Abstract

This paper gives the reader a personal tour through the field of phase retrieval and related works that lead up to or cited the paper “Phase Retrieval Algorithms: a Comparison,” [Appl. Opt. 21, 2758 (1982)].

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef]
  2. J. R. Fienup, “Improved synthesis and computational methods for computer-generated holograms,” Ph.D. Thesis (Stanford University, 1975) (ProQuest, UMI No. 7525523, or at http://www.optics.rochester.edu/workgroups/fienup/Professor.htm ).
  3. R. J. Collier, C. B. Burkhardt, and L. H. Lin, Optical Holography (Academic, 1971).
  4. A. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
  5. L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Devel. 13, 150–155 (1969).
    [CrossRef]
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  7. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).
  8. Paul Simon, “Kodachrome”.
  9. D. Kermisch, “Image reconstruction from phase information only,” J. Opt. Soc. Am. 60, 15–16 (1970).
    [CrossRef]
  10. N. C. Gallagher and B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. l2, 2328–2335 (1973).
  11. B. Liu and N. C. Gallagher, “Convergence of a spectrum shaping algorithm,” Appl. Opt. l3, 2470–2471 (1974).
  12. P. M. Hirsch, J. A. Jordan, and L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. patent 3,619,022(9Nov.1971).
  13. 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).
  14. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. l9, 297–305 (1980).
  15. R. Hanbury Brown, and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048(1956).
    [CrossRef]
  16. A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).
  17. E. Wolf, “Is a complete determination of the energy spectrum of light possible from measurements of the degree of coherence,” Proc. Phys. Soc. London 80, 1269–1272 (1962).
    [CrossRef]
  18. A. Walther, “The question of phase retrieval in optics,” Opt. Acta l0, 41–49 (1963).
  19. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978).
    [CrossRef]
  20. D. C. Chu, J. R. Fienup, and J. W. Goodman, “Multiemulsion on-axis computer generated hologram,” Appl. Opt. 12, 1386–1388 (1973).
    [CrossRef]
  21. B. R. Frieden and D. G. Currie, “On unfolding the autocorrelation function,” J. Opt. Soc. Am. 66, 1111 (1976) (Abstract).
  22. R. H. T. Bates, “Contributions to the theory of intensity interferometry,” Mon. Not. R. Astron. Soc. 142, 413–428 (1969).
  23. P. J. Napier and R. H. T. Bates, “Inferring phase information from modulus information in two-dimensional aperture synthesis,” Astron. Astrophys. Suppl. l5, 427–430 (1974).
  24. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” presented at the Annual Meeting of the OSA, Toronto, Ontario, October 1977, Abstract: J. Opt. Soc. Am. 67, 1389 (1977).
  25. J. R. Fienup, “Space object imaging through the turbulent atmosphere,” Proc. SPIE 149, 71–81 (1978).
  26. J. R. Fienup, “Space object imaging through the turbulent atmosphere,” Opt. Eng. 18, 529–534 (1979).
    [CrossRef]
  27. G. B. Feldkamp and J. R. Fienup, “Noise properties of images reconstructed from Fourier modulus,” Proc. SPIE 231, 84–93 (1980).
    [CrossRef]
  28. J. R. Fienup and G. B. Feldkamp, “Astronomical imaging by processing stellar speckle interferometry data,” Proc. SPIE 243, 95–102 (1980).
  29. T. R. Crimmins and J. R. Fienup, “Ambiguity of phase retrieval for functions with disconnected support,” J. Opt. Soc. Am. 71, 1026–1028 (1981).
    [CrossRef]
  30. J. R. Fienup, T. R. Crimmins, and W. Holsztynski, “Reconstruction of the support of an object from the support of its autocorrelation,” J. Opt. Soc. Am. 72, 610–624 (1982).
    [CrossRef]
  31. J. R. Fienup, “Phase retrieval in astronomy,” in Signal Recovery and Synthesis with Incomplete Information and Partial Constraints, digest of papers (Optical Society of America, 1983), paper ThA8-1-5.
  32. J. R. Fienup, “Image reconstruction for stellar interferometry,” in Current Trends in Optics, F. T. Arecchi and F. R. Aussenegg, eds. (Taylor and Francis and Halsted, 1981), Invited Papers from ICO-12 Meeting, Graz, Austria, September 1981, pp. 95–102.
  33. J. R. Fienup, “Comparison of phase retrieval algorithms,” presented at the Annual Meeting of the O.S.A., Kissimmee, Florida, October 1981, Abstract: J. Opt. Soc. Am. 71, 1641 (1981).
  34. M. T. Manry and J. K. Aggarwal, “The design of multidimensional FIR digital filters by phase correction,” IEEE Trans. Circuits Syst. 23, 185–199 (1976).
    [CrossRef]
  35. J. A. Marozas, “Fourier transform-based continuous phase-plate design technique: a high-pass phase-plate design as an application for OMEGA and the National Ignition Facility,” J. Opt. Soc. Am. A 24, 74–83 (2007).
    [CrossRef]
  36. S. Buhling and F. Wyrowski, “Solving tolerancing and three-dimensional beam shaping problems by multifunctional wave optical design,” Opt. Eng. 40, 1590–1597 (2001).
    [CrossRef]
  37. E. G. Johnson and J. D. Brasher, “Phase encryption of biometrics in diffractive optical elements,” Opt. Lett. 21, 1271–1273 (1996).
    [CrossRef]
  38. Y. Ivankovski and D. Mendlovic, “High-rate-long-distance fiber-optic communication based on advanced modulation techniques,” Appl. Opt. 38, 5533–5540 (1999).
    [CrossRef]
  39. J. Skaar, “Iterative design of antireflection coatings based on the direct and inverse scattering transform,” Opt. Commun. 232, 45–48 (2004).
    [CrossRef]
  40. D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. 33, 749–755 (1985).
    [CrossRef]
  41. J. N. Cederquist, J. R. Fienup, C. C. Wackerman, S. R. Robinson, and D. Kryskowski, “Wave-front phase estimation from Fourier intensity measurements,” J. Opt. Soc. Am. A 6, 1020–1026 (1989).
    [CrossRef]
  42. J. R. Fienup, J. C. Marron, T. J. Schulz, and J. H. Seldin, “Hubble Space Telescope characterized by using phase retrieval algorithms,” Appl. Opt. 32, 1747–1767 (1993).
    [CrossRef]
  43. 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).
    [CrossRef]
  44. G. R. Brady and J. R. Fienup, “Nonlinear optimization algorithm for retrieving the full complex pupil function,” Opt. Express 14, 474–486 (2006).
    [CrossRef]
  45. M. Guizar-Sicairos and J. R. Fienup, “Measurement of coherent x-ray focused beams by phase retrieval with transverse translation diversity,” Opt. Express 17, 2670–2685 (2009).
    [CrossRef]
  46. S. T. Thurman, R. T. DeRosa, and J. R. Fienup, “Amplitude metrics for field retrieval with hard-edge and uniformly illuminated apertures,” J. Opt. Soc. Am. A 26, 700–709(2009).
