I am currently reading this book by Mireille Levy. It says (on page 40) that the Gaussian beam pattern with half-power beamwidth $\beta$ is gien by:
where $A$ is the normalization constant, $\theta$ is the elevation angle and $\beta$ is the half-power beamwidth.
The context is source modelling of the initial vertical field in parabolic equation modelling. I want to understand this equation and understand where it comes from, but I can't find any information online. Could anyone derive it to me or point me to some source, so I can understand it better? Thanks.