Abstract
Phase-shifting fringe analysis using wavelength tuning has been widely applied to interferometric surface measurements of optical flats. However, when measuring the silicon wafer that has the highly reflective surface, the correlated error between the second harmonic component and phase-shift miscalibration can be a significant error in the phase distribution. In this study, a novel design method to derive a phase-extraction algorithm is proposed for the suppression of the correlated error. A new 11-frame algorithm was developed using the Blackman sampling window. The 11-frame algorithm was visualized on the frequency space and complex plane, and its compensation capability was confirmed by numerical error analysis comparing with other algorithms. Finally, the silicon wafer surface was profiled by applying the 11-frame algorithm and Fizeau interferometer.
Similar content being viewed by others
References
F. Miao, S. Ahn, Y. H. Moon and Y. Kim, Surface profilometry of silicon wafer using wavelength-tuned phase-shifting interferometry, Journal of Mechanical Science and Technology, 33(11) (2019) 5327–5335.
Y. Kim, Interferometric profilometry of absolute optical thickness of transparent plate using wavelength tuning fringe analysis, Journal of Mechanical Science and Technology, 33(6) (2019) 2841–2846.
J. Park, J. A. Kim, H. Ahn, J. Bae and J. Jin, A review of thickness measurements of thick transparent layers using optical interferometry, International Journal of Precision Engineering and Manufacturing, 20 (2019) 463–477.
P. de Groot, Measurement of transparent plates with wavelength-tuned phase-shifting interferometry, Applied Optics, 39(16) (2000) 2658–2663.
J. Burke, K. Hibino, R. Hanayama and B. F. Oreb, Simultaneous measurement of several near-parallel surfaces with wavelength-shifting interferometry and a tunable phase-shifting method, Optics and Lasers in Engineering, 45(2) (2007) 326–341.
Y. Kim, K. Hibino, N. Sugita and M. Mitsuishi, Simultaneous measurement of surface shape and optical thickness using wavelength tuning and a polynomial window function, Optics Express, 23(25) (2015) 32869–32880.
Y. Kim, W. Bae, Y. H. Moon, K. Hibino and M. Mitsuishi, Fourier interferometry of multi-layer sample using wavelength tuning and partially negative window, Optics and Lasers in Engineering, 137 (2020) 106350.
K. Hibino, B. F. Oreb, D. I. Farrant and K. G. Larkin, Phase shifting for nonsinusoidal waveforms with phase-shift errors, Journal of the Optical Society of America A, 12(4) (1995) 761–768.
K. G. Larkin and B. F. Oreb, Design and assessment of symmetrical phase-shifting algorithms, Journal of the Optical Society of America A, 9(10) (1992) 1740–1748.
Y. Kim, Precision interferometric surface metrology of transparent thin film using wavelength tuning, Journal of Mechanical Science and Technology, 31(11) (2017) 5423–5428.
K. Hibino, B. F. Oreb, D. I. Farrant and K. G. Larkin, Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts, Journal of the Optical Society of America A, 14(4) (1997) 918–930.
K. Creath, Phase measurement interferometry techniques, Progress in Optics, E. Wolf (Ed.), North-Holland (1988).
J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White and D. J. Brangaccio, Digital wavefront measuring interferometer for testing optical surfaces and lenses, Applied Optics, 13(11) (1974) 2693–2703.
J. Schwider, R. Burow, K. E. Elssner, J. Grzanna, R. Spolaczyk and K. Merkel, Digital wave-front measuring interferometry: some systematic error sources, Applied Optics, 22(21) (1983) 3421–3432.
J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller and N. Streibl, New compensating four-phase algorithm for phase-shift interferometry, Optical Engineering, 32(8) (1993) 1883–1885.
J. Schmit and K. Creath, Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry, Applied Optics, 34(19) (1995) 3610–3619.
K. Hibino, B. F. Oreb, P. S. Fairman and J. Burke, Simultaneous measurement of surface shape and variation in optical thickness of a transparent parallel plate in wavelength-scanning Fizeau interferometer, Applied Optics, 43(6) (2004) 1241–1249.
