A method for correcting errors introduced by oblique incident light in aspherical interferometry

Abstract

This invention discloses a method for correcting errors introduced by oblique incident light in aspherical interferometry, relating to the field of optical precision measurement technology. The method includes the following steps: constructing an interferometry system and obtaining the surface shape error distribution of the aspherical surface to be measured; constructing a corresponding geometric optical model based on the actual spatial layout parameters of the interferometry system, and calculating the mapping relationship between the theoretical spatial coordinates of the interferometry results and the oblique incident angle of the non-directional beam; converting the pixel coordinates of the interferometry results into theoretical spatial coordinates, and calculating the oblique incident angle of each sampling point of the actual surface shape data on the aspherical surface to be measured using an interpolation algorithm based on the mapping relationship; finally, correcting the errors introduced by oblique incident light in the interferometry of the aspherical surface to be measured by using the relationship between the surface shape error and the oblique incident angle under oblique and normal incidence. This method is specifically designed to address the error problem introduced by oblique incident light during the interferometry of aspherical components, significantly improving the detection accuracy.

Description

Technical Field

[0001] This invention relates to the field of optical precision measurement technology, specifically to a method for correcting errors introduced by the oblique incidence of light in aspherical interferometry. Background Technology

[0002] As optical systems evolve towards higher resolution, lighter weight, and greater integration, aspherical optical elements, due to their unique geometric characteristics, are widely used in imaging systems, laser processing, precision measurement, aerospace, and other fields. However, the detection and precise control of normal surface shape errors during the manufacturing process of aspherical components remains a key technological bottleneck restricting their engineering applications.

[0003] The high performance of aspherical optical elements depends on the precise match between their surface shape and the theoretical design. Normal surface shape error, representing the deviation of the actual surface from the designed surface shape in the normal direction, directly leads to wavefront distortion, affecting the wavefront control capability and imaging quality of the optical system. At the manufacturing level, deterministic processing techniques such as magnetorheological polishing and ion beam shaping require the distribution of normal surface shape error as a parameter for iterative correction of the removal function. If the measured value deviates from the normal, processing errors will accumulate, leading to surface shape convergence failure. However, in interferometric measurement techniques for aspherical surface shape detection, aberration-free methods or the self-collimating optical path mentioned in Chinese patent CN117889780A are both oblique incidence measurement methods, and their measurement results deviate from the normal surface shape. In ultra-high precision manufacturing fields, such as extreme ultraviolet lithography and synchrotron radiation sources, directly using these methods for processing correction will introduce a significant error propagation. Therefore, it is necessary to correct for the error introduced by the oblique incidence of light.

[0004] Currently, there is a wealth of research on the correction of oblique incidence angle errors in plane mirrors, while research on aspherical surfaces is relatively scarce. Therefore, there is an urgent need to develop a correction method for errors introduced by oblique incidence of light rays in aspherical interferometry, in order to achieve high-precision measurement of aspherical components. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention aims to provide a correction method for errors introduced by oblique incident light in aspherical interferometry. This method is specifically designed to address the error problem caused by oblique incident light during interferometry measurement of aspherical components, and significantly improves the detection accuracy.

[0006] This invention is achieved through the following technical solution:

[0007] A method for correcting errors introduced by oblique incident light in aspherical interferometry includes the following steps:

[0008] S1: Construct an interferometric measurement system and obtain the surface shape error distribution of the aspherical surface to be measured;

[0009] The interferometric measurement system includes an interferometer module, a test off-axis parabolic surface module, and a mirror module. The test off-axis parabolic surface module has a test aspherical surface. The interferometer module is used to incident an undirected light beam onto the test aspherical surface, and the mirror module is used to receive the reflected light beam from the test aspherical surface and return the reflected light beam to the interferometer module along the original path.

