Method for measuring super large curvature radius of large aperture spherical mirror

Abstract

The application discloses a method for measuring a super-long curvature radius of a large-aperture spherical mirror. Main steps are as follows: (1) building a super-long curvature radius measuring optical path of the large-aperture spherical mirror; (2) adjusting a wavefront detector position to a vicinity of a system convergence point, so that a system wavefront can be completely received by a target surface of the wavefront detector; (3) fitting a wave surface obtained by the wavefront detector through a Zernike polynomial, so as to obtain a Zernike 0° Astigmatism item W6 of the system wave aberration; (4) measuring an incidence angle θ of a laser light source to a to-be-measured spherical surface by using a laser tracker; and (5) calculating a curvature radius of the to-be-measured spherical surface. The method can more accurately and objectively measure the curvature radius of the large-aperture spherical mirror, shortens the optical path length, thereby reducing the interference of environmental factors such as vibration, temperature and air flow, and the method can measure both a concave spherical surface and a convex spherical surface.

Description

Technical Field

[0001] This invention belongs to the technical field of optical testing, specifically relating to a method for detecting the ultra-large radius of curvature of a large-aperture spherical mirror, which utilizes systematic wave aberration to measure the large-curvature spherical mirror. Background Technology

[0002] Currently, the methods for measuring the curvature of large curvature spherical mirrors can be divided into two types: direct detection method and indirect detection method.

[0003] Common direct testing methods include the template method, the sphere diameter meter method, the coordinate measuring machine (CMM) method, and the laser tracking method. Among these, the template method and the sphere diameter meter method are simple to operate and fast, allowing results to be obtained simply by placing the component directly on the worktable. These are the most widely used methods for measuring the radius of curvature in optical production. However, the template method is affected by the precision of the template itself and stress variations between the measured mirrors, resulting in low measurement accuracy and susceptibility to subjective factors of the measurement personnel. The sphere diameter meter method calculates the radius of curvature by measuring the sag of the sphere and combining it with the known chord radius. This method has a measurement accuracy of approximately 30 ppm, but its accuracy decreases as the radius of curvature increases. The CMM method scans the measured spherical surface to obtain a three-dimensional point cloud of the spherical shape, then performs spherical fitting to obtain the best-fit sphere, using the radius of the fitted sphere as the measurement result for the radius of curvature. This method has a measurement accuracy of approximately 20 ppm. However, this method is inefficient and unsuitable for spherical mirrors in the fine grinding stage. The laser tracking method calculates the radius of curvature of the test sphere by measuring the defocusing amount of a laser-tracked sphere at the cat's-eye position, the defocusing amount at the confocal position, the distance between the two positions, and the radius of the tracking sphere. Its relative measurement accuracy is approximately 18 ppm, but the measurement process is relatively cumbersome. All of the above measurement methods are contact measurements, and all have the inherent drawback of easily scratching the surface of the sample being tested.

[0004] Indirect detection methods mainly include geometric optics and interferometry. Geometric optics methods include the knife-edge shadow method and the autocollimation method. The knife-edge shadow method is simple to operate, but its measurement accuracy is only 50 ppm and it is highly subjective. The autocollimation method has an accuracy of 500 ppm when measuring curvature radii larger than 5 m. Compared with geometric optics, interferometry offers higher measurement accuracy and is currently the most widely used high-precision measurement method. The classic interferometry uses a phase measurement interferometer to focus on the cat's-eye position and confocal position of the spherical surface being measured, thereby obtaining the radius of curvature. The measurement accuracy can reach 10 ppm. However, for measuring the curvature of spherical mirrors with large radii of curvature, the long optical path and environmental factors such as temperature, vibration, and airflow can significantly interfere with the interpretation of interference fringes, thus increasing the measurement error. Furthermore, the above measurement methods still have significant limitations in measuring the radius of curvature of large-curvature convex spherical mirrors, making them difficult to apply in practical engineering workshops. Summary of the Invention

[0005] To address the aforementioned shortcomings of existing technologies, this invention proposes a method for precisely measuring the ultra-large radius of curvature of a large-aperture spherical mirror using astigmatic wave aberration. This method is an indirect measurement method, which can effectively shorten the optical path for measuring the radius of curvature of a large-curvature spherical mirror, thereby effectively suppressing the influence of environmental factors on interference fringes and reducing measurement errors; and it can simultaneously measure the radius of curvature of concave and convex spherical mirrors.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for measuring the ultra-large radius of curvature of a large-aperture spherical mirror includes the following steps:

