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.

中文翻译：

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利用径向基函数的航空波前数据的保流插值：应用和分形分析

将使用径向基函数（RBF）的空间插值与标准自然邻域插值进行了比较，目的是为了填充通过航空湍流收集的光程差（OPD）波前数据中的死区。详细介绍了这两种方法以及一些其他常用的基础函数。将这些候选值应用于在整个转塔回望角范围为60度至135度的范围内，使用共形窗口半球形转塔收集的实验性小尺度湍流风洞数据。使用OPD幅度和分形（Hurst指数）分析评估插值性能。使用薄板RBF插值航空光学OPD分别使OPD量级和Hurst指数的对称平均绝对百分比误差分别降低28％和50％，与自然邻居内插法相比。改进的插值精度同样应提高后续后处理分析的质量，这些后处理需要均匀填充的矩形区域作为输入，例如光流算法。提供了伪三次样条RBF的MATLAB实现。