Single-scattering optical tomography: Simultaneous reconstruction of scattering and absorption

We report theory and numerical simulations that demonstrate the feasibility of simultaneous reconstruction of the three-dimensional scattering and absorption coefficients of a mesoscopic system using angularly resolved measurements of scattered light. Image reconstruction is based on the inversion of a generalized (broken ray) Radon transform relating the scattering and absorption coefficients of the medium to angularly resolved intensity measurements. Although the single-scattering approximation to the radiative transport equation (RTE) is used to devise the image reconstruction method, there is no assumption that only singly scattered light is measured. That is, no physical mechanism for separating single-scattered photons from the rest of the multiply-scattered light (e.g., time gating) is employed in the proposed experiments. Numerical examples of image reconstruction are obtained using samples of optical depth of up to 3.2. The forward data are obtained from numerical solution of the RTE, accounting for all orders of scattering.

Figure 1

(Color online) Illustrating the quantities used in Eq. (3) and elsewhere. “BR” denotes broken ray.

Figure 2

(Color online) The proposed experiment geometry for simultaneous reconstruction of scattering and absorption coefficients. The rectangles represent the slices in which reconstruction is performed.

Figure 3

Reconstruction of the scattering (left) and absorption (right) coefficients for the sample A for various noise levels $n$. The rows in each panel correspond to the slices $x=6h$, $13h$, and $20h$ where the inhomogeneities are placed. Scattering and absorbing inhomogeneities are present in the sample simultaneously, and in the slices $x=6$ and $x=20$, they overlap. The top and bottom panels use different color scales (since they visualize different quantities) but all plots within the same panel utilize the same color scale.

Figure 4

Same as in Fig. 3 but for the sample B.

Figure 5

Same as in Fig. 3 but for Sample C.

Figure 6

Same as in Fig. 3 but for Sample D.