[0008] Step 1: Construct the optical path system. The spherical wave laser emitted from the laser interferometer is incident at an angle onto the spherical mirror under test via a beam splitter. After being reflected by the spherical mirror under test, it is incident directly onto a standard spherical mirror. It is then reflected by the standard spherical mirror and returns along the original path to the beam splitter. After being reflected by the beam splitter, it is received by the wavefront detector. The standard spherical mirror in the optical path should satisfy R... s ≥10D s Among them, R s It is the radius of curvature of a standard spherical mirror, D. s Its aperture; the optical parameters of the spherical mirror to be tested should meet the following requirements: In the formula, D is the aperture of the spherical mirror under test; R is the nominal value of the radius of curvature of the spherical mirror under test; θ is the incident angle from the laser interferometer to the spherical mirror under test; and λ is the wavelength of the laser used for measurement. The relationship between the standard spherical mirror and the spherical mirror under test should satisfy D. s ≥1.3D.

[0009] Step 2: Adjust the position of the wavefront detector to near the system focus so that the system wavefront can be completely received by the wavefront detector target surface, and obtain the system wave aberration from the wavefront detector.

[0010] Step 3: Fit the wavefront obtained by the wavefront detector with a Zernike polynomial to obtain the Zernike 0° Asrigmatism term W6 of the wavefront.

[0011] Step 4: Measure the incident angle from the laser interferometer to the spherical surface under test using a laser tracker. Place the laser tracker head near the center normal of the spherical mirror under test, and use the target ball of the laser tracker to sample feature points on the mirror surface and outer contour of the spherical mirror under test, obtaining the mirror point coordinate data set: A1: (x1, y1, z1), (x2, y2, z2), ..., (x i y i , z i ), …(x n y n , z n); External contour data set: A2: (x1, y1, z1), (x2, y2, z2), ..., (x i y i , z i ), …(x n y n , z n The closest plane is fitted using the A1 point set sampled on the mirror surface of the mirror under test; the cylindrical surface containing the outer contour of the mirror under test is fitted using the A2 point set sampled along the generatrix of the cylindrical surface of the outer contour of the mirror under test. The center of the fitted cylindrical surface is projected onto the fitted plane to obtain the center point M of the mirror surface under test. The straight line passing through the center point M and perpendicular to the closest plane is the normal l of the mirror under test. The spatial position of the laser interferometer focus 0 is then located. The target ball of the laser tracker is placed near the focus of the laser interferometer lens. An interference pattern appears on the screen of the laser interferometer host. From the interference pattern, the Zernike Power term coefficient in the wave aberration caused by the defocusing of the target ball can be obtained. Then, the formula is used... Calculate the geometric defocus of the target sphere. Based on the current position of the target sphere and the defocus, spatially locate the focal point O of the laser interferometer. The line OM connecting the interferometer focal point O to the center point M of the sphere under test is the principal optical axis of the system. The angle between the normal l of the mirror under test and the principal optical axis OM of the system can be obtained from the above, denoted as θ.

[0012] Step 5: Substitute the measured parameters and the aperture D of the spherical mirror to be measured into the formula. The radius of curvature R′ of the spherical mirror under test can then be calculated. In the formula, W6 is the Zernike 0°Astigmatism term obtained in step 3, θ is the angle between the normal of the spherical mirror under test and the principal optical axis of the system, and λ is the wavelength of the laser used for detection.

[0013] Compared with the prior art, the beneficial effects of the present invention are:

[0014] This invention provides a method for measuring the radius of curvature of large-curvature spherical mirrors. It can measure the radius of curvature of both concave and convex spherical mirrors. It shortens the test optical path used in traditional methods, effectively suppresses the influence of environmental factors such as airflow and vibration, improves measurement accuracy, and reduces measurement errors. Furthermore, this method is simple to implement, requiring only a simple detection optical path setup. It does not require high-precision optical platforms or instruments such as grating rulers, or complex algorithm programming. It has low environmental requirements and can be implemented in an optical workshop. Attached Figure Description

[0015] Figure 1 This is a flowchart of a method for precisely measuring the ultra-large radius of curvature of a large-aperture spherical mirror using astigmatic wave aberration;

[0016] Figure 2It is an optical path diagram built in optical design software to precisely measure the ultra-large radius of curvature of a large-aperture spherical mirror using astigmatic aberration.

[0017] Figure 3 This is a schematic diagram of the optical path and instrument position for a precision measurement of the ultra-large radius of curvature of a large-aperture spherical mirror using astigmatic aberration.

[0018] Figure 4 This is a schematic diagram of a wavefront detected by a wavefront detector;

[0019] Figure 5 This is a schematic diagram of a laser tracker measuring the angle of incidence of a laser interferometer onto the surface to be measured.

