On the applicability of asymptotic formulas of retrieving “optical” turbulence parameters from pulse lidar sounding data: I–equations

Abstract

Asymptotic solutions for the problem of retrieving the distribution of the structure characteristic of refractive index fluctuations from measurement data on the backscattering enhancement factor have been found. The solutions are written in terms of fractional derivatives of the enhancement factor in the case of receivers with a small aperture or via usual derivatives in the case of receivers with a large aperture. Properties of the kernel of the integral equation from which the asymptotic formulas follow have been studied in detail. Attention is paid to the fact that the kernel is oscillating in the general case. The kernel oscillations slightly affect the magnitude of the enhancement factor; however, their effect on derivatives of this factor can be significant.