A spherical reference mirror calibration method based on multi-sphere randomness

Abstract

The present invention discloses a spherical reference mirror calibration method based on multi-ball randomness. The method is as follows: First, build a random ball measurement platform; then randomly select small balls from multiple random balls and fix them at the base position, turn on the interferometer, adjust the relative position between the spherical reference mirror and the random ball to cause interference between the spherical reference mirror and the random ball, and measure the data once; then remove the random ball, repeat multiple groups of random ball measurements, obtain multiple groups of random ball measurement results, perform weighted averaging on the multiple measurement results, and the result after weighted averaging is the calibration result of the spherical reference mirror; finally, use the Zernike polynomial to perform aberration analysis on the calibration result of the spherical reference mirror. The present invention avoids the overlap of the random ball measurement areas during the calibration process of the spherical reference mirror, reduces the coherence of the measurement results, and improves the accuracy of the measurement results. The measurement platform has a simple structure and is easy to operate.

Description

Technical Field

[0001] The present invention relates to the technical field of optical interference metrology, and in particular to a spherical reference mirror calibration method based on multi-sphere randomness. Background Art

[0002] With the development of technology, the requirements for the surface shape accuracy of optical components are getting higher and higher. The spherical absolute testing method was first proposed by Jenson and applied in a Twyman interferometer. Since then, Zygo Corporation (Truax B E. Absolute interferometric testing of spherical surfaces[J]. Proceedings of SPIE - The International Society for Optical Engineering, 1989, 966.) and Wkyo Corporation (Creath K, Wyant J C. Absolute measurement of spherical surfaces[J]. Proceedings of SPIE - The International Society for Optical Engineering, 1991, 1332:2 - 7.) have utilized the characteristics of Zernike polynomials to separate the surface shape error of the measured spherical surface from that of the reference surface, and completed the absolute testing of spherical surfaces respectively.

[0003] The calibration methods of spherical reference mirrors include the two-sphere method, the translation-rotation method, the three-sphere method, and the random sphere method. During the measurement process of the two-sphere method, the measurement of the cat's-eye position with non-common optical paths will introduce additional aberrations and is susceptible to environmental noise, resulting in inaccurate detection results. During the measurement process of the translation-rotation method, the translation operation will introduce tilt, making it difficult to eliminate the astigmatism term in the measurement results. The three-sphere method requires three spherical reference mirrors with comparable accuracies, and in actual measurement, the position requirements for the spherical mirrors are strict. The random sphere method has a simple measurement principle, higher efficiency, and it is easier to obtain the surface shape result of the spherical reference mirror.

[0004] The random ball method was first proposed by Parks (Parks, R.E., Evans, C.J. and L. Shao. Calibration of interferometer transmission spheres [J]. Optical Fabrication and Testing Workshop OSA Technical Digest Series, 1998, 12, 80 - 83.). He used a chrome-plated metal ball to interfere with the reference surface of the interferometer, averaged the measurement results, and obtained the surface shape error of the spherical reference mirror. Griesmann (Griesmann U, Wang Q, Soons J, et al. A simple ball averager for reference sphere calibrations [J]. Optical Manufacturing & Testing VI, 2005.) et al. used an automatic rotation device for random balls to study the convergence of the mean value of random balls under random motion. Yue (Yue Z, Ghim Y S, Davies A. Self calibration for slope-dependent errors in optical profilometry by using the random ball test [J]. Proceedings of SPIE - The International Society for Optical Engineering, 2012, 8493(10): 729 - 740.) et al. combined the random ball method with the transmission wavefront detection of microlenses and studied the hysteresis error. However, during each measurement of the random ball and the spherical reference mirror, there is an overlap problem on the measured surface of the random ball, and the coherence of the measurement results of the spherical reference mirror is relatively high, reducing the accuracy of the measurement results. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for calibrating a spherical reference mirror based on multi-ball randomness, so as to avoid the problem of overlapping measurement areas of random balls in the static random ball calibration method, reduce the coherence of the measurement results of the spherical reference mirror, and improve the accuracy of the measurement results of the spherical reference mirror calibration method.

