Mr. Poole --
I ran across your discussions of Coolpix 4500 rings in photomicrography while surfing the Internet. I tried sending an e-mail earlier, but I don't think it went through.
I encountered the ring problem using the Coolpix 4500 with my Nikon Optiphot microscope. I found that setting up Koehler illumination eliminated the problem. Specifically, I think that proper adjustment of the microscope field diaphragm reduces or eliminates stray light reflections within the microscope objective, and that those stray light reflections with an improperly adjusted field diaphragm may contribute to the ring problem. The stray light reflections are clearly visible with a phase telescope as several concentric bright rings when the field diaphragm is left open wider than it should be. The field diaphragm must be adjusted with each change in objective to maintain the reduced internal reflections and Koehler illumination. I have no clue why the stray light contributes to the rings, assuming my observations are correct, but I have had no problem with rings since I started paying attention to Koehler illumination and proper adjustment of the field diaphragm.
I don't know what microscope you use, but, if it lacks a field diaphragm, this solution may not be helpful. I am not sure whether adjusting the condenser diaphragm alone does the trick.
I also have encountered the small, circular artifacts you described and photographed. I found that they were eliminated when I used compressed air to blow dust off the front element of the Coolpix 4500 lens and the top element of the eyepiece in the microscope photo tube.
I hope this is helpful. If you have learned more about the Coolpix 4500 ring problem, I would be interested in hearing about it.
fwgastrojim at gmail dot com