Optimized diffusion approximation.

We show that the diffusion approximation (DA) to the radiative transport equation, which is commonly used in biomedical optics to describe propagation of light in tissues, contains a previously unexplored adjustable parameter. This parameter is related to the rate of exponential decay of the reduced intensity. In conventional theories, there are two distinct choices for this parameter. However, neither of these choices is optimal. When the optimal value for the parameter is used, the resulting DA becomes much more accurate near the medium boundaries, e.g., at the depth of up to a few ℓ, where ℓ is the transport mean free path (typically, about 1 mm in tissues). We refer to the new adjustable parameter as the reduced extinction coefficient. The proposed technique can reduce the relative error of the predicted diffuse density of the optical energy from about 30% to less than 1%. The optimized DA can still be inaccurate very close to an interface or in some other physical situations. Still, the proposed development extends the applicability range of the DA significantly. This result can be useful, for instance, in tomographic imaging of relatively shallow (up to a few ℓ deep) layers of tissues in the reflection geometry.