[0006] The technical solution for achieving the purpose of the present invention is: A method for calibrating a spherical reference mirror based on multi-ball randomness, comprising the following steps:

[0007] Step 1, Build a random ball measurement platform;

[0008] Step 2: Randomly select small balls from multiple random balls and fix the random balls at the base position;

[0009] Step 3: Turn on the interferometer, adjust the relative position of the spherical reference mirror and the random ball so that the spherical reference mirror and the random ball interfere, and measure the data once;

[0010] Step 4: Remove the random ball, repeat multiple groups of random ball measurements, obtain multiple groups of random ball measurement results, perform weighted averaging on the multiple measurement results, and the result after weighted averaging is the calibration result of the spherical reference mirror;

[0011] Step 5: Use the Zernike polynomial to perform aberration analysis on the calibration result of the spherical reference mirror.

[0012] Compared with the prior art, the significant advantages of the present invention are: (1) avoiding the overlap of the random ball measurement areas during the calibration process of the spherical reference mirror, reducing the coherence of the measurement results; (2) the weighted averaging algorithm improving the accuracy of the measurement results; (3) the simple structure of the measurement platform and easy operation. Brief Description of the Drawings

[0013] Figure 1 It is a schematic flow chart of the method for calibrating a spherical reference mirror based on multi-ball randomness of the present invention.

[0014] Figure 2 It is a schematic structural diagram of the random ball measurement platform in the present invention. Detailed Embodiment

[0015] A method for calibrating a spherical reference mirror based on multi-ball randomness of the present invention includes the following steps:

[0016] Step 1: Build a random ball measurement platform;

[0017] Step 2: Randomly select small balls from multiple random balls and fix the random balls at the base position;

[0018] Step 3: Turn on the interferometer, adjust the relative position of the spherical reference mirror and the random ball so that the spherical reference mirror and the random ball interfere, and measure the data once;

[0019] Step 4: Remove the random ball, repeat multiple groups of random ball measurements, obtain multiple groups of random ball measurement results, perform weighted averaging on the multiple measurement results, and the result after weighted averaging is the calibration result of the spherical reference mirror;

[0020] Step 5: Use the Zernike polynomial to perform aberration analysis on the calibration result of the spherical reference mirror.

[0021] As a specific example, the building of the random ball measurement platform described in Step 1 is as follows:

[0022] The random sphere measurement platform includes a Fizeau interferometer 1, a spherical reference mirror 2, a random sphere base 3, and an adjustment bracket 4. The spherical reference mirror 2 is fixed in the Fizeau interferometer 1, and the random sphere base 3 is fixed in the adjustment bracket 4 to complete the construction of the random sphere measurement platform.

[0023] As a specific example, for randomly selecting a small sphere from multiple random spheres and fixing the random sphere at the base position in step 2, it is as follows:

[0024] Prepare multiple random spheres as the random spheres for the experiment. Randomly select one small sphere during the experiment and fix it on the random sphere base 3.

[0025] As a specific example, for the random spheres described in step 2, small spheres with the same precision, the same diameter, and the same material are selected.

[0026] As a specific example, the number of the random spheres described in step 2 is 20.

[0027] As a specific example, for turning on the interferometer and adjusting the relative positions of the spherical reference mirror and the random sphere to cause interference between the spherical reference mirror and the random sphere and measure a set of data in step 3, it is as follows:

[0028] Turn on the interferometer. By adjusting the position of the adjustment bracket 4, make the center of the random sphere confocal with the spherical reference mirror, cause interference between the spherical reference mirror and the random sphere, and measure a set of data. The single measurement result is:

[0029]

[0030] Among them, W R is the wavefront reflected by the spherical reference mirror, is the wavefront reflected by the surface of the random sphere, and W n is the test wavefront obtained by the superposition of the two.

