Estimation of the orientation term of the general quadrature transform from a single n-dimensional fringe pattern

Thumbnail Image
Full text at PDC
Publication Date
Servín Guirado, Manuel
Marroquín Zaleta, José Luis
Crespo Vázquez, Daniel
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Optical Society of America
Google Scholar
Research Projects
Organizational Units
Journal Issue
The spatial orientation of the fringe has been demonstrated to be a key point in the reliable phase demodulation from a single n-dimensional fringe pattern regardless of the frequency spectrum of the signal. The recently introduced general n-dimensional quadrature transform (GQT) makes explicit the importance of the fringe orientation in the demodulation process. The GQT is a quadrature operator that transforms cos φ into -sin φ-where φ is the modulating phase-and it is composed of two terms: an orientation factor directly related to the fringe's spatial orientation and an isotropic n-dimensional generalization of the one-dimensional Hilbert transform. We present a method for the determination of the orientation factor in a general n-dimensional case and its application to the demodulation of a single fringe pattern by the GQT. We have tested the algorithm with simulated as well as real photoelastic fringe patterns with good results.
© 2005 Optical Society of America. We acknowledge the economic support of this work given by project DPI2002-02104 of the Ministerio de Ciencia y Tecnología of Spain and by Consejo Nacional de Ciencia y Tecnología, México. Figure 6(a) is courtesy of NDT Expert, Toulouse, France;
1. T. Kreis, Holographic Interferometry (Akademie Verlag, Berlin, 1996). 2. J. L. Marroquín, R. Rodríguez-Vera, and M. Servín, ‘‘Local phase from local orientation by solution of a sequence of linear systems”, J. Opt. Soc. Am. A 15, 1536–44 (1998). 3. M. Servín, J. L. Marroquín, and F. J. Cuevas, ‘‘Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms”, J. Opt. Soc. Am. A 18, 689–695 (2001). 4. 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). 5. 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). 6. J. A. Quiroga, M. Servín, and F. J. Cuevas, ‘‘Modulo 2 p fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm”, J. Opt. Soc. Am. A 19, 1524–1531 (2002). 7. X. Zhou, J. P. Baird, and J. F. Arnold, ‘‘Fringe-orientation estimation by use of a Gaussian gradient filter and neighboring-direction averaging”, Appl. Opt. 38,795–804 (1999). 8. J. A. Quiroga and M. Servín, ‘‘Isotropic n-dimensional fringe pattern normalization”, Opt. Commun. 224, 221–227 (2003). 9. K. Ramesh, Digital Photoelasticity (Springer-Verlag, Berlin, 2000)