[0010] S2: Based on the actual spatial layout parameters of the interferometric measurement system, construct the corresponding geometric optical model and calculate the mapping relationship between the theoretical spatial coordinates of the interferometric measurement results and the oblique incidence angle of the illegal beam;

[0011] S3: Convert the pixel coordinates of the interferometric measurement results into theoretical spatial coordinates, and based on the mapping relationship, calculate the oblique incidence angle of each sampling point of the actual surface shape data on the aspherical surface to be measured using an interpolation algorithm;

[0012] S4: Finally, by using the relationship between the surface shape error and the oblique incidence angle under oblique and normal incidence, the error introduced by the oblique incidence of light in the interferometric detection of the aspherical surface under test is corrected.

[0013] Compared to existing technologies, conventional oblique incidence measurement methods in interferometric measurement for aspherical surface shape detection often result in deviations between the measurement results and the normal surface shape. In ultra-high precision manufacturing fields, such as extreme ultraviolet lithography and synchrotron radiation sources, directly using these methods for processing correction introduces a significant error propagation problem. This invention provides a method for correcting errors introduced by oblique incidence in aspherical interferometric detection. The method described in this invention is based on ray tracing and derives the normal vector formula for general aspherical surfaces through precise mathematical modeling, establishing a mapping relationship between the theoretical spatial coordinates of the interferometric measurement results and the oblique incidence angle of the aspherical surface. Based on this, the pixel coordinates obtained from actual measurements are converted into corresponding actual spatial coordinates, and interpolation is performed using the above mapping relationship to obtain the oblique incidence angle of each sampling point in the actual surface shape data. Subsequently, based on the relationship between the surface shape error and the oblique incidence angle under oblique and normal incidence, error correction is completed, ultimately obtaining an accurate normal surface shape error distribution. This method effectively corrects errors caused by oblique incidence angles, is suitable for the application of aspherical interferometric measurement technology in industrial settings, and has good practical value and broad application prospects.

[0014] Further optimization involves constructing an interferometric measurement system using the aberration-free method or the self-collimation principle.

[0015] Furthermore, the interferometer module includes an interferometer main unit and a transmission standard mirror located at the light outlet of the interferometer main unit;

[0016] The off-axis parabolic surface module to be tested includes a mirror body to be tested and a first clamping mechanism for clamping the crystal to be tested, wherein the aspherical surface to be tested is disposed on the mirror body to be tested;

[0017] The reflector module includes a reflector assembly and a second clamping mechanism for holding the reflector assembly.

[0018] Furthermore, the interferometric measurement system also includes an adjustment control mechanism and a computer processing module, wherein the adjustment control mechanism is used to adjust the poses of the first clamping mechanism and the second clamping mechanism respectively;

[0019] The computer processing module includes a data analysis and processing unit, which processes the data measured by the interferometer host to obtain the surface shape error of the aspherical surface to be measured.

[0020] Furthermore, the specific steps for obtaining the surface shape error distribution of the aspherical surface under test include:

[0021] S11: The interferometer module emits a test beam, which is obliquely incident on the aspherical surface to be tested at an incident angle θ.

[0022] S12: The aspherical surface under test reflects the light beam to the mirror module, and after being reflected by the mirror module, the reflected light beam returns to the aspherical surface under test and the interferometer module in sequence along the original path, forming interference fringes inside the interference cavity and acquiring the measured phase data;

[0023] S13: Finally, the surface shape error distribution W(x,y) of the aspherical surface to be measured is obtained based on the measured phase data.

[0024] To further optimize this process, in step S2, a corresponding geometric optical model is constructed using ray tracing technology.

[0025] Further optimization is achieved by including the following specific steps in step S2 for calculating the mapping relationship:

[0026] S21: Assume the mathematical expression for an aspherical surface is:

[0027]

[0028] In the formula, k is the conic coefficient, c is the curvature, and r 2 =x 2 +y 2 A 2m These are higher-order aspherical coefficients;

[0029] S22: Solve for the normal vector n(x,y,z) of the aspherical surface to be measured; Let:

[0030]

[0031] S23: Subsequently, the three partial derivatives of g(x,y,z) were calculated respectively:

[0032] In the formula, B2m=2mA 2m ;

[0033] S24: The normal vector n of the aspherical surface at the point (x,y,z) can be expressed as: In ray tracing, if we let the direction vector of the ray incident obliquely on the aspherical surface be v(x,y,z), then the oblique incidence angle can be calculated as:

[0034]

[0035] S25: Finally, establish the theoretical spatial coordinates (x) of the interferometric measurement results. mir ,y mir The mapping relationship f:(x) to the oblique incidence angle θ(x,y,z) corresponding to each coordinate. mir ,y mir )→θ.

