The depth of the banana and the impulse stripe illumination for diffuse optical tomography

The stripe illumination lies between the illumination in the spatial-frequency domain and the point illumination. Although the stripe illumination has a periodic structure as the illumination in the spatial-frequency domain, light from the stripe illumination can reach deep regions in biological tissue since it can be regarded as an array of point illuminations. For a pair of a source and a detector, the shape of light paths which connect the source and detector is called the banana shape. First, we investigate the depth of the banana. In the case of the zero boundary condition, we found that the depth of the center of the banana is $d_{\rm SD}/(2\sqrt{2})$, where $d_{\rm SD}$ is the distance between the source and detector on the boundary. In general, the depth is about $0.3d_{\rm SD}$ when $d_{\rm SD}\approx2\,{\rm cm}$ and the ratio of refractive indices on the boundary is about $1.37$. Next, we perform diffuse optical tomography for the stripe illumination against forward data taken by Monte Carlo simulation. We consider an impulse illumination of the shape of a stripe. This time-resolved measurement is more informative than conventional continuous-wave measurements in the spatial-frequency domain.