A review of iterative phase retrieval for measurement and encryption

Abstract Phase retrieval technique is regarded as one of the most significant tools to solve optical inverse problems. Several phase retrieval algorithms are discussed in this review. The occurrence of ill-posed conditions often makes the calculation difficult. As a synthesis, the multiple-image phase retrieval technology is invented to obtain more accurate convergence result in iterative computation. The multiple-input retrieval scheme can attach new constraints on convergence as a new limitation. As an indirect measuring method, it will make it possible to reconstruct the distribution of intensity and phase in an imaging or measurement system, where data processing is executed by computer. Moreover, the retrieval method has been applied for image encryption successfully. Finally, the development and application of the iterative phase retrieval are overviewed.

[1]  Linfei Chen,et al.  Phase retrieval encryption in an enhanced optical interference by key phase constraint. , 2015, Applied optics.

[2]  Nobuharu Nakajima,et al.  Lensless coherent imaging by a deterministic phase retrieval method with an aperture-array filter. , 2008, Journal of the Optical Society of America. A, Optics, image science, and vision.

[3]  L J Allen,et al.  Exit wave reconstruction at atomic resolution. , 2004, Ultramicroscopy.

[4]  Bahram Javidi,et al.  Advances in optical security systems , 2014 .

[5]  Kaikai Guo,et al.  Optimization of sampling pattern and the design of Fourier ptychographic illuminator. , 2015, Optics express.

[6]  Hai Yu,et al.  Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains , 2015 .

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

[8]  G. Pedrini,et al.  Phase retrieval using multiple illumination wavelengths. , 2008, Optics letters.

[9]  G. Pedrini,et al.  Lensless phase microscopy using phase retrieval with multiple illumination wavelengths. , 2012, Applied optics.

[10]  A. G. Cullis,et al.  Transmission microscopy without lenses for objects of unlimited size. , 2007, Ultramicroscopy.

[11]  X. F. Meng,et al.  Image watermarking based on an iterative phase retrieval algorithm and sine–cosine modulation in the discrete-cosine-transform domain , 2007 .

[12]  J. Rodenburg,et al.  High resolution transmission imaging without lenses , 2010 .

[13]  Wolfgang Osten,et al.  High-resolution quantitative phase microscopic imaging in deep UV with phase retrieval. , 2011, Optics letters.

[14]  Wenqi He,et al.  Optical multiple-image hiding based on interference and grating modulation , 2012 .

[15]  John T. Sheridan,et al.  Collision in double random phase encoding , 2008 .

[16]  Alex Shenfield,et al.  Evolutionary determination of experimental parameters for ptychographical imaging , 2011 .

[17]  Zhengjun Liu,et al.  Image watermarking by using phase retrieval algorithm in gyrator transform domain , 2010 .

[18]  Muhammad Rafiq Abuturab,et al.  An asymmetric single-channel color image encryption based on Hartley transform and gyrator transform , 2015 .

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

[20]  A. Alfalou,et al.  Recent Advances in Optical Image Processing , 2015 .

[21]  Kehar Singh,et al.  Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane , 2015 .

[22]  Wave form reconstruction of photoconductive switch using minimum phase retrieval algorithm , 1998 .

[23]  R. Horstmeyer,et al.  Wide-field, high-resolution Fourier ptychographic microscopy , 2013, Nature Photonics.

[24]  Victor A. Soifer,et al.  Iteractive Methods For Diffractive Optical Elements Computation , 1997 .

[25]  B Javidi,et al.  Optical image encryption based on input plane and Fourier plane random encoding. , 1995, Optics letters.

[26]  Zhengjun Liu,et al.  A Recovery Method of Double Random Phase Encoding System With a Parallel Phase Retrieval , 2016, IEEE Photonics Journal.

[27]  Daomu Zhao,et al.  Color image hiding based on the phase retrieval technique and Arnold transform. , 2011, Applied optics.

[28]  Zhengjun Liu,et al.  Double image encryption based on iterative fractional Fourier transform , 2007 .

[29]  I. Robinson,et al.  Collagen imaged by Coherent X-ray Diffraction: towards a complementary tool to conventional scanning SAXS , 2010 .

[30]  Ayman Alfalou,et al.  Optical image compression and encryption methods , 2009 .

[31]  Lu-Zhong Cai,et al.  Information security system by iterative multiple-phase retrieval and pixel random permutation. , 2006, Applied optics.

[32]  Andrew V. Martin,et al.  Phase imaging from a diffraction pattern in the presence of vortices , 2007 .

[33]  James R Fienup,et al.  Phase retrieval algorithms: a personal tour [Invited]. , 2013, Applied optics.

[34]  Peng Zhang,et al.  Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain. , 2006, Optics letters.

[35]  Sanguo Zhang,et al.  Optical image encryption via ptychography. , 2013, Optics letters.

[36]  Zeev Zalevsky,et al.  Multi-stage phase retrieval algorithm based upon the gyrator transform. , 2010, Optics express.

[37]  G. Pedrini,et al.  Wave-front reconstruction from a sequence of interferograms recorded at different planes. , 2005, Optics letters.

[38]  Wei Liu,et al.  Optical security validation using Michelson interferometer , 2015 .

[39]  L. Waller,et al.  Phase-space measurement and coherence synthesis of optical beams , 2012, Nature Photonics.

[40]  J. Rodenburg,et al.  A phase retrieval algorithm for shifting illumination , 2004 .

[41]  C. David,et al.  Influence of finite spatial coherence on ptychographic reconstruction , 2015 .

[42]  J. Kirz,et al.  Biological imaging by soft x-ray diffraction microscopy , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[43]  Shutian Liu,et al.  Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms , 2015 .

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

[45]  Yukio Takahashi,et al.  Precession x-ray ptychography with multislice approach , 2015 .

[46]  L J Allen,et al.  Retrieval of a complex-valued object from its diffraction pattern. , 2004, Physical review letters.

[47]  Wen Chen,et al.  Optical Encryption and Authentication Based on Phase Retrieval and Sparsity Constraints , 2015, IEEE Photonics Journal.

[48]  Shutian Liu,et al.  Generation of hollow Gaussian beam by phase-only filtering. , 2008, Optics express.

[49]  In-Kwon Lee,et al.  Modified computational integral imaging-based double image encryption using fractional Fourier transform , 2015 .

[50]  Feng Zhang,et al.  Asymmetric multiple-image encryption based on the cascaded fractional Fourier transform , 2015 .

[51]  Keng S. Liang,et al.  Quantitative phase retrieval in transmission hard x-ray microscope , 2007 .

[52]  Eduardo Peters,et al.  Complex wavefront reconstruction from multiple-image planes produced by a focus tunable lens. , 2015, Optics letters.

[53]  J. H. Seldin,et al.  Hubble Space Telescope characterized by using phase-retrieval algorithms. , 1993, Applied optics.

[54]  Zhengjun Liu,et al.  Precision influence of a phase retrieval algorithm in fractional Fourier domains from position measurement error. , 2015, Applied optics.

[55]  Xiaogang Wang,et al.  Optical image hiding using double-phase retrieval algorithm based on nonlinear cryptosystem under vortex beam illumination , 2015 .

[56]  R. Mittra,et al.  Digital and optical reconstruction of images from suboptical diffraction patterns. , 1974, Applied optics.

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

[58]  Zhengjun Liu,et al.  Securing color image by using phase-only encoding in Fresnel domains , 2015 .

[59]  Bahram Javidi,et al.  Optical encryption using multiple intensity samplings in the axial domain. , 2013, Journal of the Optical Society of America. A, Optics, image science, and vision.

[60]  B Y Gu,et al.  Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison. , 1994, Applied optics.

[61]  Shutian Liu,et al.  Randomization of the Fourier transform. , 2007, Optics letters.

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

[63]  Chuang Lin,et al.  Image encryption by encoding with a nonuniform optical beam in gyrator transform domains. , 2010, Applied optics.

[64]  Jingjuan Zhang,et al.  Multiple-image encryption by wavelength multiplexing. , 2005, Optics letters.