The preceding seven papers of this series present a systematic procedure for computing the effect of an optical system on the state of polarization of the light that passes through it. The M-matrices discussed in the first six papers represent the over-all effect of an optical system; the N-matrices described in Paper VII are essentially path derivatives of the M-matrices and represent the local optical properties at a given point along the light-path.
In this paper we suppose that the medium is an anisotropic crystal and note that the description of the local optical properties by the N-matrices must be closely related to the description of the local properties by the dielectric and gyration tensors that are employed in standard crystal optics. We find the exact relation between the N-matrix and the above-mentioned tensors. It is shown how one can compute the dielectric and gyration tensors from a knowledge of the N-matrices for several different directions of the light-path in the crystal. It is also shown how one can compute the N-matrix for any given light direction from a knowledge of the dielectric and gyration tensors; the computation entails finding the square root of a two-by-two complex matrix.
Taken together, the eight papers of this series present a compact and systematic procedure for the solution of problems in crystal optics. The N-matrices have the advantage that circular birefringence and circular dichroism are treated in the same framework used for linear birefringence and linear dichroism.
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