Examples of optimal orthogonal systems of functions for the microwave absorption coefficient and refractive index

Systems of orthogonal vectors are determined, providing an optimal (in the statistical sense) approximation of the vertical distributions of the molecular absorption coefficient at characteristic microwave wavelengths associated with atmospheric windows and the absorption resonances of O₂ and H₂O, as well as the distribution of the refractive index of the atmosphere in the range 1 mm. Certain properties of the orthogonal vectors are analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 12, pp. 1742–1749, December, 1978.The authors are indebted to M. B. Zinicheva for running the computer calculations of the correlation matrices.