The scattering and absorption of light by randomly oriented, discretely scattering, red blood cells imbedded in a homogeneous plasma medium can be described by the P1 approximation to the one-speed transport equation, where the cells have the dual role of anisotropic sources for first scattering events and of scattering and absorption sites for subsequent scattering events. Equations for diffuse reflectance defined for a finite size receiver in the plane of a normally incident cylindrical photon beam are derived and compared with experimental data to fundamentally justify the basic sending-receiving characteristics of a fiber optic catheter model. A model of the fiber optic catheter used for the spectrophotometric measurement of oxygen content in blood is developed from the theory and compared with experimental results to further substantiate the theoretical approach.

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In vivo measurement of the oxygen saturation levels in blood may be obtained from relative amounts of backscattered monochromatic light at two different wavelengths, as measured with a fiber-optic catheter oximeter. Because of the short mean free path length of light in blood, the backscattering can be well approximated by a previously-derived, one-wavelength transport theory solution for the half-space searchlight problem. This solution, unlike simple diffusion approximations has the advantage that the boundary condition describing illumination of a localized area of blood by a monodirectional light beam can be rigorously satisfied. Sample calculations using the solution are compared with experimental values of the reflectance of blood.

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