Diffuse reflection of light from a dense random medium using fibres dipped into the medium

Diffuse reflection of a narrow collimated light beam from a slab of a dense random medium is considered theoretically and experimentally for the case of the source and the detector fibres dipped into the random medium, as is the case for an endoscopic catheter. By use of the diffusion approximation, a simple and physically clear analytical expression is derived for the distribution of the diffuse reflectance of the light beam along the surface of the random medium slab. We include the effects of reflections from the top and bottom surfaces of the slab. The analytical expression derived predicts that, in the case of small absorption, the relative reflectance is a universal function defined by the geometrical parameters and is independent of specific properties of the random medium. The theoretical prediction is found to show good agreement with the results of measurements.