Would a perfectly collimated laser beam have a flat intensity distribution? I'm trying to simulate a collimated laser beam in some FORTRAN and am wondering about the intensity distribution of a perfectly collimated beam: would it be a flat distribution (equal intensity across the beam) or it would be more of a gaussian? I know that a perfectly collimated beam wouldn't disperse, but would this translate to equal intensity across the beam?
 A: Collimation means that all pencil ("bundle") of light rays emitted from one specific point in the object plane is "translated" by the collimator to a pencil of rays that have a specific angle.
In this case, the object is the output surface of the laser cavity or the output of an optical fiber.
Imagine you have a point light source, then a collimator could create a beam that consists of rays of only one angle, and a homogeneous intensity distribution would be possible. Such a light source doesn't exist, though.
Additionally, diffraction laws make it impossible to create a light source that emits light at only one angle, so even if you'd try to eliminate the need for a collimator by fixing the problem at the source, that's not possible.
By the way, the best physically possible light source (i.e. with minimum divergence) actually has a Gaussian intensity profile (in far-field approximation) and its divergence angle $\theta$ is
$$
\theta = \frac \lambda {\pi w_0},
$$
where $\lambda$ is the wavelength and $w_0$ is the beam waist (i.e. the emitter diameter or the collimator output diameter, depending on which divergence angle you're interested in).
A: "Top hat" optics can provide a nearly flat intensity distribution across a beam.  A Gaussian beam is nearly flat near its center, so simply passing it through a circular aperture yields a nearly flat beam.  A beam that is slightly nonuniform can be corrected by passing it through a customized gray-level filter to reduce intensity in the high-intensity regions.  In practice, you can create a beam with intensity pattern and/or phase pattern you want, using a combination of phase and intensity spatial light modulators.