[0031] As a specific example, for removing the random sphere in step 4, repeating multiple groups of random sphere measurements, obtaining multiple groups of random sphere measurement results, and performing weighted averaging on the multiple measurement results, and the result after weighted averaging is the calibration result of the spherical reference mirror, it is as follows:

[0032] Step 4.1: Remove the measured random sphere, randomly select a small sphere from multiple random spheres and fix it on the random sphere base 3 to keep the spherical reference mirror and the random sphere in interference, and measure a set of data;

[0033] Step 4.2: Repeat step 4.1 until all 20 random spheres have interfered with the spherical reference mirror;

[0034] Step 4.3: Perform weighted averaging on the multiple measurement results of the random spheres, and the result after weighted averaging is the calibration result of the spherical reference mirror.

[0035] As a specific example, the weighted average of the multiple measurement results of the random sphere in step 4.3 is taken, and the result after the weighted average is the calibration result of the spherical reference mirror, which is specifically as follows:

[0036] Step 4.3.1: Take the average of the multiple measurement results of the random sphere, and the average result is:

[0037]

[0038] where N is the number of measurements of the random sphere, and W n is the test wavefront superimposed by the two, and W R is the wavefront reflected by the spherical reference mirror, is the wavefront reflected by the light from the surface of the random sphere, is the mean value of the surface shape distribution of the random sphere;

[0039] Step 4.3.2: Subtract the single measurement result of the random sphere from the average result of the random sphere respectively:

[0040]

[0041] where Δ is the difference between the single measurement result of the random sphere and the average result of the random sphere, and the correlation between the single measurement result of the random sphere and the average measurement result of the random sphere is judged according to the magnitude of the difference;

[0042] Step 4.3.3: Based on Δ, the single measurement results of the random sphere are weighted and averaged according to the magnitude of the correlation;

[0043] Step 4.3.4: The actual measurement result of the random sphere is obtained as:

[0044]

[0045] where a n is the weighting coefficient,

[0046] As a specific example, the aberration analysis of the calibration result of the spherical reference mirror using Zernike polynomials in step 5 is specifically as follows:

[0047] The calibration result of the spherical reference mirror is W R , which is represented by the following Zernike polynomial:

[0048]

[0049] where (x, y) is the normalized Cartesian coordinate system, and Z j (x, y) is the j-th order Zernike term, and a jis the weight coefficient of the corresponding j-th order Zernike term. Aberration analysis is performed on the calibration result of the spherical reference mirror according to the above formula.

[0050] The following further elaborates on the present invention in detail in conjunction with the accompanying drawings and specific embodiments.

[0051] Embodiment

[0052] Combined with Figures 1 to 2 , the spherical reference mirror calibration method based on multi-sphere randomness of the present invention includes the following steps:

[0053] Step 1: Build a random sphere measurement platform, specifically as follows:

[0054] The random sphere measurement platform includes a Fizeau interferometer 1, a spherical reference mirror 2, a random sphere base 3, and an adjustment bracket 4;

[0055] Fix the spherical reference mirror 2 in the Fizeau interferometer 1, and fix the random sphere base 3 in the adjustment bracket 4 to complete the construction of the random sphere measurement platform.

[0056] Step 2: Randomly select a small sphere from multiple random spheres and fix the random sphere at the base position, specifically as follows:

[0057] Prepare 20 small spheres with the same precision, diameter, and material as the experimental random spheres. Randomly select one small sphere during the experiment and fix it at the position of the random sphere base 3.

[0058] Step 3: Turn on the interferometer, adjust the relative positions of the spherical reference mirror and the random sphere to cause interference between the spherical reference mirror and the random sphere, and measure a set of data, specifically as follows:

[0059] Turn on the interferometer. By adjusting the position of the adjustment bracket 4, make the center of the random sphere confocal with the spherical reference mirror, cause interference between the spherical reference mirror and the random sphere, and measure a set of data. The single measurement result is:

[0060]

[0061] where W R is the wavefront reflected by the spherical reference mirror, is the wavefront reflected from the surface of the random sphere, and W n is the test wavefront obtained by superimposing the two.

