ADP: Automatic differentiation ptychography

Ptychography is an imaging technique which aims to recover the complex-valued exit wavefront of an object from a set of its diffraction pattern magnitudes. Ptychography is one of the most popular techniques for sub-30 nanometer imaging as it does not suffer from the limitations of typical lens based imaging techniques. The object can be reconstructed from the captured diffraction patterns using iterative phase retrieval algorithms. Over time many algorithms have been proposed for iterative reconstruction of the object based on manually derived update rules. In this paper, we adapt automatic differentiation framework to solve practical and complex ptychographic phase retrieval problems and demonstrate its advantages in terms of speed, accuracy, adaptability and generalizability across different scanning techniques.

[1]  J. Fienup,et al.  Phase retrieval with transverse translation diversity: a nonlinear optimization approach. , 2008, Optics express.

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

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

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

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

[6]  Martín Abadi,et al.  TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems , 2016, ArXiv.

[7]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[8]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[9]  Youssef S. G. Nashed,et al.  Distributed Automatic Differentiation for Ptychography , 2017, ICCS.

[10]  S. Marchesini,et al.  Iterative Algorithms for Ptychographic Phase Retrieval , 2011, 1105.5628.

[11]  Laura Waller,et al.  Nonlinear Optimization Algorithm for Partially Coherent Phase Retrieval and Source Recovery , 2016, IEEE Transactions on Computational Imaging.

[12]  Ian K Robinson,et al.  Continuous scanning mode for ptychography. , 2014, Optics letters.

[13]  R. J.,et al.  Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint , 2002 .

[14]  Tie Zhou,et al.  Numerical Optimization Algorithm of Wavefront Phase Retrieval from Multiple Measurements , 2016, 1607.01861.

[15]  A. Huiser,et al.  Ambiguity of the phase-reconstruction problem. , 1980, Optics letters.

[16]  Tom Peterka,et al.  Continuous Motion Scan Ptychography: Characterization for Increased Speed in Coherent X-ray Imaging References and Links Chemical Composition Mapping with Nanometre Resolution by Soft X-ray Microscopy, " Nature , 2022 .

[17]  Tom Peterka,et al.  Parallel ptychographic reconstruction. , 2014, Optics express.

[18]  James R Fienup,et al.  Applications of algorithmic differentiation to phase retrieval algorithms. , 2014, Journal of the Optical Society of America. A, Optics, image science, and vision.

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

[20]  Louis B. Rall,et al.  Automatic Differentiation: Techniques and Applications , 1981, Lecture Notes in Computer Science.

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

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

[23]  W. Hoppe.  Beugung im inhomogenen Primärstrahlwellenfeld. I. Prinzip einer Phasenmessung von Elektronenbeungungsinterferenzen , 1969 .