I am working on theoretical laser amplifier model for a pulsed input beam. However, my model is based on a top hat pump beam and laser beam profile, I want to update to a super gaussian and gaussian distribution respectively. The parameters I know are: beam radius w Pulse Energy E and therefore the Fluence of the seed beam if it is a top hot profile E/Area Pulse Width tp I know a gaussian beam takes the form f(r) = (-2*e^((r/w)^2))). My ultimate question is, for a guassian distribution, how do I calculate fluence E0 for the equation: E = E0*f(r) where E is the fluence (energy / area)? I feel this should be obvious, and I'm missing something very easy.