    [CrossRef]
  47. B. H. Dean and C. W. Bowers, “Diversity selection for phase-diverse phase retrieval,” J. Opt. Soc. Am. A 20, 1490–1504 (2003).
    [CrossRef]
  48. H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
    [CrossRef]
  49. M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16, 7264–7278 (2008).
    [CrossRef]
  50. J. S. Smith, D. L. Aronstein, B. H. Dean, and D. S. Acton, “Phase retrieval on broadband and under-sampled images for the JWST testbed telescope,” Proc. SPIE 7436, 7436D (2009).
    [CrossRef]
  51. G. R. Brady and J. R. Fienup, “Effect of broadband illumination on reconstruction error of phase retrieval in optical metrology,” Proc. SPIE 6617, 66170I (2007).
    [CrossRef]
  52. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983).
    [CrossRef]
  53. D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
    [CrossRef]
  54. R. Trebino and D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. A 10, 1101–1111 (1993).
    [CrossRef]
  55. R. G. Lane, “Blind deconvolution of speckle images,” J. Opt. Soc. Am. A 9, 1508–1514 (1992).
    [CrossRef]
  56. C. M. Vest and I. Prikryl, “Tomography by iterative convolution: empirical study and application to interferometry,” Appl. Opt. 23, 2433–2440 (1984).
    [CrossRef]
  57. G. K. Datta and R. M. Vasu, “Non-interferometric methods of phase estimation for application in optical tomography,” J. Mod. Opt. 46, 1377–1388 (1999).
    [CrossRef]
  58. M. H. Maleki and A. J. Devaney, “Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086–1092 (1993).
    [CrossRef]
  59. R. P. Yu, D. M. Paganin, and M. J. Morgan, “Inferring generalized time-dependent complex Ginzburg-Landau equations from modulus and gauge-field information,” Phys. Rev. B. 77, 134512 (2008).
    [CrossRef]
  60. M. Carmody, E. Landree, L. D. Marks, and K. L. Merkle, “Determination of the current density distribution in Josephson junctions,” Phys. C 315, 145–153 (1999).
    [CrossRef]
  61. V. Elser, I. Rankenburg, and P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. 104, 418–423 (2007).
    [CrossRef]
  62. J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987).
    [CrossRef]
  63. J. R. Fienup, “Lensless coherent imaging by phase retrieval with an illumination pattern constraint,” Opt. Express 14, 498–508 (2006).
    [CrossRef]
  64. J. R. Fienup and A. M. Kowalczyk, “Phase retrieval for a complex-valued object by using a low-resolution image,” J. Opt. Soc. Am. A 7, 450–458 (1990).
    [CrossRef]
  65. P. S. Idell, J. R. Fienup, and R. S. Goodman, “Image synthesis from nonimaged laser speckle patterns,” Opt. Lett. 12, 858–860 (1987).
    [CrossRef]
  66. D. Sayre, “Some implications of a theorem due to Shannon,” Acta Cryst. 5, 843 (1952).
    [CrossRef]
  67. K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54, 27–32 (2001).
    [CrossRef]
  68. J. N. Cederquist, J. R. Fienup, J. C. Marron, and R. G. Paxman, “Phase retrieval from experimental far-field data,” Opt. Lett. 13, 619–621 (1988).
    [CrossRef]
  69. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
    [CrossRef]
  70. H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–2000 (2006).
    [CrossRef]
  71. J. H. Seldin and J. R. Fienup, “Numerical investigation of the uniqueness of phase retrieval,” J. Opt. Soc. Am. A 7, 412–427 (1990).
    [CrossRef]
  72. J. R. Fienup and C. C. Wackerman, “Phase retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986).
    [CrossRef]
  73. H. Takajo, T. Takahashi, H. Kawanami, and R. Ueda, “Numerical investigation of the iterative phase-retrieval stagnation problem: territories of convergence objects and holes in their boundaries,” J. Opt. Soc. Am. A 14, 3175–3187 (1997).
    [CrossRef]
  74. H. Takajo, T. Takahashi, R. Ueda, and M. Taninaka, “Study on the convergence property of the hybrid input output algorithm used for phase retrieval,” J. Opt. Soc. Am. A 15, 2849–2861 (1998).
    [CrossRef]
  75. H. Takajo, T. Takahashi, and T. Shizuma, “Further study on the convergence property of the hybrid input–output algorithm used for phase retrieval,” J. Opt. Soc. Am. A 16, 2163–2168 (1999).
    [CrossRef]
  76. R. G. Lane, “Phase retrieval using conjugate gradient minimization,” J. Mod. Opt. 38, 1797–1813 (1991).
    [CrossRef]
  77. J. R. Fienup, “Phase-retrieval algorithms for a complicated optical system,” Appl. Opt. 32, 1737–1746 (1993).
    [CrossRef]
  78. J. R. Fienup, “Wave front sensing by nonlinear optimization,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper FML2.
  79. T. R. Crimmins, J. R. Fienup, and B. J. Thelen, “Improved bounds on object support from autocorrelation support and application to phase retrieval,” J. Opt. Soc. Am. A 7, 3–13 (1990).
    [CrossRef]
  80. D. C. Youla, “Generalized image restoration by method of alternating orthogonal projections,” IEEE Trans. Circuits Syst. 25, 694–702 (1978).
    [CrossRef]
  81. D. C. Youla and H. Webb, “Image restoration by the method of convex projections: Part 1—theory,” IEEE Trans. Med. Imag. 1, 81–94 (1982).
    [CrossRef]
  82. H. H. Bauschke, P. L. Combettes, and D. R. Luke, “Phase retrieval, error reduction algorithms, and Fienup variants: a view from convex optimization,” J. Opt. Soc. Am. A 19, 1334–1345 (2002).
    [CrossRef]
  83. H. H. Bauschke, P. L. Combettes, and D. R. Luke, “A hybrid projection reflection method for phase retrieval,” J. Opt. Soc. Am. A 20, 1025–1034 (2003).
    [CrossRef]
  84. V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am A 20, 40–55 (2003).
    [CrossRef]
  85. J. R. Fienup, “Phase retrieval with continuous version of hybrid input–output,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2003), paper ThI3.
  86. J. R. Fienup, “Invariant error metrics for image reconstruction,” Appl. Opt. 36, 8352–8357 (1997).
    [CrossRef]
  87. M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156–158 (2008).
    [CrossRef]
  88. R. H. T. Bates, “Astronomical speckle imaging,” Phys. Rep. 90, 203–297 (1982).
    [CrossRef]
  89. J. C. Dainty and J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” Image Recovery: Theory and Application, H. Stark, ed. (Academic, 1987), pp. 231–275.
  90. W. O. Saxton, Computer Techniques for Image Processing in Electron Microscopy (Academic, 1978).
  91. R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A 7, 394–411 (1990).
    [CrossRef]
  92. K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99 (2010).
    [CrossRef]

