On the noise in statistics of PIV measurements

TL;DR

This paper analyzes the sources of noise in PIV turbulence measurements, identifying quantization and non-uniformity as key contributors, and discusses their statistical independence and dependence on particle count within interrogation volumes.

Contribution

It provides a detailed theoretical framework for understanding and quantifying noise sources in PIV measurements of turbulence.

Findings

Noise variances depend inversely on particle count in interrogation volume.

Quantization and non-uniformity noises are statistically independent across realizations.

Finite interrogation window filters the spatially distributed noise contributions.

Abstract

It is argued herein that when PIV is used to measure turbulence, it can be treated as a time-dependent signal. The `output' velocity consists of three primary contributions: the time-dependent velocity, a noise arising from the quantization (or pixelization), and a noise contribution from the fact that the velocity is not uniform inside the interrogation volume. For both of the latter their variances depend inversely on the average number of particles or images) in this interrogation volume. All three of these are spatially filtered by the finite extent of the interrogation window. Since the above noises are associated directly with the individual particles (or particle images), the noise between different realizations and different interrogation volumes is statistically independent.