Optical invariants of LCD 'splay' retardation films

Retardation liquid crystal films with a profiled titled optic axis (splay films) of both nematic and discotic types are used as compensation films for twisted nematic displays (TN-LCD). A new method is developed to characterize retardation vs. inclination (retardation profile) of splay films by three parameters: "full retardation" $d^{\ast}{\triangle}n$, "inplane retardation" $R_0$ and "retardation difference" $R_d$ . Splay films with the same retardation profile but with different tilt profile (retardation invariants) are discovered. Splay films with different structure parameters but belong to the same retardation invariant have the same compensation opportunities for TN-LCD.