Methods for compensating for errors in grating shearing interference systems caused by grating defocus

Abstract

A method for compensating for grating defocusing errors in grating shearing interferometry systems involves replacing the coefficients of the Z4 and Z9 Zernike polynomials of the fitted wavefront measured after the image-plane grating has defocused with the corresponding coefficients when the image-plane grating is located at the focal plane. This refits the wavefront to achieve algorithmic compensation for the system error. Simultaneously, the method calculates the actual defocus distance of the image-plane grating, enabling mechanical compensation by adjusting the grating to the imaging focal plane. This method eliminates the defocusing error introduced by image-plane grating defocusing, improving the accuracy of grating shearing interferometry detection optical systems.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of optical detection technology, and relates to a system error compensation method of a grating shearing interferometer, in particular to a system error compensation method of imaging defocus of a to-be-detected optical system caused by defocusing of an image plane grating of a grating shearing interferometer. BACKGROUND

[0002] The grating shearing interferometer is a kind of transverse shearing interferometer, has the advantages of common optical path structure, no need for reference surface, zero fringe detection, high detection sensitivity, etc., and is one of the technical means for realizing wave aberration detection of an imaging optical system.

[0003] Prior Art 1 (d. K. Van, A. Mark, W. D. Boeij, H. Kok, M. Silova, J. Baselmans, M. Hemerik, and B. W. Smith, "Full optical column characterization of DUV lithographic projection tools," Proc. SPIE 5377, 1960-1970 (2004)) proposes a double-grating wave aberration detection technology based on Ronchi shearing interferometry, which realizes high-speed and high-precision in-situ detection of wave aberration of a projection objective.

[0004] Prior Art 2 (F. Wu, F. Tang, X. Wang, J. Li, and Y. Li, "Phase retrieval errors analysis of Ronchi phase-shifting shearing interferometer," Acta Opt. Sin. 35, 0612004 (2015).) studies the phase shift error, detector error, vibration error, grating period error and light source spatial coherence error of the double-grating wave aberration detection technology.

[0005] Prior Art 3 (Yang Liu, Feng Tang, Sikun Li, Xiangzhao Wang, and Rong Su, "Effects of illumination non-uniformity on the double-Ronchi lateral shearing interference field," Appl. Opt. 61, 10299-10308 (2022)) studies the influence of illumination uniformity on the interference field when the illumination of the double-grating wave aberration detection technology is a non-uniform light source.

[0006] Prior art 4 (a compensation method in a grating lateral shearing interference wavefront reconstruction process, CN113432731B) simultaneously compensates for pupil coordinate distortion and shear amount change in the grating lateral shearing interference wavefront reconstruction process, and improves the detection accuracy of the large-NA optical system.

[0007] The above-mentioned technologies all analyze and compensate for system errors when the image plane grating is located at the imaging focal plane of the optical system to be measured. In actual interferometer operation, the defocus of the image plane grating is an important problem affecting the interference field, and brings system errors to the interferometer measurement. SUMMARY

[0008] The purpose of the present application is to overcome the shortcomings of the prior art, and to provide a compensation method for system errors in grating shearing interference technology. This method can eliminate the defocus error of the imaging system caused by the defocus of the image plane grating, and improve the accuracy of the grating shearing interference technology in detecting optical systems.

[0009] The technical scheme of the present application is as follows:

[0010] 1. A system error compensation method for defocus of an image plane grating in grating shearing interference technology, characterized in that the method comprises the following steps:

[0011] 1) When the image plane grating of the grating shearing interferometer coincides with the imaging focal plane of the optical system to be measured, the X and Y direction shearing interference patterns of the optical system to be measured are generated by using the grating lateral shearing interferometer, and the interference patterns I * x (x d ,y d ) and I * y (x d ,y d ) are received by using a two-dimensional photoelectric sensor, wherein (x d ,y d ) is the pixel position coordinate system on the two-dimensional photoelectric sensor;

[0012] 2) The differential phases S * x (x d ,y d ) and S * y (x d ,y d ) in the X and Y directions are extracted from the X and Y direction shearing interference patterns;

[0013] 3) The differential phases S * x (x d ,y d ) and S *y (x d ,y d ) reconstructs the wavefront W * to be measured, and the first m Zernike polynomials are used to fit the reconstructed wavefront W * , and the coefficients C * i (i = 1, 2, …, m) are obtained, and the fitting expression of the reconstructed wavefront W * :

[0014]

[0015] wherein Z i represents the i-th polynomial, and the coefficients corresponding to Z4 and Z9 are C * 4 and C * 9, respectively.

[0016] 4) When the image plane grating of the grating shearing interferometer deviates from the imaging focal plane of the optical system to be measured, the shearing interferograms of the optical system to be measured in the X and Y directions are generated by using the grating lateral shearing interferometer, and the interference patterns I x (x d ,y d ) and I y (x d ,y d ) are received by using a two-dimensional photoelectric sensor, wherein (x d ,y d ) is the pixel position coordinate system on the two-dimensional photoelectric sensor.

