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>if you took a typical 1 meter mirror and scaled it up to the size of the United States, the biggest deformity from a perfect curve would be less than you are tall

My father, who worked on the Hubble Space Telescope and its servicing missions, used virtually that exact wording when describing the precision of its mirror to me as a child. So that's evidently a popular metaphor for optically oriented parents :)

Even currently, many world class high-precision mirrors are ground and polished by hand. I believe the machines you're describing are just copying the same procedure that is done by hand (a robot or swivel arm imitates the motion that a hand would make), and this process produces surfaces that have an average roughness of less than 1 Angstrom across the optic.

However, there have been other technologies that will polish out tiny non-uniformities and 'bumps' on the order of nanometers tall across a few square microns. These technologies, such as MRF finishing https://qedmrf.com/en/mrfpolishing/mrf-technology/how-it-wor... are the current state of the art to get the best surface finish.

Over a decade ago I worked at one of the big semiconductor manufacturing R&D outfits (there's very few of those in the world) and the mirror making for EUV lithography R&D was done by polishing by hand at the end by two guys with metallurgy PhDs. Good chuckles were had.

Hand techniques are still used for reference surfaces in machining. Granite surface plates (highly accurate planes) are hand lapped[1], and metal bearing surfaces on machine tools and cast iron reference tools are sometimes hand scraped[2].

[1] On location calibration and lapping of granite surface plates: https://www.youtube.com/watch?v=EWqThb9Z1jk [2] Hand scraping (effectively chiseling) of reference cast iron surfaces: https://www.youtube.com/watch?v=nOJrhrne80s

It's interesting that you mention measurement. I've been involved in a number of exercises to source optical components in China, and have learned to judge a vendor by what measurements they're capable of.

I think there's an analogue to test-driven development in software. Many designs that you look at make no sense until you understand what can be measured readily and what can't, while making the parts and assembling them into a system.

What impressed me when I was polishing an 8" mirror was that you could easily see the effect of the thermal expansion of the glass where you touched it briefly with a finger.

I'd love to grind my own mirror, but are there health concerns with the fine powder for the skin and respiratory systems?

I'm guessing these are done with wet sand paper for the coarser grits (< ~3000), or polished with a soft cloth and paste/polish for the extremely fine grits. At least that's common for related techniques such as lapping, car paint detailing etc. So the fine powder should be carried away in a slurry.

Edit: from TFA:

"Always work wet! Sprinkle some water on the grit before you start grinding! Glass dust is very dangerous and can cause silicosis, a serious lung disease if inhaled!"

> for the coarser grits (< ~3000)

I love it how you casually throw that out there. For the un-initiated, outside of grinding lenses: grit 3000 is approximately 6 micron particles and very fine indeed but for this purpose (and gem polishing) it is still considered 'coarse'.

The finest polishing grits go to 100,000, ~0.25 u across.

And for knife sharpening people: 3000 grit (and a leather strip) is enough to almost reach razor sharpness ... with good steel, that is :)

Even with the wet grinding, eventually the slurry dries out, right? So wouldn't you have to keep your work area wet or mop up regularly during the process?

Unless you are a complete slob, you will clean your work area when you are done for the day, right?

In my experience grinding and polishing samples for petrography, Because the grit etc was once wet, it gets caked-on to everything once it dries. So caked-on that it can be hard to clean everything once it is dry, and if you want to remove it you have to wet it all again. Unless you are stirring up the air with a fan, or trying to remove caked-on grit with compressed air, I do not expect much dust will get airborne. So, clean up whilst it is still wet, and there will be no problems.

I'd imagine the math to be off-the-charts complicated, but I'm interested in the signal processing software people have created for correcting optical aberration (and how effective it is). I believe they pioneered this technology for the hubble's mirror defect. If it's effective, then manufacturers could reduce costs by not even needing to try for perfection, just staying within the limits of what software can fix.

Yeah this is an interesting area of research - I think the term you're looking for is deconvolution. Here's a document about some of the work done for Hubble in this regard (large PDF): http://www.stsci.edu/hst/HST_overview/documents/Restorationo...

However, my understanding is that you can improve things but you can't "truly" correct it, generally speaking, because the optical aberration causes information to be lost. eg. if point A on your mirror focuses to point A' on the resulting image, and point B on your mirror, due to an aberration, also focuses to A', there's no way to determine from the image which point on the mirror a photon came from.

This is why Hubble eventually needed a hardware fix... from the linked paper: "it is clear that many image restoration methods are highly successful at deriving images that 'look good' from HST data. These restored images may be qualitatively faithful to the true (unknown) image. However, for most astronomical purposes qualitative agreement with reality is not sufficient; we want quantitative agreement as well."

The approach most advanced people use now is deformable mirrors. They work in concert with a laser that emits from the detector, bounces off the atmosphere, and produces a real time map for the deformation (you have to solve an inverse problem here IIRC). You can also use a wavefront sensor.

For small problems, you can just buy these things off the shelf: https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=32... "only" $17.5K

The history behind wavefront sensors is pretty fascinating. It was developed in the 60's by Hartmann, in order to better image satellites from earth, and then largely ignored by the astronomy community, even though he presented it to them, until the 80's.

I can't find the original paper that I read, but here's a bit of history [1].

[1] https://pdfs.semanticscholar.org/d1ed/a97dd2cf70f54f24b85abc...

WHen I started grad school in Biophysics (1995), a microscope professor mentioned adaptive optics and asked the incoming students if they thought similar processes could be done in microscopy. If you said yes, he let you join his lab (they were already working on this).

Oh interesting!

Were they working with some sort of fluid interface? Maybe layered liquids, or fluids that you don't want to dip an objective lens into? Or maybe temperature gradients?

I wonder if it would be possible to make a deformable mirror using a combination of liquid mercury chemically bonded with a ferromagnetic metal (if mercury isn't already magnetic). Then theoretically, you could use an electric current in a coil to shape the liquid into a precise shape.

Maybe? I wouldn't touch mercury for any reason, though.