To find a diffraction pattern for a given aperture, you need to apply the theory of Fraunhofer diffraction.
To do this, define an aperture function in cylindrical coordinates as follows;
a(r) = 1 for r less than or equal to a.
a(r) = 0 for r greater than a.
Where a is the radius of the aperture.
The resultant diffraction pattern is a 2D Fourier transform of this function (i.e. the Airy function). I'm sure you can find the gory details of this calculation somewhere (or maybe post in the math forums).