Correction method for light oblique incidence introduction error in aspheric interference detection

Abstract

The invention discloses a method for correcting an error introduced by oblique incidence of light in aspheric surface interference detection, which relates to the technical field of optical precision measurement and comprises the following steps of: constructing an interference measurement system, and obtaining surface shape error distribution of an aspheric surface to be measured; constructing a corresponding geometrical optical model according to actual space layout parameters of an interference measurement system, and calculating a mapping relation between theoretical space coordinates of an interference measurement result and an illegal oblique incidence angle of a light beam; pixel coordinates of the interference measurement result are converted into theoretical space coordinates, and the oblique incidence angle of each sampling point of the actual surface shape data on the aspheric surface to be measured is calculated through an interpolation algorithm based on the mapping relation; and finally, through the relationship between the surface shape error during oblique incidence and normal incidence and the oblique incidence angle, completing the correction of the light oblique incidence introduction error in the to-be-detected aspheric interference detection. According to the method, the problem of errors caused by oblique incidence of light rays in the interference measurement process of the aspheric element is solved, and the detection precision is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of optical precision measurement, and particularly relates to a method for correcting errors introduced by oblique incidence of light rays in aspheric interference detection. Background Art

[0002] With the development of optical systems towards high resolution, lightweight, and integration, due to their unique geometric characteristics, aspheric optical elements have been widely used in imaging systems, laser processing, precision measurement, aerospace, and other fields. However, the detection and precise control of the normal surface shape error during the manufacturing process of aspheric surfaces have always been the key technical bottlenecks restricting their engineering applications.

[0003] The high performance of aspheric optical elements depends on the precise coincidence of their surface shapes with the theoretical design. The normal surface shape error represents the deviation of the actual surface relative to the designed surface in the normal direction, which will directly lead to wavefront distortion and affect the wavefront control ability and imaging quality of the optical system. At the manufacturing level, deterministic processing techniques such as magnetorheological polishing and ion beam figuring require the normal surface shape error distribution as the parameter for iterative correction of the removal function. If the measured value deviates from the normal direction, it will lead to the accumulation of processing errors and the failure of surface shape convergence. However, in the interference measurement technology for aspheric surface shape detection, the non-image point method or the self-collimation optical path mentioned in Chinese Patent CN117889780A both belong to oblique incidence measurement means, and there is a deviation between their measurement results and the normal surface shape. In the field of ultra-high precision manufacturing, such as extreme ultraviolet lithography and synchrotron radiation light sources, if directly used for processing and correction, it will introduce non-negligible error transmission. Therefore, it is necessary to correct the errors introduced by the oblique incidence of light rays.

[0004] Currently, there is relatively rich research on the correction of oblique incidence angle errors of plane mirrors, while the related research on aspheric surfaces is relatively scarce. In view of this, there is an urgent need to develop a method for correcting errors introduced by the oblique incidence of light rays in aspheric interference detection to achieve high-precision measurement of aspheric elements. Summary of the Invention

[0005] In order to solve the deficiencies of the prior art, the purpose of the present invention is to provide a method for correcting errors introduced by oblique incidence of light rays in aspheric interference detection. This method specifically addresses the problem of errors introduced by the oblique incidence of light rays during the interference measurement of aspheric elements, significantly improving the detection accuracy.

[0006] The present invention is achieved through the following technical solutions:

[0007] A method for correcting errors introduced by oblique incidence of light rays in aspheric interference detection, comprising the following steps:

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

[0009] The interferometric measurement system includes an interferometer module, an off-axis paraboloid module to be measured, and a mirror module. The off-axis paraboloid module to be measured has an aspheric surface to be measured. The interferometer module is used to incident a non-normal beam on the aspheric surface to be measured, and the mirror module is used to receive the reflected beam of the aspheric surface to be measured and make the reflected beam return to the interferometer module along the original path.

[0010] S2: According to the actual spatial layout parameters of the interferometric measurement system, construct a corresponding geometric optical model, and calculate the mapping relationship between the theoretical spatial coordinates of the interferometric measurement result and the oblique incidence angle of the non-normal beam.

