Phase-shifting interferometry by a covariance-based method

Applied Optics

Volumn 44, Issue 27, 2005, Pages 5778-5785

  Patil, Abhijit ^a   Rastogi, Pramod ^a   Raphael, Benny ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ACTUATORS; CALIBRATION; COMPUTER SIMULATION; DATA STRUCTURES; GAUSSIAN NOISE (ELECTRONIC); PHASE SHIFT; PIEZOELECTRIC DEVICES; SET THEORY; WAVEFORM ANALYSIS;

DATA SETS; MISCALIBRATION; PHASE-SHIFTING INTERFEROMETRY; PIEZOACTUATOR DEVICES;

INTERFEROMETRY;

EID: 27144548521     PISSN: 1559128X     EISSN: 15394522     Source Type: Journal    
DOI: 10.1364/AO.44.005778     Document Type: Conference Paper

References (34)

1. P. Carré, "Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures," Metrologia 2, 13-23 (1966).
2. 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," Appl. Opt. 13, 2693-2703 (1974).
3. K. Creath, "Phase-shifting holographic interferometry," in Holographic Interferometry, P. K. Rastogi, ed., Vol. 68 of Springer Series in Optical Sciences (Springer-Verlag, 1994), pp. 109-150.
4. T. Kreis, Holographic Interferometry: Principles and Methods (Akademie Verlag, 1996), pp. 101-170.
5. J. E. Greivenkamp and J. H. Bruning, "Phase shifting interferometry," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 501-598.
6. J. Schwider, R. Burow, K. E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, "Digital wave-front measuring interferometry: some systematic error sources," Appl. Opt. 22, 3421-3432 (1983).
7. Y. Zhu and T. Gemma, "Method for designing error-compensating phase-calculation algorithms for phase-shifting interferometry," Appl. Opt. 40, 4540-4546 (2001).
8. P. Hariharan, B. F. Oreb, and T. Eiju, "Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm," Appl. Opt. 26, 2504-2506 (1987).
9. J. Schwider, O. Falkenstorfer, H. Schreiber, and A. Zoller, "New compensating four-phase algorithm for phase-shift interferometry," Opt. Eng. 32, 1883-1885 (1993).
10. Y. Surrel, "Phase stepping: a new self-calibrating algorithm," Appl. Opt. 32, 3598-3600 (1993).
11. Y. Surrel, "Design of algorithms for phase measurements by the use of phase stepping," Appl. Opt. 35, 51-60 (1996).
12. J. van Wingerden, H. J. Frankena, and C. Smorenburg, "Linear approximation for measurement errors in phase shifting interferometry," Appl. Opt. 30, 2718-2729 (1991).
13. K. G. Larkin and B. F. Oreb, "Design and assessment of symmetrical phase-shifting algorithms," J. Opt. Soc. Am. A 9, 1740-1748 (1992).
14. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, "Phase shifting for nonsinusoidal waveforms with phase-shift errors," J. Opt. Soc. Am. A 12, 761-768 (1995).
15. Y.-Y. Cheng and J. C. Wyant, "Phase-shifter calibration in phase-shifting interferometry," Appl. Opt. 24, 3049-3052 (1985).
16. B. Zhao, "A statistical method for fringe intensity-correlated error in phase-shifting measurement: the effect of quantization error on the N-bucket algorithm," Meas. Sci. Technol. 8, 147-153 (1997).
17. B. Zhao and Y. Surrel, "Effect of quantization error on the computed phase of phase-shifting measurements," Appl. Opt. 36, 2070-2075 (1997).
18. R. Józwicki, M. Kujawinska, and M. Salbut, "New contra old wavefront measurement concepts for interferometric optical testing," Opt. Eng. 31, 422-433 (1992).
19. P. de Groot, "Vibration in phase-shifting interferometry," J. Opt. Soc. Am. A 12, 354-365 (1995).
20. P. de Groot and L. L. Deck, "Numerical simulations of vibration in phase-shifting interferometry," Appl. Opt. 35, 2172-2178 (1996).
21. C. Rathjen, "Statistical properties of phase-shift algorithms, " J. Opt. Soc. Am. A 12, 1997-2008 (1995).
22. P. L. Wizinowich, "Phase-shifting interferometry in the presence of vibration: a new algorithm and system," Appl. Opt. 29, 3271-3279 (1990).
23. C. Joenathan and B. M. Khorana, "Phase measurement by differentiating interferometric fringes," J. Mod. Opt. 39, 2075-2087 (1992).
24. K. Kinnnstaetter, A. W. Lohmann, J. Schwider, and N. Streibl, "Accuracy of phase shifting interferometry," Appl. Opt. 27, 5082-5089 (1988).
25. C. J. Morgan, "Least squares estimation in phase-measurement interferometry," Opt. Lett. 7, 368-370 (1982).
26. J. E. Greivenkamp, "Generalized data reduction for heterodyne interferometry," Opt. Eng. 23, 350-352 (1984).
27. R. Roy and T. Kailath, "ESPRIT - Estimation of signal param-eters via rotational invariance techniques," IEEE Trans. Acoust. Speech Signal Process. 37, 984-995 (1989).
28. J. J. Fuchs, "Estimating the number of sinusoids in additive white noise," IEEE Trans. Acoust. Speech Signal Process. 36, 1846-1853 (1988).
29. T. Söderström and P. Stoica, "Accuracy of high-order Yule-Walker methods for frequency estimation of complex sine waves," IEE Proc. F 140, 71-80 (1993).
30. R. Kumaresan and D. W. Tufts, "Estimating the angles of arrival of multiple plane waves," IEEE Trans. Aerosp. Electron. Syst. 19, 134-139 (1983).
31. M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities (Dover, 1992), pp. 15-16.
32. K. M. Hoffman and R. Kunze, Linear Algebra, 2nd ed. (Prentice-Hall, 1971).
33. P. K. Rastogi, "Phase shifting applied to four-wave holographic interferometers," Appl. Opt. 31, 1680-1681 (1992).
34. P. K. Rastogi, "Phase-shifting holographic moiré: phase-shifter error-insensitive algorithms for the extraction of the difference and sum of phases in holographic moiré," Appl. Opt. 32, 3669-3675 (1993).