Iterative phase retrieval algorithms. I: optimization.

Two modified Gerchberg-Saxton (GS) iterative phase retrieval algorithms are proposed. The first we refer to as the spatial phase perturbation GS algorithm (SPP GSA). The second is a combined GS hybrid input-output algorithm (GS/HIOA). In this paper (Part I), it is demonstrated that the SPP GS and GS/HIO algorithms are both much better at avoiding stagnation during phase retrieval, allowing them to successfully locate superior solutions compared with either the GS or the HIO algorithms. The performances of the SPP GS and GS/HIO algorithms are also compared. Then, the error reduction (ER) algorithm is combined with the HIO algorithm (ER/HIOA) to retrieve the input object image and the phase, given only some knowledge of its extent and the amplitude in the Fourier domain. In Part II, the algorithms developed here are applied to carry out known plaintext and ciphertext attacks on amplitude encoding and phase encoding double random phase encryption systems. Significantly, ER/HIOA is then used to carry out a ciphertext-only attack on AE DRPE systems.

[1]  J. Rodenburg,et al.  Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm. , 2004, Physical review letters.

[2]  R. Gerchberg.  A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[3]  Peng Zhang,et al.  Known-plaintext attack on optical encryption based on double random phase keys. , 2006, Optics letters.

[4]  G. Pedrini,et al.  Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm. , 2003, Optics express.

[5]  James R. Fienup,et al.  Improved bounds on object support from autocorrelation support and application to phase retrieval , 1990 .

[6]  Unnikrishnan Gopinathan,et al.  Generalized in-line digital holographic technique based on intensity measurements at two different planes. , 2008, Applied optics.

[7]  J. Rodenburg,et al.  Phase retrieval based on wave-front relay and modulation , 2010 .

[8]  Peng Xiang,et al.  Ciphertext-only attack on double random phase encoding optical encryption system , 2007 .

[9]  Marcus C Newton,et al.  Compressed sensing for phase retrieval. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  S. Marchesini,et al.  X-ray image reconstruction from a diffraction pattern alone , 2003, physics/0306174.

[11]  James R. Fienup,et al.  Reconstruction of objects having latent reference points , 1983 .

[12]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[13]  K. Nugent,et al.  Phase retrieval in x-ray imaging based on using structured illumination , 2008 .

[14]  Xiaojing Huang,et al.  Phase retrieval of diffraction from highly strained crystals , 2010 .

[15]  James R. Fienup,et al.  Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint , 1987 .

[16]  J. Miao,et al.  Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects , 1998 .

[17]  Unnikrishnan Gopinathan,et al.  A known-plaintext heuristic attack on the Fourier plane encryption algorithm. , 2006, Optics express.

[18]  Martin Kohl,et al.  Improved success rate and stability for phase retrieval by including randomized overrelaxation in the hybrid input output algorithm , 2012, 1206.3619.

[19]  Veit Elser.  Phase retrieval by iterated projections. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[20]  J. Miao,et al.  Phase retrieval of diffraction patterns from noncrystalline samples using the oversampling method , 2003 .

[21]  Irad Yavneh,et al.  Approximate Fourier phase information in the phase retrieval problem: what it gives and how to use it. , 2011, Journal of the Optical Society of America. A, Optics, image science, and vision.

[22]  Q. Shen,et al.  Wave propagation and phase retrieval in Fresnel diffraction by a distorted-object approach , 2005 .

[23]  P. Scott,et al.  Phase retrieval and twin-image elimination for in-line Fresnel holograms , 1987 .

[24]  Wen Chen,et al.  Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain. , 2010, Optics express.

[25]  Hiroyuki Shioya,et al.  K-means clustering for support construction in diffractive imaging. , 2014, Journal of the Optical Society of America. A, Optics, image science, and vision.

[26]  J R Fienup,et al.  Reconstruction of an object from the modulus of its Fourier transform. , 1978, Optics letters.

[27]  A. Fannjiang,et al.  Phase retrieval with random phase illumination. , 2012, Journal of the Optical Society of America. A, Optics, image science, and vision.

[28]  James R. Fienup,et al.  Phase-retrieval stagnation problems and solutions , 1986 .

[29]  John T. Sheridan,et al.  Optical double image encryption employing a pseudo image technique in the Fourier domain , 2014 .

[30]  John T. Sheridan,et al.  Digital image watermarking spread-space spread-spectrum technique based on Double Random Phase Encoding , 2013 .

[31]  James R. Fienup,et al.  Phase retrieval using boundary conditions , 1986 .

[32]  James R. Fienup,et al.  Reconstruction of the support of an object from the support of its autocorrelation , 1982 .