[0017] 5) The differential phases S x (x d ,y d ) and S y (x d ,y d ) in the X and Y directions are extracted from the shearing interferograms in the X and Y directions.

[0018] 6) The wavefront W to be measured is reconstructed by using the differential phases S x (x d ,y d ) and S y (x d ,y d ), and the first m Zernike polynomials are used to fit the reconstructed wavefront W i (i = 1, 2, …, m) are obtained, and the fitting expression of the reconstructed wavefront W is:

[0019]

[0020] wherein Z irepresents the ith polynomial; the coefficients corresponding to the Z4, Z9 terms are C4, C9;

[0021] 7) replace the coefficients C4, C9 corresponding to the Z4, Z9 terms of the polynomial obtained in step 6) with the coefficients C4, C9 of the Z4, Z9 terms obtained in step 3) * 4, C * 9, use the replaced polynomial coefficients C i fit the to-be-measured wavefront again, and output the to-be-measured wavefront after system error compensation;

[0022] 8) calculate the Z4 term coefficient C4 of the wavefront fitting when the image plane grating is defocused, and the Z4 term coefficient C4 when the image plane grating is at the focal plane position * 4 calculate the defocus distance z of the image plane grating as:

[0023]

[0024] wherein NA is the numerical aperture of the to-be-measured optical system;

[0025] 9) move the image plane grating by a distance z, and adjust the image plane grating of the grating lateral shearing interferometer to coincide with the imaging focal plane of the to-be-measured optical system.

[0026] The technical effect of the present application is:

[0027] The system error compensation method of the grating shearing interference technology can eliminate the defocus error of the imaging system caused by the defocus of the image plane grating, and improve the accuracy of the grating shearing interference technology in detecting the optical system. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 System error compensation method flowchart

[0029] Figure 2 is the experimental principle diagram related to embodiment 1 of the present application

[0030] Figure 3 is the interference pattern I when the image plane grating is defocused x (x d ,y d ) and I y (x d ,y d )

[0031] Figure 4 Reconstructed to-be-measured wavefront pattern when the image plane grating is defocused

[0032] Figure 5 Comparison diagram of the to-be-measured wavefront after system error compensation and the ideal to-be-measured wavefront, wherein (a) is the to-be-measured wavefront diagram after eliminating the system error; (b) is the to-be-measured wavefront diagram when the image plane grating is at the focal plane. Detailed Implementation

[0033] The present invention will be further described below with reference to the embodiments and accompanying drawings, but the scope of protection of the present invention should not be limited by these embodiments.

[0034] Example 1:

[0035] use Figure 2 The dual-grating Ronchi grating shearing interferometer shown measures the wavefront aberration of a projection lens system. The interferometer consists of an illumination source (wavelength λ = 532 nm), an object grating period (To = 80 μm), the projection lens system under test (NA = 0.3), an image grating period (Ti = 20 μm), and a detector. The object grating is located on the front focal plane of the focusing lens; the image grating is located on the rear focal plane of the projection lens system under test; the two-dimensional photoelectric sensor is parallel to the image grating, and its distance to the image grating satisfies a 0th-order diffraction sampling number of 256 × 256 pixels. The measurement steps are as follows:

[0036] 1) When the image plane grating of the grating shearing interferometer coincides with the imaging focal plane of the optical system under test, the shearing interferogram of the optical system under test in the X and Y directions is generated using the grating transverse shearing interferometer, and the interferogram I is received using a two-dimensional photoelectric sensor. * x (x d ,y d ) and I * y (x d ,y d ), where (x d ,y d () represents the pixel position coordinate system on the two-dimensional photoelectric sensor;

[0037] 2) Extract the differential phase S in the X and Y directions from the shearing interferograms in the X and Y directions. * x (x d ,y d ) and S * y (x d ,y d );

[0038] 3) Utilizing differential phase S * x (x d ,y d ) and S * y (x d ,y d Reconstructing the wavefront W to be measured * The wavefront W was reconstructed using the first m terms of the Zernike polynomial with fringe.* By fitting the polynomials, the coefficients C corresponding to each polynomial are obtained. * i (i = 1, 2, ..., m), reconstruct wavefront W * The fitted expression:

[0039]

[0040] Among them, Z i Let Z4 and Z9 be the coefficients of the i-th polynomial. * 4. C * 9;

[0041] 4) When the image plane grating of the grating shearing interferometer deviates from the imaging focal plane of the optical system under test, a differential wavefront interferogram of the optical system under test in the X and Y directions is generated using a grating transverse shearing interferometer, and the interferogram I is received using a two-dimensional photoelectric sensor. x (x d ,y d ) and I y (x d ,y d ),like Figure 3 As shown;

[0042] 5) Extract the differential phase S in the X and Y directions from the interferogram. x (x d ,y d ) and S y (x d ,y d );

