Optical velocimetry correction in Fabry-Perot measurements taken through cylindrically expanding shocked fluids with no dispersion

A correction is needed in interpreting optical velocity measurements made by reflected frequency versus time measurements through cylindrically expanding air or fluids. The reflected frequency seen by the velocimeter will be higher than it would be in a planar geometry, even if the fluid obeys the Gladstone–Dale model for the index of refraction versus compression. This has been pointed out by Wackerle, Stacy, and Dallman [Proc. Int. Soc. Opt. Eng. 832, 72 (1987)], who develop a general Lagrangian treatment of one-dimensional planar, cylindrical, and spherical geometries. Our work, developed independently, uses a different, very simple, and rigorous treatment for a special case of cylindrical geometry. It also provides physical insight into the processes that lead to this frequency change. The magnitude of the correction is very small for air, but for a realistic constant density versus radius model is about 5%–10% for fluids such as water, for cylindrically expanding shocks with radii of curvature near 3 cm.