[0011] S3: Convert the pixel coordinates of the interferometric measurement result into theoretical spatial coordinates, and based on the mapping relationship, calculate the oblique incidence angles of each sampling point of the actual surface shape data on the aspheric surface to be measured through an interpolation algorithm.

[0012] S4: Finally, complete the correction of the error introduced by the oblique incidence of light in the interferometric detection of the aspheric surface to be measured through the relationship between the surface shape error at oblique incidence and normal incidence and the oblique incidence angle.

[0013] Compared with the prior art, in the interferometric measurement technology for aspheric surface shape detection, the conventional oblique incidence measurement method has a deviation between its measurement result and the normal surface shape. In the field of ultra-high precision manufacturing, such as extreme ultraviolet lithography, synchrotron radiation light source, etc., if it is directly used for processing and correction, the problem of non-negligible error transmission will be introduced. The present invention provides a method for correcting the error introduced by the oblique incidence of light in the interferometric detection of an aspheric surface. The method of the present invention is based on ray tracing, and through precise mathematical modeling, the normal vector formula of a general aspheric surface is derived, and the mapping relationship between the theoretical spatial coordinates of the interferometric measurement result and the oblique incidence angle of the aspheric surface is established. On this basis, the pixel coordinates obtained in the actual measurement are converted into corresponding actual spatial coordinates, and the above mapping relationship is used for interpolation calculation to obtain the oblique incidence angles of each sampling point of the actual surface shape data. Subsequently, according to the relationship between the surface shape error at oblique incidence and normal incidence and the oblique incidence angle, the error correction is completed, and finally the accurate normal surface shape error distribution is obtained. The method realizes the effective correction of the error caused by the oblique incidence angle, is applicable to the application of the aspheric surface interferometric measurement technology in the industrial field, and has good practical value and broad application prospects.

[0014] For further optimization, the interferometric measurement system is constructed by the method of stigmatic points or the principle of autocollimation.

[0015] For further optimization, the interferometer module includes an interferometer main body and a transmissive reference mirror located at the light exit of the interferometer main body.

[0016] The off-axis paraboloid module to be measured includes a mirror body to be measured and a first clamping mechanism for clamping the crystal to be measured, and the aspherical surface to be measured is provided on the mirror body to be measured;

[0017] The mirror module includes a mirror group and a second clamping mechanism for clamping the mirror group.

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

[0019] The computer processing module includes a data analysis and processing unit, and the data analysis and processing unit is used to process the data results 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 to be measured include:

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

[0022] S12: The aspherical surface to be measured reflects the beam to the mirror module, and after being reflected by the mirror module, the reflected beam returns to the aspherical surface to be measured and the interferometer module in turn along the original path, forming interference fringes inside the interference cavity and obtaining measurement phase data;

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

[0024] Furthermore, in step S2, a corresponding geometric optical model is constructed by ray tracing technology.

[0025] Furthermore, in step S2, the specific steps for calculating the mapping relationship include:

[0026] S21: Assume that the mathematical expression of the aspherical surface is:

[0027]

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

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

[0030]

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

[0032] where B2m = 2mA 2m ;

[0033] S24: The normal vector n at the point (x, y, z) of the aspherical surface can be expressed as During the ray tracing process, assume that the ray direction vector of the obliquely incident aspherical surface is v(x, y, z), then the obliquely incident angle can be calculated as:

[0034]

[0035] S25: Finally, establish the mapping relationship f: (x mir , y mir ) → θ between the theoretical space coordinates (x mir , y mir ) of the interference measurement result and the corresponding obliquely incident angle θ(x, y, z) for each coordinate.

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

[0037] S31: Convert the pixel coordinates (x pix , y pix ) of the surface shape data into the corresponding space coordinates (x i , y i ) on the surface of the aspherical workpiece to be measured based on the calibration parameters of the interference measurement system;

[0038] S32: Based on the obliquely incident angle spatial distribution mapping model f: (x mir , y mir ) → θ, calculate the corresponding obliquely incident angle θ of (x i , y i ) through the interpolation algorithm, that is, θ(x i , y i ) = f(x i , y i ).

