Remote atmospheric probing on a line‐of‐sight path, using spatial filter concepts: 1. Theory

Abstract

A rigorous treatment is given to a spatial filtering method for remotely determining the transverse wind velocity and the atmospheric structure constant along a line‐of‐sight path, assuming a Kolmogorov spectrum of refractivity and weak scattering. The results are applicable from the millimeter‐wave range to the optical range for linear array configurations at either one end or both ends of the path. Various methods of signal detection are considered, such as coherent, quasi‐coherent (knowledge of relative phases), and incoherent. In order to determine the two parameters the integral for the time covariance or the spectrum of the wave fluctuations must be inverted. For simple arrangements of single elements or pairs of elements at the transmitting and receiving locations the inversion is ill conditioned and yields only three or four resolution cells along the path. A statement of the problem in spectral form for line apertures representing narrow bandpass‐type spatial filters leads to optimal orthogonality of the inversion problem. In the limiting case of ideally sharp spatial filters, the inversion is shown to degenerate into a simple one‐to‐one relationship between spectral measurements of the spatially filtered wave fluctuations and the values of the parameters at a specified location along the path. A subsequent paper will be devoted to an experimental application of the principle in the mm‐wave region.