[0036] Furthermore, step S3 also includes the following specific steps:

[0037] S31: Based on the calibration parameters of the interferometric measurement system, the pixel coordinates (x) of the surface data are... pix ,y pix Convert the coordinates (x, y) to the spatial coordinates (x, y) of the surface of the aspherical workpiece being measured. i ,y i );

[0038] S32: Based on the spatial distribution mapping model of oblique incidence angle f:(x mir ,y mir )→θ, and calculate (x) using an interpolation algorithm. i ,y i The oblique incident angle θ corresponding to ) is θ(x i ,y i )=f(x i ,y i ).

[0039] Further optimization is achieved in step S4, where the corrected surface shape is as follows:

[0040]

[0041] Furthermore, the interpolation algorithm is optimized to be one of nearest neighbor interpolation, linear interpolation, bilinear interpolation, and cubic spline interpolation.

[0042] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0043] This invention provides a method for correcting errors introduced by oblique incident light in aspherical interferometry. By calculating the oblique incident angle at different positions on the aspherical surface, the method corrects the error introduced by the test light not being incident along the normal direction of the aspherical surface in interferometry using aberration-free methods or autocollimating optical paths, thereby obtaining the aspherical surface normal shape error distribution. Attached Figure Description

[0044] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0045] Figure 1 A structural diagram of the interferometric measurement system provided by the present invention;

[0046] Figure 2 A comparison diagram before and after the error correction caused by the oblique incidence angle provided by the present invention.

[0047] The attached diagram shows the markings and corresponding component names:

[0048] 1-Interferometer main unit, 2-Transmission standard mirror, 3-Aspherical surface to be measured, 4-First clamping mechanism, 5-Reflector group, 6-Second clamping mechanism, 7-Computer processing module. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0050] Example 1:

[0051] This embodiment 1 provides the specific structure of the interferometric measurement system, such as... Figure 1 As shown, Figure 1 The optical path diagram for off-axis parabolic interferometry based on the aberration-free method includes an interferometer module, an off-axis parabolic surface module to be measured, a high-precision spherical reflector module, an adjustment and control mechanism, and a computer processing module.

[0052] The interferometer module includes an interferometer host 1 and an interferometer projection standard mirror 2; the off-axis parabolic mirror module includes an off-axis parabolic mirror 3 and a parabolic mirror clamping mechanism 4; the high-precision spherical mirror module includes a spherical mirror 5 and a spherical mirror clamping and adjustment mechanism 6.

[0053] The interferometer host 1 generates a parallel light beam. Part of this beam is reflected by the interferometer's transmission standard mirror 2 to form a reference beam; the other part passes through the transmission standard mirror 2 to form a test beam, which is incident on the off-axis parabolic surface to be tested, i.e., the aspherical surface to be tested, fixed by the first clamping mechanism 4. After reflection, it is projected onto the high-precision spherical reflecting mirror 5 fixed by the second clamping structure 6. Subsequently, the light returns to the interferometer host along the original path, encounters the reference beam inside the interferometer, and interferes to generate an interference pattern. The data is processed by the computer processing module 7 to obtain the surface shape error distribution of the off-axis parabolic surface to be tested.

[0054] The adjustment control mechanism is used to control the position and orientation of the parabolic mirror and the spherical mirror. The computer processing module 7 includes a data analysis and processing unit, which processes the data results measured by the interferometer to obtain the surface shape error of the off-axis parabolic surface to be measured.

