New indices of coherence for one or two-dimensional fields

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.Comment: 14 pages, 5 figures, 10 example

Modelling attenuation and velocity of ultrasonics in reconstituted milk powder

In the context of food quality control, ultrasonics provide proven methods which are able to replace manual controls. The latter are subject to the lack of objectivity of human judgement. Automatic control increases reliability and reduces costs. This paper revisits data coming from ultrasonics through reconstituted milk powder. Two characteristics are studied using five productions of a well known manufacturer. Measured attenuation and dispersion of ultrasonics are explained through stable probability laws and random propagation times. We have proved elsewhere that this model is available in many propagation problems,in acoustics, ultrasonics and in the electromagnetic world.Comment: 13 pages, 11 figure