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The modified Beer-Lambert law (MBL) and the spatially resolved spectroscopyare used to measure the tissue oxidation in muscles and brains by thecontinuous wave near-infrared spectroscopy. The spatially resolved spectroscopypredicts the change in the concentration of the absorber by measuring the slopeof attenuation data according to the separation and calculating the absorptioncoefficients of tissue on the basis of the slop in attenuation at theseparation distance satisfying the linearity of this slop. This study analyzedthe appropriate source-detector separation distance by using the diffuseapproximation resolution for photon migration when predicting the absorptioncoefficient by the spatially resolved spectroscopy on the basis of thereflective image of the tissue. We imagine the 3 dimensional attenuation imagewith the absorption coefficient, reduced scattering coefficient and separationdistance as its axes and obtained the attenuation data cube by calculating theattenuation on a certain interval of coordinate on the basis of the diffuseapproximation expression. We predicted the separation distance appropriate forthe application of the spatially resolved spectroscopy by calculating andanalyzing the first derivatives and second derivatives of attenuation withrespect to the coordinates and also doing the differential pathlength factorsand first derivatives of the attenuation with respect to the absorptioncoefficient from the attenuation data cube. When analyzing the hemoglobinderivatives in tissues, the appropriate separation distances are 3-5cm and thevalue of its corresponding differential pathlength factors are from 3.5 to 5.These data agree with the preceding experimental data.

Theoretical prediction of the source-detector separation distance suited  to the application of the spatially resolved spectroscopy from the  near-infrared attenuation data cube of tissues