I'm not that confident the tailstock on the lathe will be very near the axis…
ANyway you asked for pictures:
This is the bit of microscope, the one existing rod is in place, screwed in a the point arrowed. It IS steel of some sort that it goes into. As you can see the rod goes through a large hole. Quite why they break I don't know.

It's moving a filter cube in the fluorescence illumination head of a 'scope. There are two filters and a dichroic mirror in the cube. You use light of wavelength X, which reflects through the objective lens onto the subject, which you preload with fluorophores which emit at a different wavelength Y. None of X gets up the eyepiece / camera, so you only see your excited bit of subject, emitting in its own colour. Then you use a different excitation wavelength and cube and different fluorophore, for a different bit of your subject. The light source is usually a mercury arc lamp, though LEDs are replacing them because they're made with a narrow colour bandwidth.
Normally you tag a protein or drug or whatever so you can see where it's got to. You can tag cancer cells or TB cells, or things smaller than a wavelength of light. They emit so you know they're there.
Here's a picture c/o Zeiss of a bit of gut, with ten different fluorophores and sets of cubes/filters.

Edited By Chris R 1 on 25/01/2019 01:46:02
Edited By Chris R 1 on 25/01/2019 01:49:03