Frequency Domain Analysis of Photon Migration Based on the Microscopic Beer-Lambert Law

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Abstract
Exact analytic solutions for frequency domain responses of photon migration in variously shaped turbid media are derived based on a model in which the microscopic Beer-Lambert law holds. We show that the system function specified by the Fourier transform of the impulse response is a regular function, and that the temporal or spatial changes in the macroscopic absorption coefficient and the concentration of the absorber can therefore be determined from macroscopic observables such as amplitude, phase and modulation frequency of the probe light. The feasibility of using this technique in spectroscopy to determine the absolute concentration of an absorber in turbid media is also discussed. The advantage of these methods is that we do not need to take the boundary conditions into account. Similar approaches may also yield simple techniques to determine physical properties in various scientific fields.