We introduce a set of corrections to the integral equations of scattering theory within the diffusion approximation to the radiative transport equation. We use this result to obtain an image reconstruction algorithm for optical tomography with spatial resolution below the transport mean free path.
A geometrical optics approach (GOA) to the optics of the nematic liquid crystals whose optic axis (director) varies in two or three space dimensions is presented. Two examples of the GOA applications are considered: calculation of light transmittance (1) through a liquid crystal (LC) film with two-dimensional (2D) director which combines the concepts of in-plane switching and vertical alignment, and (2) through a three-dimensional (3D) LC cell associated with a homeotropic to multidomainlike transition (HMD cell). Important details of the GOA applications for both cases are described. The GOA results are compared with those obtained from the quasi-one-dimensional Jones calculus and the beam propagation method (BPM) where the latter is applicable. Comparison between the results of different methods of calculating the near zone electromagnetic field (the radiation at points just on the exit of the analyzer) as well as the far zone diffraction pattern is provided. It is found that the GOA is about as fast as the Jones method for calculating optical properties of LC films with any number of dimensions of director variations, yet the GOA has the advantage of being more accurate than the Jones calculus.