Effectiveness of Iterative Algorithms for Recovering Phase in the Presence of Noise for Coherent Diffractive Imaging

Abstract

Methods of coherent diffractive imaging (CDI) rely on iterative algorithms to reconstruct the complex exit-surface wave (ESW) of the object being imaged from the measured diffraction intensity only. In this thesis we investigate by simulation the artifacts on reconstruction when noise are present in the measurement. We first confrmed the results obtained by Williams et al. [1, 2, 3] for plane-wave CDI, for reconstructions from simulated measurement data with various amount of shot-noise, non-sample beam scatter and background levels. Two kinds of iterative reconstruction algorithms were tested, error-reduction (ER) and hybrid-input output (HIO). An analogous examination of the effects of noise for Fresnel coherent diffractive imaging (FCDI) was then undertaken. The technique of FCDI requires a separate algorithm to recover the phase of the illumination, prior to the use of ER or HIO algorithm for obtaining the ESW of the object. Thus we simulated measurements of both the illumination and the diffracted intensity, with a certain amount of shot-noise and additionally equal or different amounts of background noise. This resulted in distinct artifacts on the reconstruction for the different noise types. A wide range of different error metrics was investigated for each noise type and level, for the reconstructed ESW and it's derived transmission function. Our results show that certain error metrics are very useful for identifying a good estimate to the generally unknown true solution, in any amount and type of noise tested. These observations will help to design FCDI experiments for optimal use of the available signal and to design new algorithms for iterative phase retrieval that can be applied to noisy data.