Fluid flows are most often studied today by measuring the velocity fields using particle image velocimetry. This has been the standard approach for over thirty years and has proven to be an effective and reliable technique. However, recent work has shown that it is possible to produce measurements with the same equipment but much higher accuracy and detail by using a different method for processing the images. The aim of this project is to develop and validate a new algorithm to obtain velocity measurements from particle images to replace the current state of the art. The new algorithm will significantly advance the capabilities of fluid flow measurement systems employed in academia, industry, and national laboratories. The finished algorithms and validations will be disseminated to a wide range of potential users.<br/><br/>This research focuses on the development of a novel algorithm for velocimetry from pairs of images of tracer particles illuminated by a laser sheet. The new algorithm will substitute directly for the cross-correlation based approaches used in state-of-the-art particle image velocimetry processing software, but the approach does not require any new equipment, such as cameras or lasers, since the acquired images input to the software are the same for both algorithms. It is well known that even the most advanced correlation-based algorithms suffer from a loss in spatial resolution when computing the velocity field from images due primarily to the use of finite-sized interrogation windows employed during processing. The new method will utilize advanced mathematics coupled with the governing laws of fluid mechanics to form a robust, physics-inspired method that will address the shortcomings of current algorithms. The novel algorithm will allow researchers to measure velocities in turbulent flows with significantly greater accuracy, resolution, and dynamic range than has been possible to date, while using conventional experimental hardware. The vision for the end of the project is to disseminate the thoroughly tested, final version of the algorithm to the widest group of fluid dynamic experimenters as possible, after conducting a study to determine the optimal mode of distribution.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.