Optical flow of non-integer order in particle image velocimetry techniques

High resolution particle image velocimetry (PIV) is an experimental method that has recently improved the measurement of particles velocity in flows after the advent of high resolution cameras. Nonetheless, the improvement in spatial resolution, the accuracy and performance of the velocity measurement techniques developed so far, are prone to improvements by new mathematical tools. As the current techniques are based on conventional calculus, the non-integer order or fractional calculus is becoming a more attractive technique since it predicts better than conventional calculus several phenomena in areas like complex fluids, mechanics and electrodynamics, among others. In this article, three main optical flow algorithms used in PIV are expressed in terms of fractional calculus for improvement of their performance in velocity measurements. The experimental results show the accuracy improvement obtained from the use of fractional calculus for velocity measurements.