The Minimum Spanning Tree method applied to the study of optical speckle fields: spatial characterization of a Gaussian transition and its phase singularities

Abstract

The optical speckle field generated by the scattering of a laser beam on a rough surface contains useful information about the surface properties especially in the case of the incident beam illuminates only a few correlation cells of the surface roughness. The study of the transition from the non Gaussian to the Gaussian regime of the speckle field can increase the amount of accessible information concerning the surface roughness. The probability density function of intensity is helpful to characterize an optical speckle field, but we do not obtain information about the qualification of spatial distribution of the field. To qualify this spatial intensity distribution, we propose to use the Minimum Spanning Tree methodology. From the tree constructed from the set of points of the local maxima of the intensity distributions in an observation plane, we determine the mean and the standard deviation of the edges length of the tree and we qualify the distributions of this points (ordered, cluster, random...). Using high resolution images, we will present the first results concerning the study of a Gaussian transition of a speckle field by the Minimum Spanning Tree method and some preliminary results about the study of the spatial distribution of phase singularities in this transition. At the end, we will highlight that this new approach appears to be a very robust way to characterize the correlation length of a surface roughness and its illumination conditions, and offers a new criterion to study the optical speckle field.