Phase retardation of both extraordinary and ordinary polarized rays passing through a liquid crystal (LC) cell with homogeneous and inhomogeneous LC director distribution is calculated as a function of the LC pretilt angle θ₀ on the cell substrates in the range 0 ≤ θ₀ ≤ 90°. The LC pretilt on both substrates can have the same or opposite direction, thereby forming homogeneous, splay, or bend director configurations. At the same pretilt angle value, the largest phase retardation ΔΦ is observed in splay LC cells, whereas the smallest phase retardation is observed in bend cells. For the θ₀ values close to 0, 45°, and 90°, analytical approximations are derived, showing that phase retardation depends on LC birefringence variation.

Optical and electro-optical methods of liquid crystal (LC) director pretilt angle measurement are described for LC cells with homogeneous and inhomogeneous LC director distribution. The LC pretilt on both LC substrates can have the same or opposite direction. The phase retardation difference of both extraordinary and ordinary polarized rays passing through an LC cell with homogeneous and inhomogeneous LC director distribution has been calculated versus the LC pretilt angle θ(0) on the cell's substrates in the range 0≤θ(0)≤90°. The experimental procedure for phase retardation difference determination by measurement of the LC cell transmission between crossed polarizers for cells with LC tilted alignment is described. The method developed can also be used in optical compensator design.

New optical and electro-optical methods of LC director average tilt angle measurement are described in LC cells with homogeneous and inhomogeneous LC director distribution. The LC pretilt on both LC substrates can have the same or opposite direction. Both LC pretilt angle and polar anchoring energy values have been measured for both polar and weak polar liquid crystal materials on aligning films of organosilicon compounds (OC) of different molecular structure. The method developed can be used also in optical compensator design.

The phase retardation difference, ΔΦ, is calculated for hybrid liquid crystal (LC) cells as a function of LC pretilt angles, θ0(1), θ0(2), on the opposite substrates of the cell for the case of an arbitrary angle of light incidence in the range from 0 to 90°. An LC director configuration is suggested for its application in optical compensators. Design and fabrication methods of hybrid aligned nematic (HAN) cells with an arbitrary LC pretilt angle are described. The LC pretilt angle is measured in the HAN cells with a given planar or vertical LC alignment on one of the substrates.

Liquid crystal (LC) director distribution and optical transmission for different types of heterophase systems with different LC boundary conditions is simulated. The first type is a transparent isotropic material with spherical or cylindrical liquid crystalline objects. There are polymer dispersed liquid crystal, LC fiber, lyotropic LC in polarizing films, LC in microgroove and nanogrooves and pores. The second type is an LC layer incorporating an isotropic transparent or non‐transparent object like microparticles and nanoparticles, spacers, protrusions in multi‐domain vertical alignment LC display et al. The system parameters' influence on LC display performances is discussed.