We calculate the elements of the 4 × 4 matrix that completely describes the geometrical optic properties of a planar surface of an anisotropic crystal as an optical instrument. The linear and angular magnification submatrices clearly demonstrate the lack of rotational symmetry about the principal ray. The results also show that the astigmatism produced by the surface has in general, nonorthogonal axes. The calculations apply to crystals of arbitrary symmetry, surfaces of arbitrary orientation, and rays of arbitrary direction. The results are applicable to sound waves as well as light waves. Byproducts of this calculation are the ratio of solid angles of ray vectors inside and outside the crystals, as well as the demagnification of a source volume. These factors are combined to relate the ratio of scattered to incident power outside the crystal to the corresponding ratio inside the crystal for a general scattering experiment such as Raman or Brillouin scattering.
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