2010 (1)

K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99 (2010).
[CrossRef]

2009 (3)

2008 (3)

2007 (3)

V. Elser, I. Rankenburg, and P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. 104, 418–423 (2007).
[CrossRef]

G. R. Brady and J. R. Fienup, “Effect of broadband illumination on reconstruction error of phase retrieval in optical metrology,” Proc. SPIE 6617, 66170I (2007).
[CrossRef]

J. A. Marozas, “Fourier transform-based continuous phase-plate design technique: a high-pass phase-plate design as an application for OMEGA and the National Ignition Facility,” J. Opt. Soc. Am. A 24, 74–83 (2007).
[CrossRef]

2006 (4)

2004 (2)

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef]

J. Skaar, “Iterative design of antireflection coatings based on the direct and inverse scattering transform,” Opt. Commun. 232, 45–48 (2004).
[CrossRef]

2003 (3)

2002 (1)

2001 (2)

S. Buhling and F. Wyrowski, “Solving tolerancing and three-dimensional beam shaping problems by multifunctional wave optical design,” Opt. Eng. 40, 1590–1597 (2001).
[CrossRef]

K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54, 27–32 (2001).
[CrossRef]

1999 (5)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

M. Carmody, E. Landree, L. D. Marks, and K. L. Merkle, “Determination of the current density distribution in Josephson junctions,” Phys. C 315, 145–153 (1999).
[CrossRef]

G. K. Datta and R. M. Vasu, “Non-interferometric methods of phase estimation for application in optical tomography,” J. Mod. Opt. 46, 1377–1388 (1999).
[CrossRef]

Y. Ivankovski and D. Mendlovic, “High-rate-long-distance fiber-optic communication based on advanced modulation techniques,” Appl. Opt. 38, 5533–5540 (1999).
[CrossRef]

H. Takajo, T. Takahashi, and T. Shizuma, “Further study on the convergence property of the hybrid input–output algorithm used for phase retrieval,” J. Opt. Soc. Am. A 16, 2163–2168 (1999).
[CrossRef]

1998 (1)

1997 (2)

1996 (1)

1993 (5)

1992 (1)

1991 (1)

R. G. Lane, “Phase retrieval using conjugate gradient minimization,” J. Mod. Opt. 38, 1797–1813 (1991).
[CrossRef]

1990 (4)

1989 (1)

1988 (1)

1987 (2)

1986 (1)

1985 (1)

D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. 33, 749–755 (1985).
[CrossRef]

1984 (1)

1983 (1)

1982 (4)

J. R. Fienup, T. R. Crimmins, and W. Holsztynski, “Reconstruction of the support of an object from the support of its autocorrelation,” J. Opt. Soc. Am. 72, 610–624 (1982).
[CrossRef]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef]

D. C. Youla and H. Webb, “Image restoration by the method of convex projections: Part 1—theory,” IEEE Trans. Med. Imag. 1, 81–94 (1982).
[CrossRef]

R. H. T. Bates, “Astronomical speckle imaging,” Phys. Rep. 90, 203–297 (1982).
[CrossRef]

1981 (1)

1980 (3)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. l9, 297–305 (1980).

G. B. Feldkamp and J. R. Fienup, “Noise properties of images reconstructed from Fourier modulus,” Proc. SPIE 231, 84–93 (1980).
[CrossRef]

J. R. Fienup and G. B. Feldkamp, “Astronomical imaging by processing stellar speckle interferometry data,” Proc. SPIE 243, 95–102 (1980).

1979 (1)

J. R. Fienup, “Space object imaging through the turbulent atmosphere,” Opt. Eng. 18, 529–534 (1979).
[CrossRef]

1978 (3)

J. R. Fienup, “Space object imaging through the turbulent atmosphere,” Proc. SPIE 149, 71–81 (1978).

D. C. Youla, “Generalized image restoration by method of alternating orthogonal projections,” IEEE Trans. Circuits Syst. 25, 694–702 (1978).
[CrossRef]

J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978).
[CrossRef]

1976 (2)

B. R. Frieden and D. G. Currie, “On unfolding the autocorrelation function,” J. Opt. Soc. Am. 66, 1111 (1976) (Abstract).

M. T. Manry and J. K. Aggarwal, “The design of multidimensional FIR digital filters by phase correction,” IEEE Trans. Circuits Syst. 23, 185–199 (1976).
[CrossRef]

1974 (2)

P. J. Napier and R. H. T. Bates, “Inferring phase information from modulus information in two-dimensional aperture synthesis,” Astron. Astrophys. Suppl. l5, 427–430 (1974).

