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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 1 — Jan. 1, 2000
  • pp: 46–52

Phase reconstruction from undersampled intensity patterns

Gonzalo Paez and Marija Strojnik  »View Author Affiliations

JOSA A, Vol. 17, Issue 1, pp. 46-52 (2000)

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We demonstrate the uniqueness and convergence of phase recovery from high-spatial-frequency and undersampled intensity data. Furthermore, this is accomplished without the ambiguities that arise in phase unwrapping and without the need to employ a priori information. The method incorporates the technique of line integration of the phase gradient to find the first approximation to the phase and the algorithm of synthetic interferograms to find the unknown phase with high accuracy. The method may be used with any experimental method that at a certain data processing step obtains generalized sine and cosine intensity functions.

© 2000 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval
(100.6640) Image processing : Superresolution
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(220.1250) Optical design and fabrication : Aspherics
(220.4840) Optical design and fabrication : Testing

Original Manuscript: December 10, 1998
Revised Manuscript: September 3, 1999
Manuscript Accepted: April 12, 1999
Published: January 1, 2000

Gonzalo Paez and Marija Strojnik, "Phase reconstruction from undersampled intensity patterns," J. Opt. Soc. Am. A 17, 46-52 (2000)

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  1. G. Páez, M. Strojnik Scholl, “Thermal contrast detected with a thermal detector,” Infrared Phys. Technol. 40, 109–116 (1999). [CrossRef]
  2. G. Paez, M. Strojnik Scholl, “Thermal contrast detected with a quantum detector,” Infrared Phys. Technol. 40, 261–265 (1999). [CrossRef]
  3. G. Paez, M. Strojnik, “Fringe analysis and phase reconstruction from modulated intensity patterns,” Opt. Lett. 22, 1669–1971 (1997). [CrossRef]
  4. G. Paez, M. Strojnik, “Convergent, recursive phase reconstruction from noisy, modulated intensity patterns using synthetic interferograms,” Opt. Lett. 23, 406–408 (1998). [CrossRef]
  5. D. W. Robinson, “Phase unwrapping methods,” in Interferogram Analysis, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, 1993), pp. 195–229.
  6. M. Kujawinska, “Fresnel-field analysis of double-grating systems and their application in phase-stepping grating interferometers,” J. Opt. Soc. Am. A 5, 849–857 (1988). [CrossRef]
  7. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based tomography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  8. T. Kreis, “Digital holographic interference-phase measurement using Fourier transform method,” J. Opt. Soc. Am. A 3, 847–855 (1986). [CrossRef]
  9. J. H. Bruning, D. R. Herriott, J. D. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974). [CrossRef] [PubMed]
  10. G. Paez, M. Strojnik, “Phase-shifted interferometry without phase unwrapping: reconstruction of a decentered wave front,” J. Opt. Soc. Am. A 16, 475–480 (1999). [CrossRef]
  11. M. Strojnik, G. Paez, “Testing the aspherical surfaces with the differential rotational-shearing interferometer,” in Fabrication and Testing of Aspherics, Vol. 24 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1999), pp. 119–123.
  12. M. S. Scholl, “Recursive exact ray trace equations through the foci of the tilted off-axis confocal prolate spheroids,” J. Mod. Opt. 43, 1583–1588 (1996). [CrossRef]
  13. G. Páez Padilla, M. Strojnik School, “Recursive relations for ray-tracing through three-dimensional reflective confocal prolate spheroids,” Rev. Mex. Fis. 43, 875–886 (1997).
  14. J. L. Flores, G. Paez, M. Strojnik, “Design of a diluted aperture by use of the practical cutoff frequency,” Appl. Opt. 38, 6010–6018 (1999). [CrossRef]

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