Iterative Algorithms for Ptychographic Phase Retrieval

Ptychography promises diffraction limited resolution without the need for high resolution lenses. To achieve high resolution one has to solve the phase problem for many partially overlapping frames. Here we review some of the existing methods for solving ptychographic phase retrieval problem from a numerical analysis point of view, and propose alternative methods based on numerical optimization.

[1]  B. C. McCallum,et al.  Resolution beyond the 'information limit' in transmission electron microscopy , 1995, Nature.

[2]  Stefano Marchesini,et al.  Phase retrieval and saddle-point optimization. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[3]  David J. Thuente,et al.  Line search algorithms with guaranteed sufficient decrease , 1994, TOMS.

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

[5]  Andreas Menzel,et al.  Probe retrieval in ptychographic coherent diffractive imaging. , 2009, Ultramicroscopy.

[6]  Ken Kreutz-Delgado,et al.  The Complex Gradient Operator and the CR-Calculus ECE275A - Lecture Supplement - Fall 2005 , 2009, 0906.4835.

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

[8]  R. Remmert,et al.  Theory of Complex Functions , 1990 .

[9]  J. Rodenburg,et al.  The theory of super-resolution electron microscopy via Wigner-distribution deconvolution , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

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

[11]  H. Chapman Phase-retrieval X-ray microscopy by Wigner-distribution deconvolution , 1996 .

[12]  Carl Tim Kelley,et al.  Iterative methods for optimization , 1999, Frontiers in applied mathematics.

[13]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[14]  J. Rodenburg Ptychography and Related Diffractive Imaging Methods , 2008 .

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

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

[17]  T. Steihaug The Conjugate Gradient Method and Trust Regions in Large Scale Optimization , 1983 .

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