B. Liu and N. C. Gallagher, “Convergence of a spectrum shaping algorithm,” Appl. Opt. l3, 2470–2471 (1974).

1973 (2)

N. C. Gallagher and B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. l2, 2328–2335 (1973).

D. C. Chu, J. R. Fienup, and J. W. Goodman, “Multiemulsion on-axis computer generated hologram,” Appl. Opt. 12, 1386–1388 (1973).
[CrossRef]

1972 (1)

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).

1970 (2)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

D. Kermisch, “Image reconstruction from phase information only,” J. Opt. Soc. Am. 60, 15–16 (1970).
[CrossRef]

1969 (2)

R. H. T. Bates, “Contributions to the theory of intensity interferometry,” Mon. Not. R. Astron. Soc. 142, 413–428 (1969).

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Devel. 13, 150–155 (1969).
[CrossRef]

1967 (1)

1963 (1)

A. Walther, “The question of phase retrieval in optics,” Opt. Acta l0, 41–49 (1963).

1962 (1)

E. Wolf, “Is a complete determination of the energy spectrum of light possible from measurements of the degree of coherence,” Proc. Phys. Soc. London 80, 1269–1272 (1962).
[CrossRef]

1956 (1)

R. Hanbury Brown, and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048(1956).
[CrossRef]

1952 (1)

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Cryst. 5, 843 (1952).
[CrossRef]

Acton, D. S.

J. S. Smith, D. L. Aronstein, B. H. Dean, and D. S. Acton, “Phase retrieval on broadband and under-sampled images for the JWST testbed telescope,” Proc. SPIE 7436, 7436D (2009).
[CrossRef]

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).
[CrossRef]

Aggarwal, J. K.

M. T. Manry and J. K. Aggarwal, “The design of multidimensional FIR digital filters by phase correction,” IEEE Trans. Circuits Syst. 23, 185–199 (1976).
[CrossRef]

Aronstein, D. L.

J. S. Smith, D. L. Aronstein, B. H. Dean, and D. S. Acton, “Phase retrieval on broadband and under-sampled images for the JWST testbed telescope,” Proc. SPIE 7436, 7436D (2009).
[CrossRef]

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).
[CrossRef]

Barty, A.

Bates, R. H. T.

R. H. T. Bates, “Astronomical speckle imaging,” Phys. Rep. 90, 203–297 (1982).
[CrossRef]

P. J. Napier and R. H. T. Bates, “Inferring phase information from modulus information in two-dimensional aperture synthesis,” Astron. Astrophys. Suppl. l5, 427–430 (1974).

R. H. T. Bates, “Contributions to the theory of intensity interferometry,” Mon. Not. R. Astron. Soc. 142, 413–428 (1969).

Bauschke, H. H.

Beetz, T.

Bowers, C. W.

Brady, G. R.

G. R. Brady and J. R. Fienup, “Effect of broadband illumination on reconstruction error of phase retrieval in optical metrology,” Proc. SPIE 6617, 66170I (2007).
[CrossRef]

G. R. Brady and J. R. Fienup, “Nonlinear optimization algorithm for retrieving the full complex pupil function,” Opt. Express 14, 474–486 (2006).
[CrossRef]

Brasher, J. D.

Buhling, S.

S. Buhling and F. Wyrowski, “Solving tolerancing and three-dimensional beam shaping problems by multifunctional wave optical design,” Opt. Eng. 40, 1590–1597 (2001).
[CrossRef]

Burkhardt, C. B.

R. J. Collier, C. B. Burkhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Carmody, M.

M. Carmody, E. Landree, L. D. Marks, and K. L. Merkle, “Determination of the current density distribution in Josephson junctions,” Phys. C 315, 145–153 (1999).
[CrossRef]

Cederquist, J. N.

Chapman, H. N.

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Chu, D. C.

Collier, R. J.

R. J. Collier, C. B. Burkhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Combettes, P. L.

Crimmins, T. R.

Cui, C.

Currie, D. G.

B. R. Frieden and D. G. Currie, “On unfolding the autocorrelation function,” J. Opt. Soc. Am. 66, 1111 (1976) (Abstract).

Dainty, J. C.

J. C. Dainty and J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” Image Recovery: Theory and Application, H. Stark, ed. (Academic, 1987), pp. 231–275.

Datta, G. K.

G. K. Datta and R. M. Vasu, “Non-interferometric methods of phase estimation for application in optical tomography,” J. Mod. Opt. 46, 1377–1388 (1999).
[CrossRef]

Dean, B. H.

J. S. Smith, D. L. Aronstein, B. H. Dean, and D. S. Acton, “Phase retrieval on broadband and under-sampled images for the JWST testbed telescope,” Proc. SPIE 7436, 7436D (2009).
[CrossRef]

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).
[CrossRef]

B. H. Dean and C. W. Bowers, “Diversity selection for phase-diverse phase retrieval,” J. Opt. Soc. Am. A 20, 1490–1504 (2003).
[CrossRef]

DeRosa, R. T.

Devaney, A. J.

Elser, V.

V. Elser, I. Rankenburg, and P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. 104, 418–423 (2007).
[CrossRef]

V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am A 20, 40–55 (2003).
[CrossRef]

Faulkner, H. M. L.

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef]

Feldkamp, G. B.

G. B. Feldkamp and J. R. Fienup, “Noise properties of images reconstructed from Fourier modulus,” Proc. SPIE 231, 84–93 (1980).
[CrossRef]

J. R. Fienup and G. B. Feldkamp, “Astronomical imaging by processing stellar speckle interferometry data,” Proc. SPIE 243, 95–102 (1980).

Fienup, J. R.

