抄録
Cross-correlation function used in the binary image cross-correlation method developed by Uemura, T., Yamamoto, F., and Koukawa, M. is used without mathematical strict proof, although their method is thought to be convenient and efficient to analyze the particle images due to the high speed algorithm for particle identification. In the present study, the binary image crosscorrelation function is derived from mathematical foundations, and the generality is discussed. Since the velocity vectors are computed discretely at the particle positions, some interpolation methods are needed to rearrange the velocity vectors at the grid points in order to extract the other physical informations. The three following new mathematical interpolation methods (differential form of equation of continuity, integral form of equation of continuity, and boundary element method) are proposed in the present paper.
