• Laser & Optoelectronics Progress
  • Vol. 47, Issue 8, 81001 (2010)
Liao Tianhe1、*, Gao Qiong2, Cui Yuanfeng3, and Song Kaiyang1
Author Affiliations
  • 1[in Chinese]
  • 2[in Chinese]
  • 3[in Chinese]
  • show less
    DOI: 10.3788/lop47.081001 Cite this Article Set citation alerts
    Liao Tianhe, Gao Qiong, Cui Yuanfeng, Song Kaiyang. Phase Retrieval Problem in Fractional Fourier Domain[J]. Laser & Optoelectronics Progress, 2010, 47(8): 81001 Copy Citation Text show less
    References

    [1] H. M. Ozaktas,Z. Zalevsky,M. A. Kutay. The Fractional Fourier Transform with Applications in Optics and Signal Processing [M]. New York:Wiley,2000

    [2] V. Namias. The fractional Fourier transform and its application to quantum mechanics [J]. J. Inst. Maths. Appl.,1980,25:241-265

    [3] A. C. Mcbride,F. H. Kerr. On Namias's fractional Fourier transform[J]. IMA J. Appl. Math,1987,39:159-175

    [4] H. M. Ozaktas,D. Mendlovic. Fourier transforms of fractional order and their optical interpretation [J]. Opt. Commun.,1993,101:163-169

    [5] D. Mendlovic,H. M. Ozaktas. Fractional Fourier transforms and their optical implementation:I [J]. J. Opt. Soc. Am. A,1993,10(9):1875-1880

    [6] H. M. Ozaktas,D. Mendlovic. Fractional Fourier transforms and their optical implementation:II [J]. J. Opt. Soc. Am. A,1993,10(12):2522-2531

    [7] H. M. Ozaktas. Image rotation,wigner rotation,and the fractional Fourier transform [J]. J. Opt. Soc. Am. A,1993,10(10):2181-2186

    [8] D. Mendlovic,H. M. Ozaktas,A. W. Lohmann. Gradient-index fibers,wigner distribution functions,and the fractional Fourier transform [J]. Appl. Opt.,1994,33(26):6188-6193

    [9] L. B. Almeida. The fractional Fourier transform and time-frequency representation [J]. IEEE Trans. Signal Process,1994,42(11):3084-3091

    [10] H. M. Ozaktas,B. Barshan,D. Mendlovic et al.. Convolution,filtering,and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms [J]. J. Opt. Soc. Am. A,1994,11(2):547-559

    [11] Z. Zalevsky,D. Mendlovic. Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain [J]. Opt. Lett.,1996,21(12):842-844

    [12] B. Dong,Y. Zhang,B. Gu et al.. Numerical investigation of phase retrieval in a fractional Fourier transform [J]. J. Opt. Soc. Am. A,1997,14(10):2709-2714

    [13] W. Cong,N. Chen,B. Gu. Recursive algorithm for phase retrieval in the fractional Fourier transform domain [J]. Appl. Opt.,1998,37(29):6906-6910

    [14] M. G. Ertosun,H. Atli,H. M. Ozaktas et al.. Complex signal recovery from multiple fractional Fourier-transform intensities [J]. Opt. Commun.,2005,244:6170

    [15] M. G. Ertosun,H. Atli,H. M. Ozaktas et al.. Complex signal recovery from multiple fractional Fourier-transform intensities [J]. Appl. Opt.,2005,44(23):4902-4908

    [16] T. H. Liao,Q. Gao. Image recovery from double amplitudes in fractional Fourier domain [J]. Chin. Phys.,2006,15(2):347-352

    [17] Cui Yuanfeng,Liao Tianhe,Gao Qiong. Hybrid input-output algorithm for phase retrieval of 2-D complex image in fractional Fourier domain [J]. J. Appl. Opt.,2008,29(4):653-656

    [18] Cui Yuanfeng. The Phase Retrieval Problem of Complex Images in The Fractional Fourier Domain [D]. Zhengzhou:Information and Engineering University,2008

