Whole field spatial frequency analysis of double-or multiple-exposed PIV images

Speckle Velocimetry or high-image density PIV gives a velocity vector map of a twodimensional flow field by point-by-point spatial frequency analysis of local pattern at an interrogation spot in a double- or a multiple-exposed image of laser speckle or pseudo-speckle pattern generated by pulsed laser-light-sheet illuminations of a plane in the flow densely seeded with fine particles. The whole field spatial frequency analysis of the double- or multiple-exposed PIV image gives more useful information of the flow field. Optical Fourier transform is a conventional technique not only for the local spatial frequency analysis but for the whole field analysis. Filtering of spatial frequency is one of the typical techniques for the latter which can reconstruct a velocity contour or a component velocity contour map of the flow. Fundamentally this technique is a simple and efficient analogue method to get more information in the velocity field analysis of the flow than a digital image processing, but in practical applications the measurement is restricted to simple flows because of optical noise and low spatial resolution. In order to improve the technique, the fundamental characteristics of the filtering and the noise yielded in the filtering process must be investigated. Meanwhile, wavelet analysis can also be applied to the whole field spatial frequency analysis of PIV image. In this paper the filtering technique is examined by numerical convolution integral, and the results obtained are compared with ones obtained by the wavelet analysis.