[0039] Furthermore, in the step S4, the corrected surface shape result is:

[0040]

[0041] Furthermore, the interpolation algorithm is 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] A method for correcting the error introduced by the oblique incidence of light in aspheric interference detection calculates the oblique incidence angles at different positions of the aspheric surface, thereby correcting the error introduced due to the test light not being incident along the normal direction of the aspheric surface in the interference measurement of the non-image point method or the autocollimation optical path, and obtaining the normal surface shape error distribution of the aspheric surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, without creative efforts, other related drawings can also be obtained based on these drawings. In the drawings:

[0045] Figure 1 is a structural diagram of the interference measurement system provided by the present invention;

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

[0047] Marks in the drawings and corresponding component names:

[0048] 1 - Interferometer main body, 2 - Transmission standard mirror, 3 - Aspheric surface to be measured, 4 - First clamping mechanism, 5 - Mirror group, 6 - Second clamping mechanism, 7 - Computer processing module. DETAILED DESCRIPTION OF THE EMBODIMENTS

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

[0050] Embodiment 1:

[0051] This Embodiment 1 provides the specific structure of the interference measurement system, as Figure 1 shown, Figure 1 is an off-axis paraboloid interference measurement optical path diagram based on the non-image point method, including an interferometer module, an off-axis paraboloid module to be measured, a reflecting mirror module of a high-precision spherical surface, an adjustment control mechanism, and a computer processing module.

[0052] The interferometer module includes an interferometer main body 1 and an interferometer projection standard mirror 2; the off-axis paraboloid module to be measured includes an off-axis paraboloid mirror 3 to be measured and a paraboloid mirror clamping mechanism 4; the high-precision spherical surface reflecting mirror module includes a spherical surface reflecting mirror 5 and a spherical mirror clamping and adjustment mechanism 6.

[0053] The interferometer main body 1 generates a parallel light beam. A part of it is reflected by the transmissive reference mirror 2 of the interferometer to form a reference beam; another part passes through the transmissive reference mirror 2 to form a test beam, which is incident on the off-axis paraboloid to be measured on the mirror body to be measured fixed by the first clamping mechanism 4, that is, in the aspheric surface 3 to be measured. After reflection, it is projected onto the reflecting mirror 5 with a high-precision spherical surface fixed by the second clamping structure 6. Subsequently, the light returns along the original path to the interferometer main body, meets the reference beam inside the interferometer and interferes to generate an interference pattern. The data processing is completed by the computer processing module 7 to obtain the surface shape error distribution of the off-axis paraboloid to be measured.

[0054] Among them, the adjustment and control mechanism is used to control the pose states of the parabolic mirror and the spherical mirror. The computer processing module 7 includes a data analysis and processing unit, and the data analysis and processing unit processes the measurement data results of the interferometer to obtain the surface shape error of the off-axis paraboloid to be measured.

[0055] Embodiment 2:

[0056] This Embodiment 2 provides a correction method for the error introduced by the oblique incidence of light in aspheric interferometric detection, including the following specific steps:

[0057] S1. System construction and measurement:

[0058] Based on the non-image-point method or the autocollimation principle, an aspheric oblique incidence interferometric measurement system is built. The system mainly involves the interferometer CCD surface and the aspheric surface 3 to be measured. During measurement, the test beam exits from the interferometer and obliquely incides on the surface of the aspheric surface 3 to be measured at an incident angle θ. After being reflected by a high-precision mirror group, it returns to the interferometer along the original path, forms interference fringes inside the interference cavity and obtains measurement phase data. In the case of only using a high-precision mirror as an auxiliary reflection system, the obtained measurement results can directly reflect the surface shape of the aspheric surface 3 to be measured, or the surface shape error distribution W(x, y) of the aspheric surface can be accurately obtained through absolute detection technology.

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

[0060] Optical modeling is carried out on the interferometric measurement system built in step S1, and the mapping relationship between the oblique incidence angle of the aspheric surface 3 to be measured and the coordinates of the interferometer measurement results is established through the ray tracing method.

