Quiroga Mellado, Juan AntonioMarroquín Zaleta, José LuisServín Guirado, Manuel2023-06-202023-06-202004-031. D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Chap. 1. 2. M. Takeda, H. Ina, and S. Kobayashi, ‘‘Fourier-transform method of fringe pattern analysis’’, J. Opt. Soc. Am. 72, 156–160 (1982). 3. D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998), Chap. 6. 4. G. Cloud, Optical Methods of Engineering Analysis (Cambridge U. Press, Cambridge, UK, 1995). 5. K. G. Larkin, D. J. Bone, and M. A. Oldfield, ‘‘Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform’’, J. Opt. Soc. Am. A 18, 1862–1870 (2001). 6. M. Servín, J. A. Quiroga, and J. L. Marroquín, ‘‘General n-dimensional quadrature transform and its application to interferogram demodulation’’, J. Opt. Soc. Am. A 20, 925–934 (2003). 7. J. A. Quiroga, M. Servín, and F. J. Cuevas, ‘‘Módulo 2 π fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm’’, J. Opt. Soc. Am. A 19, 1524–1531 (2002). 8. M. Servín, J. L. Marroquin, and F. J. Cuevas, ‘‘Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms’’, J. Opt. Soc. Am. A 18, 689–695 (2001). 9. M. Servín and R. Rodríguez-Vera, ‘‘Two dimensional phase locked loop demodulation of carrier frequency interferograms’’, J. Mod. Opt. 40, 2087–2094 (1993). 10. J. Kozlowski and G. Serra, ‘‘New modified phase locked loop method for fringe pattern demodulation’’, Opt. Eng. 36, 2025–2030 (1997). 11. J. Kozlowski and G. Serra, ‘‘Complex phase tracing method for fringe pattern demodulation’’, Appl. Opt. 38, 2256–2262 (1999). 12. B. Ströbel, ‘‘Processing of interferometric phase maps as complex-valued phasor images’’, Appl. Opt. 35, 2192–2198 (1996). 13. C. W. Groetsch, Inverse Problems in the Mathematical Sciences (Vieweg, Braunschweig, Germany, 1993).1084-752910.1364/JOSAA.21.000411https://hdl.handle.net/20.500.14352/50817© 2004 Optical Society of America. M. Servín and J. L. Marroquín were partially supported by grants 33429-E and 42523, respectively, from Consejo Nacional de Ciencia y Tecnología (CONACYT), México.A new sequential phase demodulator based on a regularized quadrature and phase tracker system (RAPT) is applied to demodulate two-dimensional fringe patterns. This RQPT system tracks the fringe pattern's quadrature and phase in a sequential way by following the path of the fringes. To make the RAPT system more robust to noise, the modulating phase around a small neighborhood is modeled as a plane and the quadrature of the signal is estimated simultaneously with the fringe's modulating phase. By sequentially calculating the quadrature of the fringe pattern, one obtains a more robust sequential demodulator than was previously possible. This system may be applied to the demodulation of a single interferogram having closed fringes.engjournal articlehttp://dx.doi.org/10.1364/JOSAA.21.000411http://www.opticsinfobase.orgopen access535Pattern-AnalysisDemodulationTransformÓptica (Física)2209.19 Óptica Física