I admire your persistence for quality and accuracy. That’s what separates a good machinist from a bad one. You had a idea and you will see it all the way through improving the design the whole way, until its right. My hats off to you Bucket. 
Thanks for sharing.
Good job! The top didn’t have good contrast and the image was tilted 1* so I leveled it and only used the bottom contour. It’s definitely a paraboloid. The pilot is a good idea but at that diameter, your LED will need a shim. You only needed to go a little further (indicated by the green dotted line) to make the pilot slightly smaller and eliminate shimming.
If the length is where I drew red lines, that a good ratio and will have about a 60* spill.
Amazing that you have achieved such accuracy without cnc.
Thanks. I will take a little credit, but have to say that manual lathes are capable of pretty good precision if used carefully. In this case, I just did the same thing that a CNC machine would do one data point at a time. Albeit a lot slower. The big thing that I can't do that CNC can is move directly from point to point. I have to back out, then come back in. To overcome that, I made the distance between my points small.
On to news.
I have succeeded in creating a bit that cuts aluminum (again). It still takes more force to make it cut than I like but it is what it is. I may try some very careful grinding later to make better relief angles behind the cutting edge.
Here is the first reflector made with the new bit. The reflector is not polished yet. The grooves that you see should polish out fine.
I have just started testing beam pattern with it. I'll let you know how it goes.
There ya go, polish, send it my way, and we’ll fire it up! 
Looks to me like it should work perfectly, I’m really eager to see what the beam pattern and hot spot look like from your work. I do believe you’re finally there!
It's looking good so far. I put an XM-L2 on a heat sink with a couple of D cells driving it at a whopping 100ma just to see how things looked. I don't have anything quantifiable, but it has a decent hot spot. I am pleased so far. I'm modding a light to put it in so that I can do some better analysis on how far to shave the bottom off for best focus.
On the down side, my Dremel is done for. My repair didn't hold up. 15 seconds of polishing was all I got out of it. Amazon is shipping me a Proxxon which will hopefully be here Friday.
I love hearing about the success, and look forward as well to your impressions on the Proxxon.
I have the most success polishing with the paper on the back of 600 grit wet/dry, just using my finger to press it in place. Works better than felt pads in my experience.
Of course, I don’t have the part in a lathe, but I do spin it up to 2500 rpm sometimes.
I put together a video of working on the lathe and some rather Mickey Mouse hot spot testing. I am not happy with how said testing is going. So as a side project I am modifying an old Elektrolumens XM-3 2AA flashlight. I'm gutting it and converting it to a single 18650 with a 3 amp driver. Once it's done, I'll be able to do better testing with a camera with constant aperture, shutter speed and ISO settings.
nice video, I like the moving pictures of the lathe work. The beam testing could indeed use some refinement ;-)
I keep watching this thread :-)
Perhaps set up 2 stands that hold a piece of paper as you were in the video but at a constant height and then trace the hot spot as you whittle it down bit by bit until you reach optimal focus?
I'm going to do the good old fixed distance from the wall bit. The wall has a sheet of peg board hanging on it with 1 inch between centers of the holes.
Pictures at constant aperture ISO and shutter speed will tell the tale.
Lack of updates is due to the wife's honey-do crap getting in the way of more important business. Out of the blue, we needed a new kitchen faucet. I hate plumbing. It's done now, back to modifying the old XM-3.
You could fab entire heads for lights like this. Just thread the stock at either end for a bezel and a body on the appropriate sides. I bet that would help some of the higher driven lights. Fascinating thread either way. It’s a treat to follow you chip away until you nail it. There are so many snags and dead-ends in my work-a-day world that can wear a person down. Following your progress has been educating and up lifting. Thanks.
You really can’t measure the hot spot from 2’ away, pretty irrelevant unless you’re trying to make a light for working on the bench. As such, you then wouldn’t want a hot spot at all most likely. The hot-spot, in my way of thinking, is a matter of throw. How does it perform at a distance, so we can see an object or animal or person that we’re looking for in the dark. I would think 20-30’ away would be a bare minimum for a hot spot, and more like 30+ yards.
I was thinking the same at that distance I would think you’d want to see a dark flower petal with it shifting to a hotspot further away
Very impressive lathe work btw bucket
I've done some testing on the first reflector. Not exactly promising so far.
Ok, I have eliminated another rather LARGE mistake from my spreadsheet. Since my parabola has a vertex of 0,0 the x coordinate is the radius of the parabola at coordinate y. I failed to account for that in my spread sheet and removed material in terms of diameter when making the bit. What I made is still a parabola, but it doesn't have the focus point that I wanted.
Lightme, this totally explains why the focus point is where you pointed to in your previous post and not where I thought it would be.
I'm going to make another bit eventually, but for now I'm going to keep going with what I have and see if my math works out for it. It may be that it is usable the way it is.
I made a second reflector with the same (fourth) bit and it works pretty well. My Proxxon just came today so my testing was done before polishing. I know you guys don't buy my method, but I used my DSLR in manual mode to take pictures of the beam shot on the wall. I used small aperture and fastish shutter speed to make the pictures very dark such that all spill was eliminated. In fact, in some of the pictures it's just blackness. I then compared the pictures to see when the focused light was brighter after machining .010" off of the bottom each time. It was basically a "Brighter / Not Brighter test".
I started with what was effectively a .125" shim in bottom thickness. I have not measured what remains on the bottom, but it is it in ballpark of .050-.075" below where the parabolic curve ends.
This is the one I'll be sending to DBCstm. I'll get it polished up and in the mail as long as my little buffing wheel holds up ok.
Now I’ll be watching for Santa with passion!
I'll have to make a sleeve so it fits in your light properly. I could also use your address :)
On to more results. I polished it as best I can with the only felt bob that I have. I can't get all of the way down into the bottom with it. The good or even great news is that what polishing I was able to do made a very large difference. I am happy, happy, happy to quote Phil Robertson. The hot spot is well defined and throws decently. I have some pics I need to upload. I'll try to get that done tonight.
By the way, I am really digging the Proxxon. It is twice the machine my old Dremel was. I really can't overstate how nice it is in comparison. The Dremel vibrated like it was going to come apart compared to the buttery smoothness of the Proxxon.
Does the total height of 1 1/32 include the shoulder height (on the bottom)?
17/32 seems kind of big for the shoulder....
I've tested the reflector without a shoulder. If I put a shoulder on it, it will put the die deeper in the reflector- which is fine, but you will likely need to shim it. It's actually better if I put a shoulder on it and let you adjust it as needed for best focus. In fact, since I'm making a spacer ring I have an idea that might work out.