[0055] Example 2:

[0056] This embodiment 2 provides a method for correcting errors introduced by the oblique incidence of light in aspherical interferometry, including the following specific steps:

[0057] S1. System Construction and Measurement:

[0058] A non-aspheric oblique incidence interferometry system is constructed based on the aberration-free method or the self-collimation principle. The system mainly involves the CCD surface of the interferometer and the aspheric surface 3 to be measured. During measurement, the test beam exits the interferometer and is obliquely incident on the surface of the aspheric surface 3 at an incident angle θ. After being reflected by a high-precision mirror group, it returns to the interferometer along its original path, forming interference fringes inside the interference cavity and acquiring the measured phase data. Using only high-precision mirrors as an auxiliary reflection system, the obtained measurement results can directly reflect the surface shape of the aspheric surface 3, or the surface shape error distribution W(x,y) can be accurately obtained through absolute detection technology.

[0059] S2. Geometric optical modeling and establishment of mapping relationships:

[0060] Optical modeling is performed on the interferometric measurement system built in step S1, and the mapping relationship between the oblique incidence angle of the three aspherical mirrors under test and the coordinates of the interferometer measurement results is established by ray tracing method.

[0061] First, calculate the normal vector of the aspherical surface. Assume the general expression for an aspherical surface is:

[0062]

[0063] In the formula, k is the conic coefficient, c is the curvature, and r 2 =x 2 +y 2 A 2mThese are higher-order coefficients.

[0064] To solve for the oblique incidence angle at any point on an aspherical surface, we first need to solve for its corresponding normal vector n(x,y,z). Let

[0065]

[0066] Then, calculate the three partial derivatives of g(x,y,z) separately. For example, the calculation process for the partial derivative in the x-direction is as follows:

[0067]

[0068] In the formula, B 2m =2mA 2m Similarly, the partial derivatives in the y and z directions can be calculated, thus obtaining the three partial derivatives of g(x,y,z):

[0069]

[0070] Therefore, the normal vector n of the aspherical surface at the point (x,y,z) can be expressed as:

[0071] In ray tracing, if we let the direction vector of the ray incident obliquely on the aspherical surface be v(x,y,z), then the oblique incidence angle can be calculated as:

[0072]

[0073] Thus, the theoretical spatial coordinates (x) of the interferometric measurement results were established. mir ,y mir The mapping relationship f:(x) to the oblique incidence angle θ(x,y,z) corresponding to each coordinate. mir ,y mir )→θ.

[0074] S3. Coordinate Transformation and Interpolation:

[0075] Based on the mapping relationship obtained in step S2, the pixel coordinates of the interference test results are transformed into test coordinates of the theoretical optical path model, and the oblique incidence angle corresponding to the aspherical 3 mirrors under test is obtained by interpolation.

[0076] First, based on the calibration parameters of the interferometry system (such as the interferometer pixel spacing, the off-axis amount of the aspherical surface, etc.), the pixel coordinates (x, y, z) of the surface shape data are determined. pix ,y pix Convert the coordinates (x, y) to the spatial coordinates (x, y) of the surface of the aspherical workpiece being measured. i ,y i According to the spatial distribution mapping model f:(x) of the oblique incidence angle in step S2. mir ,y mirBy applying an appropriate interpolation algorithm, (x) → θ can be calculated. i ,y i The oblique incident angle θ corresponding to ) is θ(x i ,y i )=f(x i ,y i ).

[0077] S4. Error Correction:

[0078] After interpolating the oblique incidence angle at S3, the interferometric measurement results can be angularly corrected. The corrected surface shape is as follows:

[0079]

[0080] The method for correcting errors introduced by oblique incident light in aspherical interferometry detection can be one of nearest neighbor interpolation, linear interpolation, bilinear interpolation, and cubic spline interpolation.

