I recently decided to upgrade my microscope to LED illumination. Instead of building the power supply into the microscope itself, I put the power supply and current regulator circuit into a dedicated enclosure.
The circuit is a simple current regulator. Using a trimmer on the back of the enclosure the maximum current can be set, the potentiometer on the front will then regulate the current relative to this set limit. For DC power I'm using a standard 5V SMPS supply module, I've exposed the 5V rail through a DC jack on the back as well, so that I can also use the supply for further accessories. The LED that goes into the base of the microscope is connected using the DIN connector.