Robert W. Schmieder

Stokes-Algebra Formalism

A unified treatment of the algebra of Stokes parameters and the coherency matrix is presented. Explicit formulas are given which relate the Jones and Mueller matrix formulations to the coherency matrix, and to themselves. The general method involves the trace of products of matrices, and the algebra is both useful and capable of generalization.

Operator Formulation of Plane Mirror Systems

A terminology limited to point objects is introduced to distinguish between finite and infinite, transparent and opaque mirrors. A basic image-producing operator is defined, and its properties are examined in detail. An operational form of the basic operator is derived, two general definitions are presented, and a formal expression for the images of a system of plane mirrors is written. Some simple systems are analyzed in detail to illustrate the applications of the theory. Finally, indication is given of possible directions for future development of the subject, and of its relationship to existing mathematical theories.