[0081] In summary, this invention establishes a ray-tracing geometric optical model of an off-axis paraboloid, calculates the normal vector n(x,y,z) and incident vector v(x,y,z) of the aspherical surface to be measured, and then determines the oblique incident angle θ(x,y,z), establishing the theoretical spatial coordinates (x,y,z) of the interferometric measurement results. mir ,y mir The mapping relationship between f:(x,y,z) and the oblique incidence angle θ(x,y,z) mir ,y mir )→θ. Then, using the above mapping relationship f, and employing an appropriate interpolation algorithm, the spatial coordinates (x, y, θ) of each sampling point in the actual surface shape data are used to determine the interpolation result. i ,y i Solve for the corresponding oblique incidence angle θ(x) i ,y i After obtaining the oblique incidence angle corresponding to the surface shape data, the error introduced by the oblique incidence angle in the interferometric detection can be corrected based on the relationship between the surface shape error and the oblique incidence angle under oblique and normal incidence, thereby obtaining a more accurate normal surface shape error distribution.

[0082] The above-mentioned correction method for errors introduced by oblique incident light in aspherical interferometry calculation corrects the error introduced by the test light not being incident along the normal direction of the aspherical surface in interferometry without aberration points or autocollimating optical paths, by calculating the oblique incident angle at different positions of the aspherical surface. Thus, the distribution of the normal surface shape error of the aspherical surface can be obtained.

[0083] Example 3:

[0084] This embodiment 3, based on embodiment 2, provides a specific implementation example, such as... Figure 2As shown, a simulation measurement of an off-axis parabolic mirror based on the aberration-free method is performed.

[0085] The parabolic mirror used has a circular aperture of 15 mm in diameter, a radius of curvature of 100 mm, and an off-axis distance of 50 mm. Measurements were performed using an interferometer with a wavelength of 632.8 nm, resulting in an image resolution of 201 pixels × 201 pixels. Without correction for the oblique incidence angle error, the surface shape error distribution is as follows: Figure 2 As shown in (a), its PV value is 1263.92 nm and its RMS value is 119.33 nm. After correcting for the error introduced by the oblique incidence of light, the surface shape error distribution is as follows. Figure 2 As shown in (b), its PV value is 1432.52 nm and its RMS value is 133.94 nm. Subtracting the results from the two cases yields the difference distribution diagram, as shown below. Figure 2 As shown in (c), the PV value of this difference map is 180.73 nm, and the RMS value is 14.79 nm. This demonstrates a significant difference in surface morphology before and after correction for the oblique incidence angle error. Such a difference can have a significant impact on ultra-precision optical inspection and processing. This method can effectively correct the error introduced by oblique light incidence in aspherical interferometry, thereby improving measurement accuracy.

[0086] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., 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 correcting errors introduced by oblique incident light in aspherical interferometry, characterized in that, Includes the following steps: S1: Construct an interferometric measurement system and obtain the surface error distribution of the aspherical surface (3) to be measured; The interferometric measurement system includes an interferometer module, a test off-axis parabolic surface module, and a reflector module. The test off-axis parabolic surface module has a test aspherical surface (3). The interferometer module is used to incident an undirected beam onto the test aspherical surface, and the reflector module is used to receive the reflected beam from the test aspherical surface and return the reflected beam to the interferometer module along the original path. S2: Based on the actual spatial layout parameters of the interferometric measurement system, construct the corresponding geometric optical model and calculate the mapping relationship between the theoretical spatial coordinates of the interferometric measurement results and the oblique incidence angle of the illegal beam; S3: Convert the pixel coordinates of the interferometric measurement results into theoretical spatial coordinates, and based on the mapping relationship, calculate the oblique incidence angle of each sampling point of the actual surface shape data on the aspherical surface to be measured using an interpolation algorithm; S4: Finally, by using the relationship between the surface shape error and the oblique incidence angle under oblique and normal incidence, the error introduced by the oblique incidence of light in the interferometric detection of the aspherical surface under test is corrected.

2. The method for correcting errors introduced by tilted incident light in aspherical interferometry detection according to claim 1, characterized in that, An interferometric measurement system can be constructed using the aberration-free method or the self-collimation principle.

