Publication:
Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections

Loading...
Thumbnail Image
Full text at PDC
Publication Date
2011-03-28
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
The Optical Society Of America
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
In this work, we propose a robust and versatile approach for the characterization of the complex field amplitude of holographically generated coherent-scalar paraxial beams. For this purpose we apply an iterative algorithm that allows recovering the phase of the generated beam from the measurement of its Wigner distribution projections. Its performance is analyzed for beams of different symmetry: Laguerre-Gaussian, Hermite-Gaussian and spiral ones, which are obtained experimentally by a computer generated hologram (CGH) implemented on a programmable spatial light modulator (SLM). Using the same method we also study the quality of their holographic recording on a highly efficient photopolymerizable glass. The proposed approach is useful for the creation of adaptive CGH that takes into account the peculiarities of the SLM, as well as for the quality control of the holographic data storage.
Description
© 2011 Optical Society of America. The financial support of the Spanish Ministry of Science and Innovation under project TEC2008-04105 is acknowledged. José A. Rodrigo gratefully thanks a “Juan de la Cierva” grant and A. Cámara acknowledges the financial support of the “Comunidad de Madrid” and the European Social Fund.
Keywords
Citation
1. A. E. Siegman, Lasers (University Science Books, 1986). 2. F. M. Dickey, S. C. Holswade, and D. L. Shealy, eds., Laser Beam Shaping Applications (CRC Press, 2005). 3. A. Ashkin, Optical Trapping and Manipulation of Neutral Particles Using Lasers: A Reprint Volume With Commentaries (World Scientific Publishing Company, 2006). 4. J. P. Kirk and A. L. Jones, “Phase-only complex-valued spatial filter”, J. Opt. Soc. Am. 61, 1023–1028 (1971). 5. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters”, Appl. Opt. 38, 5004–5013 (1999). 6. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields”, J. Opt. Soc. Am. A 24, 3500–3507 (2007). 7. B. Hennelly, J. Ojeda-Castañeda, and M. Testorf, eds., Phase Space Optics: Fundamentals and Applications (McGraw-Hill, 2009). 8. T. Alieva and J. A. Rodrigo, “Iterative phase retrieval from Wigner Distribution Projections”, in “Signal Recovery and Synthesis”, (Optical Society of America, 2009), p. STuD2. 9. A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase space tomography reconstruction of the Wigner distribution for optical beams separable in Cartesian coordinates”, J. Opt. Soc. Am. A 26, 1301–1306 (2009). 10. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999). 11. J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays”, Appl. Opt. 46, 5667–5679 (2007). 12. J. D. Schmidt, M. E. Goda, and B. D. Duncan, “Aberration production using a high-resolution liquid-crystal spatial light modulator”, Appl. Opt. 46, 2423–2433 (2007). 13. A. Jesacher, A. Schwaighofer, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image”, Opt. Express 15, 5801–5808 (2007). 14. C. López-Quesada, J. Andilla, and E. Martín-Badosa, “Correction of aberration in holographic optical tweezers using a Shack-Hartmann sensor”, Appl. Opt. 48, 1084–1090 (2009). 15. L. Paterson, M. P. MacDonald, J. Arlt,W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles”, Science 292, 912–914 (2001). 16. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons”, Nature 412, 313–316 (2001). 17. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons”, Nat. Phys. 3, 305–310 (2007). 18. Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions”, Phys. Rev. E 54, R50–R53 (1996). 19. E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams”, Sov. Phys. Usp. 47, 1177 (2004). 20. T. Alieva, E. Abramochkin, A. Asenjo-Garcia, and E. Razueva, “Rotating beams in isotropic optical system”, Opt. Express 18, 3568–3573 (2010). 21. J. P. Guigay, “Fourier-transform analysis of Fresnel diffraction patterns and in-line holograms”, Optik 49, 121–125 (1977). 22. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution”, J. Opt. Soc. Am. 73, 1434–1441 (1983). 23. T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation”, Opt. Commun. 133, 339–346 (1997). 24. U. Gopinathan, G. Situ, T. J. Naughton, and J. T. Sheridan, “Noninterferometric phase retrieval using a fractional Fourier system”, J. Opt. Soc. Am. A 25, 108–115 (2008). 25. 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). 26. Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, “Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain”, Opt. Lett. 21, 842–844 (1996). 27. 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). 28. J. A. Rodrigo, H. Duadi, T. Alieva, and Z. Zalevsky, “Multi-stage phase retrieval algorithm based upon the gyrator transform”, Opt. Express 18, 1510–1520 (2010). 29. D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral”, J. Mod. Opt. 44, 407 (1997). 30. J. B. Bentley, J. A. Davis, M. A. Bandres, and J. C. Gutiérrez-Vega, “Generation of helical Ince-Gaussian beams with a liquid-crystal display”, Opt. Lett. 31, 649–651 (2006). 31. N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators”, J. Opt. Soc. Am. A 25, 1642–1651 (2008). 32. T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators”, Opt. Lett. 34, 34–36 (2009). 33. A. Lizana, A. Márquez, L. Lobato, Y. Rodange, I. Moreno, C. Iemmi, and J. Campos, “The minimum euclidean distance principle applied to improve the modulation diffraction efficiency in digitally controlled spatial light modulators”, Opt. Express 18, 10581–10593 (2010). 34. I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics”, Opt. Express 16, 16711–16722 (2008). 35. R. J. Noll, “Zernike polynomials and atmospheric turbulence”, J. Opt. Soc. Am. 66, 207–211 (1976). 36. V. Arrizón, G. Méndez, and D. S. de La-Llave, “Accurate encoding of arbitrary complex fields with amplitude only liquid crystal spatial light modulators”, Opt. Express 13, 7913–7927 (2005). 37. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms”, J. Mod. Opt. 45, 231–1237 (1998). 38. F. del Monte, O. Martínez, J. Rodrigo, M. Calvo, and P. Cheben, “A volume holographic sol-gel material with large enhancement of dynamic range by incorporation of high refractive index species”, Adv. Mater. 18, 2014–2017 (2006). 39. O. Martínez-Matos, J. A. Rodrigo, M. P. Hernández-Garay, J. G. Izquierdo, R.Weigand, M. L. Calvo, P. Cheben, P. Vaveliuk, and L. Bañares, “Generation of femtosecond paraxial beams with arbitrary spatial distribution”, Opt. Lett. 35, 652–654 (2010).
Collections