M. Guizar-Sicairos and J. R. Fienup, “Measurement of coherent x-ray focused beams by phase retrieval with transverse translation diversity,” Opt. Express 17, 2670–2685 (2009).
[CrossRef]

S. T. Thurman, R. T. DeRosa, and J. R. Fienup, “Amplitude metrics for field retrieval with hard-edge and uniformly illuminated apertures,” J. Opt. Soc. Am. A 26, 700–709(2009).
[CrossRef]

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16, 7264–7278 (2008).
[CrossRef]

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156–158 (2008).
[CrossRef]

G. R. Brady and J. R. Fienup, “Effect of broadband illumination on reconstruction error of phase retrieval in optical metrology,” Proc. SPIE 6617, 66170I (2007).
[CrossRef]

J. R. Fienup, “Lensless coherent imaging by phase retrieval with an illumination pattern constraint,” Opt. Express 14, 498–508 (2006).
[CrossRef]

G. R. Brady and J. R. Fienup, “Nonlinear optimization algorithm for retrieving the full complex pupil function,” Opt. Express 14, 474–486 (2006).
[CrossRef]

J. R. Fienup, “Invariant error metrics for image reconstruction,” Appl. Opt. 36, 8352–8357 (1997).
[CrossRef]

J. R. Fienup, “Phase-retrieval algorithms for a complicated optical system,” Appl. Opt. 32, 1737–1746 (1993).
[CrossRef]

J. R. Fienup, J. C. Marron, T. J. Schulz, and J. H. Seldin, “Hubble Space Telescope characterized by using phase retrieval algorithms,” Appl. Opt. 32, 1747–1767 (1993).
[CrossRef]

J. R. Fienup and A. M. Kowalczyk, “Phase retrieval for a complex-valued object by using a low-resolution image,” J. Opt. Soc. Am. A 7, 450–458 (1990).
[CrossRef]

J. H. Seldin and J. R. Fienup, “Numerical investigation of the uniqueness of phase retrieval,” J. Opt. Soc. Am. A 7, 412–427 (1990).
[CrossRef]

T. R. Crimmins, J. R. Fienup, and B. J. Thelen, “Improved bounds on object support from autocorrelation support and application to phase retrieval,” J. Opt. Soc. Am. A 7, 3–13 (1990).
[CrossRef]

J. N. Cederquist, J. R. Fienup, C. C. Wackerman, S. R. Robinson, and D. Kryskowski, “Wave-front phase estimation from Fourier intensity measurements,” J. Opt. Soc. Am. A 6, 1020–1026 (1989).
[CrossRef]

J. N. Cederquist, J. R. Fienup, J. C. Marron, and R. G. Paxman, “Phase retrieval from experimental far-field data,” Opt. Lett. 13, 619–621 (1988).
[CrossRef]

J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987).
[CrossRef]

P. S. Idell, J. R. Fienup, and R. S. Goodman, “Image synthesis from nonimaged laser speckle patterns,” Opt. Lett. 12, 858–860 (1987).
[CrossRef]

J. R. Fienup and C. C. Wackerman, “Phase retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986).
[CrossRef]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef]

J. R. Fienup, T. R. Crimmins, and W. Holsztynski, “Reconstruction of the support of an object from the support of its autocorrelation,” J. Opt. Soc. Am. 72, 610–624 (1982).
[CrossRef]

T. R. Crimmins and J. R. Fienup, “Ambiguity of phase retrieval for functions with disconnected support,” J. Opt. Soc. Am. 71, 1026–1028 (1981).
[CrossRef]

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. l9, 297–305 (1980).

G. B. Feldkamp and J. R. Fienup, “Noise properties of images reconstructed from Fourier modulus,” Proc. SPIE 231, 84–93 (1980).
[CrossRef]

J. R. Fienup and G. B. Feldkamp, “Astronomical imaging by processing stellar speckle interferometry data,” Proc. SPIE 243, 95–102 (1980).

J. R. Fienup, “Space object imaging through the turbulent atmosphere,” Opt. Eng. 18, 529–534 (1979).
[CrossRef]

J. R. Fienup, “Space object imaging through the turbulent atmosphere,” Proc. SPIE 149, 71–81 (1978).

J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978).
[CrossRef]

D. C. Chu, J. R. Fienup, and J. W. Goodman, “Multiemulsion on-axis computer generated hologram,” Appl. Opt. 12, 1386–1388 (1973).
[CrossRef]

J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” presented at the Annual Meeting of the OSA, Toronto, Ontario, October 1977, Abstract: J. Opt. Soc. Am. 67, 1389 (1977).

J. R. Fienup, “Phase retrieval in astronomy,” in Signal Recovery and Synthesis with Incomplete Information and Partial Constraints, digest of papers (Optical Society of America, 1983), paper ThA8-1-5.

J. R. Fienup, “Wave front sensing by nonlinear optimization,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper FML2.

J. R. Fienup, “Improved synthesis and computational methods for computer-generated holograms,” Ph.D. Thesis (Stanford University, 1975) (ProQuest, UMI No. 7525523, or at http://www.optics.rochester.edu/workgroups/fienup/Professor.htm ).

J. R. Fienup, “Phase retrieval with continuous version of hybrid input–output,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2003), paper ThI3.

J. R. Fienup, “Image reconstruction for stellar interferometry,” in Current Trends in Optics, F. T. Arecchi and F. R. Aussenegg, eds. (Taylor and Francis and Halsted, 1981), Invited Papers from ICO-12 Meeting, Graz, Austria, September 1981, pp. 95–102.

J. C. Dainty and J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” Image Recovery: Theory and Application, H. Stark, ed. (Academic, 1987), pp. 231–275.

J. R. Fienup, “Comparison of phase retrieval algorithms,” presented at the Annual Meeting of the O.S.A., Kissimmee, Florida, October 1981, Abstract: J. Opt. Soc. Am. 71, 1641 (1981).

Frieden, B. R.

B. R. Frieden and D. G. Currie, “On unfolding the autocorrelation function,” J. Opt. Soc. Am. 66, 1111 (1976) (Abstract).

Gallagher, N. C.

B. Liu and N. C. Gallagher, “Convergence of a spectrum shaping algorithm,” Appl. Opt. l3, 2470–2471 (1974).

N. C. Gallagher and B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. l2, 2328–2335 (1973).

Gerchberg, R. W.

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).

Goodman, J. W.

D. C. Chu, J. R. Fienup, and J. W. Goodman, “Multiemulsion on-axis computer generated hologram,” Appl. Opt. 12, 1386–1388 (1973).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

Goodman, R. S.

Guizar-Sicairos, M.

Gureyev, T. E.

K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54, 27–32 (2001).
[CrossRef]

Hanbury Brown, R.

R. Hanbury Brown, and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048(1956).
[CrossRef]

Hau-Riege, S. P.

He, H.

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Devel. 13, 150–155 (1969).
[CrossRef]

P. M. Hirsch, J. A. Jordan, and L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. patent 3,619,022(9Nov.1971).

Holsztynski, W.

