An absolute surface shape testing method based on optical interference detection

Abstract

The application relates to an absolute surface shape testing method based on optical interference detection, and particularly relates to a calibration method of absolute surface shape error suitable for planes and spherical surfaces. The method has high testing precision, simple testing mode and can reserve full-spectrum error of a testing element.

Description

Technical Field

[0001] This invention belongs to the field of optical detection, specifically an absolute surface shape testing method for optical interferometry, which is particularly suitable for absolute surface shape testing of planes and spheres. It can obtain the absolute surface shape of planes and spheres, and its testing method is simple, has high testing accuracy, and can preserve the full spectrum error of the test element. Background Technology

[0002] The surface shape inspection of optical components typically employs an interferometer to measure the wavefront error between the component and a reference surface. The surface shape error of the optical component is then calculated based on the surface shape error of the reference surface, usually using a Fizzo interferometer. Since the surface shape error of the reference surface introduces wavefront error, a three-sided absolute inspection method is generally used to obtain the absolute surface shape of each component. This three-sided mutual inspection method typically involves testing three components in pairs, and obtaining the absolute surface shape of the component through addition and subtraction operations, rotation to eliminate asymmetric terms, and least squares fitting. However, this method has limitations in computational accuracy, inability to obtain high-frequency surface shape errors within the component, and the need for multiple component rotations and testing during the process. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and propose an absolute surface shape detection method for optical interferometry.

[0004] The technical solution adopted by this invention to solve the technical problem is as follows:

[0005] An optical interferometric detection method for absolute surface shape detection, comprising the following steps:

[0006] Step 1: Let the test surfaces of components a, b, and c be A, B, and C, respectively, and let the radii of the three test surfaces be equal, denoted as Radius; set the calibration distance D, and D... <Radius;

[0007] Mark the center positions of test surfaces A, B, and C, and mark the positive x-axis direction (D, 0) and positive y-axis direction (0, D);

[0008] Step 2: In the interferometer test optical path, align the center mark point on test surface A of component a and the center mark point on test surface B of component b. At the same time, align the mark point on test surface A of component a in the positive y-axis direction with the mark point on test surface B of component b in the positive y-axis direction. Perform the interferometric test and obtain the measured value M1(x,y) using the calibration coordinate system of test surface B as the reference.

[0009] Step 3: Align the center mark on test surface B of component b with the center mark on test surface C of component c. At the same time, align the mark on test surface B of component b in the positive y-axis direction with the mark on test surface C of component c in the positive y-axis direction. Perform an interference test and obtain the measured value M2(x, y) using the calibration coordinate system of test surface C as the reference.

[0010] Step 4: Align the center mark on test surface C of component c with the center mark on test surface A of component a. At the same time, align the mark on test surface C of component c in the positive y-axis direction with the mark on test surface A of component a in the positive y-axis direction. Perform an interference test and obtain the measured value M3(x,y) using the calibration coordinate system of test surface A as the reference.

[0011] Step 5: When converting rectangular coordinates to polar coordinates, M represents the total number of samples along the angular direction. Calculate the total number of effective signal frequencies NF(θ) under different rotation angles θ, using the following formula:

[0012] NF(θ)=M-num(θ·m / 360)

[0013] Where m takes values ​​of 0, 1, 2…M-1, and num(Δ) is the number of non-zero values ​​in Δ;

[0014] Step Six: Select different rotation angles θ1, θ2…θ l , where l is the total number of selected angles, ensuring that the total number of effective signal frequencies is greater than αM, where α is between 0 and 1;

[0015] Step 7: In the interferometer test optical path, align the center mark on test surface A of component a with the center mark on test surface B of component b. Simultaneously align the mark on test surface A of component a with the mark on test surface B of component b along the positive y-axis. Rotate component b clockwise around the center of test surface B by different angles θ1, θ2…v. l Interference tests were conducted, and the test results M4(x,y), M5(x,y)...M were obtained. 3+l (x, y);

[0016] Step 8: Calculate the even-symmetric surface shape error A of test surfaces A, B, and C. even (x, y), B even (x, y) and C even (x, y), as shown in the following formula.

[0017]

[0018]

[0019]

[0020] Step 9: Calculate the test surface shapes M4(x,y), M5(x,y)...M 3+l The difference between (x, y) and M1(x, y), RD1(x, y), RD2(x, y)...RD l (x, y), as shown in the following formula.

[0021]

[0022]

[0023] Step 10: RD1(x, y), RD2(x, y), ... RD l (x, y), using bispline surface interpolation, RD1(x, y), RD2(x, y), ... RD in polar coordinate form. l (x,y) is RD1(n,m), RD2(n,m),…RD l (n, m), where n is the discrete sample 0, 1, ..., N with an interval of ΔR in the radial direction, and m is the discrete sample 0, 1, ..., M with an interval of Δθ in the angular direction, where N and M are the total number of samples;

[0024] Step 11: Calculate RD1(x, y), RD2(x, y), ... RD l The signal processing matrices SM1(n,m), SM2(n,m), ...SM2(n,m) of (x,y) are: l (n, m), as shown in the following formula.

