A method for improving wavefront measurement accuracy of optical focusing system

Abstract

The present invention discloses a method for improving the wavefront measurement accuracy of an optical focusing system, comprising the following steps: 1) obtaining the focal position of the optical focusing system to be measured; 2) correcting the wavefront measurement error; 3) calculating the corrected wavefront. The method of the present invention is simple to operate, has strong applicability, reduces the requirements for mirror processing accuracy, and has great promotion value.

Description

Technical Field

[0001] The present invention relates to the technical field of optical systems, and in particular to a method for improving the wavefront measurement accuracy of an optical focusing system. Background Art

[0002] As a typical optical performance index, wavefront aberration can guide the optimization design of optical path, phase modulation and imaging analysis, and is easy to detect, so it is often used to evaluate optical systems. The inverse Hartmann detection method uses non-special devices such as screens for projecting stripes, CCD cameras, and translation stages. It is highly versatile and has high theoretical accuracy. However, the actual measurement accuracy is easily affected by system errors. At present, there are two main methods for correcting system structural errors. The first method is based on high-precision calibration components to realize the calculation of structural parameters and errors in the system, thereby suppressing the influence of errors from the source. The second method analyzes the influence of various system errors on wavefront measurement, removes the influence of errors from the measured wavefront aberration, and suppresses the influence of errors from the results. In response to the overcorrection problem, a high-precision structural error correction method based on Zernike polynomials is further proposed. Different Zernike polynomial coefficient weight distributions are introduced for different types of structural errors, and different types of structural errors are corrected step by step, thereby effectively avoiding the problem of overcorrection and achieving high-precision measurement of free-form surfaces with a large dynamic range.

[0003] However, this error correction method requires the known parameters of the measured mirror surface, and is only applicable when the processed surface shape is not much different from the designed surface shape. This places extremely high demands on the processing method and is not universal and applicable. It is difficult to find a simple and universal method to improve the measurement accuracy of the existing inverse Hartmann wavefront measurement method. Summary of the invention

[0004] In view of the above-mentioned defects or deficiencies in the prior art, it is desired to provide a method for improving the wavefront measurement accuracy of an optical focusing system, which is simple to operate, has strong applicability, reduces the requirements for mirror processing accuracy, and has great promotion value.

[0005] The present invention provides a method for improving the wavefront measurement accuracy of an optical focusing system, comprising the following steps:

[0006] 1) Obtaining the focal position of the optical focusing system under test;

[0007] 2) Wavefront measurement error correction: Assume that the ideal wavefront of the measured optical focusing system is A(x, y), the random error of the measurement system at time t is η(x, y, t), the reference position is defined at the focal position of the measured optical focusing system, and the measured optical focusing system is conjugate translated s in the orthogonal direction of the reference position in sequence. The measured wavefront W(x, y) of the measured optical focusing system is obtained as follows:

[0008]

[0009] The detected differential wavefronts of the optical focusing system under test in two orthogonal directions are calculated:

[0010]

[0011] The Taylor formula expansion of the detected differential wavefront of the optical focusing system under test in two orthogonal directions yields:

[0012]

[0013] in, and is the ideal differential wavefront; is the error term;

[0014] It can be seen that when the translation distance s of the optical focusing system under test increases, the error term decreases and the detection error is effectively suppressed; however, when the translation distance s is too large, algorithm error will be introduced;

[0015] Through ray tracing, the wavefront simulation of the optical focusing system under test is carried out, and it is found that the translation distance s is greater than s max When the algorithm error exceeds the allowable error range, the optimization algorithm is used to set the translation distance s as the input value, and the translation distance s ranges from 0 to s max , the wavefront PV value is the objective function. When the wavefront PV value does not exceed the allowable error range, the correction translation distance s is obtained. a Range value of

[0016] In the correction translation distance s a The value within the range of is taken as the translation distance s, and the corrected differential wavefront is calculated as:

[0017]

[0018] 3) Calculate the corrected wavefront:

[0019]

[0020] Where (x, y) represents the normalized sampling point of the optical focusing system under test in the rectangular coordinate system, C k is the coefficient of the kth Zernike polynomial, Zk (x,y) is the kth orthogonalized Zernike polynomial;

[0021] C=(ΔZ T ΔZ) -1 ΔZ T ΔW a ;

[0022] Where C is the Zernike polynomial coefficient and ΔZ is the Zernike polynomial basis function.