Howells, M. R.

Idell, P. S.

Ivankovski, Y.

Jacobsen, C.

Johnson, E. G.

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Devel. 13, 150–155 (1969).
[CrossRef]

P. M. Hirsch, J. A. Jordan, and L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. patent 3,619,022(9Nov.1971).

Kane, D. J.

R. Trebino and D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. A 10, 1101–1111 (1993).
[CrossRef]

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

Kawanami, H.

Kermisch, D.

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Kowalczyk, A. M.

Kryskowski, D.

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Landree, E.

M. Carmody, E. Landree, L. D. Marks, and K. L. Merkle, “Determination of the current density distribution in Josephson junctions,” Phys. C 315, 145–153 (1999).
[CrossRef]

Lane, R. G.

R. G. Lane, “Blind deconvolution of speckle images,” J. Opt. Soc. Am. A 9, 1508–1514 (1992).
[CrossRef]

R. G. Lane, “Phase retrieval using conjugate gradient minimization,” J. Mod. Opt. 38, 1797–1813 (1991).
[CrossRef]

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Devel. 13, 150–155 (1969).
[CrossRef]

P. M. Hirsch, J. A. Jordan, and L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. patent 3,619,022(9Nov.1971).

Lin, L. H.

R. J. Collier, C. B. Burkhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Liu, B.

B. Liu and N. C. Gallagher, “Convergence of a spectrum shaping algorithm,” Appl. Opt. l3, 2470–2471 (1974).

N. C. Gallagher and B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. l2, 2328–2335 (1973).

Lohmann, A. W.

Luke, D. R.

Maleki, M. H.

Manry, M. T.

M. T. Manry and J. K. Aggarwal, “The design of multidimensional FIR digital filters by phase correction,” IEEE Trans. Circuits Syst. 23, 185–199 (1976).
[CrossRef]

Marchesini, S.

Marks, L. D.

M. Carmody, E. Landree, L. D. Marks, and K. L. Merkle, “Determination of the current density distribution in Josephson junctions,” Phys. C 315, 145–153 (1999).
[CrossRef]

Marozas, J. A.

Marron, J. C.

Mendlovic, D.

Merkle, K. L.

M. Carmody, E. Landree, L. D. Marks, and K. L. Merkle, “Determination of the current density distribution in Josephson junctions,” Phys. C 315, 145–153 (1999).
[CrossRef]

Miao, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Millane, R. P.

Morgan, M. J.

R. P. Yu, D. M. Paganin, and M. J. Morgan, “Inferring generalized time-dependent complex Ginzburg-Landau equations from modulus and gauge-field information,” Phys. Rev. B. 77, 134512 (2008).
[CrossRef]

Morris, D.

D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. 33, 749–755 (1985).
[CrossRef]

Napier, P. J.

P. J. Napier and R. H. T. Bates, “Inferring phase information from modulus information in two-dimensional aperture synthesis,” Astron. Astrophys. Suppl. l5, 427–430 (1974).

Noy, A.

Nugent, K. A.

K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99 (2010).
[CrossRef]

K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54, 27–32 (2001).
[CrossRef]

Paganin, D.

K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54, 27–32 (2001).
[CrossRef]

Paganin, D. M.

R. P. Yu, D. M. Paganin, and M. J. Morgan, “Inferring generalized time-dependent complex Ginzburg-Landau equations from modulus and gauge-field information,” Phys. Rev. B. 77, 134512 (2008).
[CrossRef]

Paris, D. P.

Paxman, R. G.

Prikryl, I.

Rankenburg, I.

V. Elser, I. Rankenburg, and P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. 104, 418–423 (2007).
[CrossRef]

Robinson, S. R.

Rodenburg, J. M.

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef]

Rosen, R.

Saxton, W. O.

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).

W. O. Saxton, Computer Techniques for Image Processing in Electron Microscopy (Academic, 1978).

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Cryst. 5, 843 (1952).
[CrossRef]

Schulz, T. J.

Seldin, J. H.

Shapiro, D.

Shiri, R.

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).
[CrossRef]

Shizuma, T.

Simon, Paul

Paul Simon, “Kodachrome”.

Skaar, J.

J. Skaar, “Iterative design of antireflection coatings based on the direct and inverse scattering transform,” Opt. Commun. 232, 45–48 (2004).
[CrossRef]

Smith, J. S.

J. S. Smith, D. L. Aronstein, B. H. Dean, and D. S. Acton, “Phase retrieval on broadband and under-sampled images for the JWST testbed telescope,” Proc. SPIE 7436, 7436D (2009).
[CrossRef]

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).
[CrossRef]

Spence, J. C. H.

Takahashi, T.

Takajo, H.

Taninaka, M.

Teague, M. R.

Thelen, B. J.

Thibault, P.

V. Elser, I. Rankenburg, and P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. 104, 418–423 (2007).
[CrossRef]

Thurman, S. T.

Trebino, R.

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

R. Trebino and D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. A 10, 1101–1111 (1993).
[CrossRef]

Twiss, R. Q.

R. Hanbury Brown, and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048(1956).
[CrossRef]

Ueda, R.

Vasu, R. M.

G. K. Datta and R. M. Vasu, “Non-interferometric methods of phase estimation for application in optical tomography,” J. Mod. Opt. 46, 1377–1388 (1999).
[CrossRef]

Vest, C. M.

Wackerman, C. C.

Walther, A.

A. Walther, “The question of phase retrieval in optics,” Opt. Acta l0, 41–49 (1963).

Webb, H.

D. C. Youla and H. Webb, “Image restoration by the method of convex projections: Part 1—theory,” IEEE Trans. Med. Imag. 1, 81–94 (1982).
[CrossRef]

Weierstall, U.

Wolf, E.

E. Wolf, “Is a complete determination of the energy spectrum of light possible from measurements of the degree of coherence,” Proc. Phys. Soc. London 80, 1269–1272 (1962).
[CrossRef]

Wyrowski, F.

S. Buhling and F. Wyrowski, “Solving tolerancing and three-dimensional beam shaping problems by multifunctional wave optical design,” Opt. Eng. 40, 1590–1597 (2001).
[CrossRef]

Youla, D. C.

