Singularities in Speckled Speckle: Statistics

TL;DR

This paper investigates the complex statistical properties of speckled speckle patterns generated by random optical fields with two correlation lengths, revealing anomalous distributions and densities of critical points through analytical and simulation methods.

Contribution

It introduces the concept of speckled speckle and provides a detailed analysis of their critical points, highlighting significant anomalies in their spatial arrangements and densities.

Findings

Anomalous spatial arrangements of critical points

Order of magnitude anomalies in their densities

Significant deviations in zero crossing densities

Abstract

Random optical fields with two widely different correlation lengths generate far field speckle spots that are themselves highly speckled. We call such patterns speckled speckle, and study their critical points (singularities and stationary points) using analytical theory and computer simulations. We find anomalous spatial arrangements of the critical points and orders of magnitude anomalies in their relative number densities, and in the densities of the associated zero crossings.