    [19] R. Gerchberg,W. Saxton. A practical algorithm for the determination of phase from image and diffraction plane pictures [J]. Optik,1972,35:237-246

    [20] J. R. Fienup. Phase retrieval algorithms:a comparison [J]. Appl. Opt.,1982,21(15):2758-2769

    [21] Yang Guozhen,Gu Benyuan. On the amplitude-phase retrieval problem in optical system [J]. Acta. Physica. Sinica. 1981,30(3):410-413

    [22] D. C. Dobson. Phase reconstruction via nonlinear least-aquares [J]. Inverse Probl,1992,8:541-557

    [23] B. Hofmann,B. Kaltenbacher,C. Poschl et al.. A convergence rates result for tikhonov regularization in banach spaces with non-smooth operators [J]. Inverse Probl.,2007,23:987-1010

    [24] H. H. Bauschke,P. L. Combettes,D. R. Luke. Phase retrieval,error reduction algorithm,and Fienup variants:a view from convex optimization [J]. J.Opt. Soc. Am. A,2002,19(7):1334-1345

    [25] T. Alieva,M. J. Bastiaans,L. Stankovic. Signal reconstruction from two close fractional Fourier power spectra [J]. IEEE Trans. Signal Process,2003,51(1):112-123

    [26] U. Gopinathan,G. Sita,T. J. Naughton et al.. Noninterferometric phase retrieval using a fractional Fourier system [J]. J.Opt. Soc. Am. A,2008,25(1):108-115

    [27] D. F. McAlister,M. Beck,L. Clarke et al.. Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms [J]. Opt. Lett.,1995,20(10):1181-1183

    [28] A. Semichaevsky,M. Testorf. Phase-space interpretation of deterministic phase retrieval [J]. J. Opt. Soc. Am. A,2004,21(11):2173-2179

    [29] C. Candan,M. A. Kutay,H. M. Ozaktas. The discrete fractional Fourier transform [J]. IEEE Trans. Signal Process,2000,48(5):1329-1337

    [30] S. C. Pei,J. J. Ding. Closed-form discrete fractional and affine fourier transforms [J]. IEEE Trans. Signal Process,2000,48(5):1338-1353

    [31] S. C. Pei,M. H. Yeh,C. C. Tseng. Discrete fractional Fourier transform based on orthogonal projections[J]. IEEE Trans. Signal Process,1999,47(5):1335-1348

    [32] S. C. Pei,M. H. Yeh. Two dimensional discrete Fourier transform [J]. Signal Process,1998,67:99-108

    [33] A. Bultheel,A. H. Sulbaran. Computation of fractional Fourier transform [J]. Appl. And Comp. Harmon. Anal,2004,16:182-202

    [34] A. Bultheel,A. H. Sulbaran. http://www.cs.kuleuven.be/cwis/research/nalag/research /software/FRFT (2004)

    [35] Gerchberg Saxton,Yang Gu. Algorithms for phase retrieval in a nonunitary transform system:a comparison [J]. Appl. Opt.,1994,33(2):209-218

    [36] Q. Gao,T. H. Liao,Y. F. Cui. Solving the phase-retrieval problem of a complex signal in the fractional Fourier domain by nonlinear least-squares [J]. Opt. Lett.,2008,33(15):1899-1901

    [37] J. Nocedal,S. J. Wright. Numerical Optimization [M]. 1999,Berlin:Springer

    [38] Yuan Yaxiang,Sun Wenyu. Theory and Methods of Optimization [M]. Beijing:Science Press,1997

    CLP Journals

    [1] Cui Wenda, Du Shaojun. Phase Retrieval Based on Fractional Fourier Transform[J]. Laser & Optoelectronics Progress, 2013, 50(9): 91003

    Liao Tianhe, Gao Qiong, Cui Yuanfeng, Song Kaiyang. Phase Retrieval Problem in Fractional Fourier Domain[J]. Laser & Optoelectronics Progress, 2010, 47(8): 81001
    Download Citation