[0023] Furthermore, obtaining the focal position of the optical focusing system under test comprises the following steps:

[0024] Acquire a first unwrapped phase of the optical focusing system under test, and extract a transverse phase and a longitudinal phase and a corresponding first pixel index in the first unwrapped phase; acquire a second unwrapped phase of the optical focusing system under test corresponding to the first unwrapped phase, and extract a transverse phase and a longitudinal phase and a corresponding second pixel index in the second unwrapped phase;

[0025] A plurality of groups of corresponding first pixel indexes and second pixel indexes are obtained, the point spacing between each group of corresponding first pixel indexes and second pixel indexes is subtracted, and a difference curve is fitted. When the difference is 0, the focal position of the optical focusing system under test is obtained.

[0026] Further, the first unwrapped phase is obtained on a small-period four-step phase-shifted fringe set by spatial unwrapping, and the small-period four-step phase-shifted fringe set is a small-period four-step phase-shifted fringe set projected horizontally and vertically on a screen by a mapping device through a measured optical focusing system, and the screen is located at position 1 on the optical axis of the measured optical focusing system;

[0027] The second unwrapped phase is obtained on a small-period four-step phase-shifted fringe set by spatial unwrapping, and the small-period four-step phase-shifted fringe set is a set of small-period four-step phase-shifted fringe sets in horizontal and vertical directions projected on a screen by a mapping device through the optical focusing system under test, and the screen is located at position 2 on the optical axis of the optical focusing system under test; the position 2 is the position where the screen located at position 1 moves a certain distance along the optical axis of the optical focusing system under test.

[0028] Furthermore, the transverse phase and the longitudinal phase are four points selected in a "cross" manner at the center of the first unfolding phase or the second unfolding phase.

[0029] Furthermore, each group of corresponding first pixel indexes and second pixel indexes is obtained after the position of the image acquisition device is moved along the optical axis of the optical focusing system under test.

[0030] Furthermore, the image acquisition device includes a CCD camera.

[0031] Furthermore, the focus position is the pinhole aperture position of the CCD camera corresponding to when the difference is 0.

[0032] Compared with the prior art, the beneficial effects of the present invention are:

[0033] (1) The method of the present invention obtains the correction translation distance s by the conjugate difference method and the optimization algorithm. a The range value is corrected by the translation distance s a The range value can greatly reduce random errors and systematic errors of the measurement system, effectively improving the measurement accuracy and reliability of wavefront detection. It does not need to measure the surface parameters of the mirror, does not require difficult mirror processing methods and stringent processing requirements, and is more universal and applicable.

[0034] (2) The method of the present invention focuses the optical focusing system under test through a phase-assisted focusing algorithm, which can quickly and accurately determine the focal position, improve the focusing efficiency and accuracy, eliminate defocus errors, and further improve the accuracy of wavefront detection.

[0035] It should be understood that the contents described in the summary of the invention are not intended to limit the key or important features of the embodiments of the present invention, nor are they intended to limit the scope of the present invention. Other features of the present invention will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0037] Figure 1 Schematic diagram of the position before and after defocusing;

[0038] Figure 2 This is the flow chart of the phase-assisted focusing algorithm;

[0039] Figure 3 This is the optical path diagram of the phase-assisted focusing algorithm;

[0040] Figure 4 centered is a point spacing difference curve diagram of the first pixel index and the second pixel index;

[0041] Figure 5 is a schematic diagram of the translation distance s of the optical focusing system under test;

[0042] Figure 6 Figure a is a schematic diagram of the ideal wavefront of the optical focusing system under test; Figure b is a schematic diagram of the detected wavefront after Gaussian noise is added to the ideal wavefront; Figure c is a schematic diagram of the wavefront difference obtained by the ideal wavefront without adding noise error;

[0043] Figure 7 Figure a is a schematic diagram of the relationship curve between the translation distance s and the reconstruction error simulated by the wavefront difference reconstruction algorithm under a fixed random error; Figure b is a schematic diagram of the relationship curve between the translation distance s and the reconstruction error simulated by the wavefront difference reconstruction algorithm under different random errors. DETAILED DESCRIPTION

[0044] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the relevant inventions, rather than to limit the invention. It should also be noted that, for ease of description, only the parts related to the invention are shown in the accompanying drawings.

