Abstract
In this paper, a calibration method is proposed which eliminates the zeroth order effect in lateral shearing interferometry. An analytical expression of the calibration error function is deduced, and the relationship between the phase-restoration error and calibration error is established. The analytical results show that the phase-restoration error introduced by the calibration error is proportional to the phase shifting error and zeroth order effect. The calibration method is verified using simulations and experiments. The simulation results show that the phase-restoration error is approximately proportional to the phase shift error and zeroth order effect, when the phase shifting error is less than 2° and the zeroth order effect is less than 0.2. The experimental result shows that compared with the conventional method with 9-frame interferograms, the calibration method with 5-frame interferograms achieves nearly the same restoration accuracy.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Y. Q. Yu, Y. F. Zhang, Z. L. Ou, X. Chen, Q. D. Huang, and S. C. Ruan, “Simultaneous measurement of one dimensional bending and temperature based on Mach-Zehnder interferometer,” Photonic Sensors, 2015, 5(4): 376–384.
L. C. Zhang, X. K. Cai, and G. Shi, “Optical coatings for DUV lithography,” Chinese Optics, 2015, 8(2): 169–181.
S. T. Gao, D. C. Wu, and E. L. Miao, “Distortion correcting method when testing large-departure asphere,” Chinese Optics, 2017, 10(3): 383–390.
F. Wang, X. Z. Wang, M. Y. Ma, D. Q. Zhang, W. J. Shi, and J. M. Hu, “Aberration measurement of projection optics in lithographic tools by use of an alternating phase-shifting mask,” Applied Optics, 2006, 45(2): 281–287.
F. Z. Dai, J. Li, X. Z. Wang, and Y. Bu, “Exact two-dimensional zonal wavefront reconstruction with high spatial resolution in lateral shearing interferometry,” Optics Communications, 2016, 367: 367–264.
M. Takeda and S. Kobayashi, “Lateral aberration measurements with a digital Talbot interferometer,” Applied Optics, 1984, 23(11): 1760–1764.
M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, et al., “Recent progress of EUV wave-front metrology in EUVA,” SPIE, 2004, 5533: 5533–27.
H. Schreiber and J. Schwider, “Lateral shearing interferometer based on two Ronchi gratings in series,” Applied Optics, 1997, 36(22): 5321–5324.
F. Z. Bai, X. Q. Wang, K. Z. Huang, and F. Tian, “Analysis of spatial resolution and pinhole size for single-shot point-diffraction interferometer using in closed-loop adaptive optics,” Optics Communications, 2013, 297(12): 27–31.
S. H. Lee, P. Naulleau, K. A. Goldberg, F. Piao, W. Oldham, and J. Bokar, “Phase-shifting point-diffraction interferometry at 193 nm,” Applied Optics, 2013, 39(31): 5768–5772.
K. A. Goldberg, P. Naulleau, P. Denham, and E. H. Anderson, “EUV interferometric testing and alignment of the 0.3-NA MET optic,” SPIE, 2004, 5374(7): 64–73.
P. Gao, I. Harder, V. Nercissian, K. Mantel, and B. Yao, “Phase-shifting point-diffraction interferometry with common-path and in-line configuration for microscopy,” Optics Letters, 2010, 35(5): 712–714.
R. Miyakawa, P. Naulleau, and K. Goldberg, “Analysis of systematic errors in lateral shearing interferometry for EUV optical testing,” SPIE, 2009, 7272: 7272–1.
Y. C. Zhu, K. Sugisaki, C. Ouchi, M. Hasegawa, M. Niibe, A. Suzuki, et al., “Lateral shearing interferometer for EUVL: theoretical analysis and experiment,” in Proceeding of Conference on Emerging Lithographic Technologies VIII, Santa Clara, CA, USA, 2004, pp. 824–832.
C. Fang, Y. Xiang, K. Q. Qi, C. L. Zhang, and C. S. Yu, “An 11-frame phase shifting algorithm in lateral shearing interferometry,” Optics Express, 2013, 21(23): 28325–28333.
P. Hariharan, “Digital phase-stepping interferometry: effects of multiply reflected beams,” Applied Optics, 1987, 26(13): 2506–2507.
Acknowledgment
This work was supported by the National S&T (Science and Technology) Special Program (No. 2009ZX02202005).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Fang, C., Xiang, Y., Qi, K. et al. Calibration Method to Eliminate Zeroth Order Effect in Lateral Shearing Interferometry. Photonic Sens 8, 255–262 (2018). https://doi.org/10.1007/s13320-018-0500-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13320-018-0500-2