[0020] The markings in the diagram are: 1-Laser interferometer, 2-Spherical mirror under test, 3-Standard spherical mirror, 4-Wavefront detector, 5-Beam splitter, 6-Laser tracker, 7-Laser tracker target sphere. Detailed Implementation

[0021] The invention will now be described in further detail with reference to the accompanying drawings and optical design software.

[0022] This invention discloses a method for measuring the ultra-large radius of curvature of a large-aperture spherical mirror, using apparatus and components such as... Figure 3 The system includes a laser interferometer (1), a spherical mirror under test (2), a standard spherical mirror (3), a wavefront detector (4), a beam splitter (5), a laser tracker (6), and a laser tracker target sphere (7). It utilizes astigmatic wave aberration to precisely measure the ultra-large radius of curvature of large-aperture spherical mirrors, enabling more accurate measurement of the radius of curvature of concave and convex spherical mirrors.

[0023] This embodiment uses a spherical mirror with a curvature radius of 30m and an aperture of 400mm as an example. The method for measuring the ultra-large curvature radius of a large-aperture spherical mirror is as follows: Figure 1 As shown, the specific steps include the following:

[0024] Step 1: Build such a system in optical design software Figure 2 The optical path is shown, where the design parameters of the spherical mirror 2 under test are D′=400mm; R′=30000mm, and the design parameters of the standard spherical mirror 3 are D=500mm; R=7000mm; the incident angle is designed to be θ=10°. The actual testing setup is as follows... Figure 3 The optical path is shown. A spherical laser beam emitted from the laser interferometer is incident at an angle onto the spherical surface under test via a beam splitter. After reflection from the surface under test, it is incident directly onto a standard spherical surface. Reflected again by the standard spherical surface, it returns along the same path to the beam splitter, where it is reflected and received by a wavefront detector. Fine-tuning the pitch and yaw angles of the spherical mirror allows the wavefront of the reflected laser to be observed on the wavefront detector.

[0025] Step 2: Adjust the position of the wavefront detector to near the convergence point of the system so that the wavefront of the system can be completely received by the target surface of the wavefront detector.

[0026] Step 3: Fit the wavefront obtained by the wavefront detector with a Zernike polynomial to obtain the Zernike 0° Astigmatism term W6 of the wavefront.

[0027] Step 4: Use laser tracker 6 to measure the incident angle from laser interferometer 1 to the spherical surface under test. Use laser tracker target sphere 7 to sample feature points of the spherical mirror under test and its outer contour. The sampled mirror point coordinate data set is denoted as: A1: (x1, y1, z1), (x2, y2, z2), ..., (x i y i , z i ), …(x n y n , z n The external contour data set of the mirror is denoted as: A2: (x1, y1, z1), (x2, y2, z2), ..., (x i y i , z i ), …(x n y n , z n The plane mirror surface is fitted using the A1 point set sampled from the mirror surface of the mirror under test; the cylindrical surface containing the outer contour of the mirror under test is fitted using the A2 point set sampled from the generatrix of the cylindrical surface of the outer contour of the mirror under test. The center of the fitted cylindrical surface is projected onto the fitted mirror surface to obtain the center point M of the mirror surface of the mirror under test. The spatial position of the laser interferometer focal point is then located. The laser tracker target sphere is placed near the focal point of the laser interferometer lens. Since the reflective surface of the laser tracker target sphere is a corner prism, an interference pattern appears on the screen of the laser interferometer host. From the interference pattern, the Zernike Power term coefficient in the wave aberration caused by the defocusing of the target sphere can be obtained. Then, the formula... The geometric defocus of the target sphere is calculated. Based on the current position of the target sphere and the defocus, the spatial positioning of the laser interferometer's focus is completed. The line connecting the interferometer's focus to the center point of the sphere under test is the system's principal optical axis. The angle between the normal of the mirror under test and the system's principal optical axis can be obtained from the above, denoted as θ. A schematic diagram of the laser tracker measurement and sampling point distribution, showing θ = 9.982°, is shown below. Figure 5 As shown.

[0028] Step 5: Substitute the measured parameters and the aperture D′ of the spherical mirror to be measured into the formula. The radius of curvature R′ of the spherical mirror under test can then be calculated. In the formula, W6 is the Zernike 0° Astigmatism term obtained in step 2, θ is the incident angle from the laser interferometer to the spherical surface under test measured in step 3, and λ is the laser wavelength used by the laser source. Using this formula and measurement data, the radius of curvature of the spherical surface under test is calculated to be R′=29976.1mm, with a relative error of 0.09%, which meets the requirements for accurately measuring the radius of curvature of a large-curvature spherical mirror.

