The Hartley transform applied to particle image velocimetry

Abstract

The measurement principle of particle image velocimetry (PIV) is based on cross-correlation analysis of flow images. By using the cross-correlation property and fast algorithm of the Fourier transform, the analysis in PIV can be implemented easily and quickly. The Hartley transform is an integral transform similar to the Fourier transform and has most of the characteristics of the Fourier transform. The Hartley transform also has some better properties and a faster algorithm than the Fourier transform. The cross-correlation property of the Hartley transform based on separable kernels is presented in detail and the application to PIV analysis is introduced. The advantage of the Hartley transform can be shown from the comparison of numbers of operations in theory and computation time in practice.