PHOTON-MEASUREMENT DENSITY-FUNCTIONS .1. ANALYTICAL FORMS

This paper addresses the problem of tomographic reconstruction of abso rption and scattering parameters in the optical region from measuremen ts of transilluminated light. Specifically, the question of the sensit ivity of different measurement schemes on the boundary of an object to perturbations of the optical parameters within the object are address ed. The concept of a photon-sampling volume [Appl. Opt. 33, 448 (1994) ] and a photon-hitting density [Appl. Opt. 32, 448 (1993)] is extended to a photon-measurement density function (PMDF). The PMDF is derived from the Green's function of the diffusion equation and can be express ed for measurements such as the time-varying intensity, integrated int ensity, temporal moments, and phase shift, as well as for both absorpt ion and diffusion perturbations. Closed-form solutions are given for a number of these functions in infinite space, half-space, and slab geo metries. Example results are given in terms of three-dimensional image s. (C) 1995 Optical Society of America