Extended Area of Irradiation

The unconvenient equations of the former sections can be substituted by the much simpler /Vapproximation that is equivalent to classical diffusion theory. After integra- 

The total emitted fluorescence radiation without any reabsorption is then 

On diffuse irradiation, Eqs. (8.10) through (8.15) become much simpler since all terms with the factor (3/m - 2) vanish, j (3/m - 2)fiod/xo = 0. Helpwise, collimated irradiation under //o = 2/3 (ao = 48.2°) has the same effect, but only for weak absorption. With increasing absorption the light fluxes inside the sample deviate more and more from the condition of diffuse irradiation. It has been often shown that the two-flux model derived first by Schuster 30) and then by Kubelka and Munk(28) has formally the same analytical solutions as the Pi-approximation under diffuse irradiation. Kubelka 

For semi-infinite layers the radiation fluxes simplify to single exponentials 

For weakly absorbing, or weakly scattering, or very thin layers, the equations simplify to 

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Under an extended area of irradiation, Tc is only a function of z. Under spot irradiation the lateral coordinates also have to be treated as variables. For simplicity we use cylindrical Gaussian profiles and //o = 1. Then... 

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