[0025]

[0026] Where Imag{Δ} represents the imaginary part of Δ, and FFT[Δ] represents the Fourier transform of Δ. j is the imaginary number sign;

[0027] Step 12: Calculate the test surface shape B and the odd-symmetric surface shape error B. odd (x, y), as shown in the following formula.

[0028]

[0029] Where Rect{Δ} represents the real part of Δ, and FFT -1 [Δ] represents the inverse Fourier transform of Δ;

[0030] Step 13: Calculate and determine the absolute surface shapes of test surfaces A, B, and C as A(x, y), B(x, y), and C(x, y), as shown in the following formula.

[0031] B(x, y) = B odd(x, y) + B even (x, y),

[0032] A(x,-y)=M1(x,y)-B(x,y),

[0033] C(x,y)=M2(x,y)-B(x,-y).

[0034] The advantages of this invention patent are:

[0035] This invention can test and calibrate the absolute surface shape of planar and spherical optical elements. The method has high testing accuracy and simple testing method, while preserving the full spectrum error of the tested element. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of an interference test for a test element.

[0037] Figure 2 To calculate the effective frequency count under different rotation angles;

[0038] Figure 3 To verify the calculation results of the absolute surface shape testing method for optical interferometry.

[0039] Figure 3 (a) represents the test results M1(x,y), M2(x,y), M3(x,y), M4(x,y), and M5(x,y).

[0040] Figure 3 (b) is the even-symmetric surface shape error A of test surfaces A, B, and C. even (x, y), B even (x, y) and C even (x, y),

[0041] Figure 3 (c) Calculate the differences between the test surface shapes M4(x,y), M5(x,y) and M1(x,y), RD1(x,y), RD2(x,y).

[0042] Figure 3 (d) Calculate the odd symmetry surface shape error B of the test surface shape B. odd (x, y),

[0043] Figure 3 (e) is for calculating the absolute surface shape results A(x,y), B(x,y), and C(x,y). Detailed Implementation

[0044] The present invention will be further described below with reference to embodiments, but these should not be construed as limiting the scope of protection of the present invention.

[0045] An absolute surface shape testing method based on optical interferometry is adopted, including the following steps:

[0046] 1) See Figure 2 Calculate the total number of effective signal frequencies at different discrete angles (1°, 2°, 3°…365°) when the number of discrete signals in polar coordinate angles is 360°. Figure 2 As shown, according to the calculation, the total effective frequency is 365 when the rotation angle is 10° and 20°, which meets the test requirements. Therefore, the rotation angle is set to 10° and 20°.

[0047] 2) See Figure 1 For components a, b, and c, the test surfaces are A, B, and C, respectively, and all three test surfaces have the same radius of 150 mm. The calibration distance is set to 120 mm. Using a coordinate measuring machine, marks are made at the center positions of test surfaces A, B, and C, and also on the positive x-axis (120 mm, 0 mm) and positive y-axis (0 mm, 120 mm) of test surfaces A, B, and C.

[0048] 3) See Figure 1 , 3 In the interferometer test optical path, the centers of test surface A and test surface B and the marked points in the positive y-axis direction are aligned to perform an interferometric test. The measured value is M1(x,y) with the calibration coordinate system of test surface B as the reference. The centers of test surface B and test surface C and the marked points in the positive y-axis direction are aligned to perform an interferometric test. The measured value is M2(x,y) with the calibration coordinate system of test surface C as the reference. The centers of test surface C and test surface A and the marked points in the positive y-axis direction are aligned to perform an interferometric test. The measured value is M3(x,y) with the calibration coordinate system of test surface A as the reference.

[0049] 4) See Figure 1 , 3 Align the center of test surface A and test surface B with the mark point in the positive direction of the y-axis, rotate surface B counterclockwise by 10° and 20°, test the wavefront error of surface A and the rotated surface B, and obtain the measured values ​​M4(x,y) and M5(x,y).

[0050] 5) Calculate A even (x, y), B even (x, y) and C even (x, y), as shown in the following formula.

[0051]

[0052]

[0053]

[0054] 6)Reference Figure 3 The calculated differences between the test surfaces M4(x,y), M5(x,y) and M1(x,y) are obtained as RD1(x,y) and RD2(x,y), as shown in the following formula.

[0055] RD1(x,y)=M4(x,y)-M1(x,y),

[0056] RD2(x,y)=M4(x,y)-M1(x,y);

[0057] 7) Convert RD1(x,y) and RD2(x,y) into polar coordinates RD1(n,m) and RD2(n,m) using double spline surface interpolation, where n is the discrete sample 0, 1, ..., 301 with an interval of 0.5mm in the radial direction, and m is the discrete sample 0, 1, ..., 359 with an interval of 1° in the angular direction;

[0058] 8) After performing Fourier transforms on RD1(n, m) and RD2(n, m), multiply by the del coefficients, and take the imaginary part of the calculation result to obtain SM1(n, m) and SM2(n, m), where j is the imaginary number sign;

[0059] 9)Reference Figure 3 After averaging SM1(n,m) and SM2(n,m) to obtain SM(n,m), perform an inverse Fourier transform on SM(n,m) and take the real part to obtain the odd symmetry surface shape error B of the test surface shape B. odd (x, y);

[0060] 10)Reference Figure 3 The absolute shapes of test surfaces A, B, and C are calculated and determined as A(x, y), B(x, y), and C(x, y), respectively, as shown in the following formula.