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

[0062]

[0063] In the formula, k is the conic coefficient, c is the curvature, r 2 =x 2 +y 2 A 2mis the high-order coefficient.

[0064] To solve the oblique incidence angle at any point on the aspheric surface, it is necessary to first solve its corresponding normal vector n(x, y, z). Let

[0065]

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

[0067]

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

[0069]

[0070] Thus, the normal vector n at the point (x, y, z) on the aspheric surface can be expressed as

[0071] During the ray tracing process, assume that the ray direction vector of the obliquely incident aspheric surface is v(x, y, z). Then, the oblique incidence angle can be calculated as:

[0072]

[0073] Thus, a mapping relationship f: (x mir , y mir ) → θ between the theoretical space coordinates (x mir , y mir ) of the interference measurement result and the oblique incidence angle θ(x, y, z) corresponding to each coordinate is established.

[0074] S3. Coordinate transformation and interpolation:

[0075] Based on the mapping relationship obtained in step S2, convert the pixel coordinates of the interference test result into the test coordinates of the theoretical optical path model, and obtain the oblique incidence angle corresponding to the aspheric surface 3 mirror to be measured through interpolation.

[0076] First, based on the calibration parameters of the interference measurement system (such as the pixel pitch of the interferometer, the off-axis amount of the aspheric surface, etc.), convert the pixel coordinates (x pix , y pix ) of the surface shape data into the spatial coordinates (x i , y i ) corresponding to the surface of the aspheric workpiece to be measured. According to the oblique incidence angle spatial distribution mapping model f: (x mir , y mir) → θ, by applying an appropriate interpolation algorithm, the oblique incidence angle θ corresponding to (x i , y i ) can be calculated, that is, θ(x i , y i ) = f(x i , y i ).

[0077] S4. Error correction:

[0078] After obtaining the oblique incidence angle through interpolation in S3, the interference measurement result can be corrected for the angle, and the corrected surface shape result is:

[0079]

[0080] In the method for correcting the error introduced by the oblique incidence of light in aspheric interference detection, the interpolation method can be one of nearest neighbor interpolation, linear interpolation, bilinear interpolation, cubic spline interpolation, etc.

[0081] In summary, the present invention establishes a ray tracing geometric optical model of an off-axis paraboloid, calculates the normal vector n(x, y, z) and the incident vector v(x, y, z) of the aspheric surface to be measured, and then determines the oblique incidence angle θ(x, y, z), and establishes the mapping relationship f between the theoretical space coordinates (x mir , y mir ) of the interference measurement result and the oblique incidence angle θ(x, y, z): (x mir , y mir ) → θ. Subsequently, using the above mapping relationship f and adopting an appropriate interpolation algorithm, the corresponding oblique incidence angle θ(x i , y i ) is solved according to the spatial coordinates (x i , y i ) of each sampling point of the actual surface shape data. After obtaining the oblique incidence angle corresponding to the surface shape data, based on the relationship between the surface shape error during oblique incidence and normal incidence and the oblique incidence angle, the error introduced by the oblique incidence of light in interference detection can be corrected, so as to obtain a more accurate normal surface shape error distribution.

[0082] The above-provided method for correcting the error introduced by the oblique incidence of light in aspheric interference detection calculates the oblique incidence angles at different positions of the aspheric surface, thereby correcting the error introduced because the test light does not enter along the normal direction of the aspheric surface in the interference measurement of the non-image point method or the autocollimation optical path, and the normal surface shape error distribution of the aspheric surface can be obtained.

[0083] Example 3:

[0084] This Example 3 provides a specific implementation case on the basis of Example 2, such as Figure 2As shown below. A simulation measurement is carried out on an off-axis parabolic mirror based on the method of non-image point.

