The intention of this exploration was to demonstrate the usefulness and effects possible with non-uniform bokeh.
Foliage was created by placing real leaves on a flatbed scanner, and mapping the resulting images to simple geometric meshes.
In optics, bokeh is the distribution of light across a lense's focus disk or the circle of confusion. Idiosyncrasies in manufacturing techniques, optical glass quality, and diaphragm (aperture) shape can create unique effects.
The above image makes use of an exponential distribution across the bokeh disk, which creates pronounced ringing effects. Further, it uses 22 aperture blades, creating a nearly-circular ring pattern.
The top image on the left similarly uses an exponential distribution, but instead of a round aperture, six aperture blades are used. This creates an effect similar to a lens with non-rounded aperture blades, resulting in hard edged, geometric shapes.
The second image on the left makes use of an inverse-exponential distribution across the bokeh disk, with a high power setting. This mimics the effect of a catadioptric system, however certain aspherical lenses are also capable of producing this effect, sometimes referred to as "soap bubble bokeh," due to the apparent visual similarity.
The final image on the left demonstrates a uniform distribution. No ringing effects are produced, and bokeh is perfectly circular.
In terms of practical use, I used this scene to compare bokeh distributions in contribution to the LuxCoreRender open source project.
As a result of the submission of this comparison, non-uniform bokeh was added to the program, giving users further render options.
LuxRender 1.2.1 & Blender 2.65a