Different options are available. Most of the halogen bulbs operate on 6V, 12V and 24V supply. There is no need to rectifier the AC supply but step down transformer is needed. Also, industry also produce halogen bulb that operates directly on 230V or 110V.
The common power supply for hallogen microscopes is 6v and its not to differ between dc or ac current and i suggest u you can creat a dimmer for it between 6v to 24v range if possible
However the hallogen lamps is very warmer than other one and it possible to damage your microscope system and accuracy
In another word direct current as better than alternate 50hz current because of light stability