Nick Cook, University of North Carolina, Chapel Hill


Light paths in a fluid medium of varying density: forward and inverse problems

Abstract: The density of a fluid in a tank often varies spatially and temporally, resulting in a proportional variation of the index of refraction. This causes light to take warped paths to an observer, and objects in the fluid will appear distorted and often in multiple copies. We investigate the case of a diffusive medium with a low density layer on top of a higher density layer. We have derived a second order nonlinear differential equation for ray paths in this medium, determined by the density profile: an error function fixed by four parameters. The "forward problem" of finding the light paths is solved by specifying these four parameters. An "inverse problem" for this equation is to infer the parameters of the density profile given partial information about the light paths. A solution to this problem would provide a non-invasive tool for the measurement of fluid density.

Mentors: Roberto Camassa, Richard McLaughlin, Peter Mucha (University of North Carolina, Chapel Hill)