Two noise-robust axial scanning multi-image phase retrieval algorithms based on Pauta criterion and smoothness constraint.

We proposed two noise-robust iterative methods for phase retrieval and diffractive imaging based on the Pauta criterion and the smoothness constraint. The work is to address the noise issue plaguing the application of iterative phase retrieval algorithms in coherent diffraction imaging. It is demonstrated by numerical analysis and experimental results that our proposed algorithms have higher retrieval accuracy and faster convergence speed at a high shot noise level. Moreover, they are proved to hold the superiority to cope with other kinds of noises. Due to the inconvenience of conventional iteration indicators in experiments, a more reliable retrieval metric is put forward and verified its effectiveness. It should be noted that the proposed methods focus on exploiting the longitudinal diversity. It is anticipated that our work can further expand the application of iterative multi-image phase retrieval methods.

[1]  J. Rodenburg,et al.  An improved ptychographical phase retrieval algorithm for diffractive imaging. , 2009, Ultramicroscopy.

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

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

[4]  Sayre,et al.  On possible extensions of X-ray crystallography through diffraction-pattern oversampling , 2000, Acta crystallographica. Section A, Foundations of crystallography.

[5]  J. Miao,et al.  Atomic electron tomography: 3D structures without crystals , 2016, Science.

[6]  Chao Yang,et al.  Augmented projections for ptychographic imaging , 2012, 1209.4924.

[7]  R. Horstmeyer,et al.  Diffraction tomography with Fourier ptychography. , 2015, Optica.

[8]  Jianwei Miao,et al.  Emerging opportunities in structural biology with X-ray free-electron lasers. , 2012, Current opinion in structural biology.

[9]  Ian Robinson,et al.  Effectiveness of iterative algorithms in recovering phase in the presence of noise. , 2007, Acta crystallographica. Section A, Foundations of crystallography.

[10]  Garth J. Williams,et al.  Single mimivirus particles intercepted and imaged with an X-ray laser , 2011, Nature.

[11]  Yonina C. Eldar,et al.  Sparsity-based single-shot sub-wavelength coherent diffractive imaging , 2011, 2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel.

[12]  Percival F Almoro,et al.  Numerical correction of aberrations via phase retrieval with speckle illumination. , 2009, Optics letters.

[13]  J. Rodenburg,et al.  Ptychographic microscope for three-dimensional imaging. , 2014, Optics express.

[14]  Andreas Menzel,et al.  Reconstructing state mixtures from diffraction measurements , 2013, Nature.

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

[16]  Percival F Almoro,et al.  Wavefront sensing using speckles with fringe compensation. , 2008, Optics express.

[17]  Hong Qi,et al.  Application of multi-phase particle swarm optimization technique to inverse radiation problem , 2008 .

[18]  Wolfgang Osten,et al.  Shape and deformation measurements of 3D objects using volume speckle field and phase retrieval. , 2009, Optics letters.

[19]  Yibo Zhang,et al.  Wide-field computational imaging of pathology slides using lens-free on-chip microscopy , 2014, Science Translational Medicine.

[20]  Zhengjun Liu,et al.  A review of iterative phase retrieval for measurement and encryption , 2017 .

[21]  Kazuto Yamauchi,et al.  Towards high-resolution ptychographic x-ray diffraction microscopy , 2011 .

[22]  P. Thibault,et al.  Maximum-likelihood refinement for coherent diffractive imaging , 2012 .

[23]  Chunmin Zhang,et al.  Wide-spectrum reconstruction method for a birefringence interference imaging spectrometer. , 2010, Optics letters.

[24]  Chunmin Zhang,et al.  Static hyperspectral imaging polarimeter for full linear Stokes parameters. , 2012, Optics express.

[25]  Laura Waller,et al.  Experimental robustness of Fourier Ptychography phase retrieval algorithms , 2015, Optics express.

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

[27]  Tim Salditt,et al.  Near-field ptychography using lateral and longitudinal shifts , 2015 .

[28]  Steen G. Hanson,et al.  Object wave reconstruction by speckle illumination and phase retrieval , 2009 .

[29]  J. Miao,et al.  Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities. , 2012, Journal of applied crystallography.

[30]  J. Rodenburg,et al.  Noise limit on practical electron ptychography , 2010 .

[31]  D. R. Luke.  Relaxed Averaged Alternating Reflections for Diffraction Imaging , 2004, math/0405208.

[32]  V. Elser.  Solution of the crystallographic phase problem by iterated projections. , 2002, Acta crystallographica. Section A, Foundations of crystallography.

[33]  Qian Chen,et al.  Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy. , 2016, Optics express.

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

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

[36]  O. Bunk,et al.  High-Resolution Scanning X-ray Diffraction Microscopy , 2008, Science.

[37]  G. Pedrini,et al.  Phase microscopy of technical and biological samples through random phase modulation with a diffuser. , 2010, Optics letters.

[38]  Talita Perciano,et al.  SHARP: a distributed, GPU-based ptychographic solver , 2016, 1602.01448.

[39]  Zhengjun Liu,et al.  Coherent diffraction imaging by moving a lens. , 2016, Optics express.

[40]  K. Nugent.  Coherent methods in the X-ray sciences , 2009, 0908.3064.

[41]  A. Ozcan,et al.  Synthetic aperture-based on-chip microscopy , 2015, Light: Science & Applications.

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

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

[44]  Henry C. Kapteyn,et al.  Subwavelength coherent imaging of periodic samples using a 13.5 nm tabletop high-harmonic light source , 2017, Nature Photonics.

[45]  Andrew V. Martin,et al.  Noise-robust coherent diffractive imaging with a single diffraction pattern , 2012 .

[46]  S. Marchesini,et al.  High-resolution ab initio three-dimensional x-ray diffraction microscopy. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[47]  J. Miao,et al.  Quantitative image reconstruction of GaN quantum dots from oversampled diffraction intensities alone. , 2005, Physical review letters.

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

[49]  K. Nugent,et al.  Atom-scale ptychographic electron diffractive imaging of boron nitride cones. , 2012, Physical review letters.