Mike B wrote:

This is for a searchlight application where the light source shines
backwards into the reflector which then reflects the light forwards
producing a narrow beam.
The reflector needs to be about 2 to 3 inches in diameter with a focal
point about 2 to 3 inches in front.

Presumably this was possible in the days before CNC machinery, so how did
they do it?
If you have a lathe with calibrated dials, you can do this
with HNC - that's Human numeric control. You use a program
to print out a list of coordinates, then you turn the dials
of the crossslide and compound to the right settings, perhaps
every .010". After all that is done, then you use a Cratex
rubberized abrasive wheel in a die grinder or Dremel tool to
remove the ridges and then polish on the lathe with jeweler's
rouge. I did an ellipsoidal mirror for a 200 W Hg arc lamp
some years ago this way, it worked very well.

Jon