The circular apeture is a system where only a small amount of the incident light can penetrate into the system. 

circular.gif (4734 bytes)      

(Left)  Schematic for a pinhole of radius R.  (Right)  Step function observed of the emitted light from the pinhole.

The Fraunhofer pattern for this system can be found as the following:

       (Fowles 118)

where u = y/R, and r = kRsinq.  The intensity for the Fraunhofer pattern can then be found by:

       (Fowles 118)

       When the above intensity equation is plotted in Mathematica, we can find the following theoretical Fraunhofer pattern.

      

(Left)  2D Fraunhofer pattern for the pinhole.  (Right)  3D Fraunhofer pattern for the pinhole.