On the Occurrence of Systematic Errors in Cross-Correlation based Measurements for Aerodynamics

Abstract

The scope of this paper is the investigation of sub-pixel displacement estimation in crosscorrelation based measurement techniques used in aerodynamics. We will show, that a systematic error will occur when using one-dimensional sub-pixel displacement estimation algorithms to decompose elliptically shaped correlation peaks. First, an analytical description of this error will be derived and it will be shown, that it can lead to a systematic influence of more than one pixel. Additionally, a general linear two-dimensional Gaussian algorithm based on least squares estimation will be presented to allow for sub-pixel displacement estimation of elliptically shaped correlation peaks without any significant bias error. The performance of the here presented algorithms for sub-pixel displacement estimation, as well as algorithms provided by commercial software packages, will be tested with artificial image pairs of random dot patterns.