[0061] B(x, y) = B odd (x, y) + B even (x, y),

[0062] A(x,-y)=M1(x,y)-B(x,y),

[0063] C(x,y)=M2(x,y)-B(x,-y).

Claims

1. An absolute surface shape testing method based on optical interferometry, the method comprising the following steps: 1) Let the test surfaces of components a, b, and c be A, B, and C, respectively, and let the radii of the three test surfaces be equal and denoted by Radius; set the calibration distance D, and D... <Radius; Mark the center positions of test surfaces A, B, and C, and mark the positive x-axis direction (D, 0) and positive y-axis direction (0, D); 2) In the interferometer test optical path, align the center mark point on test surface A of component a and the center mark point on test surface B of component b. At the same time, align the mark point on test surface A of component a in the positive y-axis direction with the mark point on test surface B of component b in the positive y-axis direction. Perform the interferometric test and obtain the measured value M1(x,y) with the calibration coordinate system of test surface B as the reference. Align the center mark on test surface B of component b with the center mark on test surface C of component c, and align the mark on test surface B of component b in the positive y-axis direction with the mark on test surface C of component c in the positive y-axis direction. Perform an interference test and obtain the measured value M2(x,y) using the calibration coordinate system of test surface C as the reference. Align the center mark on test surface C of component c with the center mark on test surface A of component a, and align the mark on test surface C of component c with the mark on test surface A of component a in the positive y-axis direction. Perform an interference test and obtain the measured value M3(x,y) using the calibration coordinate system of test surface A as the reference. 3) When converting rectangular coordinates to polar coordinates, M represents the total number of samples along the angular direction. The total number of effective signal frequencies NF(θ) under different rotation angles θ is calculated using the following formula: NF(θ)=M-num(θ·m / 360) (1) Where m takes values ​​of 0, 1, 2…M-1, and num(Δ) is the number of non-zero values ​​in Δ; 4) Select different rotation angles θ1, θ2…θ l , where l is the total number of selected angles, ensuring that the total number of effective signal frequencies is greater than αM, where α is between 0 and 1; 5) In the interferometer test optical path, align the center mark on test surface A of component a with the center mark on test surface B of component b. Simultaneously align the mark on test surface A of component a with the mark on test surface B of component b in the positive y-axis direction. Rotate component b clockwise around the center of test surface B by different angles θ1, θ2…θ l Interference tests were conducted, and the test results M4(x,y), M5(x,y)...M were obtained. 3+l (x,y); 6) Calculate the even-symmetric surface shape error A of test surfaces A, B, and C. even (x, y), B even (x, y) and C even (x, y), as shown in the following formula. 7) Calculate the measured values ​​M4(x, y), M5(x, y)...M 3+l The differences between (x, y) and M1(x, y) are RD1(x, y), RD2(x, y), ... RD l (x, y), as shown in the following formula. RD1(x,y)=M4(x,y)-M1(x,y), RD2(x,y)=M5(x,y)-M1(x,y), RD l (x,y)=M 3+l (x,y)-M1(x,y); (5) 8) Use bispline surface interpolation to interpolate RD1(x,y), RD2(x,y), ... RD in polar coordinate form. l (x, y) is transformed into RD1(n, m), RD2(n, m), ... RD l (n, m), where n is the discrete sample 0, 1, ..., N with an interval of ΔR in the radial direction, and m is the discrete sample 0, 1, ..., M with an interval of Δθ in the angular direction, where N and M are the total number of samples; 9) Calculate RD1(x, y), RD2(x, y), ... RD l The signal processing matrices SM1(n,m), SM2(n,m), ...SM2(n,m) of (x,y) are: l (n, m), as shown in the following formula. SM1(n,m)=Imag{del·FFT[RD1(n,m)]}, SM2(n,m)=Imag{del·FFT[RD2(n,m)]}, SM l (n,m)=Imag{del·FFT{RD l (n,m)]}, (6) Where Imag{Δ} represents the imaginary part of Δ, and FFT[Δ] represents the Fourier transform of Δ. j is the imaginary number sign; 10) Calculate the test surface shape B, odd symmetry surface shape error B odd (x, y), as shown in the following formula. Where Rect{Δ} represents the real part of Δ, and FFT -1 [Δ] represents the inverse Fourier transform of Δ; 11) Calculate the absolute shapes A(x, y), B(x, y), and C(x, y), as shown in the following formula. B(x,y)=B odd (x,y)+B even (x,y) (8) A(x,-y)=M1(x,y)-B(x,y) (9) C(x,y)=M2(x,y)-B(x,-y) (10).

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