Mathematical background of statistical PIV evaluation

Abstract

A detailed mathematical description of statistical PIV evaluation has been given by Adrian [36]. This early work from 1988 concentrated on autocorrelation methods and was later expanded to cross-correlation analysis [65]. Most of the characteristics and limitations of the statistical PIV evaluation have been described therein. The most complete and careful mathematical description of digital PIV has been given by Westerweel [7]. In this chapter a simplified mathematical model of the recording and subsequent statistical evaluation of PIV images will be presented. For this purpose the two-dimensional spatial estimator for the correlation will be referred to as the correlation. First, we analyze the cross-correlation of two frames of singly exposed recordings, then we expand the theory for the evaluation of doubly exposed recordings. The motivation for why auto- and cross-correlation methods are employed in PIV evaluation will be given in chapter 5.