The Effect of roughness on the polarization of thermal emission from a surface

Abstract

The observation of the polarization of the thermal emission from a largely dielectric smooth surface may be used to infer the dielectric constant of the medium. The method was suggested by Troitsky [Astron. Zhur. 31, 511, 1954) for lunar observations, and has since then actually been used to evaluate the dielectric constant of the moon by Soboleva [Astron. Zhur. 39, 1124, 1962], Heiles and Drake [Icarus 2, 281 , 1963) , Baars et aI., [Astron. J. 70, 132 , 1965), and Davies and Gardner (this meeting). The same method basically was also used by Clark and Kuzmin [private communication) to study the surface material of Venus. Quite generally the radiometrically determined dielectric constants have been consistently lower than values derived from radar data by studying cross sections [Evans and Pettengill, J. Geophys. Res. 68,423 , 1963) and Evans, private communication [1965). In view of this persistent discrepancy, and because of many suggestions that surface roughness might play some part in the apparent disagreement, a fairly rigorous theory was developed for the emission of electromagnetic waves from a dielectric medium with an undulating boundary surface. In the following few paragraphs we briefly outline the basic procedure, state the several simplifying assumptions used, and finally present some numerical results in the form of diagrams in order to show the effect of surface roughness on the emission. The boundary between the dielectric material and free space is plane in the mean, but deviates from this plane by an amount Z (x, y) which depends on the position (x, y) on the mean plane. The random vari· able is taken to be Gaussian with zero mean and with root-mean-square value ho. The covariance of Z is defined by