In the last few years, works have been published about demodulating Single Fringe Pattern Images (SFPI) with closed fringes. The two best known methods are the regularized phase tracker (RPT), and the two-dimensional Hilbert Transform method (2D-HT). In both cases, the demodulation success depends strongly on the path followed to obtain the expected estimation. Therefore, both RPT and 2D-HT are path dependent methods. In this paper, we show a novel method to demodulate SFPI with closed fringes which follow arbitrary sequential paths. Through the work presented here, we introduce a new technique to demodulate SFPI with estimations within the function space C²; in other words, estimations where the phase curvature is continuous. The technique developed here, uses a frequency estimator which searches into a frequency discrete set. It uses a second order potential regularizer to force the demodulation system to look into the function space C². The obtained estimator is a fast demodulator system for normalized SFPI with closed fringes. Some tests to demodulate SFPI with closed fringes using this technique following arbitrary paths are presented. The results are compared to those from RPT technique. Finally, an experimental normalized interferogram is demodulated with the herein suggested technique.

© 2006 Optical Society of America

1. A. Mujeeb, V. U. Nayar and V. R. Ravindran, "Electronic Speckle Pattern Interferometry techniques for nondestructive evaluation: a review," INSIGHT 45275-281 (2006). [CrossRef]
2. J. N. Butters and J. A. Leendertz, "A double exposure technique for speckle pattern interferometry," J. Phys. E: Sci. Instrum. 4277-279 (1971). [CrossRef]
3. J. A. Quiroga and M. Servin, "Isotropic n-dimensional fringe pattern normalization," Opt Commun. 224221- 227 (2003). [CrossRef]
4. J. A. Guerrero, J. L. Marroquin, and M. Rivera, "Adaptive monogenic filtering and normalization of ESPI fringe patterns," Opt. Lett. 30318-320 (2005). [CrossRef]
5. M. Takeda, H. Ina, and S. Kobayashi, "Fourier transform methods of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982). [CrossRef]
6. K. A. Stetson andW. R. Brohinsky, "Fringe-shifting technique for numerical analysis of time-average holograms of vibrating objects," J. Opt. Soc. Am. A 51472 (1988). [CrossRef]
7. J. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfel, A. D. White, and D. J. Brangaccio, "Digital wavefront measuring interferometer for testing optical surface and lenses," Appl. Opt. 132693-2703 (1974). [CrossRef] [PubMed]
8. M. Servin, J. L. Marroquin and F. J. Cuevas, "Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms," J. Opt. Soc. Am. A 18689-695 (2001). [CrossRef]
9. K. G. Larkin, DonaldJ. Bone, and Michael A. Oldfield, "Natural demodulation of two-dimensional fringe patterns. i. general background of the spiral phase quadrature transform," J. Opt. Soc. Am. A 181862-1870 (2001). [CrossRef]
10. K. G. Larkin, "Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform," J. Opt. Soc. Am. A 181871-1881 (2001). [CrossRef]
11. K. Larkin, "Uniform estimation of orientation using local and nonlocal 2-D energy operators," Opt. Express 138097-8121 (2005). [CrossRef] [PubMed]
12. J. A. Quiroga, Manuel Servin and Francisco Cuevas, "Modulo 2 fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm," J. Opt. Soc. Am. A 191524-1531 (2002). [CrossRef]
13. J. Villa, I. De la Rosa and G. Miramontes, "Phase recovery from a single fringe pattern using an orientational vector-field-regularized estimator," J. Opt. Soc. Am. A 222766-2773 (2005). [CrossRef]
14. M. Servin and R. Rodriguez-Vera, "Two-dimensional phase locked loop demodulation of interferograms," J. Mod. Opt. 402087-2094 (1993). [CrossRef]
15. MuntherA. Gdeisat, David R. Burton and Michael J. Lalor, "Real-Time Fringe Pattern Demodulation with a Second-Order Digital Phase-Locked Loop," Appl. Opt. 395326-5336 (1993). [CrossRef]
16. Jorge Nocedal and Stephen J. Wright, Numerical Optimization. Springer, 1999. [CrossRef]

Appl. Opt.

• J. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfel, A. D. White, and D. J. Brangaccio, "Digital wavefront measuring interferometer for testing optical surface and lenses," Appl. Opt. 132693-2703 (1974). [CrossRef] [PubMed]
• MuntherA. Gdeisat, David R. Burton and Michael J. Lalor, "Real-Time Fringe Pattern Demodulation with a Second-Order Digital Phase-Locked Loop," Appl. Opt. 395326-5336 (1993). [CrossRef]

INSIGHT

• A. Mujeeb, V. U. Nayar and V. R. Ravindran, "Electronic Speckle Pattern Interferometry techniques for nondestructive evaluation: a review," INSIGHT 45275-281 (2006). [CrossRef]

J. Mod. Opt.

• M. Servin and R. Rodriguez-Vera, "Two-dimensional phase locked loop demodulation of interferograms," J. Mod. Opt. 402087-2094 (1993). [CrossRef]

J. Opt. Soc. Am.

• M. Takeda, H. Ina, and S. Kobayashi, "Fourier transform methods of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982). [CrossRef]

J. Opt. Soc. Am. A

• K. A. Stetson andW. R. Brohinsky, "Fringe-shifting technique for numerical analysis of time-average holograms of vibrating objects," J. Opt. Soc. Am. A 51472 (1988). [CrossRef]
• J. A. Quiroga, Manuel Servin and Francisco Cuevas, "Modulo 2 fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm," J. Opt. Soc. Am. A 191524-1531 (2002). [CrossRef]
• J. Villa, I. De la Rosa and G. Miramontes, "Phase recovery from a single fringe pattern using an orientational vector-field-regularized estimator," J. Opt. Soc. Am. A 222766-2773 (2005). [CrossRef]
• M. Servin, J. L. Marroquin and F. J. Cuevas, "Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms," J. Opt. Soc. Am. A 18689-695 (2001). [CrossRef]
• K. G. Larkin, DonaldJ. Bone, and Michael A. Oldfield, "Natural demodulation of two-dimensional fringe patterns. i. general background of the spiral phase quadrature transform," J. Opt. Soc. Am. A 181862-1870 (2001). [CrossRef]
• K. G. Larkin, "Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform," J. Opt. Soc. Am. A 181871-1881 (2001). [CrossRef]

J. Phys. E: Sci. Instrum.

• J. N. Butters and J. A. Leendertz, "A double exposure technique for speckle pattern interferometry," J. Phys. E: Sci. Instrum. 4277-279 (1971). [CrossRef]

Opt Commun.

• J. A. Quiroga and M. Servin, "Isotropic n-dimensional fringe pattern normalization," Opt Commun. 224221- 227 (2003). [CrossRef]

Opt. Express

• K. Larkin, "Uniform estimation of orientation using local and nonlocal 2-D energy operators," Opt. Express 138097-8121 (2005). [CrossRef] [PubMed]

Opt. Lett.

• J. A. Guerrero, J. L. Marroquin, and M. Rivera, "Adaptive monogenic filtering and normalization of ESPI fringe patterns," Opt. Lett. 30318-320 (2005). [CrossRef]

Other

• Jorge Nocedal and Stephen J. Wright, Numerical Optimization. Springer, 1999. [CrossRef]

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