I'm parabolizing my telescope mirror - I've ground it to a sphere shape, and now I'm grinding a tiny bit more to change its shape precisely into a parabola.

I've done 3 grinding sessions for a total of 34 minutes of grinding. Here's a Ronchi picture of my current progress. Mel's online Ronchi calculator has overlaid some semi-transparent white lines which show the ideal Ronchi grid of a somewhat parabolized mirror. Looks like the center is fine, but the edge is focusing light too close - similar to what happened in parabolizing attempt #1. I'll need to think to figure out how to solve this.

I'm in the home stretch - my goal is to turn this sphere shaped mirror into a parabola shaped mirror.

The final stage of mirror grinding is called either parabolizing, because you're making a parabola, or figuring, because you have to measure carefully and that involves numbers which are also called figures. You use a stroke that goes up and down fast and side to side slowly in a big zigzag, called a W stroke, to remove a tiny bit of glass from both the center and the edge, as seen in the first picture (from Mel Bartels' site).

This stage involves removing very small amounts of glass, so parabolizing is very quick. After 15 minutes of a W stroke - which is crazy fast compared to hours and hours it took to get to spherical - my center was slightly deepened, enough to match a parabola! My mirror edge, however, still had very straight bands. The Ronchi test calculator said my edge wasn't where it should be.

Then I made a mistake: the amateur astronomers in the discord said I had a turned edge, and I needed to return to spherical. A mirror edge that's too low can only be fixed by grinding the rest of the rest of the mirror down to that height. So I spent anouther two hours undoing all my hard parabolizing work.

But in retrospect, I didn't need to do that at all - my edge was focusing light too close, so if I wore down the edge it would have focused light at a longer radius of curvature, which is what I wanted! I could have done that! I mistook the error for "turned down edge" when actually the edge wasn't turned down enough!

Anyway, I'm back at a sphere. Parabolization attempt #2: begin!

This site is my secret weapon: https://www.bbastrodesigns.com/ronchi.html

It's a slightly janky javascript app made by some old telescope maker in Oregon, and it lets you get quantitative measurements from all those Ronchi pictures. Very important.

Looks like my outer zone focuses light at around 0.066 in from my desired radius of curvature, and inner zone focuses light at around 0.1 in. (There's probably big error bars on both those numbers). Only the relative number of "inner zone focuses 0.1-0.66in = 0.03 in closer than outer zone" really matters.

Since the focal length is half the radius of convergence, that means my mirror focuses space light to 0.015" of where a spherical mirror would. Not bad!

CLOSE ENOUGH! SPHERE-ISH ACHIEVED!!

But my goal is to focus space light. A sphere will bounce light from center point back to itself, but to focus parallel light rays from space to a single point, I need a parabola.

Jean Texereau's book says the formula for "parabolic abberation", how different a parabola is from a sphere, is that the zone with radius h from the mirror should focus a distance Δp = h^2 / R further from the radius of curvature. Tape measure and eyeball says as I move my tester backwards, the ronchi switches from bands get wider to bands get smaller at 89 + 1/16", so that's the radius of curvature of my mirror (which is twice the focal length). By that formula, my goal is to have the very edge focus h^2/R = (1*8/2)^2/89 + 1/16" = 0.1796" further from the front.

Above I calculated that the edge focuses 0.03in closer than the front. Wow, I went so far past parabolic in my quest to get to spherical. I think I'm ready to parabolize.

To parabolize, I have to deepen this curve around six times its current amount. That's doable! The open astronomy discord recommended I start by smoothing out the division between the two zones with long strokes, and then begin using a different stroke to deepen the center. Let's do this

Total grinding time: 21 hours

I'M SO CLOSE TO A SPHERE

(You know you're a sphere when the lines are completely straight. See this infographic for more)

total mirror grinding time: TWENTY GODDAMN HOURS