OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 24 — Nov. 23, 2009
  • pp: 21867–21881

The general theory of phase shifting algorithms

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


Optics Express, Vol. 17, Issue 24, pp. 21867-21881 (2009)
http://dx.doi.org/10.1364/OE.17.021867


View Full Text Article

Enhanced HTML    Acrobat PDF (227 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We have been reporting several new techniques of analysis and synthesis applied to Phase Shifting Interferometry (PSI). These works are based upon the Frequency Transfer Function (FTF) and how this new tool of analysis and synthesis in PSI may be applied to obtain very general results, among them; rotational invariant spectrum; complex PSI algorithms synthesis based on simpler first and second order quadrature filters; more accurate formulae for estimating the detuning error; output-power phase noise estimation. We have made our cases exposing these aspects of PSI separately. Now in the light of a better understanding provided by our past works we present and expand in a more coherent and holistic way the general theory of PSI algorithms. We are also providing herein new material not reported before. These new results are on; a well defined way to combine PSI algorithms and recursive linear PSI algorithms to obtain resonant quadrature filters.

© 2009 OSA

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

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: September 1, 2009
Revised Manuscript: October 28, 2009
Manuscript Accepted: October 29, 2009
Published: November 13, 2009

Citation
M. Servin, J. C. Estrada, and J. A. Quiroga, "The general theory of phase shifting algorithms," Opt. Express 17, 21867-21881 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-24-21867


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. K. Freischlad and C. L. Koliopoulos, “Fourier description of digital phase-measuring interferometry,” J. Opt. Soc. Am. A 7(4), 542–551 (1990). [CrossRef]
  2. D. W. Phillion, “General methods for generating phase-shifting interferometry algorithms,” Appl. Opt. 36(31), 8098–8115 (1997). [CrossRef] [PubMed]
  3. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35(1), 51–60 (1996). [CrossRef] [PubMed]
  4. D. Malacara, M. Servin, and Z. Malacara, Interferogram analysis for Optical Testing, 2th ed., (Marcel Deker, 2003).
  5. M. Servin, J. C. Estrada, and J. A. Quiroga, “Spectral analysis of phase shifting algorithms,” Opt. Express 17(19), 16423–16428 (2009). [CrossRef] [PubMed]
  6. J. G. Proakis, and D. G. Manolakis, Digital Signal Processing, 4th-ed., (Prentice Hall, 2007). [PubMed]
  7. J. Schmit and K. Creath, “Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry,” Appl. Opt. 34(19), 3610–3619 (1995). [CrossRef] [PubMed]
  8. 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(7), 5618–5623 (2009). [CrossRef] [PubMed]
  9. M. Servin, J. C. Estrada, J. A. Quiroga, J. F. Mosiño, and M. Cywiak, “Noise in phase shifting interferometry,” Opt. Express 17(11), 8789–8794 (2009). [CrossRef] [PubMed]
  10. J. C. Estrada, M. Servin, and J. A. Quiroga, “Easy and straightforward construction of wideband phase-shifting algorithms for interferometry,” Opt. Lett. 34(4), 413–415 (2009). [CrossRef] [PubMed]
  11. K. G. Larkin, and B. F. Oreb, “Propagation of errors in different phase-shifting algorithms: a special property of the arctangent function,” presented at the SPIE International Symposium on Optical Applied Science and Engineering, San Diego, California, SPIE, 1755, 219–227 (1992).
  12. F. G. Stremler, Introduction to Communications Systems, 3rd ed., (Addison-Wesley, 1990).
  13. 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). [CrossRef] [PubMed]
  14. K. Hibino, “Susceptibility of systematic error-compensating algorithms to random noise in phase-shifting interferometry,” Appl. Opt. 36(10), 2084–2093 (1997). [CrossRef] [PubMed]
  15. C. J. Morgan, “Least-squares estimation in phase-measurement interferometry,” Opt. Lett. 7(8), 368–370 (1982). [CrossRef] [PubMed]
  16. V. K. Madisetti, and D. B. Williams, eds., Digital Signal Processing Handbook, (CRC Press, IEEE Press, 1998).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited