Analytic MTF Expression for a Turbid Medium

The multiple light scattering in a turbid medium degrades imaging through the medium. The degradation can be quantitatively described by the modulation transfer function (MTF). Knowledge of the MTF of a turbid medium is important for imaging system design, imaging processing, and related areas The MTF of a turbid medium is equivalent to the transmitted radiance distribution from the medium under isotropic diffuse illumination with unit intensity. By solving the radiative transfer problem we could obtain the MTF in full spatial frequency range and investigate effects of any kind of scattering parameters on the MTF. The radiative transfer problem in a typical turbid medium could only be solved numerically, and an explicit analytical expression of the MTF is impossible to be given in a general manner. A convenient analytical MTF expression is useful and necessary for application. The widely used MTF expression is obtained from the small-angle-approximation (SAA) analysis The SAA approximation is valid only for a rather narrow frequency range. Though the MTF is affected by the whole scattering properties of the turbid medium the SAA MTF expression depends only on the scattering and absorption optical thickness. An analytical MTF expression for a turbid medium is obtained as a function of some main scattering parameters. It is found that the analytical expression of MTF is with high accuracy at practical frequencies for a typical optical thickness.