Analysis of the conoscopic measurement for uniaxial liquid-crystal tilt angles.

Conoscopy as an optical method for accurate measurement of crystal tilt angles from interference figures is analyzed for the special case of uniaxial crystals. The displacement of interference figures is related to the crystal tilt angle in an explicit, noniterative manner that is accurate to within ~2%. The analysis applies to uniaxial nematic liquid-crystal monodomains and homogeneous crystals when a symmetrical center of the conoscopic interference figure is visible. The equations developed are also used to derive other previously reported expressions that are approximations with a limited range of applicability.