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Methods using transfer matrices of higher dimensionality, that is 3 × 3, 4 × 4, and 6 × 6, are also used in optical analysis. [9] In particular, 4 × 4 propagation matrices are used in the design and analysis of prism sequences for pulse compression in femtosecond lasers .
Mueller calculus is a matrix method for manipulating Stokes vectors, which represent the polarization of light. It was developed in 1943 by Hans Mueller . In this technique, the effect of a particular optical element is represented by a Mueller matrix—a 4×4 matrix that is an overlapping generalization of the Jones matrix .
The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium; a stack of thin films. [ 1 ] [ 2 ] This is, for example, relevant for the design of anti-reflective coatings and dielectric mirrors .
Finding the Jones matrix, J(α, β, γ), for an arbitrary rotation involves a three-dimensional rotation matrix. In the following notation α , β and γ are the yaw, pitch, and roll angles (rotation about the z-, y-, and x-axes, with x being the direction of propagation), respectively.
Visulization of flux through differential area and solid angle. As always ^ is the unit normal to the incident surface A, = ^, and ^ is a unit vector in the direction of incident flux on the area element, θ is the angle between them.
In applied mathematics, the transfer matrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable functions. Refinable functions play an important role in wavelet theory and finite element theory.
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Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances. The simplifying assumptions of geometrical optics include that light rays: