Holographic phase retrieval and reference design

A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a ‘reference’ portion of the signal to be recovered via phase retrieval is a priori known from experimental design. A generic formula is also derived for the expected recovery error when the measurement data is corrupted by Poisson shot noise. This facilitates an optimization perspective towards reference design and analysis. We employ this optimization perspective towards quantifying the performance of various reference choices.

[1]  O. Papaspiliopoulos.  High-Dimensional Probability: An Introduction with Applications in Data Science , 2020 .

[2]  Holger Sambale,et al.  Concentration inequalities for polynomials in α-sub-exponential random variables , 2019, Electronic Journal of Probability.

[3]  Emmanuel J. Candès,et al.  Dual-Reference Design for Holographic Coherent Diffraction Imaging , 2019, ArXiv.

[4]  David Halliday,et al.  FIFTH EDITION , 2004 .

[5]  Roman Vershynin,et al.  High-Dimensional Probability , 2018 .

[6]  David A. Barmherzig,et al.  On Block-Reference Coherent Diffraction Imaging , 2018 .

[7]  Anton Barty,et al.  Femtosecond X-ray Fourier holography imaging of free-flying nanoparticles , 2017, 1707.09424.

[8]  Jianwei Miao,et al.  In situ coherent diffractive imaging , 2017, Nature Communications.

[9]  Ju Sun,et al.  A Local Analysis of Block Coordinate Descent for Gaussian Phase Retrieval , 2017, ArXiv.

[10]  Yonina C. Eldar,et al.  Fourier Phase Retrieval: Uniqueness and Algorithms , 2017, ArXiv.

[11]  Adrian Stern,et al.  Optical Compressive Imaging , 2016 .

[12]  J. Rothhardt,et al.  Influence of detector noise in holographic imaging with limited photon flux. , 2016, Optics express.

[13]  Kishore Jaganathan,et al.  Convex Programming-Based Phase Retrieval: Theory and Applications , 2016 .

[14]  Oliver Cossairt,et al.  High dynamic range coherent imaging using compressed sensing. , 2015, Optics express.

[15]  Yonina C. Eldar,et al.  Phase Retrieval: An Overview of Recent Developments , 2015, ArXiv.

[16]  Yonina C. Eldar,et al.  Phase retrieval with masks using convex optimization , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[17]  J. Miao,et al.  Beyond crystallography: Diffractive imaging using coherent x-ray light sources , 2015, Science.

[18]  Yonina C. Eldar,et al.  Phase Retrieval with Application to Optical Imaging: A contemporary overview , 2015, IEEE Signal Processing Magazine.

[19]  Xiaodong Li,et al.  Phase Retrieval via Wirtinger Flow: Theory and Algorithms , 2014, IEEE Transactions on Information Theory.

[20]  Yonina C. Eldar,et al.  Phase Retrieval via Matrix Completion , 2011, SIAM Rev..

[21]  R. Harder,et al.  Coherent X-Ray Diffraction Imaging and Characterization of Strain in Silicon-on-Insulator Nanostructures , 2014, Advanced materials.

[22]  Xiaodong Li,et al.  Phase Retrieval from Coded Diffraction Patterns , 2013, 1310.3240.

[23]  Gábor Lugosi,et al.  Concentration Inequalities - A Nonasymptotic Theory of Independence , 2013, Concentration Inequalities.

[24]  Chao Yang,et al.  Alternating direction methods for classical and ptychographic phase retrieval , 2012 .

[25]  T. Latychevskaia,et al.  Fourier Transform Holography: A Lensless Non-Destructive Imaging Technique , 2012, Microscopy and Microanalysis.

[26]  W. H. Benner,et al.  Fractal morphology, imaging and mass spectrometry of single aerosol particles in flight , 2012, Nature.

[27]  Leslie J. Allen,et al.  Fast deterministic approach to exit-wave reconstruction , 2012 .

[28]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[29]  J. Fienup,et al.  High-resolution X-ray lensless imaging by differential holographic encoding. , 2009, Physical review letters.

[30]  William F. Trench,et al.  Inverses of lower triangular Toeplitz matrices , 2009 .

[31]  Manuel Guizar-Sicairos,et al.  Direct image reconstruction from a Fourier intensity pattern using HERALDO. , 2008, Optics letters.

[32]  Leslie J. Allen,et al.  Direct retrieval of a complex wave from its diffraction pattern , 2008 .

[33]  Joshua W. Shaevitz,et al.  Massively parallel X-ray holography , 2008 .

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

[35]  L. Pelkmans,et al.  Ameobal Pathogen Mimivirus Infects Macrophages through Phagocytosis , 2008, PLoS pathogens.

[36]  O. Bunk,et al.  Coherent diffractive imaging using phase front modifications. , 2008, Physical review letters.

[37]  Manuel Guizar-Sicairos,et al.  Holography with extended reference by autocorrelation linear differential operation. , 2007, Optics express.

[38]  D. Paganin,et al.  A non-iterative reconstruction method for direct and unambiguous coherent diffractive imaging. , 2007, Optics express.

[39]  O. Bunk,et al.  Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels. , 2007, Acta crystallographica. Section A, Foundations of crystallography.

[40]  V Elser,et al.  Searching with iterated maps , 2007, Proceedings of the National Academy of Sciences.

[41]  S Marchesini,et al.  Invited article: a [corrected] unified evaluation of iterative projection algorithms for phase retrieval. , 2006, The Review of scientific instruments.

[42]  W. H. Benner,et al.  Femtosecond diffractive imaging with a soft-X-ray free-electron laser , 2006, physics/0610044.

[43]  S. Marchesini,et al.  Invited article: a [corrected] unified evaluation of iterative projection algorithms for phase retrieval. , 2006, The Review of scientific instruments.

[44]  D. R. Luke.  Relaxed averaged alternating reflections for diffraction imaging , 2004, math/0405208.

[45]  S. Eisebitt,et al.  Lensless imaging of magnetic nanostructures by X-ray spectro-holography , 2004, Nature.

[46]  D Russell Luke.  Relaxed averaged alternating reflections for diffraction imaging , 2004 .

[47]  Robert M. Rioux,et al.  Lawrence Berkeley National Laboratory , 2004 .

[48]  V. Elser.  Phase retrieval by iterated projections. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[49]  I. Robinson,et al.  Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction. , 2001, Physical review letters.

[50]  Arkadi Nemirovski,et al.  Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[51]  J. Miao,et al.  Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens , 1999, Nature.

[52]  Alan V. Oppenheim,et al.  Discrete-time signal processing (2nd ed.) , 1999 .

[53]  H. Sahinoglou,et al.  On phase retrieval of finite-length sequences using the initial time sample , 1991 .

[54]  Monson H. Hayes,et al.  Phase retrieval using two Fourier-transform intensities , 1990 .

[55]  Rick P. Millane,et al.  Phase retrieval in crystallography and optics , 1990 .

[56]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[57]  Katta G. Murty,et al.  Some NP-complete problems in quadratic and nonlinear programming , 1987, Math. Program..

[58]  M. Hayes.  The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform , 1982 .

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

[60]  S. Kikuta,et al.  X-ray holography of lensless Fourier-transform type , 1972 .

[61]  J. Goodman.  Introduction to Fourier optics , 1969 .

[62]  A. Walther.  The Question of Phase Retrieval in Optics , 1963 .

[63]  E. Leith,et al.  Reconstructed Wavefronts and Communication Theory , 1962 .

[64]  D. Gabor.  A New Microscopic Principle , 1948, Nature.

[65]  W. Schottky.  Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern , 1918 .