Cell thickness and surface pretilt angle measurements of a planar liquid-crystal cell with obliquely incident light

Abstract

Two simple and fast optical methods are presented for the cell thickness and the surface pretilt angle measurements of a planar-oriented liquid-crystal (LC) cell, in which the LC director always lies in a plane of a Cartesian coordinate system. The methods employ an obliquely incident light propagating in the same plane containing the liquid-crystal molecules. Simple analytic formulas for the angular-dependent optical transmission are obtained. The phase retardation between the ordinary and extraordinary waves is used to measure the cell thickness with the use of a compensator. Independent data can be obtained for the cell thickness measurement by varying the angle of incidence of the incident light. The phase retardation-extremum method is used to measure the pretilt angle. Approximate formulas relating the pretilt angle and the angle of incidence corresponding to the transmission minimum are also obtained for the pretilt angle measurement for vertically and parallel-oriented LC cells with a small pretilt angle. For the parallel cell, the approximate formula agrees with that obtained by Birecki and Kahn [The Physics and Chemistry of Liquid Crystal Devices, edited by G. J. Sprokel (Plenum, New York, 1980), p. 115]. The methods are applicable to a planar LC cell, including the planar parallel nematic LC, homeotropic nematic LC cell, obliquely oriented nematic LC cell, and the planar-oriented ferroelectric smectic LC cell.