Mathematical background of statistical PIV evaluation
A detailed mathematical description of statistical PIV evaluation has been given by Adrian . This early work from 1988 concentrated on autocorrelation methods and was later expanded to cross-correlation analysis . 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 . 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.
KeywordsParticle Image Velocimetry Intensity Field Particle Image Point Spread Function Light Sheet
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