ANALYZING SHADOWGRAPH IMAGES: A NEW ALGORITHM

Abstract

A new algorithm for constructing shadowgraph images from approximate density fields is presented with the primary motivation of performing accurate laboratory shadowgraph analysis. Available image construction algorithms are noisy and produce discontinuous errors even for small gradient density fields. Discontinuity errors are serious, being indistinguishable from real optical focusing which occurs frequently. The new algorithm completely eliminates these errors. Image improvements are demonstrated for realistic synthetic refractive index fields. Favorable comparisons of the new algorithm are also demonstrated with laboratory shadowgraph of natural convection flows in a cavity which feature large density gradients. A second motivation of the paper is to accurately analyze approximate shadowgraph images derived from a linearized analytical model for refraction. The linearized shadowgraph images are correlated with the artificial shadowgraph images of the new algorithm. Preliminary results indicate that quantitative information from shadowgraph images of larger gradient density fields could be obtained by iterating about the linear solution.