[0043] 6) Utilizing differential phase S x (x d ,y d ) and S y (x d ,y d Reconstructing the wavefront W to be measured Figure 4 As shown, the reconstructed wavefront W is fitted using the first m terms of the Zernike polynomial, and the coefficients C corresponding to each polynomial are obtained. i As shown in (i = 1, 2, ..., m), the fitted expression for reconstructing the wavefront W is:

[0044]

[0045] Among them, Z i Represent the i-th polynomial;

[0046] 7) Replace the coefficients C4 and C9 of the Z4 and Z9 polynomials obtained in step 6) with the coefficients C of the Z4 and Z9 polynomials obtained in step 3). * 4. C *9) the replaced polynomials Z i corresponding coefficients C i The measured wavefront is fitted again, and the comparison between the compensated measured wavefront and the ideal measured wavefront is shown in FIG. 6. Figure 5

[0047] 8) At the same time, the Z4 polynomial coefficient C4 of the image plane grating when the image plane grating is offset from the focal plane and the Z4 polynomial coefficient C * 4) The defocus distance z of the image plane grating is calculated as:

[0048]

[0049] wherein NA is the numerical aperture of the measured optical system;

[0050] 9) The image plane grating is moved by 5x10 4 nm, and the image plane grating of the lateral shearing interferometer is adjusted to coincide with the imaging focal plane of the measured optical system.

[0051] The details of the present application are known in the art.

[0052] The above examples are only for illustrating the technical concept and characteristics of the present application, and the purpose is to enable those skilled in the art to understand the content of the present application and to implement it, and it cannot limit the protection scope of the present application. Any equivalent changes or modifications made according to the spirit and essence of the present application shall be covered within the protection scope of the present application.​

Claims

1. A method for compensating for errors in a grating shearing interference system caused by grating defocus, characterized in that, The method comprises the following steps: 1) When the image plane grating of the grating shearing interferometer coincides with the imaging focal plane of the optical system to be measured, the shearing interferograms of the optical system to be measured in X and Y directions are generated by using the grating transverse shearing interferometer, and the interferograms I * x (x d , y d ) and I * y (x d , y d ) are received by using a two-dimensional photoelectric sensor, wherein (x d , y d ) is the pixel position coordinate system on the two-dimensional photoelectric sensor; 2) extracting the differential phases Sx, Sy in the X, Y directions from the shearing interferograms in the X, Y directions * x (x d , y d ) and S * y (x d , y d ) 3) using differential phase S * x (x d , y d ) and S * y (x d , y d ) to reconstruct the wavefront W * to be measured, using the first m Zernike polynomials to fit the reconstructed wavefront W * , and obtaining the coefficients C * i (i = 1, 2, …, m) corresponding to each polynomial, and the fitting expression of the reconstructed wavefront W * . wherein Z i represents the ith polynomial, the coefficients of the Z4, Z9 terms are C * 4, C * 9; 4) When the image plane grating of the grating shearing interferometer deviates from the imaging focal plane of the optical system to be measured, the shearing interferograms of the optical system to be measured in X and Y directions are generated by using the grating transverse shearing interferometer, and the interferograms I x (x d ,y d ) and I y (x d , y d ) are received by using a two-dimensional photoelectric sensor, wherein (x d , y d ) is the pixel position coordinate system on the two-dimensional photoelectric sensor; 5) extracting the differential phases Sx, Sy in the X, Y directions from the shearing interferograms in the X, Y directions x (x d , y d ) and S y (x d , y d ); 6) using differential phase S x (x d , y d ) and S y (x d , y d ) to reconstruct the wavefront W to be measured, fitting the reconstructed wavefront W with the first m Zernike polynomials to obtain the coefficients C i (i = 1, 2,..., m) corresponding to each polynomial, and the fitting expression of the reconstructed wavefront W: wherein Z i represents the ith polynomial; the coefficients corresponding to the Z4, Z9 terms are C4, C9; 7) replace the coefficients C4, C9 of the Z4, Z9 terms of the polynomials obtained in step 6) with the coefficients C4, C9 of the Z4, Z9 terms obtained in step 3) * 4, C * 9, using the replaced polynomial coefficients C i fit the wavefront to be measured again, and output the wavefront to be measured after compensation of the system error; 8) Z4 term polynomial coefficient C4 of wavefront fitting when the image plane grating is off the focal plane and Z4 term coefficient C4 when the image plane grating is at the focal plane position * 4 Calculate the defocus distance z of the image plane grating as ， NA is the numerical aperture of the optical system to be measured; 9) Moving the image plane grating by a distance z, the image plane grating of the grating lateral shearing interferometer is adjusted to coincide with the imaging focal plane of the optical system to be measured.

2. The method of claim 1, wherein the method further comprises: The grating lateral interferometer is a four-wave grating shearing interferometer, a Talbot grating shearing interferometer or a Ronchi shearing interferometer.

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