[0062] Step 4: Remove the random sphere, repeat multiple sets of random sphere measurements, and obtain multiple sets of random sphere measurement results. The average result of multiple measurements is the calibration result of the spherical reference mirror, specifically as follows:

[0063] Step 4.1: Remove the measured random ball, arbitrarily select a small ball from multiple random balls and fix it on the random ball base 3, keep the spherical reference mirror in interference with the random ball, and measure the data once.

[0064] Step 4.2: Repeat Step 4.1 until all 20 random balls are in interference with the spherical reference mirror.

[0065] Step 4.3: Perform weighted averaging on the multiple measurement results of the random ball. The result after weighted averaging is the calibration result of the spherical reference mirror, specifically as follows:

[0066] Step 4.3.1: Take the average of the multiple measurement results of the random ball. The average result is:

[0067]

[0068] where N is the number of times the random ball is measured, W n is the test wavefront superimposed by the two, W R is the wavefront reflected by the spherical reference mirror, is the wavefront reflected from the surface of the random ball, is the mean value of the surface shape distribution of the random ball.

[0069] Step 4.3.2: Subtract the single measurement result of the random ball from the average result of the random ball respectively:

[0070]

[0071] Δ is the difference between the single measurement result of the random ball and the average result of the random ball. Judge the correlation between the single measurement result of the random ball and the average measurement result of the random ball according to the size of the difference.

[0072] Step 4.3.3: Based on Δ, perform weighted averaging on the single measurement results of the random ball according to the correlation size.

[0073] Step 4.3.4: The actual measurement result of the random ball is obtained as:

[0074]

[0075] where a n is the weighting coefficient, The spherical reference mirror W R is calibrated by the above formula.

[0076] Step 5: Use the Zernike polynomial to perform aberration analysis on the calibration result of the spherical reference mirror, specifically as follows:

[0077] The calibration result of the spherical reference mirror is W R and is represented by the following Zernike polynomial:

[0078]

[0079] where x and y are in a normalized Cartesian coordinate system, and Z j (x, y) is the j-th order Zernike term, and a j is the weight coefficient corresponding to the j-th order Zernike term. Aberration analysis is performed on the calibration result of the spherical reference mirror according to the above formula.

[0080] The correction method of the spherical reference mirror based on multi-sphere randomness in the present invention avoids the overlap of the measured surfaces of the random spheres during the measurement of each random sphere and the spherical reference mirror, reduces the coherence of the measurement results of the random spheres, the weighted average algorithm improves the accuracy of the measurement results, and the measurement platform has a simple structure and is easy to operate.

Claims

1. A spherical reference mirror calibration method based on multi-sphere randomness, characterized in that, It includes the following steps: Step 1: Build a random sphere measurement platform; Step 2: Randomly select a small sphere from multiple random spheres and fix the random sphere at the base position; Step 3: Turn on the interferometer, adjust the relative position between the spherical reference mirror and the random sphere to make the spherical reference mirror interfere with the random sphere, and measure the data once; Step 4: Remove the random sphere, repeat multiple groups of random sphere measurements, obtain multiple groups of random sphere measurement results, perform weighted averaging on the multiple measurement results, and the result after weighted averaging is the calibration result of the spherical reference mirror; Step 5: Use the Zernike polynomial to perform aberration analysis on the calibration result of the spherical reference mirror; For the weighted averaging of the multiple measurement results, the result after weighted averaging is the calibration result of the spherical reference mirror, specifically as follows: Step 4.3.1: Take the average of the multiple measurement results of the random sphere, and the average result is: where N is the number of random sphere measurements, and W n is the measured wavefront superposed by the two, and W R is the wavefront reflected by the spherical reference mirror, is the wavefront reflected by the light from the surface of the random sphere, is the mean value of the surface shape distribution of the random sphere; Step 4.3.2: Subtract the single random sphere measurement result from the average result of the random sphere respectively: where Δ is the difference between the single random sphere measurement result and the average result of the random sphere, and the correlation between the single random sphere measurement result and the average measurement result of the random sphere is judged according to the magnitude of the difference; Step 4.3.3: Based on Δ, perform weighted averaging on the single random sphere measurement results according to the magnitude of the correlation; Step 4.3.4: The actual random sphere measurement result obtained is: where a n is a weighting coefficient, a n ∈(0, 1).

