Angularly selective mesoscopic tomography

We report three-dimensional tomographic reconstruction of optical parameters for the mesoscopic light-scattering regime from experimentally obtained datasets by employing angularly selective data acquisition. The approach is based on the assumption that the transport coefficient of a scattering medium differs by an order of magnitude for weakly and highly scattering regions. Datasets were obtained by imaging a weakly scattering phantom, which embeds a highly scattering cylinder of two to three photons' mean path length in diameter containing light-absorbing inclusions. Reconstruction results are presented and discussed.

Figure 1

(a)–(d) Scattered light from the numerical phantom in accordance with the Rayleigh phase function (${\epsilon }_1=0$ and ${\epsilon }_2=1$). (e)–(h) Scattered light when ${\epsilon }_1=1$ and ${\epsilon }_2=0$. Each row displays images for four angles $\phi =\{0,\pi /2,\pi ,3\pi /2\}$, where $\phi$ is the angle between the direction of the incident light, ${\mathbf{s}}_0$, and the camera normal, $\mathbf{n}$.

Figure 2

Experimental setup. D: diffuser; TL: telecentric illumination lens; TO: telecentric objective; P: phantom.

Figure 3

Diagram showing orientation and geometry of inclusions. (a) Highly scattering cylinder. (b) Two absorbing rods.

Figure 4

Images taken by the CCD camera. (a)–(d) Projection dataset $\phi ={180}^{\circ }$, where $\phi$ is the angle between the direction of the incident light, ${\mathbf{s}}_0$, and the camera normal, $\mathbf{n}$. The phantom was rotated by ${90}^{\circ }\times i$, where $i=\left\{0,1,2,3\right\}$. (e)–(h) The camera's images for $\phi ={124}^{\circ }$. The phantom was rotated by the same angles.

Figure 5

(a)–(d) Slices taken at heights $z=\left\{3,6,9,12\right\}$ mm showing reconstructed transport coefficient $\mu$. (e)–(h) Slices displaying reconstructed albedo $\lambda$ at the same heights.

Figure 6

(a) Isosurface of the transport coefficient $\mu$. (b) Isosurface of the albedo $\lambda$.

Figure 7

Simulated camera images of the phantom rotated by (a) ${160}^{\circ }$, (b) ${220}^{\circ }$, and (c) ${300}^{\circ }$, where reconstructed optical parameters were used. (d)–(f) Experimentally acquired images for the same rotation angles.