RT Journal Article T1 The general theory of phase shifting algorithms A1 Quiroga Mellado, Juan Antonio A1 Estrada, Julio César A1 Servín Guirado, Manuel AB 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. PB The Optical Society Of America SN 1094-4087 YR 2009 FD 2009-11-23 LK https://hdl.handle.net/20.500.14352/43973 UL https://hdl.handle.net/20.500.14352/43973 LA eng NO 1. K. Freischlad, and C. L. Koliopoulos, “Fourier description of digital phase-measuring interferometry,” J. Opt. Soc. Am. A 7(4), 542–551 (1990).2. D. W. Phillion, “General methods for generating phase-shifting interferometry algorithms,” Appl. Opt. 36(31), 8098–8115 (1997).3. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35(1), 51–60 (1996).4. D. Malacara, M. Servín, and Z. Malacara, Interferogram analysis for Optical Testing, 2th ed., (Marcel Deker, 2003).5. M. Servín, J. C. Estrada, and J. A. Quiroga, “Spectral analysis of phase shifting algorithms,” Opt. Express 17(19), 16423–16428 (2009).6. J. G. Proakis, and D. G. Manolakis, Digital Signal Processing, 4th-ed., (Prentice Hall, 2007).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).8. J. F. Mosiño, M. Servín, J. C. Estrada, and J. A. Quiroga, “Phasorial analysis of detuning error in temporal phase shifting algorithms,” Opt. Express 17(7), 5618–5623 (2009).9. 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).10. J. C. Estrada, M. Servín, and J. A. Quiroga, “Easy and straightforward construction of wideband phase-shifting algorithms for interferometry,” Opt. Lett. 34(4), 413–415 (2009).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).14. K. Hibino, “Susceptibility of systematic error-compensating algorithms to random noise in phase-shifting interferometry,” Appl. Opt. 36(10), 2084–2093 (1997).15. C. J. Morgan, “Least-squares estimation in phase-measurement interferometry,” Opt. Lett. 7(8), 368–370 (1982).16. V. K. Madisetti, and D. B. Williams, eds., Digital Signal Processing Handbook, (CRC Press, IEEE Press, 1998). NO © 2009 Optical Society of America.We acknowledge the valuable support of the Mexican Science Council, CONACYT. NO Mexican Science Council, CONACYT DS Docta Complutense RD 8 may 2024