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. © 2011 Optical Society of America References and links 1. R Hegerl and W Hoppe. Dynamic theory of crystalline structure analysis by electron diffraction in inhomogeneous primary wave field. Berichte Der Bunsen-Gesellschaft Fur Physikalische Chemie, 74:1148, 1970. 2. P. D. Nellist, B. C. McCallum, and J. M. Rodenburg. Resolution beyond the ’information limit’ in transmission electronmicroscopy. 374:630–632, 04 1995. 1 LBNL-4598E ar X iv :1 10 5. 56 28 v1 [ ph ys ic s. op tic s] 2 7 M ay 2 01 1 3. H N Chapman. Phase-retrieval x-ray microscopy by wigner-distribution deconvolution. Ultramicroscopy, 66:153–172, 1996. 4. H. M. L. Faulkner and J. M. Rodenburg. Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm. Phy. Rev. Lett., 93:023903, 2004. 5. J. M. Rodenburg and H. M. L. Faulkner. A phase retrieval algorithm for shifting illumination. Appl. Phy. Lett., 85:4795–4797, 2004. 6. J M Rodenburg. Ptychography and related diffractive imaging methods. volume 150 of Advances in Imaging and Electron Physics, chapter Ptychography and Related Diffractive Imaging Methods, pages 87–184. Elsevier, 2008. 7. M. Guizar-Sicairos and J. R. Fineup. Phase retrieval with transverse translation diversity: a nonlinear optimization approach. Opt. Express, 16:7264–7278, 2008. 8. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer. Probe retrieval in ptychographic coherent diffractive imaging. Ultramicroscopy, 109:338–343, 2009. 9. J. M. Rodenburg and R. H. T. Bates. The theory of super-resolution electron microscopy via wignerdistribution deconvolution. Phil. Trans. R. Soc. Lond. A, 339:521–553, 1992. 10. R. Remmert. Theory of Complex Functions. Springer-Verlag, 1991. 11. K. Kreutz-Delgado. The Complex Gradient Operator and the CR-Calculus. UCSD, 2003. 12. T. Steihaug. The conjugate gradient method and trust regions in large scale optimization. SIAM J. Num. Anal., 20:626–637, 1983. 13. S Marchesini. A unified evaluation of iterative projection algorithms for phase retrieval. Rev Sci Instrum, 78:011301, Jan 2007. 14. J. Moré and D. J. Thuente. Line search algorithms with guaranteed sufficient decrease. ACM Trans. Math. Software, 20(3):286–307, 1994. 15. J. Nocedal and S. J. Wright. Numerical Optimization. Springer-Verlag, New York, 1999. 16. J. R. Fienup. Phase retrieval algorithms: a comparison. Appl. Opt., 21:2758–2769, 1982. 17. R. Luke. Relaxed averaged alternating reflections for diffraction imaging. Inverse Problems, 21:37– 50, 2005. 18. S. Marchesini. Phase-retrieval and saddle-point optimization. arXiv:physics, 0611233v5:1–8, 2007. 19. J. M. Rodenburg. Ptychography and related diffractive imaging methods. Advances in Imaging and Electron Physics, 150, 2008. 20. C. T. Kelley. Iterative Methods for Optimization. SIAM, Philadelphia, 1999.