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Mirror grinding (scopemaking.net)
195 points by Tomte on March 10, 2017 | hide | past | favorite | 65 comments

My dad (Tom Johnson) founded Celestron. His key idea was a way to create the corrector plate at the front of a Schmidt-Cassegrain telescope. The corrector plate compensates for spherical aberration (the difference between a parabolic main mirror and a spherical main mirror). This is a very complicated curve, and the traditional way to make it was to have an optician make it by hand. This was an arduous and time-consuming process. Tom's idea was to spend that time manually creating a block that has the OPPOSITE shape from the one desired, and carve narrow grooves in it. Then, take a normal optical-quality sheet of glass, and use a vacuum to deflect that glass down onto the block. Grind the exposed surface flat, which is a quick and easy thing to do accurately. Release the vacuum, and out pops a piece of glass that is a high-quality corrector lens. As a kid, I can remember many weekends when my dad was out in the garage grinding lenses and refining the idea. Eventually Celestron became successful enough to allow him to quit his day job!

Small world. I have one of your dad's scopes right here, and I always wondered how they made the optical components.

I will think of him the next time I use it.

These kind of stories are why I come here. I'm sure we'd all love to hear more interesting history that you'd care to share.

Do you know what this process is called? This description makes it sound like the glass has to bend significantly under at most one atmosphere of (negative) pressure, which sounds strange to me. I'd like to read more about it.

I think the trick is that the glass actually doesn't need to bend much. Notice that the caption here: https://en.wikipedia.org/wiki/Schmidt_corrector_plate#/media... describes the plate as being hard to tell apart from a flat disk visually.

The process is called stress polishing. Here's an article about it: http://bobmay.astronomy.net/vacpan/vacpan.htm

I had some trouble understanding the exact procedure described above, but then I read the patent[1] for the technique, which was very helpful.

[1] - http://www.freepatentsonline.com/3837124.pdf

We've got one of the NexStar 6SEs here that my kids love to look at Jupiter and Saturn and whatnot with. Thank your dad for us - it's an awesome family activity!


Thanks for sharing this! As I get older and try to record as much family history I can, I really enjoy you and others sharing what you can about family/company history for the future. Stories like this from first hand accounts are getting harder to find and eventually we may lose these great stories and historical accounts for generations to come.

Thanks again!

My parents run a business making telescope mirrors, and I grew up around this exact process. Measurement is the biggest difference between this and what they do. Take a look at https://en.wikipedia.org/wiki/Interferometry#Engineering_and... if you want to know more about how it's done in industry.

The best metaphor I got from them about how precise a shape they make in glass is that 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 - far less than your ability to perceive.

The other thing that was impressed me is that up until recently, the last stage of high-precision mirror making was literally done by hand. My dad would literally rub on a mirror with very, very fine grit to take out bumps on the order of microns. Recently, they've switched to machines in that last step to make it faster and more accurate, but for many applications the traditional way worked just fine.

>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.

I know a few keen amateur astronomers who make extra cash by producing astronomical equipment for other amateurs. Some of them are very skilled, and could probably start a fully-fledged business if they wanted to, but they prefer to keep it as a hobby.

I paid one guy $400 to build me an equatorial platform for my 12-inch Dob. The value it provides me is way higher than the financial cost, and he could probably charge more for his work, but I think his main motivation comes from the satisfaction of building things he's proud of and that others can enjoy. Certainly, when I occasionally donate my time and knowledge at public astronomy outreach events, I find it very rewarding, especially if I can inspire children's interest.

N.B. By far the biggest weakness of Dobsonian (or any alt-azimuth mounted) telescopes is the lack of tracking, and thus having continuously to nudge the tube to keep objects centred. An equatorial platform eliminates this weakness, and I strongly recommend one to anyone who's frustrated with their alt-az scope.

It's a very small market. And at the higher volume lower end (cheap scopes for newbies) you can't compete with chinese mass production.

> An equatorial platform eliminates this weakness, and I strongly recommend one

Agreed. You own a dob, just get a platform already. It's even useful for astrophotography.

you can track with an alt-az mount, no problem. It doesn't rotate, but as long as you know an alt az pointing, and have feedback servos, you can track any celestial location. Tracking at very high azimuth is hard, though.

The larger the mirror the more you'll need it.

This is one of my favorite hobbies to take part in.

I've got a hot glass shop on my farm in Kentucky (where I will make blanks and other artistic pieces), and I have built a cold shop with some tools (my favorite is a mold that uses pennies instead of the porcelain that they use in the article) and then using a HD projector and a DSLR that I remotely trigger, I get a map on the screen of where the imperfections are relative to the "top" of the mirror (that I indicate with a dot on the side).

Once I've worked the imperfections out, I'll then take it to an observatory in Ohio to get mirrorized -- and generally speaking, I'll donate my last telescope to the observatory (for public use) once I get the one I'm building done.

I don't really understand how a perfect shape can come out of that process. Can someone explain how it's a product of the grinding technique?

The grit only works where it supports the tool. So as long as you rotate frequently it will just hit new 'high' spots while not affecting the low spots at all. By hitting the interior more often than the edge that's where you'll go deepest, it's more statistics than actual aiming for a some high spot or difference. The tool-on-top or mirror-on-top swap can help to adjust if you've gone too deep by favoring supporting the tool at the edge or supporting the tool in the center causing greater amounts of material being taken away at the edge.

Lots of simple processes can cause nearly perfect geometrical shapes to appear: bounce steel blocks on a vibrating drum for a while (and against each other) and you end up with steel balls that rival ball-bearings in roundness (but not in precision, they will be all kinds of sizes).

> bounce steel blocks on a vibrating drum

Wow, is that real? Do you have a link? I want to see.

Yes, it's real. I don't have a video and I don't have a metal workshop any more but you can easily try this yourself if you feel like it. For added speed you could add some sand, and if you're just interested in the effect mix some rocks with some wooden blocks, that will speed things up quite a bit.

It's similar to how river beds tend to round the stones that get moved around by the water. Those stones start out as sharp bits of rock.

The extraordinary precision (under 0.1 microns) is only possible because the surface is close to a sphere; when grinding two surfaces together uniformly in all directions, the result tends towards a sphere (or a flat shape, which is a sphere of infinite radius). If you had to make an arbitrary shape, things would be very different.

If there's a bump (a hill) on the surface, it tends to grind out more quickly than the rest because it's jutting out and it's more exposed to pressure from the grit. If there's a hole, it remains untouched while the surface around it is being ground down. This way everything tends towards the ideal shape. By carefully doing a uniform rotation of the pieces during grinding, the resulting shape is symmetrical - spherical or flat.

Other shapes are also used in mirrors (revolution surfaces generated by a parabola, hyperbola or ellipse), but they are all basically just small corrections to a sphere (which is a revolution surface generated by a circle).

You start with very rough grit to go faster in the beginning and remove most material. Then you just use finer and finer grit as the surface becomes more and more smooth.

In the final stages you switch to polishing. It's a different process where the tool is not hard (glass) but soft (pitch), and the grit is replaced with microscopic powders (such as iron oxide or cerium oxide) which work not only through physical mechanisms but also via surface chemistry.

Also during polishing you use testing procedures which can show surface errors as small as 0.02 microns. The testing process is steering your polishing techniques; you apply corrections, or choose different polishing strokes to deal with various surface errors. Whereas grinding is mostly automatic (with a few basic checks here and there), during polishing your brain is in the loop, a lot.

I'm not sure I can explain it fully, but my understanding is that it is related to the probability distribution of the abrasive technique.

The technique involves random rotation and random motion, using lapping blocks that are the same size or smaller than the mirror. The center of the mirror is the most likely to be contacted by any motion, so it is abraded more frequently and becomes the deepest point, while the edges are worn less. The distribution between "less" and "more" is spherical.

I can at least understand the process of grinding or lapping a surface flat. Here are a couple examples:




if you rub two things together, there are only two shapes which could possibly remain in constant contact. the first is perfectly flat which is very hard with only two surfaces (easier with three) the second is hemispheres and if you do the easiest thing possible rubbing two things together they will wear one another into matching convex and concave hemispheres. for some optics that is close enough (small diameter long focal length e.g. a 6" F8) otherwise instead of a spherical surface you may need a paraboloid (or other aspheric)in which case you need to preferentially deepen some part of the curve (~70% of the radius) a few millionths of an inch. but when you do it wrong you go back to doing the easy thing and make it spherical then try again... and again ... and again ... (but I'm not bitter). Till you decide it is good enough!

