Analytic calculation of the radiance in an anisotropically scattering turbid medium close to a source

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Abstract
We present a method to calculate the radiance due to an isotropic point source in an infinite, homogeneous, anisotropically scattering medium. The method is an extension of a well known method for the case of isotropic scattering. Its basic mathematical ingredient is the Fourier transform. Its great advantage is that it also works very close to the source and not just far away from it, as is the case with most other methods. In principle, the method works for any phase function that can be expanded in a finite number of Legendre polynomials. Here, the simple example of linear anisotropic scattering is worked out numerically and the result is compared with Monte Carlo simulation. Good agreement is found between the two.