[0085] The parabolic mirror used has a circular aperture with a diameter of 15 mm, a radius of curvature of 100 mm, an off-axis amount of 50 mm, and is measured using an interferometer with a wavelength of 632.8 nm. The image resolution is 201 pixel × 201 pixel. Without correcting the oblique incidence angle error, the surface shape error distribution is as shown in Figure 2 (a), with a PV value of 1263.92 nm and an RMS value of 119.33 nm. After correcting the error introduced by the oblique incidence of light, the surface shape error distribution is as shown in Figure 2 (b), with a PV value of 1432.52 nm and an RMS value of 133.94 nm. Subtracting the results of the above two cases gives a difference distribution map, as shown in Figure 2 (c). The PV value of this difference map is 180.73 nm and the RMS value is 14.79 nm. It can be seen that there are significant differences in the surface topography before and after correcting the oblique incidence angle error. In the process of ultra-precision optical detection and processing, this difference may have an important impact. And through this method, the error introduced by the oblique incidence of light in aspheric interference detection can be effectively corrected, thereby improving the measurement accuracy.

[0086] The specific embodiments described above further elaborate on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for correcting the error introduced by the oblique incidence of light in aspheric interferometry detection, characterized in that: The following steps are involved: S1: construct an interferometric measurement system and obtain the surface error distribution of the aspheric surface (3) to be measured; The interferometric measurement system comprises an interferometer module, an off-axis parabola module to be measured and a reflector module, wherein the off-axis parabola module to be measured is provided with an aspheric surface (3) to be measured; the interferometer module is used to irradiate an irregular light beam onto the aspheric surface to be measured, and the reflector module is used to receive a reflected light beam from the aspheric surface to be measured and return the reflected light beam to the interferometer module along the original path; S2: constructing a corresponding geometric optical model according to the actual spatial layout parameters of the interferometric measurement system, and calculating the mapping relationship between the theoretical spatial coordinates of the interferometric measurement result and the oblique incident angle of the non-normal light beam; S3: converting the pixel coordinates of the interference measurement result into theoretical space coordinates, and calculating the oblique incident angle of each sampling point of the actual surface shape data on the aspheric surface to be measured by an interpolation algorithm based on the mapping relationship; S4: Finally, the error introduced by the oblique incidence of light in the interference detection of the aspheric surface to be tested is corrected by the relationship between the surface shape error and the oblique incidence angle at oblique incidence and normal incidence.

2. The method for correcting the error introduced by the oblique incidence of light in aspheric interferometry detection according to claim 1, characterized in that: Interferometric measurement systems are constructed using the aberration-free point method or the autocollimation principle.

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

4. The method for correcting the error introduced by the oblique incidence of light in aspheric interferometry detection according to claim 3, characterized in that: The interferometric measurement system further comprises an adjustment control mechanism and a computer processing module (7), wherein the adjustment control mechanism is used to adjust the positions and postures of the first clamping mechanism (4) and the second clamping mechanism (6) respectively; The computer processing module (7) comprises a data analysis and processing unit, and the data analysis and processing unit is used to process the data results measured by the interferometer host (1) to obtain the surface error of the aspheric surface (3) to be measured.

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

6. The method for correcting the error introduced by the oblique incidence of light in aspheric interferometry detection according to claim 1, characterized in that: In step S2, a corresponding geometric optical model is constructed by using ray tracing technology.

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

8. The method for correcting the error introduced by the oblique incidence of light in aspheric interferometry detection according to claim 7, characterized in that: The step S3 also includes the following specific steps: S31: Based on the calibration parameters of the interferometric measurement system, the pixel coordinates (x pix ,y pix ) is converted into the spatial coordinates (x) corresponding to the surface of the aspheric workpiece (3) being measured i ,y i ); S32: Spatial distribution mapping model based on oblique incidence angle f:(x mir ,y mir )→θ, through the interpolation algorithm, calculate (x i ,y i ) corresponds to the oblique incident angle θ, that is, θ(x i ,y i )=f(x i ,y i ).

9. A method for correcting errors caused by oblique incidence of light in aspheric interferometry detection according to claim 8, characterized in that: In step S4, the corrected surface shape result is:

10. A method for correcting errors caused by oblique incidence of light in aspheric 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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