Abstract

We consider a set of scattering experiments in which a known scattering object is embedded in some known background medium, and is interrogated with monochromatic plane wave fields. The goal of the experiments is estimate the location of the object by means of noisy measurements of the magnitude of the wave fields transmitted by the object. These measurements are taken along straight lines that are outside the object's support volume and perpendicular to the direction of propagation of the incident waves. We employ maximum-likelihood estimation to address the problem, and we compute the log-likelihood function for additive, zero-mean, white Gaussian noise. We show that an image of this likelihood function can be generated directly from the measured intensity distributions by means of a filtered backpropagation algorithm.¹ This image closely approximates the exact log-likelihood function² generated from complete data (i.e., both the magnitude and the phase of the transmitted wave fields) as long as the measurements are performed sufficiently far from the scattering object. The Cramer-Rao bound for the estimation error is computed to measure the performance of the algorithm, and a number of examples employing both synthetic and experimental data are presented.

© 1990 Optical Society of America