Y. Surrel, Design of algorithms for phase measurements by the use of phase stepping, Applied Optics, 35(1) (1996) 51–60.
Y. Kim, K. Hibino, R. Hanayama, N. Sugita and M. Mitsuishi, Multiple-surface interferometry of highly reflective wafer by wavelength tuning, Optics Express, 22(18) (2014) 21145–21156.
Y. Kim, N. Sugita and M. Mitsuishi, Measurement of surface profile and thickness of multilayer wafer using wavelength-tuning fringe analysis, Precision Engineering, 52 (2018) 130–137.
P. J. de Groot, Correlated errors in phase-shifting laser Fizeau interferometry, Applied Optics, 53(19) (2014) 4334–4342.
Y. Kim, K. Hibino, N. Sugita and M. Mitsuishi, Design of phase shifting algorithms: fringe contrast maximum, Optics Express, 22(15) (2014) 18203–18213.
Y. Kim, K. Hibino, N. Sugita and M. Mitsuishi, Surface profile measurement of a highly reflective silicon wafer by phase-shifting interferometry, Applied Optics, 54(13) (2015) 4207–4213.
J. Park, J. You and S. W. Kim, Vibration-desensitized fiber-diffraction interferometer for industrial surface measurements, CIRP Annals-Manufacturing Technology, 58(1) (2009) 473–476.
Y. Kim, K. Hibino, N. Sugita and M. Mitsuishi, Measurement of absolute optical thickness of mask glass by wavelength-tuning Fourier analysis, Optics Letters, 40(13) (2015) 3169–3172.
N. Bobroff, Residual errors in laser interferometry from air turbulence and nonlinearity, Applied Optics, 26(13) (1987) 2676–2682.
F. J. Harris, On the use of window for harmonic analysis with the discrete Fourier transform, Proceedings of the IEEE, 66(1) (1978) 51–83.
K. Freischlad and C. L. Koliopoulos, Fourier description of digital phase-measuring interferometry, Journal of the Optical Society of America A, 7(4) (1990) 542–551.
A. Patil, B. Raphael and P. Rastogi, Generalized phase-shifting interferometry by use of a direct stochastic algorithm for global research, Optics Letters, 29(12) (2004) 1381–1383.
Y. Surrel, Design of phase-detection algorithms insensitive to bias modulation, Applied Optics, 36(4) (1997) 805–807.
Y. Kim, K. Hibino, N. Sugita and M. Mitsuishi, Measurement of optical thickness variation of BK87 plate by wavelength tuning interferometry, Optics Express, 23(17) (2015) 22928–22938.
K. Liu and M. G. Littman, Novel geometry for single-mode scanning of tunable lasers, Optics Letters, 6(3) (1981) 117–118.
Acknowledgments
This work was supported by National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (2020R1F1A1075993).
Author information
Authors and Affiliations
Corresponding author
Additional information
Jurim Jeon is a B.S. course student and an undergraduate researcher at the School of Mechanical Engineering, Pusan National University. Her research interests include precision measurement using wavelength-scanning Fizeau interferometry, and the design of phase-extraction algorithms.
Sungtae Kim is a master and doctor-integrated course student at the School of Mechanical Engineering, Pusan National University. He received his B.S. degree at the School of Mechanical Engineering, Pusan National University in 2019. His research interests include precision measurement using wavelength-scanning Fizeau interferometry and fringe analysis using phase shifting.
Yangjin Kim is an Associated Professor at the School of Mechanical Engineering, Pusan National University. He obtained his B.S. and Ph.D. degrees at the Department of Mechanical Engineering, The University of Tokyo, in 2007 and 2015, respectively. Prof. Kim was a researcher at the Korea Institute of Machinery and Materials (KIMM) from 2009 to 2012 as a military service. His research interests include precision measurement, wavelength-scanning Fizeau interferometry, fringe analysis using phase shifting.
Rights and permissions
About this article
Cite this article
Jeon, J., Kim, S. & Kim, Y. Precise interferometric surface profiling of silicon wafer using sampling window and wavelength tuning. J Mech Sci Technol 35, 2177–2184 (2021). https://doi.org/10.1007/s12206-021-0434-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-021-0434-2