[0045] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0046] Example 1

[0047] Please refer to Figure 1 to Figure 7 An embodiment of the present invention provides a method for improving the wavefront measurement accuracy of an optical focusing system, comprising the following steps:

[0048] 1) Obtaining the focal position of the optical focusing system under test;

[0049] The first unwrapped phase of the optical focusing system under test is obtained by spatial unwrapping, where the first unwrapped phase is the unwrapped phase of a set of small-period four-step phase-shifted fringes in the horizontal and vertical directions projected by the CCD camera on a screen at position 1 through the optical focusing system under test; four points are selected in a "cross" manner at the center of the first unwrapped phase to extract the horizontal phase, the vertical phase and the corresponding first pixel index;

[0050] The second unfolded phase of the optical focusing system under test is obtained by spatial unwrapping, and the second unfolded phase is the unfolded phase of the CCD camera projecting the horizontal and vertical small-period four-step phase-shifted fringe set on the screen at position 2 through the optical focusing system under test; four points are selected in a "cross" manner at the center of the second unfolded phase to extract the horizontal phase and the vertical phase and the corresponding second pixel index; Figure 3 As shown, position 2 is the position where the screen at position 1 moves a certain distance along the optical axis of the optical focusing system under test;

[0051] Acquire multiple groups of corresponding first pixel indexes and second pixel indexes, where each group of corresponding first pixel indexes and second pixel indexes is acquired after moving the position of the CCD camera along the optical axis of the optical focusing system under test; subtract the point spacing of each group of corresponding first pixel indexes and second pixel indexes, and fit the difference curve (such as Figure 4As shown), when the difference is 0, the corresponding pinhole aperture position of the CCD camera is the focal position of the optical focusing system under test;

[0052] 2) Wavefront measurement error correction;

[0053] Assume that the ideal wavefront of the measured optical focusing system is A(x, y), the random error of the measurement system at time t is η(x, y, t), the reference position is defined at the focal position of the measured optical focusing system, and the measured optical focusing system is conjugate translated s in the orthogonal direction of the reference position in sequence, and the detected wavefront W(x, y) of the measured optical focusing system is obtained as:

[0054]

[0055] The detected differential wavefronts of the optical focusing system under test in two orthogonal directions are calculated:

[0056]

[0057] The Taylor formula expansion of the detected differential wavefront of the optical focusing system under test in two orthogonal directions yields:

[0058]

[0059] in, and is the ideal wavefront difference; is the error term;

[0060] It can be seen that when the translation distance s of the optical focusing system under test increases, the error term decreases and the detection error is effectively suppressed; however, when the translation distance s is too large, algorithm error will be introduced;

[0061] Through ray tracing, the wavefront simulation of the optical focusing system under test is carried out, and it is found that the translation distance s is greater than s max When the algorithm error exceeds the allowable error range, the optimization algorithm is used to set the translation distance s as the input value, and the translation distance s ranges from 0 to s max , the wavefront PV value is the objective function. When the wavefront PV value does not exceed the allowable error range, the correction translation distance s is obtained. a Range value of

[0062] In the correction translation distance s a The value within the range of is taken as the translation distance s, and the corrected differential wavefront is calculated as:

[0063]

[0064] 3) Calculate the corrected wavefront:

[0065]

[0066] Where (x, y) represents the normalized sampling point of the optical focusing system under test in the rectangular coordinate system, C k is the coefficient of the kth Zernike polynomial, Z k (x,y) is the kth orthogonalized Zernike polynomial;

[0067] C=(ΔZ T ΔZ) -1 ΔZ T ΔW a ;

[0068] Where C is the Zernike polynomial coefficient and ΔZ is the Zernike polynomial basis function.

[0069] In this embodiment, the inspection personnel set up a reverse Hartmann optical inspection system, which includes a picture acquisition device, a measured optical focusing system and a screen arranged in sequence along the optical axis; wherein the picture acquisition device includes a CCD camera with a pinhole aperture; and the screen is fixedly mounted on a displacement table.

