Phase retrieval with transverse translation diversity: a nonlinear optimization approach

Manuel Guizar-Sicairos,James R Fienup

doi:10.1364/oe.16.007264

Abstract

We develop and test a nonlinear optimization algorithm for solving the problem of phase retrieval with transverse translation diversity, where the diverse far-field intensity measurements are taken after translating the object relative to a known illumination pattern. Analytical expressions for the gradient of a squared-error metric with respect to the object, illumination and translations allow joint optimization of the object and system parameters. This approach achieves superior reconstructions, with respect to a previously reported technique [H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004)], when the system parameters are inaccurately known or in the presence of noise. Applicability of this method for samples that are smaller than the illumination pattern is explored.

Highlights

Image reconstruction by phase retrieval, referred to as coherent diffraction imaging (CDI), is a lensless imaging technique in which conventional image forming optics are substituted by computational image reconstruction [1,2,3,4,5,6,7,8,9]
It was shown that an iterative phase retrieval technique, named ptychographical iterative engine (PIE), could be used in this case to increase the field of view (FOV) of the reconstruction, make the algorithms more robust, and achieve superior reconstructions
Whereas PIE was only shown to work for objects larger than the diameter of the illumination pattern, we show that this form of diversity provides very robust reconstructions when the object of interest is smaller than the illumination pattern

Summary

Introduction

Image reconstruction by phase retrieval, referred to as coherent diffraction (or diffractive) imaging (CDI), is a lensless imaging technique in which conventional image forming optics (e.g. lenses, mirrors or holographic optical elements) are substituted by computational image reconstruction [1,2,3,4,5,6,7,8,9]. A very practical form of diversity for CDI, along with a robust reconstruction algorithm, was introduced by Faulkner and Rodenburg [19, 20] and was experimentally demonstrated for the optical and x-ray regime [21, 22] This form of diversity, applicable when the sample can be illuminated repeatedly without significant change or damage, consists of taking a sequence of far-field intensity patterns, for which the object is displaced transversely relative to an illumination pattern that is known a priori. It was shown that an iterative phase retrieval technique, named ptychographical iterative engine (PIE), could be used in this case to increase the field of view (FOV) of the reconstruction, make the algorithms more robust, and achieve superior reconstructions The success of this technique relies, on an accurate knowledge of the illumination pattern and the transverse displacements of the object. In this case the diverse measurements are obtained by moving the object within the transverse extent of the illumination pattern

Object translation diversity

Ptychographical iterative engine

Nonlinear optimization approach

Object contained within the illumination pattern

Conclusion