Abstract
Present study considers the mathematical basis of PIV analysis for multiple-time-step image, which enables to obtain the acceleration and spatial derivatives of velocity field directly from the image information. The advantage of present approach is the possibility to get the spatial derivatives at the same time of velocity and acceleration. The algorithm keeps consistency of measurement principles whole through the procedure. Total consideration of mathematical background for higher-order terms enables to derive appropriate approaches for the modification of PIV algorithms and it will contribute to achieve higher performances.
