Optical computed tomography in a turbid medium using early arriving photons

We employ photon migration to image absorbing objects embedded in a turbid medium. For improved resolution, we use early arriving photons (a few hundred picoseconds in excess of the time of flight), a regime in which the diffusion approximation breaks down. Our image reconstruction method is based on extension of x-ray computed tomography (CT) to the optical regime. The CT algorithm must be generalized to take into account the distributions of photon paths. We express the point spread function (PSF) in terms of the Green's function for the transport equation. This PSF then provides weighting functions for use in a generalized series expansion method of x-ray CT. Experiments were performed on a turbid medium with scattering and absorption properties similar to those of human breast tissue. Multiple absorbers were embedded into the medium to mimic tumors. Coaxial transmission scans were collected in two projections, and the early-time portions were analyzed. Through accurate modeling, we could remove the blurring associated with multiple scattering and obtain high-resolution images. Our results show that the diffusion approximation PSF is inadequate to describe the early arriving photons. A PSF incorporating causality is required to reconstruct accurate images of turbid media.