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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 1 — Jan. 1, 2009
  • pp: 99–107

Phase front retrieval by means of an iterative shadowgraphic method

Dimitris Pliakis and Stefano Minardi  »View Author Affiliations


JOSA A, Vol. 26, Issue 1, pp. 99-107 (2009)
http://dx.doi.org/10.1364/JOSAA.26.000099


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Abstract

In this paper, we propose an iterative shadowgraphic method (ISM) as an interesting alternative to existing methods for self-referencing optical phase retrieval. Two defocused images of the intensity distribution of the light scattered by a weakly absorbing phase object were sufficient to retrieve the transverse phase distribution of the distorted illuminating beam. An algorithm was developed to correct for diffraction effects in phase maps retrieved with a simple shadowgraphic method. We provide a mathematical proof of the convergence of the algorithm to the true profile of the sought phase object. Several numerical tests were performed of the algorithm showing its capability of recovering the full details of the original phase distribution with increased resolution as compared with the simple shadowgraphic method. The convergence of the ISM was also compared numerically with that of a nonoptimized Gerchberg–Saxton-type algorithm and found to be faster and not affected by stagnation problems.

© 2008 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(100.2000) Image processing : Digital image processing
(100.5070) Image processing : Phase retrieval
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Image Processing

History
Original Manuscript: August 4, 2008
Manuscript Accepted: October 23, 2008
Published: December 16, 2008

Citation
Dimitris Pliakis and Stefano Minardi, "Phase front retrieval by means of an iterative shadowgraphic method," J. Opt. Soc. Am. A 26, 99-107 (2009)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-1-99