D. C. Youla and H. Webb, “Image restoration by the method of convex projections: Part 1—theory,” IEEE Trans. Med. Imag. 1, 81–94 (1982).
[CrossRef]

D. C. Youla, “Generalized image restoration by method of alternating orthogonal projections,” IEEE Trans. Circuits Syst. 25, 694–702 (1978).
[CrossRef]

Yu, R. P.

R. P. Yu, D. M. Paganin, and M. J. Morgan, “Inferring generalized time-dependent complex Ginzburg-Landau equations from modulus and gauge-field information,” Phys. Rev. B. 77, 134512 (2008).
[CrossRef]

Acta Cryst. (1)

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Cryst. 5, 843 (1952).
[CrossRef]

Adv. Phys. (1)

K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99 (2010).
[CrossRef]

Appl. Opt. (10)

Astron. Astrophys. (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Astron. Astrophys. Suppl. (1)

P. J. Napier and R. H. T. Bates, “Inferring phase information from modulus information in two-dimensional aperture synthesis,” Astron. Astrophys. Suppl. l5, 427–430 (1974).

IBM J. Res. Devel. (1)

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Devel. 13, 150–155 (1969).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. 33, 749–755 (1985).
[CrossRef]

IEEE Trans. Circuits Syst. (2)

M. T. Manry and J. K. Aggarwal, “The design of multidimensional FIR digital filters by phase correction,” IEEE Trans. Circuits Syst. 23, 185–199 (1976).
[CrossRef]

D. C. Youla, “Generalized image restoration by method of alternating orthogonal projections,” IEEE Trans. Circuits Syst. 25, 694–702 (1978).
[CrossRef]

IEEE Trans. Med. Imag. (1)

D. C. Youla and H. Webb, “Image restoration by the method of convex projections: Part 1—theory,” IEEE Trans. Med. Imag. 1, 81–94 (1982).
[CrossRef]

J. Mod. Opt. (2)

R. G. Lane, “Phase retrieval using conjugate gradient minimization,” J. Mod. Opt. 38, 1797–1813 (1991).
[CrossRef]

G. K. Datta and R. M. Vasu, “Non-interferometric methods of phase estimation for application in optical tomography,” J. Mod. Opt. 46, 1377–1388 (1999).
[CrossRef]

J. Opt. Soc. Am A (1)

V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am A 20, 40–55 (2003).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (19)

T. R. Crimmins, J. R. Fienup, and B. J. Thelen, “Improved bounds on object support from autocorrelation support and application to phase retrieval,” J. Opt. Soc. Am. A 7, 3–13 (1990).
[CrossRef]

H. H. Bauschke, P. L. Combettes, and D. R. Luke, “Phase retrieval, error reduction algorithms, and Fienup variants: a view from convex optimization,” J. Opt. Soc. Am. A 19, 1334–1345 (2002).
[CrossRef]

H. H. Bauschke, P. L. Combettes, and D. R. Luke, “A hybrid projection reflection method for phase retrieval,” J. Opt. Soc. Am. A 20, 1025–1034 (2003).
[CrossRef]

B. H. Dean and C. W. Bowers, “Diversity selection for phase-diverse phase retrieval,” J. Opt. Soc. Am. A 20, 1490–1504 (2003).
[CrossRef]

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–2000 (2006).
[CrossRef]

J. A. Marozas, “Fourier transform-based continuous phase-plate design technique: a high-pass phase-plate design as an application for OMEGA and the National Ignition Facility,” J. Opt. Soc. Am. A 24, 74–83 (2007).
[CrossRef]

S. T. Thurman, R. T. DeRosa, and J. R. Fienup, “Amplitude metrics for field retrieval with hard-edge and uniformly illuminated apertures,” J. Opt. Soc. Am. A 26, 700–709(2009).
[CrossRef]

H. Takajo, T. Takahashi, and T. Shizuma, “Further study on the convergence property of the hybrid input–output algorithm used for phase retrieval,” J. Opt. Soc. Am. A 16, 2163–2168 (1999).
[CrossRef]

H. Takajo, T. Takahashi, R. Ueda, and M. Taninaka, “Study on the convergence property of the hybrid input output algorithm used for phase retrieval,” J. Opt. Soc. Am. A 15, 2849–2861 (1998).
[CrossRef]

H. Takajo, T. Takahashi, H. Kawanami, and R. Ueda, “Numerical investigation of the iterative phase-retrieval stagnation problem: territories of convergence objects and holes in their boundaries,” J. Opt. Soc. Am. A 14, 3175–3187 (1997).
[CrossRef]

J. R. Fienup and C. C. Wackerman, “Phase retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986).
[CrossRef]

J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987).
[CrossRef]

J. N. Cederquist, J. R. Fienup, C. C. Wackerman, S. R. Robinson, and D. Kryskowski, “Wave-front phase estimation from Fourier intensity measurements,” J. Opt. Soc. Am. A 6, 1020–1026 (1989).
[CrossRef]

R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A 7, 394–411 (1990).
[CrossRef]

J. H. Seldin and J. R. Fienup, “Numerical investigation of the uniqueness of phase retrieval,” J. Opt. Soc. Am. A 7, 412–427 (1990).
[CrossRef]

J. R. Fienup and A. M. Kowalczyk, “Phase retrieval for a complex-valued object by using a low-resolution image,” J. Opt. Soc. Am. A 7, 450–458 (1990).
[CrossRef]

R. G. Lane, “Blind deconvolution of speckle images,” J. Opt. Soc. Am. A 9, 1508–1514 (1992).
[CrossRef]

M. H. Maleki and A. J. Devaney, “Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086–1092 (1993).
[CrossRef]

R. Trebino and D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. A 10, 1101–1111 (1993).
[CrossRef]

Mon. Not. R. Astron. Soc. (1)

R. H. T. Bates, “Contributions to the theory of intensity interferometry,” Mon. Not. R. Astron. Soc. 142, 413–428 (1969).

Nature (2)

R. Hanbury Brown, and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048(1956).
[CrossRef]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Opt. Acta (1)

A. Walther, “The question of phase retrieval in optics,” Opt. Acta l0, 41–49 (1963).

Opt. Commun. (1)

J. Skaar, “Iterative design of antireflection coatings based on the direct and inverse scattering transform,” Opt. Commun. 232, 45–48 (2004).
[CrossRef]

Opt. Eng. (3)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. l9, 297–305 (1980).

