Phasorial analysis of detuning error in temporal phase shifting algorithms

doi:10.1364/OE.17.005618

Phasorial analysis of detuning error in temporal phase shifting algorithms

J. F. Mosiño, M. Servin, J. C. Estrada, and J. A. Quiroga »View Author Affiliations

Optics Express, Vol. 17, Issue 7, pp. 5618-5623 (2009)
http://dx.doi.org/10.1364/OE.17.005618

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Abstract
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References (8)
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Abstract

Phase error analysis in Temporal Phase Shifting (TPS) algorithms due to frequency detuning has been to date only performed numerically. In this paper, we show an exact analytical expression to obtain this phase error due to detuning using the spectral TPS response. The new proposed method is based on the phasorial representation of the output of the TPS quadrature filter. Doing this, the detuning problem is reduced to a ratio of two symmetrical spectral responses of the quadrature filter at the detuned frequency. Finally, some popular cases of TPS algorithms are analyzed to show the usefulness of the proposed method.

OCIS Codes
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: December 17, 2008
Revised Manuscript: February 23, 2009
Manuscript Accepted: February 26, 2009
Published: March 25, 2009

Citation
J. F. Mosiño, M. Servin, J. C. Estrada, and J. A. Quiroga, "Phasorial analysis of detuning error in temporal phase shifting algorithms," Opt. Express 17, 5618-5623 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5618

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References

J. Schwider, "Advanced evaluation techniques in interferometry," in Progress in Optics, E. Wolf ed., (North Holland, Amsterdam, Oxford, New York, Tokyo, 1990).
J. H. Bruning, D. R. Herriot, J. E. Gallagher, D. P. Rosenfel, A. D. White, and D. J. Brangaccio, "Digital wavefront measuring interferometry for testing optical surfaces and lenses," Appl. Opt. 13, 2693-2703 (1974). [CrossRef] [PubMed]
H. Schreiber and J. H. Brunning, "Phase shifting interferometry," in Optical Shop Testing, D. Malacara ed., (John Wiley and Sons, Inc., Hoboken, New Jersey 2007).
M. Servin and M. Kujawinska, "Modern fringe pattern analysis in Interferometry," in Handbook of Optical Engineering, D. Malacara and B. J. Thompson eds., (Marcel Dekker, 2001).
J. Schwider, R. Burrow, 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). [CrossRef] [PubMed]
J. P. Hariharan, B. Oreb, and T. Eiju, "Digital phase shifting interferometry: a simple error compensating phase calculation algorithm," Appl. Opt. 26, 2504-2505 (1987). [CrossRef] [PubMed]
K. Freischland and C. L. Koliopoulos, "Fourier description of digital phase measuring interferometry," J. Opt. Soc. Am. A 7, 542-551 (1990). [CrossRef]
M. Servin, D. Malacara, J. L. Marroquin, and F. J. Cuevas, "Complex linear filters for phase shifting with very low detuning sensitivity," J. Mod. Opt. 44, 1269-1278 (1997). [CrossRef]

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[1] J. Schwider, "Advanced evaluation techniques in interferometry," in Progress in Optics, E. Wolf ed., (North Holland, Amsterdam, Oxford, New York, Tokyo, 1990).

[2] J. H. Bruning, D. R. Herriot, J. E. Gallagher, D. P. Rosenfel, A. D. White, and D. J. Brangaccio, "Digital wavefront measuring interferometry for testing optical surfaces and lenses," Appl. Opt. 13, 2693-2703 (1974). [CrossRef] [PubMed]

[3] H. Schreiber and J. H. Brunning, "Phase shifting interferometry," in Optical Shop Testing, D. Malacara ed., (John Wiley and Sons, Inc., Hoboken, New Jersey 2007).

[4] M. Servin and M. Kujawinska, "Modern fringe pattern analysis in Interferometry," in Handbook of Optical Engineering, D. Malacara and B. J. Thompson eds., (Marcel Dekker, 2001).

[5] J. Schwider, R. Burrow, 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). [CrossRef] [PubMed]

[6] J. P. Hariharan, B. Oreb, and T. Eiju, "Digital phase shifting interferometry: a simple error compensating phase calculation algorithm," Appl. Opt. 26, 2504-2505 (1987). [CrossRef] [PubMed]

[7] K. Freischland and C. L. Koliopoulos, "Fourier description of digital phase measuring interferometry," J. Opt. Soc. Am. A 7, 542-551 (1990). [CrossRef]

[8] M. Servin, D. Malacara, J. L. Marroquin, and F. J. Cuevas, "Complex linear filters for phase shifting with very low detuning sensitivity," J. Mod. Opt. 44, 1269-1278 (1997). [CrossRef]

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Phasorial analysis of detuning error in temporal phase shifting algorithms