Turbulence-preserving interpolation of aero-optical wavefront data using radial basis functions: application and fractal analysis

Abstract

Spatial interpolation using radial basis functions (RBFs) is compared with standard natural neighbor interpolation for the purpose of populating dead zones in optical path difference (OPD) wavefront data collected through aero-optics turbulence. Both methods, and some other commonly used basis functions, are described in detail. These candidates are applied to experimental subscale turbulent wind tunnel data collected with a conformal window hemispherical turret over a range of turret look-back angles spanning 60 deg to 135 deg. Interpolation performance is evaluated using both OPD magnitude and fractal (Hurst exponent) analysis. Interpolating aero-optical OPDs using the thin-plate RBF reduces the symmetric mean absolute percent error of the OPD magnitude and the Hurst exponent by an average of 28% and 50%, respectively, compared with the natural neighbor interpolation method. The improved interpolation accuracy should likewise increase the quality of subsequent postprocessing analysis requiring uniformly populated rectangular regions as inputs, such as optical flow algorithms. A MATLAB implementation of the pseudocubic spline RBF is provided.