The relationship between integrating sphere and diffusion theory calculations of fluence rate at the wall of a spherical cavity.

The radiant energy fluence rate has been calculated at the wall of a spherical cavity, filled with a non-scattering and non-absorbing material, in a scattering and absorbing infinite medium, illuminated by an isotropic point light source at the centre. Two methods have been used: first, diffusion theory for a spherical geometry; second, integrating sphere theory using reflection factors obtained from diffusion theory for a plane semi-infinite medium illuminated by either a broad collimated perpendicularly incident beam or a broad diffuse incident beam. The two methods give identical results if the condition for the validity of the diffusion approximation is satisfied, that is mu(a) << mu(s) (mu(a) = optical absorption coefficient, mu(s) = scattering coefficient) and if also mu(eff)r1 >> 1, where r1 is the radius of the cavity and mu(eff) is the effective optical attenuation coefficient of the medium. Under the same conditions, the two methods also give identical results when the refractive index of the medium is larger than the refractive index of the material in the cavity. A numerical estimate using optical properties of human bladder indicates that the conditions for validity of the integrating sphere approach are nearly satisfied in whole-bladder photodynamic therapy.