Truncated correlations in video microscopy of colloidal solids

TL;DR

This paper investigates how truncating real-space correlations in video microscopy of colloidal solids affects mode analysis, providing theoretical insights and practical strategies to mitigate artefacts for experimental accuracy.

Contribution

It offers a theoretical analysis of correlation truncation effects and proposes windowing methods to reduce artefacts in mode spectrum studies.

Findings

Truncation modifies the observed mode structure.

Boundary conditions are affected by correlation truncation.

Windowing strategies can mitigate artefacts.

Abstract

Studies by video microscopy on fluctuating colloids measure the real-space cross-correlations in particle motion. This set of correlations is then treated as a matrix, in order to study the spectrum and mode structure. We show that in general the modes are modified by the truncation of the full real-space correlations. We perform a theoretical analysis of the truncation, find the boundary conditions imposed by the truncation, and propose practical windowing strategies to eliminate artefacts. We study the problem from various perspectives, to compile a survey for experimentalists.