3. The method for correcting errors introduced by oblique incidence of light in aspherical interferometry detection according to claim 1, characterized in that, The interferometer module includes an interferometer host (1) and a transmission standard mirror (2) located at the light outlet of the interferometer host (1). The off-axis parabolic surface module to be tested includes a mirror body to be tested and a first clamping mechanism (4) for clamping the mirror body to be tested, and the aspherical surface (3) to be tested is disposed on the mirror body to be tested; The reflector module includes a reflector assembly (5) and a second clamping mechanism (6) for clamping the reflector assembly (5).

4. The method for correcting errors introduced by tilted incident light in aspherical interferometry detection according to claim 3, characterized in that, The interferometric measurement system also includes an adjustment control mechanism and a computer processing module (7), wherein the adjustment control mechanism is used to adjust the poses of the first clamping mechanism (4) and the second clamping mechanism (6) respectively; The computer processing module (7) includes a data analysis and processing unit, which is used to process the data results measured by the interferometer host (1) to obtain the surface shape error of the aspherical surface (3) to be measured.

5. The method for correcting errors introduced by oblique incidence of light in aspherical interferometry detection according to claim 1, characterized in that, The specific steps for obtaining the surface shape error distribution of the aspherical surface (3) to be measured include: S11: The interferometer module emits a test beam and is obliquely incident on the surface of the aspherical surface (3) to be tested at an incident angle θ; S12: The aspherical surface (3) under test reflects the light beam to the mirror module, and after being reflected by the mirror module, the reflected light beam returns to the aspherical surface (3) under test and the interferometer module in sequence along the original path, forming interference fringes inside the interference cavity and acquiring the measurement phase data; S13: Finally, the surface shape error distribution W(x, y) of the aspherical surface to be measured (3) is obtained based on the measured phase data.

6. The method for correcting errors introduced by tilted incident light in aspherical interferometry detection according to claim 1, characterized in that, In step S2, a corresponding geometric optical model is constructed using ray tracing technology.

7. The method for correcting errors introduced by tilted incident light in aspherical interferometry detection according to claim 1, characterized in that, In step S2, the specific steps for calculating the mapping relationship include: S21: Assume the mathematical expression for an aspherical surface is: ； In the formula, k is the conic coefficient, c is the curvature, and r 2 =x 2 +y 2 A 2m These are higher-order aspherical coefficients; S22: Solve for the normal vector n(x, y, z) of the aspherical surface (3) to be measured; Let: ； S23: Subsequently, the three partial derivatives of g(x, y, z) were calculated respectively: In the formula, B2m = 2mA 2m ; S24: The normal vector n of an aspherical surface at point (x, y, z) can be expressed as n(x, y, z) = In the process of ray tracing, let the direction vector of the ray incident obliquely on the aspherical surface be v(x, y, z), then the oblique incidence angle can be calculated as: ； S25: Finally, establish the theoretical spatial coordinates (x) of the interferometric measurement results. mir , y mir The mapping relationship f:(x, y, z) between the x and z coordinates and the corresponding oblique incidence angle θ(x, y, z). mir , y mir )→θ.

8. The method for correcting errors introduced by tilted incident light in aspherical interferometry detection according to claim 7, characterized in that, Step S3 further includes the following specific steps: S31: Based on the calibration parameters of the interferometric measurement system, the pixel coordinates (x) of the surface data are... pix , y pix (3) Convert to the spatial coordinates (x) of the workpiece surface corresponding to the measured aspherical surface. i , y i ); S32: Based on the spatial distribution mapping model of oblique incidence angle f:(x mir , y mir )→θ, and through an interpolation algorithm, (x) is calculated. i ,y i The oblique incident angle θ corresponding to ) is θ(x i , y i ) = f(x i , y i ).

9. The method for correcting errors introduced by tilted incident light in aspherical interferometry detection according to claim 8, characterized in that, In step S4, the corrected surface shape result is as follows: 。 10. A method for correcting errors introduced by oblique incidence of light rays in aspherical interferometry detection according to any one of claims 1 to 9, characterized in that, The interpolation algorithm is one of nearest neighbor interpolation, linear interpolation, bilinear interpolation, and cubic spline interpolation.

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