Focusing through random media: eigenchannel participation number and intensity correlation

TL;DR

This paper links the focusing contrast in random media to the eigenchannel participation number, providing a theoretical framework supported by microwave experiments to optimize focusing and imaging limits.

Contribution

It introduces a novel relationship between focusing contrast, eigenchannel participation, and intensity correlation, supported by experimental validation.

Findings

Contrast is proportional to 1 + N_{eff}

N_{eff} is the inverse of the intensity correlation degree

Experimental results confirm theoretical predictions

Abstract

Using random matrix calculations, we show that, the contrast between maximally focused intensity through random media and the background of the transmitted speckle pattern for diffusive waves is, \mu_N =1 +N_{eff}, where N eff is the eigenchannel participation number for the transmission matrix. For diffusive waves, N_{eff} is the inverse of the degree of intensity correlation, \kappa. The profile of the focused beam relative to the ensemble average intensity is expressed in terms of the square of the normalized spatial field correlation function, F(\Delta r), and \kappa. These results are demonstrated in microwaves experiments and provide the parameters for optimal focusing and the limits of imaging.