TESTING SCATTERING MATRICES - A COMPENDIUM OF RECIPES

Scattering matrices describe the transformation of the Stokes paramete rs of a beam of radiation upon scattering of that beam. The problems o f testing scattering matrices for scattering by one particle and for s ingle scattering by an assembly of particles are addressed. The treatm ent concerns arbitrary particles, orientations and scattering geometri es. A synopsis of tests that appear to be the most useful ones from a practical point of view is presented. Special attention is given to ma trices with uncertainties due, e.g., to experimental errors. In partic ular, it is shown how a matrix E(mod) can be constructed which is clos est (in the sense of the Frobenius norm) to a given real 4 x 4 matrix E such that E(mod) is a proper scattering matrix of one particle or of an assembly of particles, respectively, Criteria for the rejection of E are also discussed. To illustrate the theoretical treatment a pract ical example is treated. Finally, it is shown that all results given f or scattering matrices of one particle are applicable for all pure Mue ller matrices, while all results for scattering matrices of assemblies of particles hold for sums of pure Mueller matrices.