An Exponential Model of a Three-Layered Medium Mimics Astrocytoma in Visible and Near-Infrared Ranges

Development of an exponential model of diffuse reflectance of three-layered media has been accomplished over visible and near-infrared ranges of wavelength. The optical properties of these layers were selected to mimic astrocytoma, grey matter, and white matter respectively. The medium was considered to be homogenous and mismatched boundaries were not taken into account. Then, the refractive index of these three layers was the same and equaled 1.4. The thickness of the tumor layer turned out to be varied between 100 µm and 1 cm and from 0.1 cm to 0.5 cm for the grey matter. The lowest layer, which mimics white matter, was considered to be a semi-infinite medium. Reflectance was estimated theoretically based on the Monte-Carlo algorithm and fitted to the developed model. Finally, the relative error of the presented model was varied from 10% at 450 nm to 1% at 1064 nm. The simplicity and robustness of the presented model make it a good choice for estimating reflectance and reproducing the thickness of the upper layer in real-time.