Estimating Spectral Indices from Transforms of Discrete Representations of Density Functions

摘要

Structuring of plasma in the high altitude disturbed atmosphere can adversely impact the operation of optical detectors. This paper considers idealized functions of one variable that may represent scan functions that are obtained from three-dimensional optical sources observed by remote sensors. The authors establish the relationship between singular properties of these functions or their derivatives and the spectral index of their transforms, and describe the limitations on obtaining reliable spectral indices where there is no clear separation of scales in a spatial profile. The ability to extract a good estimate of the spectral index depends on the complexity of the spatial emission profile, the adequacy of resolution, and aliasing errors that necessarily result from the analysis. They illustrate these competitive effects by numerical examples using spatial profiles of a top hat, circular arc and trapezoid. (Author)