A diffusion model of noninvasive absorption spectroscopy was used to determine how the change in signal resulting from a point absorber depends on the position of that absorber relative to the source and detector. This is equivalent to calculating the relative probability that a photon will visit a certain location in tissue before its detection. Experimental mapping of the point-target response in tissue-simulating materials confirmed the accuracy of the model. For steady-state spectroscopy a simple relation was derived between the mean depth visited by detected photons, the source-detector separation, and the optical penetration depth. It was also demonstrated theoretically that combining a pulsed source with time-gated detection provides additional control over the spatial distribution of the photon-visit probability.