J. R. Fienup, “Space object imaging through the turbulent atmosphere,” Opt. Eng. 18, 529–534 (1979).
[CrossRef]

S. Buhling and F. Wyrowski, “Solving tolerancing and three-dimensional beam shaping problems by multifunctional wave optical design,” Opt. Eng. 40, 1590–1597 (2001).
[CrossRef]

Opt. Express (4)

Opt. Lett. (5)

Optik (1)

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).

Phys. C (1)

M. Carmody, E. Landree, L. D. Marks, and K. L. Merkle, “Determination of the current density distribution in Josephson junctions,” Phys. C 315, 145–153 (1999).
[CrossRef]

Phys. Rep. (1)

R. H. T. Bates, “Astronomical speckle imaging,” Phys. Rep. 90, 203–297 (1982).
[CrossRef]

Phys. Rev. B. (1)

R. P. Yu, D. M. Paganin, and M. J. Morgan, “Inferring generalized time-dependent complex Ginzburg-Landau equations from modulus and gauge-field information,” Phys. Rev. B. 77, 134512 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef]

Phys. Today (1)

K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54, 27–32 (2001).
[CrossRef]

Proc. Natl. Acad. Sci. (1)

V. Elser, I. Rankenburg, and P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. 104, 418–423 (2007).
[CrossRef]

Proc. Phys. Soc. London (1)

E. Wolf, “Is a complete determination of the energy spectrum of light possible from measurements of the degree of coherence,” Proc. Phys. Soc. London 80, 1269–1272 (1962).
[CrossRef]

Proc. SPIE (6)

J. S. Smith, D. L. Aronstein, B. H. Dean, and D. S. Acton, “Phase retrieval on broadband and under-sampled images for the JWST testbed telescope,” Proc. SPIE 7436, 7436D (2009).
[CrossRef]

G. R. Brady and J. R. Fienup, “Effect of broadband illumination on reconstruction error of phase retrieval in optical metrology,” Proc. SPIE 6617, 66170I (2007).
[CrossRef]

J. R. Fienup, “Space object imaging through the turbulent atmosphere,” Proc. SPIE 149, 71–81 (1978).

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).
[CrossRef]

G. B. Feldkamp and J. R. Fienup, “Noise properties of images reconstructed from Fourier modulus,” Proc. SPIE 231, 84–93 (1980).
[CrossRef]

J. R. Fienup and G. B. Feldkamp, “Astronomical imaging by processing stellar speckle interferometry data,” Proc. SPIE 243, 95–102 (1980).

Other (14)

J. R. Fienup, “Improved synthesis and computational methods for computer-generated holograms,” Ph.D. Thesis (Stanford University, 1975) (ProQuest, UMI No. 7525523, or at http://www.optics.rochester.edu/workgroups/fienup/Professor.htm ).

R. J. Collier, C. B. Burkhardt, and L. H. Lin, Optical Holography (Academic, 1971).

P. M. Hirsch, J. A. Jordan, and L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. patent 3,619,022(9Nov.1971).

J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” presented at the Annual Meeting of the OSA, Toronto, Ontario, October 1977, Abstract: J. Opt. Soc. Am. 67, 1389 (1977).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

Paul Simon, “Kodachrome”.

J. R. Fienup, “Phase retrieval in astronomy,” in Signal Recovery and Synthesis with Incomplete Information and Partial Constraints, digest of papers (Optical Society of America, 1983), paper ThA8-1-5.

J. R. Fienup, “Image reconstruction for stellar interferometry,” in Current Trends in Optics, F. T. Arecchi and F. R. Aussenegg, eds. (Taylor and Francis and Halsted, 1981), Invited Papers from ICO-12 Meeting, Graz, Austria, September 1981, pp. 95–102.

J. R. Fienup, “Comparison of phase retrieval algorithms,” presented at the Annual Meeting of the O.S.A., Kissimmee, Florida, October 1981, Abstract: J. Opt. Soc. Am. 71, 1641 (1981).

J. R. Fienup, “Wave front sensing by nonlinear optimization,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper FML2.

J. R. Fienup, “Phase retrieval with continuous version of hybrid input–output,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2003), paper ThI3.

J. C. Dainty and J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” Image Recovery: Theory and Application, H. Stark, ed. (Academic, 1987), pp. 231–275.

W. O. Saxton, Computer Techniques for Image Processing in Electron Microscopy (Academic, 1978).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Next input value as a function of the output value for (a) error-reduction, (b) HIO, and (c) CHIO algorithms.

Fig. 2.
Fig. 2.

Object.

Fig. 3.
Fig. 3.

Magnitude of the Fourier transform of the object.

Fig. 4.
Fig. 4.

Support constraint.

Fig. 5.
Fig. 5.

Reconstructed images after 160 iterations by (a) HIO and (b) CHIO.

Fig. 6.
Fig. 6.

Convergence as a function of iteration number for HIO and CHIO. Top: object-domain error metric, bottom: absolute error (with respect to the true object).

Fig. 7.
Fig. 7.

Next input value as a function of the output value for the HPR algorithm.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

g k + 1 ( x , y ) = { g k ( x , y ) , ( x , y ) γ g k ( x , y ) β g k ( x , y ) , ( x , y ) γ ,
g k + 1 ( x , y ) = { g k ( x , y ) , ( x , y ) S & α g k ( x , y ) g k ( x , y ) g k ( x , y ) ( 1 α α ) g k ( x , y ) , 0 g k ( x , y ) α g k ( x , y ) g k ( x , y ) β g k ( x , y ) , otherwise .
E o 2 = ( x , y ) γ | g k ( x , y ) | 2 ( x , y ) | g k ( x , y ) | 2 ,
E a b s 2 = min ( x o , y o ) ( x , y ) | g k ( x x o , y y o ) f ( x , y ) | 2 ( x , y ) | f ( x , y ) | 2 ,
g k + 1 ( x , y ) = { g k ( x , y ) , ( x , y ) S & g k ( x , y ) / ( 1 + β ) g k ( x , y ) g k ( x , y ) β g k ( x , y ) , otherwise ,

Metrics