Publication: Multi-stage phase retrieval algorithm based upon the gyrator transform
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The Optical Society Of America
The gyrator transform is a useful tool for optical information processing applications. In this work we propose a multi-stage phase retrieval approach based on this operation as well as on the well-known Gerchberg-Saxton algorithm. It results in an iterative algorithm able to retrieve the phase information using several measurements of the gyrator transform power spectrum. The viability and performance of the proposed algorithm is demonstrated by means of several numerical simulations and experimental results.
© 2010 Optical Society of America. The financial support of the Spanish Ministry of Science and Innovation under project TEC2008-04105 and the Santander-Complutense project PR-34/07-15914 are acknowledged. José A. Rodrigo gratefully thanks a “Juan de la Cierva” grant.
1. D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948). 2. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123– 1128 (1962). 3. E. N. Leith and J. Upatnieks, “Wavefront reconstruction with continuous-tone objects,” J. Opt. Soc. Am. 53, 1377–1381 (1963). 4. E. N. Leith and J. Upatnieks, “Wavefront reconstruction with diffused illumination and three-dimensional objects,” J. Opt. Soc. Am. 54, 1295–1301 (1964). 5. J. P. Guigay, “Fourier-transrorm analysis of Fresnel diffraction patterns and in-line holograms,” Optik 49, 121– 125 (1977). 6. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). 7. T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133, 339 – 346 (1997). 8. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972). 9. M. Nieto-Vesperinas, R. Navarro, and F. J. Fuentes, “Performance of a simulated-annealing algorithm for phase retrieval,” J. Opt. Soc. Am. A 5, 30–38 (1988). 10. J. H. Seldin and J. R. Fienup, “Iterative blind deconvolution algorithm applied to phase retrieval,” J. Opt. Soc. Am. A 7, 428–433 (1990). 11. J. R. Fienup, “Phase-retrieval algorithms for a complicated optical system,” Appl. Opt. 32, 1737–1746 (1993). 12. D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D: Applied Physics 6, L6–L9 (1973). 13. D. C. Redding, S. Basinger, A. Lowman, A. Kissil, P. Bely, R. Burg, R. Lyon, G. Mosier,M. Femiano, M.Wilson, R. G. Schunk, L. Craig, D. Jacobson, J. Rakoczy, and J. Hadaway, “Wavefront Sensing and Control for a Next- Generation Space Telescope,” Proc. SPIE 3356, 758 (1998). 14. D. S. Acton, P. D. Atcheson, M. Cermak, L. K. Kingsbury, F. Shi, and D. C. Redding, “James Webb Space Telescope wavefront sensing and control algorithms,” Proc. SPIE 5487, 887 (2004). 15. G. R. Brady and J. R. Fienup, “Nonlinear optimization algorithm for retrieving the full complex pupil function,” Opt. Express 14, 474–486 (2006). 16. B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, “Phase retrieval algorithm for JWST Flight and Testbed Telescope,” Proc. SPIE 6265, 626511 (2006). 17. Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, “Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21, 842 (1996). 18. J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Experimental implementation of the gyrator transform,” J. Opt. Soc. Am. A 24, 3135–3139 (2007). 19. J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Optical system design for orthosymplectic transformations in phase space,” J. Opt. Soc. Am. A 23, 2494–2500 (2006).