Physical optics treatment of the shadowgraph

We present an analysis of the shadowgraph method of visualizing convective flows based on physical optics, treating the refractive-index perturbation caused by the flow as a transmission grating. Various patterns in thermal convection of an isotropic fluid as well as normal rolls in electroconvection of a nematic liquid crystal are considered. The results differ significantly from those of geometrical optics, showing that use of the shadowgraph as a quantitative tool for amplitude measurements should not, in general, be based on geometrical optics.