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Mathematical background of statistical PIV evaluation

  • Markus Raffel
  • Christan E. Willert
  • Jürgen Kompenhans
Part of the Experimental Fluid Mechanics book series (FLUID)

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.

Keywords

Particle Image Velocimetry Intensity Field Particle Image Point Spread Function Light Sheet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Markus Raffel
    • 1
  • Christan E. Willert
    • 1
  • Jürgen Kompenhans
    • 1
  1. 1.Deutsche Forschungsanstalt für Luft-und Raumfahrt e.V.GöttingenGermany

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