New indices of coherence for one or two-dimensional fields

TL;DR

This paper introduces new coherence indices for stationary fields that quantify their similarity, extending the concept of correlation to optical coherence with invariance under basis changes.

Contribution

It proposes novel, basis-invariant indices of coherence for one- and two-dimensional stationary fields, addressing their asymmetry and non-uniqueness.

Findings

Indices range from 0 to 1, indicating uncorrelation to linear dependence.

Indices are generally not symmetric or unique.

Illustrations demonstrate the application to 1D and 2D fields.

Abstract

The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article, we attempt to measure the proximity of two stationary fields by a real and positive number between 0 and 1. The extremal values will correspond to uncorrelation and linear dependence, similar to a correlation coefficient which measures linear links between random variables. We show that these "indices of coherence" are generally not symmetric, and not unique. We study and we illustrate this problem together for one-dimensional and two-dimensional fields in the framework of stationary processes.