Mueller calculus

Transmission by Anisotropic Media The Jones and Mueller Calculus... 

The basic concept of the Stokes-Mueller calculus is that the transformation of the state of a beam under the action of an optical element could unequivocally be described by multiplying its Stokes vector So by a matrix M (Mueller matrix) from the left. The resulting new Stokes vector Sr represents the altered state of the beam. 

Let us consider some examples for the application of the Stokes-Mueller calculus. 

The appearance of Stokes publication, in which the concept of a vector representation of the beam description parameters was introduced, renders back to 1852. It, however, has remained for many years unnoticed (Shurcliff, 1962). The need for a general systematic and effective procedure for solving the exponentially growing quantity of optical problems has led to the rediscovery of Stokes approach to polarized radiation. Mueller s contribution consists of developing a matrix calculus for evaluation of the four elements of the Stokes vector which are a set of quantities describing the intensity and polarization of a light beam. 

A macroscopic, quantitative way to analyze birefringence is through Jones (33-40) and Mueller (41) calculus and the Poincare sphere (42). Those tools are widely used in the optical industry and references on them abound. Another active field of birefringence applications is the combination of the technique with polymer rheology, called flow-birefringence (43,44). 

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