View source for Overfill

==Mathematical representation==
The fraction of power {{math|''P''<sub>trans</sub>}} transmitted through a circular aperture of radius {{math|''r''}} for a Gaussian beam with a {{math|1/''e<sup>2</sup>''}} beam waist of {{math|''w''}} is given by<math display="block">P_{\text{trans}} = P_{\text{total}} \left( 1 - e^{-2r^2/w^2} \right).</math>In an overfill condition where {{math|''w''}} is significantly larger than {{math|''r''}}, the transmitted power becomes a small fraction of the total, but the intensity profile within {{math|''r''}} approaches a constant:<math display="block">\lim_{w \to \infty} I(r) = I_{\text{max}}.</math>