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We probe volar-side fingertip capillary beds with near-infrared laser light and collect Raman, Rayleigh, and Mie scattered light and fluorescence. The results are interpreted using radiation transfer theory in the single-scattering approximation. The surface topography of the skin is modeled using the Fresnel equations. The skin is treated as a three-layer material, with a mean-field treatment of tissue composition and related optical properties. The model, with a reasonable choice of tissue parameters, gives a remarkably accurate account of the features of actual measurements. It predicts the optimal values for the incident angle of the laser beam and the distance between beam and detector. It explains the correlated temporal changes in the intensities of elastically and inelastically scattered light caused by heart-driven pulses and why they are out of phase. With appropriate boundary conditions, the model can be used to discuss the scattering from ridged skin extruded conformally into an aperture in a metal surface under constant light pressure. The probing results suggest an inherent regularity and similarity in the anatomy and composition of surface and subsurface tissues of a wide range of skin types.