| The circular apeture
is a system where only a small amount of the incident light can penetrate
into the system.
(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:
where u = y/R, and r = kRsinq. The intensity for the Fraunhofer pattern can then be found by:
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.