Optical Quantitation of Absorbers in Variously Shaped Turbid Media Based on the Microscopic Beer-Lambert Law: A New Approach to Optical Computerized Tomography

To determine the concentrations of an absorber in variously shaped turbid media such as human tissue, we propose analytical expressions for diffuse re-emission in time and frequency domains, based on the microscopic Beer-Lambert law that holds true when we trace a zigzag photon path in the medium. Our expressions are implicit for the scattering properties, the volume shape, and the source-detector separation. We show that three observables are sufficient to determine the changes in the concentration and the absolute concentrations of an absorber in scattering media as long as the scattering property remains constant. The three observables are: the re-emission, the mean pathlength or group delay, and the extinction coefficient of the absorber. We also show that our equations can be extended to describe photon migration in nonuniform media. The validity of the predictions is confirmed by measuring a tissue-like phantom.