dimensional normal vector matrix of the front surface according to the vector refraction formula, and obtain the two-dimensional ray matrix after the first refraction. Step S2.2.4: Based on the two-dimensional ray matrix obtained in step S2.2.3, calculate the physical intersection point of the ray at each pixel with the rear surface of the lens, and obtain the intersection point matrix of the two-dimensional ray with the rear surface of the lens; Step S2.2.5: Based on the two-dimensional normal vector matrix of the lens back surface obtained in step S2.2.2, calculate the refraction of the two-dimensional ray matrix and the two-dimensional normal vector matrix of the back surface through the intersection matrix of the two-dimensional ray and the lens back surface and the vector refraction formula, and obtain the outgoing two-dimensional ray matrix. Step S2.2.6: Select different combinations of curvature radii according to the coarse optimization step size, use the newly selected curvature radius value as the initial value for calculation, and repeat steps S2.2.1 to S2.2.5 to obtain the simulated deflection tangent value under different combinations of curvature radii.

[0034] The standard sag formula described in step S2.2.1 is in the following form: z(x, y)={R-[R^2-(x^2+y^2)]^0.5} Where R is the radius of curvature of the corresponding surface, x is the abscissa of the corresponding elevation point, and y is the ordinate of the corresponding elevation point.

[0035] The normal vector transformation formula described in step S2.2.2 has the following form: n(n x ,n y ,n z )={x,y,(zR)} / R Where, n(n x ,n y ,n z ) is the normal vector of the point with surface coordinates (x, y, z) at this location, and each component represents the cosine of the angle with the corresponding coordinate axis.

[0036] The vector refraction formula described in step S2.2.3 is in the following form: t=η*i+{-η*n·i-[1-η^2*(1-(-n·i)^2)]^0.5} Where t is the refracted ray vector, η is the ratio of the refractive index of the medium before and after refraction, and i is the direction vector of the incident ray.

[0037] The residual value calculation algorithm described in step S2.3 specifically involves calculating the residuals one by one with the experimental deflection angle tangents of the corresponding light rays after passing through the sample, based on the simulated deflection angle tangents under the coarse step curvature radius combination obtained in step S2.2, to obtain the coarse step residual value matrix.

[0038] The fine step size iteration method described in step S2.4 specifically involves selecting the position with the smallest residual value in the matrix obtained in step S2.3 as the center point of the curvature radius of the fine step size iteration, selecting different combinations of curvature radius values ​​according to the fine optimization step size, using the newly selected curvature radius value as the initial value for calculation, and repeating steps S2.2.1 to S2.2.5 to obtain the simulated deflection angle tangent value under the fine step size curvature radius combination.

[0039] The residual value calculation algorithm described in step S2.5 specifically involves calculating the residuals one by one with the experimental deflection angle tangents of the corresponding light rays after passing through the sample, based on the simulated deflection angle tangents obtained in step S2.4 under the combination of fine step curvature radii. This yields the fine step residual value matrix.

[0040] The selection of the radius of curvature measurement value in step S2.6 is specifically based on the fine step residual value matrix obtained in step S2.5, selecting the position with the smallest residual value in the matrix as the measurement value of the double-sided radius of curvature of the lens.

[0041] In this embodiment, the samples consist of four lens samples with high asymmetry, and the specific parameters are as follows: Figure 9 As shown.

[0042] Furthermore, the sign constraint for the radius of curvature values ​​in the table is that a surface center convex along the positive direction of the principal optical axis is positive, and a surface convex along the negative direction of the principal optical axis is negative. Therefore, if the radii of curvature of two surfaces have the same sign, it is a crescent-shaped lens; if they are opposite numbers, it is a biconvex or biconcave lens.

[0043] Furthermore, the calculation process diagram in this embodiment takes sample number 1 as an example.

[0044] Figure 2 In this embodiment of the invention, four horizontal stripe images are input to the image screen, so as to... Figure 2 (a) is based on, Figure 2(bd) The phase period of each image increases by π / 2 compared to the previous image.

[0045] Furthermore, in this embodiment, the four horizontal stripe images have a period of 28 pixels.

[0046] Figure 3 In this embodiment of the invention, four vertical stripe images are input to the image screen, with... Figure 3 (a) is based on, Figure 3 (bd) The phase period of each image increases by π / 2 compared to the previous image.

[0047] Furthermore, in this embodiment, the four vertical stripe images have a period of 28 pixels.

[0048] Figure 4 This is an example of a circular stripe image on the input image screen in this embodiment of the invention.

[0049] Furthermore, in this embodiment, the four circular stripe images have a period of 28 pixels.

[0050] Figure 5 This describes the calculation process of the lateral deflection angle tangent matrix in this embodiment of the invention.

[0051] Furthermore, Figure 5 (a) is a lateral fringe image of lens sample number 1 taken by the camera in the schlieren phase-shifting device, compared with... Figure 2 The input image in (a) corresponds to this.

[0052] Furthermore, the image pixel resolution captured by the camera in the schlieren phase-shifting device is 2160*2560, corresponding to a sample field of view of approximately 28 cm*33 cm. The effective measurement range is greater than 20 cm*20 cm, which meets the field of view requirements for most lens quality testing.

[0053] Furthermore, Figure 5 (b) is the tangent intensity matrix of the horizontal stripe image after processing by the phase shift algorithm described in step 1.2.3.

[0054] Furthermore, Figure 5 (c) is the phase value matrix of the horizontal stripe image after processing by the arctangent function in step 1.2.4.

[0055] Furthermore, Figure 5 (d) is the longitudinal phase gradient matrix of the horizontal stripe image after the gradient algorithm processing in step 1.3.1.