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References

  1. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).
  2. C. Roddier and F. Roddier, “Combined approach to the Hubble Space Telescope wave-front distortion analysis,” Appl. Opt. 32, 2992-3008 (1993). [CrossRef] [PubMed]
  3. J. Högbom, “Aperture synthesis with a non-regular distribution of interferometer baselines,” Astrophys. J., Suppl. 15, 417-426 (1974).
  4. U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179-181 (1994). [CrossRef] [PubMed]
  5. C. J. Schwarz, Y. Kuznestova, and S. R. J. Brueck, “Imaging interferometric microscopy,” Opt. Lett. 28, 1424-1426 (2003). [CrossRef] [PubMed]
  6. A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336-350 (1982). [CrossRef] [PubMed]
  7. For a historical introduction of Shack-Hartman sensors see http://www.wavefrontsciences.com/Historical%20Development.pdf.
  8. A. V. Larichev, P. V. Ivanov, I. G. Iroshnikov, and V. I. Shmal'gauzen, “Measurement of eye aberrations in a speckle field,” Quantum Electron. 31, 1108-1112 (2001). [CrossRef]
  9. J. Leach, S. Keen, M. J. Padgett, C. Saunter, and G. D. Love, “Direct measurement of the skew angle of the Poynting vector in a helically phased beam,” Opt. Express 14, 11919-11924 (2006). [CrossRef] [PubMed]
  10. D. Marcuse, “Refractive index determination by the focusing method,” Appl. Opt. 18, 9-13 (1979). [CrossRef] [PubMed]
  11. C. Roddier and F. Roddier, “Wave-front reconstruction from defocused images and the testing of ground-based optical telescopes,” J. Opt. Soc. Am. A 10, 2277-2287 (1993). [CrossRef]
  12. S. P. Trainoff and D. S. Cannell, “Physical optics treatment of shadowgraphy,” Phys. Fluids 14, 1340-1363 (2002). [CrossRef]
  13. A. Gopal, S. Minardi, and M. Tatarakis, “Quantitative two-dimensional shadowgraphic method for high-sensitivity density measurement of under-critical laser plasmas,” Opt. Lett. 32, 1238-1240 (2007). [CrossRef] [PubMed]
  14. M. R. Teague, “Irradiance moments: their propagation and use for unique retrieval of phase,” J. Opt. Soc. Am. 72, 1199-1209 (1982). [CrossRef]
  15. A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23, 817-819 (1998). [CrossRef]
  16. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237-246 (1972).
  17. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758-2769 (1982). [CrossRef] [PubMed]
  18. L. J. Allen and M. P. Oxley, “Phase retrieval for series of images obtained by defocus variation,” Opt. Commun. 199, 65-75 (2001). [CrossRef]
  19. S. Borgsmüller, S. Noethe, C. Dietrich, T. Kresse, and R. Männer, “Computer-generated stratified diffractive optical elements,” Appl. Opt. 42, 5274-5283 (2003). [CrossRef] [PubMed]
  20. S. Marchesini, “A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78, 011301 (2007). [CrossRef] [PubMed]
  21. T. E. Gureyev, A. Roberts, and K. A. Nugent, “Partially coherent fields, the transport-of-intensity equation, and phase uniqueness,” J. Opt. Soc. Am. A 12, 1942-1946 (1995). [CrossRef]
  22. J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O'Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89, 155502 (2002). [CrossRef] [PubMed]
  23. T. Kämpfe, E.-B. Kley, A. Tünnermann, and P. Dannberg, “Design and fabrication of stacked, computer-generated holograms for multicolor image generation,” Appl. Opt. 46, 5482-5488 (2003). [CrossRef]
  24. S. Minardi, A. Gopal, M. Tatarakis, A. Couairon, G. Tamosauskas, R. Piskarskas, A. Dubietis, and P. Di Trapani, “Time-resolved refractive index and absorption mapping of light plasma filaments in water,” Opt. Lett. 33, 86-88 (2008). [CrossRef]
  25. B. E. Allman, P. J. McMahon, J. B. Tiller, K. A. Nugent, D. Paganin, and A. Barty, “Noninterferometric quantitative phase-imaging with soft x rays,” J. Opt. Soc. Am. A 17, 1732-1743 (2000). [CrossRef]
  26. G. Genoud, O. Guilbaud, E. Mengotti, S.-G. Pettersson, E. Georgiadou, E. Pourtal, G.-C. Wahlström, and A. L'Hullier, “XUV digital in-line holography using higher order harmonics,” Appl. Phys. B 90, 533-538 (2008). [CrossRef]
  27. W. Merzkirch, Flow Visualization (Academic, 1987), pp. 123-124.
  28. D. Pliakis, “On the volume of nodal sets of eigenfunctions,” and “Local estimates for the amplitude growth of waves in inhomogeneous media,” in preparation ; available from the authors: stefano.minardi@uni-jena.de.
  29. A cutoff function is a smooth function that equals one in a closed ball, vanishes outside a larger closed ball, and decays smoothly in the ring.
  30. R. Courant and D. Hilbert, Methods for Mathematical Physics, Vol. I, II (Wiley Interscience, 1989).
  31. We define as approximate an equation F with respect to another equation H if we can find two constants c1 and c2 such that c1H<F<c2H.
  32. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++. The Art of Scientific Computing (Cambridge U. Press, 2002).
  33. M. Giglio, D. Borgiol, M. A. C. Potenza, and A. Valiati, “Near field scattering,” Phys. Chem. Chem. Phys. 6, 1547-1550 (2004). [CrossRef]
  34. C. Cohen-Tannoudji, B. Diu, and F. Laoe, Quantum Mechanics (Wiley-Interscience, 2006).
  35. P. H. Van Cittert, “Zum Einfluss der Spaltbreite auf die Intanstätverteilung in Spectrallinien II,” Z. Phys. 69, 298-308 (1931). [CrossRef]
  36. J. L. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach (Cambridge U. Press, 1998). [CrossRef]
  37. D. Pliakis, “On a generalized Hardy's inequality and its applications in spectral geometry,” arXiv-math.AP:0203092.

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