From geometrical optics it is clear that we get the best collimation when the object lies at the focal point of the lens. I know that this carries over into cases where diffraction happens, but have no idea how to proof it. So how can we proof that the divergence angle is smallest at the focal point when we are considering both diffraction (at the lens) and the results from geometric optics?
EDIT-Clarification of what is been asked
Let us consider a more specific case:
Consider a source that creates a cone of light apex angle $\theta$, travelling towards an infinite lens. After passing through the lens the maximum angle between one of the diffracted (and refracted) 'rays' is $\theta_d$. I am trying to show that the position of the source that minimises the angel $\theta_d$ is when it is at the focal point. How can I show this?