Abstract

The viewing characteristics of a liquid-crystal display (LCD) are most reliably computed using the 4 × 4 propagation-matrix formalism of Berreman [ J. Opt. Soc. Am. 62, 502 ( 1972)]. Each viewing direction is specified by a polar angle ψ, (angle of incidence) and an azimuthal angle η, which describes the display orientation with respect to the plane of incidence. To describe LCD viewing characteristics completely, propagation matrices must be computed for (ψ, η) pairs spanning the angular ranges 0 ≤ ψ, ≤ 90°, 0 ≤ η ≤ 360° or, equivalently, −90° ≤ ψ ≤ 90°, 0 ≤ η < 180°. We report some previously unrecognized relations between elements of liquid-crystal propagation matrices for positive and negative angles of incidence. Using these relations can, under certain conditions, reduce by almost a factor of 2 the number of computations needed to describe completely the viewing characteristics of an LCD.

© 1984 Optical Society of America

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