[0070] Move the screen to position 1, and the CCD camera projects a set of horizontal and vertical small-period four-step phase-shifted fringe sets on the screen through the optical focusing system under test. The detection system obtains the horizontal phase and vertical phase and the corresponding first pixel index through the set of small-period four-step phase-shifted fringe sets; then move the screen to position 2 to obtain the corresponding second pixel index.

[0071] Then, the CCD camera is moved to obtain multiple groups of corresponding first pixel indexes and second pixel indexes, and the difference curve is fitted to obtain the focus position of the optical focusing system under test. The focus position obtained by the phase-assisted focusing algorithm is highly accurate, ensuring the detection accuracy. Among them, the fitting difference curve is as follows: Figure 4 As shown, one curve is the horizontal pixel point spacing between the first pixel index and the second pixel index, and the other is the vertical pixel point spacing between the first pixel index and the second pixel index.

[0072] After obtaining the focal position, use it as the reference position, and sequentially conjugate translate s in the orthogonal direction of the reference position of the optical focusing system under test, and obtain the differential wavefront of the optical focusing system under test by the conjugate difference method. The Taylor formula expansion shows that the larger the translation distance s, the smaller the error term, and the random error is effectively suppressed. However, when the translation distance s is too large, the algorithm error will be introduced; therefore, the appropriate correction translation distance s is obtained. a The range of values ​​can reduce both systematic errors and random errors.

[0073] Through ray tracing, the wavefront simulation of the optical focusing system under test is carried out, and it is found that the translation distance s is greater than s maxWhen the algorithm error exceeds the allowable error range, the optimization algorithm is used to set the translation distance s as the input value, and the translation distance s ranges from 0 to s max , the wavefront PV value is the objective function. When the wavefront PV value is the minimum, the correction translation distance s is obtained. a Range of values. Figure 7 shown.

[0074] By correcting the translation distance s a Calculate the corrected differential wavefront ΔW a , and then through the corrected differential wavefront ΔW a Calculate the corrected wavefront W(x,y) a .

[0075] The corrected wavefront W(x,y) is obtained by the method of the present invention: a , effectively improving the measurement accuracy and reliability of wavefront detection, without the need to measure the surface parameters of the mirror, without the need for difficult mirror processing methods and stringent processing requirements, and is more universal and applicable.

[0076] Example 2

[0077] The plano-convex lens model is used as the optical focusing system under test for simulation verification.

[0078] S1: Get the ideal wavefront data of the plano-convex lens model, such as Figure 6 As shown in Figure a, the wavefront PV value is 118.31 μm; Figure 6 As shown in Figure c, the wavefront aberration value is 1.56μm. The detection wavefront obtained by adding Gaussian noise with a mean of 0 and a standard deviation of 1μm is as follows: Figure 6 As shown in Figure b;

[0079] S2: Set the conjugate translation distance s to 1 mm and normalize the wavefront data on the unit circle;

[0080] S3: Differentiate the noisy wavefront data in the X-axis and Y-axis directions respectively;

[0081] S4: Perform wavefront difference reconstruction, and the calculated wavefront aberration PV value is 1.61μm, and the residual error compared with the ideal wavefront difference is 50nm;

[0082] S5: Simulate the wavefront aberration of the plano-convex lens model under the traditional non-differential condition, and obtain a wavefront aberration PV value of 2.31 μm and a residual error of 750 nm.

[0083] Through comparison, it was found that the conjugate difference method greatly reduced the systematic error and random error of the measurement system. The wavefront measurement accuracy improvement method of the optical focusing system provided in the present application was applied to the reverse Hartmann optical detection system, which effectively improved the measurement accuracy and reliability. There is no need to measure the surface parameters of the mirror, and there is no need for difficult mirror processing methods and strict processing requirements. It is more universal and applicable.

