Coherent imaging without phases

TL;DR

This paper presents a method for imaging weak localized scatterers using only intensity measurements, reducing data acquisition and enabling phase retrieval for standard imaging techniques.

Contribution

It extends previous work by reducing the number of required illuminations and demonstrates phase retrieval in the paraxial regime for efficient imaging.

Findings

Imaging can be achieved with only 3N-2 illuminations.

In the paraxial regime, only six illuminations are needed.

Numerical simulations confirm robustness with noisy data.

Abstract

In this paper we consider narrow band, active array imaging of weak localized scatterers when only the intensities are recorded at an array with N transducers. We consider that the medium is homogeneous and, hence, wave propagation is fully coherent. This work is an extension of our previous paper, where we showed that using linear combinations of intensity-only measurements imaging of localized scatterers can be carried out efficiently using MUSIC or sparsity promoting optimization. Here we show the same strategy can be accomplished with only 3N-2 illuminations, therefore reducing enormously the data acquisition process. Furthermore, we show that in the paraxial regime one can form the images by using six illuminations only. In particular, this paraxial regime includes Fresnel and Fraunhofer diffraction. The key point of this work is that if one controls the illuminations, imaging with intensity-only can be easily reduced to a imaging with phases and, therefore, one can apply standard imaging techniques. Detailed numerical simulations illustrate the performance of the proposed imaging strategy with and without data noise.