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.