A New Algorithm for Computing the Radial Distribution Function in Three-Dimensional Measurement Volumes

The radial distribution function is a widely used statistical tool to characterize cloud droplet clustering from one-dimensional data-sets and in direct numerical simulations. In situ estimation of the radial distribution function from three-dimensional cloud droplet spatial positions is desired but hindered by numerical challenges in computing the radial distribution functions in 3-dimensional volumes with large aspect ratios (like those associated with modern digital holographic cloud particle imaging systems). Here, we present and test a new algorithm to compute the radial distribution function for convex 3-dimensional volumes that (i) makes optimal use of all recorded data, (ii) works in large aspect-ratio measurement domains, and (iii) enables computation of the radial distribution function on scales of the same order as the largest size of the measurement volume.