Quantitation of absorbing substances in turbid media such as human tissues based on the microscopic Beer-Lambert law

We derive analytic expressions in the form of an implicit function for the system size, volume shape, refractive-index-mismatched boundary, and source-detector separation, to determine the concentrations of absorbing substances in highly scattering media such as human tissue. The basis of our derivation is the microscopic Beer-Lambert law that holds true when we trace a zigzag photon path within the medium. The validity of our prediction is evaluated by Monte Carlo simulations for transmission and reflection from an infinitely wide, 20-mm-thick slab. Quantitative spectroscopies are compared by measuring a tissue-like, liquid phantom using photon density waves modulated at 100 MHz, where the absorption of the medium is changed (the absorption coefficient mu(a) approximate to 0.002-0.02 mm(-1) at 786 nm). (C) 1997 Elsevier Science B.V.