First-order astigmatism in a telescope mirror is when the radius of curvature on one axis is observably different than it is on another axis. Instead of focusing a round out-of-focus image into a dot, you would see an oblong out-of-focus image inside of focus, and an oblong image outside of focus rotated 90 degrees from the one inside of focus. Furthermore, the focused image would not really be focused, but rather a mess. Avoiding astigmatism includes rotating the mirror and the tool frequently, grinding the back of the mirror flat if it is irregular or thin, and moving around the barrel without any preference to a specific direction on the mirror.
Testing for Astigmatism should be done when the mirror is still spherical. If it is not astigmatic when it is a sphere, it probably won’t be after you parabolize it [first-order astig]. If the mirror is astigmatic, you could theoretically polish it out with preferential cylindrical inducing strokes, but some say you should regrind from around 220 or 320 on up again. For that reason you should check the mirror for astigmatism as soon as it is able to reflect light. You wouldn’t want to put tons of hours into the mirror’s polish only to return to grinding. If all you did was an hour, then it wouldn’t be so bad to return to fix this issue.
One method of testing astigmatism is by placing a ball bearing next to a focuser, shining a tiny light on it, allowing the reflection of the image of that tiny light in the ball bearing to reflect back to the mirror, which then reflects back to the focuser, and then imaging the “star” in an eyepiece in the focuser. The ball bearing and the focuser have the mirror’s radius of curvature as their midpoint.
However, as well as this works for slow mirrors, the faster and wider the mirror gets, the closer the ball and the focuser need to be on-axis with the mirror, to the point where they run in to each other making the test difficult to perform. One solution is an on-axis beam-splitting astigmatism tester. Here is the optical path:
The light from a small flashlight shines onto a small ball bearing, which reflects light into a cube beam-splitter, illuminating the mirror and passing back through the beam-splitter into an eyepiece. Here is a photo of our astigmatism testing device:
If your mirror shows an astigmatism in the test, it is recommended that you rotate the mirror 90o so you can determine if the astigmatism is in the mirror or if it is in your test set-up or mirror stand. If the astig rotates as you rotate the mirror, then it’s in the mirror. If it stays put or changes by a different angle, then it could be in the test set-up or both the test set-up and the mirror, and you still don’t know. You will need to eliminate the test contamination to resolve if your mirror is a surface of revolution.
Once the mirror has been established as not being astigmatic, then we can continue on to figuring.