Mathematical Background of Statistical PIV Evaluation

  • Markus Raffel
  • Christian E. Willert
  • Fulvio Scarano
  • Christian J. Kähler
  • Steven T. Wereley
  • Jürgen Kompenhans


In this chapter, a simplified mathematical model of the recording and subsequent statistical evaluation of PIV images will be presented. For this purpose the mathematical representation of the particle image locations, the image intensity field and the mean value, the auto-correlation, and the variance of a single exposure recording are described. Then, we analyze the cross-correlation of two frames of singly exposed recordings and expand the theory for the evaluation of doubly exposed recordings.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Markus Raffel
    • 1
  • Christian E. Willert
    • 2
  • Fulvio Scarano
    • 3
  • Christian J. Kähler
    • 4
  • Steven T. Wereley
    • 5
  • Jürgen Kompenhans
    • 1
  1. 1. Institut für Aerodynamik und StrömungstechnikDeutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)GöttingenGermany
  2. 2. Institut für AntriebstechnikDeutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)KölnGermany
  3. 3.Department of Aerospace EngineeringDelft University of TechnologyDelftThe Netherlands
  4. 4.Institut für Strömungsmechanik und AerodynamikUniversität der Bundeswehr MünchenNeubibergGermany
  5. 5.Department of Mechanical Engineering, Birck Nanotech CenterPurdue UniversityWest LafayetteUSA

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