Abstract
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 μa ≈ 0.002–0.02mm−1 at 786 nm).
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