Solution to reverse refraction problem
Abstract
The reverse refraction problem (determination of radial profile of refractive index in planetary atmospheres, such as Earth, from radio probe measurements) is formulated as a bistatic radar problem for a spherically symmetric medium. The modified refractive index n(r)r (aradius at which the refraction angle as function of relative distance is measured) is assumed to reach extreme values at the upper boundary r sub 1 or at observation level. Before the corresponding Fredholm equation of the first kind can be solved, it must be wellconditioned in the Tikhonov sense. This is done here by two quasioptimum integral transformation variants with respect to the measurement function and subsequent simplified regularization. The first method is two successive Fourier cosine transformations followed by an Abel transformation, with the possibility of discrete Fourier transformations and numerical Abel transformation. The second method is twofold discrete Fourier transformation. Both yield solutions readily evaluated by simple algorithms. Regularization is effected by approximating functions satisfying the two fundamental conditions for convergence required of the measurement function.
 Publication:

USSR Rept Electron Elec Eng JPRS UEE
 Pub Date:
 April 1985
 Bibcode:
 1985RpEEE....R...1P
 Keywords:

 Indexes (Ratios);
 Multistatic Radar;
 Planetary Atmospheres;
 Refractivity;
 Algorithms;
 Convergence;
 Fourier Transformation;
 Mathematical Models;
 Optimization;
 Communications and Radar