[0084] In the description of this specification, the description of the terms "one embodiment", "some embodiments", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0085] The above are only preferred embodiments of the present application and are not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for improving the wavefront measurement accuracy of an optical focusing system, characterized in that: The steps include: 1) Obtaining the focal position of the optical focusing system under test; 2) Wavefront measurement error correction: Assume that the ideal wavefront of the measured optical focusing system is A(x, y), the random error of the measurement system at time t is η(x, y, t), the reference position is defined at the focal position of the measured optical focusing system, and the measured optical focusing system is conjugate translated s in the orthogonal direction of the reference position in sequence. The measured wavefront W(x, y) of the measured optical focusing system is obtained as follows: The detected differential wavefronts of the optical focusing system under test in two orthogonal directions are calculated: The Taylor formula expansion of the detected differential wavefront of the optical focusing system under test in two orthogonal directions yields: in, and is the ideal differential wavefront; is the error term; It can be seen that when the translation distance s of the optical focusing system under test increases, the error term decreases and the detection error is effectively suppressed; however, when the translation distance s is too large, algorithm error will be introduced; Through ray tracing, the wavefront simulation of the optical focusing system under test is carried out, and it is found that the translation distance s is greater than s max When the algorithm error exceeds the allowable error range, the optimization algorithm is used to set the translation distance s as the input value, and the translation distance s ranges from 0 to s max , the wavefront PV value is the objective function. When the wavefront PV value does not exceed the allowable error range, the correction translation distance s is obtained. a Range value of The corrected differential wavefront is: 3) Calculate the corrected wavefront: Where (x, y) represents the normalized sampling point of the optical focusing system under test in the rectangular coordinate system, C k is the coefficient of the kth Zernike polynomial, Z k (x,y) is the kth orthogonalized Zernike polynomial; C=(ΔZ T ΔZ) -1 ΔZ T ·ΔW a ; Where C is the Zernike polynomial coefficient and ΔZ is the Zernike polynomial basis function.

2. The method for improving the wavefront measurement accuracy of an optical focusing system according to claim 1, characterized in that: The step of obtaining the focal position of the optical focusing system under test comprises the following steps: Acquire a first unwrapped phase of the optical focusing system under test, and extract a transverse phase and a longitudinal phase and a corresponding first pixel index in the first unwrapped phase; acquire a second unwrapped phase of the optical focusing system under test corresponding to the first unwrapped phase, and extract a transverse phase and a longitudinal phase and a corresponding second pixel index in the second unwrapped phase; A plurality of groups of corresponding first pixel indexes and second pixel indexes are obtained, the point spacing between each group of corresponding first pixel indexes and second pixel indexes is subtracted, and a difference curve is fitted. When the difference is 0, the focal position of the optical focusing system under test is obtained.

3. The method for improving the wavefront measurement accuracy of an optical focusing system according to claim 2, characterized in that: The first unwrapped phase is obtained on a small-period four-step phase-shifted fringe set by spatial unwrapping, and the small-period four-step phase-shifted fringe set is a small-period four-step phase-shifted fringe set projected horizontally and vertically on a screen by a mapping device through a measured optical focusing system, and the screen is located at position 1 on the optical axis of the measured optical focusing system; The second unwrapped phase is obtained on a small-period four-step phase-shifted fringe set by spatial unwrapping, and the small-period four-step phase-shifted fringe set is a set of small-period four-step phase-shifted fringe sets in horizontal and vertical directions projected on a screen by a mapping device through the optical focusing system under test, and the screen is located at position 2 on the optical axis of the optical focusing system under test; the position 2 is the position where the screen located at position 1 moves a certain distance along the optical axis of the optical focusing system under test.

4. The method for improving the wavefront measurement accuracy of an optical focusing system according to claim 2, characterized in that: The transverse phase and the longitudinal phase are four points selected in a "cross" manner at the center of the first unfolding phase or the second unfolding phase.

5. The method for improving the wavefront measurement accuracy of an optical focusing system according to claim 3, characterized in that: Each group of corresponding first pixel indexes and second pixel indexes is obtained after the position of the image acquisition device is moved along the optical axis of the optical focusing system under test.

6. The method for improving the wavefront measurement accuracy of an optical focusing system according to claim 3, characterized in that: The image acquisition device includes a CCD camera.

7. The method for improving the wavefront measurement accuracy of an optical focusing system according to claim 6, characterized in that: The focus position is the pinhole aperture position of the CCD camera corresponding to when the difference is 0.

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