Applicability of Time Integrated Spectroscopy Based on the Microscopic Beer-Lambert Law to Finite Turbid Media with Curved Boundaries

Finite curved boundaries are unavoidable in the practical field of non-invasive tissue spectroscopy. This being the case, a technique derived from the microscopic Beer-Lambert law (MBL) can be applied regardless of what geometry is assumed. Here, experimental tests on a type of time integrated spectroscopy based on the MBL for a tissue-like phantom with curved boundaries are presented. The experiments employed a cylindrical liquid phantom 56 mm in diameter, which resembles a human forearm. Two independent measurements were made on the surface of the phantom at various absorption levels (the absorption coefficients of the phantom were from 2.45 × 10⁻³ to 4.12 × 10⁻² mm⁻¹ at 782 nm), one in the direction along the circumference and the other along the long axis of symmetry. In both cases, the absorber concentrations were successfully recovered within error values of a few percent using a single equation.