Estimating the refractive error in optical measurements of transport phenomena

Approximate methods for calculating the error introduced by the deflection of the light beam or refractive error in schlieren, shadowgraph, interferometric, and holographic measurements of transport phenomena are investigated. Relative error is reported for the well-known correction parabola and paraxial approximations as well as for a new first-order approximation in both a linear and nonlinear refractive index field. The first-order approximation is exact in a linear field but is in about the same error as the other approximations in the nonlinear field of a boundary layer. In many cases, actual optical data can be corrected for refractive errors by using the results presented.