The recovery of polarized apparent temperature distributions of flat scenes from antenna temperature measurements

The reception theory for quasi-monochromatic partially polarized emissions is employed to describe the antenna temperature when observing a flat scene from within or above an absorbing/ emitting atmosphere. When the polarization aspects of the antenna and scene are carefully observed, the resulting integral expression for the antenna temperature differs significantly from that reported for polarization invariant temperature distributions. It is observed that the antenna couples to both emitted surface polarizations, and the phase character of the antenna introduces a term involving the product of the polarized and cross-polarized antenna patterns. A matrix approximation of the integral expression is suggested and developed as a means for inverting polarized antenna temperature observations for the underlying partially polarized apparent temperature distributions. The resulting matrix formulation is interpreted and special cases are treated. By means of sample cases, the cross-coupling effect between the antenna and the emitted field polarization vectors is illustrated. When the polarization aspects of the radiometer and the scene are ignored, inversions for the apparent temperature are shown to suffer appreciably even for a highly efficient antenna. The sensitivity of the matrix inversion technique to errors in the measurement vector is also examined.