2. The spherical reference mirror calibration method based on multi-sphere randomness according to claim 1, wherein For the building of the random sphere measurement platform described in Step 1, specifically as follows: The random sphere measurement platform includes a Fizeau interferometer (1), a spherical reference mirror (2), a random sphere base (3), and an adjustment frame (4); fix the spherical reference mirror (2) in the Fizeau interferometer (1), and fix the random sphere base (3) in the adjustment frame (4) to complete the building of the random sphere measurement platform.

3. The spherical reference mirror calibration method based on multi-sphere randomness according to claim 2, characterized in that For the randomly selecting a small sphere from multiple random spheres and fixing the random sphere at the base position described in Step 2, specifically as follows: Prepare multiple random spheres as experimental random spheres, randomly select a small sphere during the experiment, and fix it on the random sphere base (3).

4. The spherical reference mirror calibration method based on multi-sphere randomness according to claim 3, wherein For the random spheres described in Step 2, select small spheres with the same precision, the same diameter, and the same material.

5. The spherical reference mirror calibration method based on multi-ball randomness according to claim 4, wherein For the random spheres described in Step 2, the number is 20.

6. The spherical reference mirror calibration method based on multi-ball randomness according to claim 5, characterized in that For the turning on of the interferometer, adjusting the relative position between the spherical reference mirror and the random sphere to make the spherical reference mirror interfere with the random sphere, and measuring the data once described in Step 3, specifically as follows: Turn on the interferometer, by adjusting the position of the adjustment frame (4), make the center of the random sphere confocal with the spherical reference mirror, make the spherical reference mirror interfere with the random sphere, and measure the data once. The single measurement result is: Among them, W R is the wavefront reflected by the spherical reference mirror, is the wavefront of light reflected from the random spherical surface, and W n is the test wavefront obtained by superposing the two.

7. The spherical reference mirror calibration method based on multi-sphere randomness according to claim 6, wherein For the removing of the random sphere, repeating multiple groups of random sphere measurements, obtaining multiple groups of random sphere measurement results, performing weighted averaging on the multiple measurement results, and the result after weighted averaging is the calibration result of the spherical reference mirror described in Step 4, specifically as follows: Step 4.1: Remove the measured random sphere, randomly select a small sphere from multiple random spheres and fix it on the random sphere base (3) to keep the spherical reference mirror interfere with the random sphere, and measure the data once; Step 4.2: Repeat Step 4.1 until all 20 random spheres interfere with the spherical reference mirror; Step 4.3: Perform weighted averaging on the multiple measurement results of the random sphere, and the result after weighted averaging is the correction result of the spherical reference mirror.

8. The spherical reference mirror calibration method based on multi-sphere randomness according to claim 7, wherein The aberration analysis of the correction result of the spherical reference mirror using Zernike polynomials as described in Step 5 is as follows: The calibration result of the spherical reference mirror is W R , which is represented by the following Zernike polynomials: where (x, y) is the normalized Cartesian coordinate system, and Z j (x, y) is the j-th order Zernike term, and a j is the weight coefficient corresponding to the j-th order Zernike term. Aberration analysis is performed on the calibration result of the spherical reference mirror according to the above formula.

Images