Phase recovery from a single undersampled interferogram

Applied Optics

Volumn 42, Issue 34, 2003, Pages 6846-6852

  Muñoz, Jesús ^a   Strojnik, Marija ^a   Paáz, Gonzalo ^a  

^a CENTRO DE INVESTIGACIONES EN ÓPTICA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

DATA REDUCTION; FOURIER TRANSFORMS; FREQUENCY DOMAIN ANALYSIS; LEAST SQUARES APPROXIMATIONS; LIGHT MODULATION; LIGHTING; PHASE SHIFT; SENSITIVITY ANALYSIS;

ASPHERIC SURFACES; INTERFEROGRAMS; PHASE DIFFERENCES;

INTERFEROMETRY;

EID: 0345548553     PISSN: 1559128X     EISSN: 21553165     Source Type: Journal    
DOI: 10.1364/AO.42.006846     Document Type: Article

References (34)

1. 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, 2693-2703 (1974).
2. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156-160 (1982).
3. T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3, 847-855 (1986).
4. K. H. Womack, “Interferometric phase measurement using spatial synchronous detection,” Opt. Eng. 23, 391-395 (1984).
5. D. W. Robinson, “Phase unwrapping methods,” in Interfero-gram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), p. 195.
6. D. L. Fried, “Least-squares fitting of a wave-front distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370-375 (1977).
7. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375-378 (1997).
8. R. J. Noll, “Phase estimates from slope-type wave-front sensors,” J. Opt. Soc. Am. 68, 139-140 (1978).
9. B. R. Hunt, “Matrix formulation of the reconstruction of phase values from phase differences,” J. Opt. Soc. Am. 69, 393-399 (1979).
10. I. Lyuboshenko and H. Maitre, “Phase unwrapping for interferometric synthetic aperture radar by use of Helmholtz equation eigenfunctions and the first Green’s identity,” J. Opt. Soc. Am. A 16, 378-395 (1999).
11. K. Itoh, “Analysis of the phase unwrapping algorithm,” Appl. Opt. 21, 2470 (1982).
12. p-norm twodimensional phase unwrapping,” J. Opt. Soc. Am. A 13, 1999 -2013 (1996).
13. J. L. Marroquin and M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. Am. A 12, 2393-2400 (1995).
14. M. Servin, F. J. Cuevas, D. Malacara, J. L. Marroquin, and R. Rodriguez, “Phase unwrapping through demodulation by use of the regularized phase-tracking technique,” Appl. Opt. 38, 1934-1941 (1999).
15. M. V. R. K. Murty, “A compact lateral shearing interferometer based on the Michelson interferometer,” Appl. Opt. 9, 1146 -1152 (1970).
16. G. Paez, M. Strojnik, and G. Garcia-Torales, “Vectorial shearing interferometer,” Appl. Opt. 39, 5172-5178 (2000).
17. G. Garcia-Torales, G. Paez, and M. Strojnik, “Simulations and experimental results with a vectorial shearing interferometer,” Opt. Eng. 40, 767-773 (2001).
18. D. Malacara, “Hartmann test of aspherical mirrors,” Appl. Opt. 11, 99-101 (1972).
19. M. Servin, D. Malacara, J. L. Marroquin, and F. J. Cuevas, “New technique for ray aberration detection in Hart-manngrams based on regularized bandpass filters,” Opt. Eng. 35, 1677-1683 (1996).
20. M. Servin, F. J. Cuevas, D. Malacara, and J. L. Marroquin, “Direct ray aberration estimation in Hartmanngrams by use of a regularized phase-tracking system,” Appl. Opt. 38, 2862-2869 (1999).
21. O. Katsuyuki and Y. Toyohiko, “Phase measuring Ronchi test,” Appl. Opt. 27, 523-528 (1988).
22. J. E. Greivenkamp, “Sub-Nyquist interferometry,” Appl. Opt. 26, 5245-5257 (1987).
23. J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962-2969 (1996).
24. B. W. Bell and C. L. Koliopoulos, “Moire topography, sampling theory, and charged-coupled devices,” Opt. Lett. 9, 171-173 (1994).
25. J. Schwider, “Detection of undersampling from measured phase-shifting data,” Opt. Lett. 19, 231-233 (1994).
26. J. Muhoz, M. Strojnik, and G. Paez, “Detection and interpretation of high-frequency spatial interferograms,” in Infrared Spaceborne Remote Sensing IX, M. Strojnik and B. F. Andersen, eds., Proc. SPIE 4486, 523-532 (2002).
27. M. Servin, D. Malacara, and F. J. Cuevas, “Path-independent phase unwrapping of subsampled phase maps,” Appl. Opt. 35, 1643-1649 (1996).
28. J. Muhoz, G. Paez, and M. Strojnik, “Phase unwrapping of subsampled phase-shifted interferograms,” in Interferometry XI: Techniques and Analysis, K. Creath and J. Schmit, eds., Proc. SPIE 4777, 288-299 (2002).
29. M. Servin and D. Malacara, “Sub-Nyquist interferometry using a computer-stored reference,” J. Mod. Opt. 43, 1723-1729 (1996).
30. M. Servin, D. Malacara, Z. Malacara, and V. I. Vlad, “Sub-Nyquist null aspheric testing using a computer-stored compensator,” Appl. Opt. 33, 4103-4108 (1994).
31. M. Kujawinska and J. Schmidt, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” in Industrial Applications of Holographic and Speckle Measuring Techniques, W. P. Jueptner, ed., Proc. SPIE 1508, 61-67 (1991).
32. M. Pirga and M. Kujawinska, “Two-directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng. 34, 2459-2466 (1995).
33. G. Paez and M. Strojnik, “Convergent, recursive phase reconstruction from noisy, modulated intensity patterns by use of synthetic interferograms,” Opt. Lett. 23, 406-408 (1998).
34. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36, 4540-4548 (1997).