[0056] Furthermore, Figure 5(e) is the longitudinally corrected phase gradient matrix of the horizontal stripe image after the gradient correction algorithm in step 1.3.2. More specifically, the selected positive phase threshold is 1 and the selected negative phase threshold is -1.

[0057] Furthermore, Figure 5 (f) is the longitudinal deflection angle tangent matrix after step 1.4.3.

[0058] Furthermore, the tangent period value in step 1.4.1 is π.

[0059] Furthermore, the physical length of the stripe period of the image screen in steps 1.4.2 and 1.4.4 is 980 micrometers.

[0060] Furthermore, the effective focal length of the objective lens of the schlieren phase-shifting measuring device is 101.3 mm.

[0061] Figure 6 This describes the calculation process of the longitudinal deflection angle tangent matrix in this embodiment of the invention.

[0062] Furthermore, Figure 6 (a) is a longitudinal fringe image of lens sample number 1, captured by the camera in the schlieren phase-shifting device, compared with... Figure 3 The input image in (a) corresponds to this.

[0063] Furthermore, Figure 6 (b) is the tangent intensity matrix of the longitudinal stripe image after processing by the phase shift algorithm described in step 1.2.7.

[0064] Furthermore, Figure 6 (c) is the phase value matrix of the longitudinal stripe image after processing by the arctangent function in step 1.2.8.

[0065] Furthermore, Figure 6 (d) is the horizontal phase gradient matrix of the vertical stripe image after the gradient algorithm processing in step 1.3.4.

[0066] Furthermore, Figure 6 (e) is the horizontally corrected phase gradient matrix of the longitudinal stripe image after the gradient correction algorithm in step 1.3.5. More specifically, the selected positive phase threshold is 1 and the selected negative phase threshold is -1.

[0067] Furthermore, Figure 6 (f) is the matrix of tangent values ​​of the lateral deflection angle after step 1.4.6.

[0068] Figure 7This is a diagram showing the calculation process of the coarse optimization of the radius of curvature of lens sample number 1. The initial point of the radius of curvature of surface 1 in the diagram is -156.90 mm. After optimization according to the coarse optimization step size, the radius of curvature of surface 1 is -39.38 mm at the position corresponding to the minimum value of the coarse optimization residual.

[0069] Furthermore, Figure 7 The coarse optimization process in the model has a step size of 1 millimeter.

[0070] Figure 8 This is a diagram illustrating the calculation process for the fine optimization of the radius of curvature of lens sample number 1. The initial point of the radius of curvature of surface 1 in the diagram is [-39.38 mm, -83.02 mm]. Based on the fine optimization step size, the minimum value of the fine optimization residual is obtained. At the corresponding position, the radius of curvature of surface 1 is -38.93 mm, and the radius of curvature of surface 2 is -82.04 mm.

[0071] Furthermore, Figure 8 The fine-tuning process is carried out with a fine-tuning step size of 0.1 mm.

[0072] Figure 10 This is a comparison of the production nominal values, the values ​​measured by this method, and the values ​​measured by a white light interferometer for all lens samples.

[0073] Furthermore, according to Figure 10 The standard deviation calculations of the measurement results show that the maximum standard deviation between the measurement results of this method and the nominal production value is 0.61, corresponding to surface 1 of sample number 3. The maximum standard deviation between the measurement results of this method and the measurement results of the white light interferometer is 0.94, corresponding to surface 2 of sample number 4. It can be seen that the measurement results of this method are in good agreement with the nominal production value and the measurement results of the white light interferometer.

Claims

1. A method for measuring the radius of curvature of a lens on both sides based on ray tracing simulation, characterized in that, Specifically, the following steps are included: Step 1: Obtain two-dimensional refraction information of parallel light rays after passing through the lens under test; Step 2: Establish a ray tracing model based on the curvature radius parameters of the lens on both sides, and calculate the corresponding simulated two-dimensional deflection information; Step 3: Construct an objective function based on the residual between the two-dimensional deflection information and the simulated two-dimensional deflection information, and iteratively optimize the radius of curvature parameter; Step 4: Determine the radius of curvature parameter corresponding to the optimal objective function as the measured value of the double-sided radius of curvature of the lens.

2. The method for measuring the radius of curvature of a lens on both sides based on ray tracing simulation according to claim 1, characterized in that, The two-dimensional deflection information is obtained through the schlieren phase shift method.

3. The method for measuring the radius of curvature of a lens on both sides based on ray tracing simulation according to claim 1, characterized in that, The two-dimensional deflection information includes the amount of deflection in two orthogonal directions after the light passes through the lens under test.

4. The method according to claim 5, characterized in that, The deflection information is calculated based on the correspondence between the phase distribution and the geometric parameters of the imaging system.

5. The method for measuring the radius of curvature of a lens on both sides based on ray tracing simulation according to claim 1, characterized in that, The ray tracing model is based on the radius of curvature parameters of the two surfaces of the lens and is used to describe the refraction process of light on the front and back surfaces of the lens and the propagation process of light within the lens medium.

6. The method for measuring the radius of curvature of a lens on both sides based on ray tracing simulation according to claim 1, characterized in that, The objective function is based on the weighted sum of squares of the differences between experimental and simulated deflection information.

7. The method for measuring the radius of curvature of a lens on both sides based on ray tracing simulation according to claim 1, characterized in that, The iterative optimization involves searching for multiple combinations of curvature radii in the parameter space to obtain the optimal solution.

8. The method for measuring the radius of curvature of a lens based on ray tracing simulation according to claim 7, characterized in that, The search process includes a combination optimization of coarse-grained search and fine-grained search.

9. The method for measuring the radius of curvature of a lens on both sides based on ray tracing simulation according to claim 1, characterized in that, The curvature radius parameter includes the curvature radius of the front surface and the curvature radius of the rear surface of the lens.

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