[0029] The contents not described in detail in this specification are common knowledge to those skilled in the art.

[0030] In summary, this invention discloses a method for precisely measuring the ultra-large radius of curvature of a large-aperture spherical mirror using astigmatic wave aberration. The main steps are: (1) constructing a... Figure 1 The optical path for measuring the ultra-long radius of curvature of the large-aperture spherical mirror shown is as follows: (2) Adjust the position of the wavefront detector to near the convergence point of the system so that the wavefront of the system can be completely received by the target surface of the wavefront detector; (3) Record the Zernike 0° Astigmatism term in the system wave aberration; (4) Use a laser tracker to sample the feature points of the spherical mirror surface and outer contour to establish the spatial geometric model of the mirror under test; (5) Use the derived formula Calculate the radius of curvature of the spherical surface to be measured. The method of this invention can more accurately and objectively measure the radius of curvature of large curvature spherical mirrors, shorten the optical path length, thereby reducing the interference of environmental factors such as vibration, temperature and airflow, and this method can simultaneously measure concave and convex spherical surfaces.

[0031] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for measuring the ultra-large radius of curvature of a large-aperture spherical mirror, characterized in that, Includes the following steps: Step 1: Construct an optical path system for measuring the ultra-long radius of curvature of a large-aperture spherical mirror; the spherical wave laser emitted from the laser interferometer is obliquely incident on the spherical mirror under test through the beam splitter, and after being reflected by the spherical mirror under test, it is incident directly on the standard spherical mirror; after being reflected by the standard spherical mirror, it returns to the beam splitter along the original path, and after being reflected by the beam splitter, it is received by the wavefront detector; Step 2: Adjust the position of the wavefront detector to near the system focus so that the system wavefront can be completely received by the target surface of the wavefront detector, and obtain the system wavefront aberration from the wavefront detector; Step 3: Fit the wavefront obtained by the wavefront detector with Zernike polynomial to obtain the Zernike 0°Astigmatism term W6 of the wavefront; Step 4: Measure the incident angle from the laser interferometer to the spherical mirror under test, i.e., the angle θ between the normal of the spherical mirror under test and the principal optical axis of the system, using a laser tracker. This includes the following steps: Step 4-1: Place the laser tracker head near the center normal of the spherical mirror under test, and use the laser tracker target ball to sample feature points on the mirror surface and outer contour of the spherical mirror under test to obtain the mirror point coordinate data set: A1: External contour data set: A2: ; Step 4-2: Use the A1 point set obtained by sampling on the surface of the spherical mirror to fit the plane mirror surface; use the A2 point set obtained by sampling on the cylindrical surface of the outer contour of the spherical mirror to fit the cylindrical surface where the outer contour of the spherical mirror to fit the plane mirror surface; Step 4-3: Project the center of the fitted cylindrical surface onto the fitted mirror surface to obtain the center point M of the spherical mirror to be tested; the straight line passing through the center point M and perpendicular to the plane mirror surface is the normal of the spherical mirror to be tested; then locate the spatial position of the laser interferometer focus; place the laser tracker target ball near the focus of the laser interferometer lens; Step 4-4: An interference pattern appears on the laser interferometer's main screen. The Zernike Power term coefficient in the wavelet aberration caused by the target sphere defocusing is obtained from the interference pattern; then, using the formula... Calculate the geometric defocusing amount of the target sphere, where R is the nominal value of the radius of curvature of the spherical mirror to be tested; Steps 4-5: Based on the current position of the target sphere and the defocusing amount, complete the spatial positioning of the laser interferometer focus; the line connecting the interferometer focus to the center point of the spherical mirror under test is the system's principal optical axis; Steps 4-6: Determine the angle between the normal of the spherical mirror to be tested and the principal optical axis of the system, denoted as θ; Step 5: Using the formula Calculate the radius of curvature of the spherical mirror to be measured, where λ is the wavelength of the laser used for measurement and D is the aperture of the spherical mirror to be measured.

2. The method for measuring the ultra-large radius of curvature of a large-aperture spherical mirror according to claim 1, characterized in that, In step 1, the standard spherical mirror satisfies R s ≥10D s In the formula R s It is the radius of curvature of a standard spherical mirror, D. s Its aperture; the spherical mirror under test satisfies The relationship between the standard spherical mirror and the spherical mirror under test satisfies D. s ≥1.3D.

3. The method for measuring the ultra-large radius of curvature of a large-aperture spherical mirror according to claim 2, characterized in that, In step 5, substitute the measured parameters and the aperture D of the spherical mirror to be measured into the formula. The radius of curvature R′ of the spherical mirror to be tested can then be calculated.

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