Experimental determination of the optical center of a convex elliptical/spherical, parabolic,or hyperbolic mirror (I think that covers all the conic sections).
1. We don't know where the optical center of the RC secondary mirror is, but we know that GSO does a good job figuring the mirrors, otherwise we wouldn't bother with these scopes at all.
2. A laser reflecting off of the secondary mirror at a fixed circular radius away from the optical center will be reflected at an identical angle. If we can control the parameters, we can use this fact to determine the optical center experimentally.
Here is the setup:
We have my RC6 scope with the secondary cell removed. It is mounted and stationary with a well-collimated Farpoint laser mounted in the focuser. We have the RC6 secondary cell mounted on a photo tripod ball head with a hand grip to allow adjustment of position. We have the ability to rotate the secondary mirror via it's distance adjustment ring (as long as we are careful not to rotate it too far out and have the whole thing fall to the floor).
I have the laser striking the secondary a distance from the center mark (around 18mm away from the center mark). I have the secondary adjusted so that the beam is reflected back directly on top of the laser source. I mark the spot where the beam is hitting the secondary with a Sharpie. I rotate the secondary 60°. If I simply rotate and mark every 60°, I'll just be making marks equidistant from the MECHANICAL center. That doesn't do me any good. But here's the trick: I make a fine adjustment with the hand grip to re-center the reflection back on the laser source with each 60° rotation. It only takes a very small adjustment. This small centering adjustment creates the offset between the mechanical center and the center of the circle you've already figured out that I'm putting together that rings the optical center. I mark the spot again where the beam hits the secondary. I repeat this process until I've made 6 roughly equally spaced marks on the secondary, re-centering the reflection on the laser each time with a small adjustment. I photograph the secondary.
I wipe away the marks with some 91% isopropanol because Sharpie on my secondary? Yuck.
So now we have the photo of the secondary:
Making a fine mark on a mirror with a Sharpie isn't as easy as you would think. Sometimes I nailed it, other times I boogered it up. Where the mark is more a blob, I tried to make the center of the blob correspond to the laser dot. I overlaid a visual "best fit" circle over the marks on the secondary. I bisected the circle with 2 perpendicular lines across the radius, and there we have a sloppily experimentally determined optical center.
Yes, there is a LOT of room for improvement and I've not convinced myself that all assumptions are fundamentally sound. But the experiment did a pretty good job of approximating a circle, and the center did have an offset from the mechanical center mark of about 1mm. Not an authoritative test and pretty sloppily constructed. But perhaps not entirely useless either.