Publication:
Phase-shifting interferometry corrupted by white and non-white additive noise

Loading...
Thumbnail Image
Full text at PDC
Publication Date
2011-05-09
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
The Optical Society Of America
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
The standard tool to estimate the phase of a sequence of phase-shifted interferograms is the Phase Shifting Algorithm (PSA). The performance of PSAs to a sequence of interferograms corrupted by non-white additive noise has not been reported before. In this paper we use the Frequency Transfer Function (FTF) of a PSA to generalize previous white additive noise analysis to non-white additive noisy interferograms. That is, we find the ensemble average and the variance of the estimated phase in a general PSA when interferograms corrupted by non-white additive noise are available. Moreover, for the special case of additive white-noise, and using the Parseval's theorem, we show (for the first time in the PSA literature) a useful relationship of the PSA's noise robustness; in terms of its FTF spectrum, and in terms of its coefficients. In other words, we find the PSA's estimated phase variance, in the spectral space as well as in the PSA's coefficients space.
Description
© The Optical Society of America. We appreciate the support of the Mexican Science and Technology Council CONACYT.
Keywords
Citation
1. 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(11), 2693–2703 (1974). 2. D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing, Taylor & Francis CRC Press, 2th edition (2005). 3. M. Servín, J. C. Estrada, J. A. Quiroga, J. F. Mosiño, and M. Cywiak, “Noise in phase shifting interferometry,” Opt. Express 17(11), 8789–8794 (2009). 4. M. Servín, J. C. Estrada, and J. A. Quiroga, “The general theory of phase shifting algorithms,” Opt. Express 17(24), 21867–21881 (2009). 5. C. P. Brophy, “Effect of intensity error correlation on the computed phase of phase-shifting interferometry,” J. Opt. Soc. Am. A 7(4), 537–541 (1990). 6. C. Rathjen, “Statistical properties of phase-shift algorithms,” J. Opt. Soc. Am. 12(9), 1997–2008 (1995). 7. Y. Surrel, “Additive noise effect in digital phase detection,” Appl. Opt. 36(1), 271–276 (1997). 8. K. Hibino, “Susceptibility of systematic error-compensating algorithms to random noise in phase-shiftinginterferometry,” Appl. Opt. 36, 2064–2093 (1997). 9. A. Papoulis, Probability Random Variables and Stochastic Processes, McGraw-Hill Series in Electrical Engineering, 4th edition (2001). 10. C. J. Morgan, “Least-squares estimation in phase-measurement interferometry,” Opt. Lett. 7(8), 368–370 (1982). 11. 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(21), 3421–3432 (1983). 12. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26(13), 2504–2506 (1987).
Collections