The minimum standard for good enough is a under a quarter wavelength in the short end of the spectrum of interest . this is because an extra quarter down plus the same quarter back up and you are a half wave out with another part of the mirror which when combined by your eye results in destructive interference of both parts of the mirror.

one last point on the final smoothness, the interplay of glass, water, pitch, metal oxide and mechanical force is imperfectly understood. crudely it may be closer to planing than grinding but that does not explain the oxide particles which are found beneath the surface of a figured mirror. another thought is the an atom in the glass is "stretched" up and snaps back into a lower energy configuration which is more atomically flat

I'm not sure in this specific case, but in general, grinding mechanisms to obtain flat planes, angles, and spheres are pretty well-established. For flat planes, the term is "automatic generation of gages" and is a subtle and clever way to grind three faces in pairs. For curves, you'll need a rotor. Interestingly, you can use a fairly coarse system to methodically generate a very precise curved surface.

Depends on what you mean by perfect. its very precise, but I'm sure if you examined the surface with an electron microscope you'd still see imperfections.

Edit: was incorrect about what I said below. Leaving it for posterity

It's important to remember that the final surface - the one that actually reflects photons - is created chemically by releasing a gas inside a vacuum that very evenly coats the surface with reflective metal atoms. I'd wager that process fills in the ~last nanometers~ or so of imperfections. Or at least averages them out enough to not affect the optical performance.

No, it's not needed. Nanometers don't matter, that's the atomic level, far below what visible light could resolve. The metallic coating doesn't change the shape.

Once you're below 20 nanometers it basically doesn't matter. The wavelength of visible light is on the order of 400 nanometers.

In a different universe where the wavelength of visible light would be comparable to, or smaller than, the size of atoms, it would be very hard to make mirrors.

Source: I make telescope mirrors.

And indeed x-ray mirrors are a bitch

(Although that's more because of destructive self interference than imperfections)

Thanks, I corrected my response. Was I partially correct about the gaseous reflective coating helping to smooth over any micro-imperfections?

You don't even need nanometer precision, since light has a wavelength of a few hundred nanometers. Random imperfections on a nanometer scale will be literally invisible.

This appears to be incomplete. It explains coarse and fine grinding but that's not enough to make a usable mirror. You need to continue with polishing and figuring before getting it aluminized. Here's an explanation of the whole process:


A much more extensive guide is at Stellafane:


Keep in mind this is a long term project. If you're looking for something to do with your hands, a physical object in the real world, that would keep you busy for months (assuming you're not working on it full time) - you've found it.

Keep at it and you'll make a very high quality instrument. My first parabolic mirror came out at lambda/25 precision (and no ripples, no turned edge), whereas many commercial mirrors are only lambda/4 or 6 and the edge is sometimes questionable.

As for the instrument itself (everything except the optics), it's not much harder than making a simple cabinet, and in some ways it's easier. Go slow, read a lot, think ahead, and you'll succeed.

There is also a 90 minutes film »Telescope building with John Dobson« [1], inventor of the Dobsonian telescope [2], going through the entire process of building a 16" telescope from scratch.

[1] https://www.youtube.com/watch?v=snz7JJlSZvw

[2] https://en.wikipedia.org/wiki/Dobsonian_telescope

From a previous HN thread for this article ...

> I grinded some mirror. Nice experience but at end monotonous and boring. Also grinding powder is lethal, I had my appendix removed since I eat some :-(


Random semi-related question I was thinking about last night:

Could you:

1) make a coarse "random" mirror that was bumpy at the large scale

2) buff out all the fine texture so you get clear fragments of an image all across the lens at random focal planes

3) put it on a track with a LCD screen on one side and a camera on the other

4) use some sort of gradient descent algorithm to move the image and camera around and reverse engineer the normal map for the lens

5) Use that displacement map to generate a light field from an image

6) Use the light field to generate any (clear, in focus) image you want in the light field volume.

In other words, can you make a Very Bad but Smooth lens, and then make up for it in software?

My guess: you could, but for any given focal plane you'd recover very little resolution because probabalistically few of the microlens fragments are focused there.

1) Yes, ThorLabs sells them: https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=11...

2) You mean like a fun house mirror?

3) So you mean have a screen shine through a wonky lens at a camera?

4) Yes, this is commonly done with interferometers in many junior physics lab classes, though the set-up is different. https://en.wikipedia.org/wiki/Optical_coherence_tomography

5) So, try to figure out how the surface deforms the light image.

6) Yes, we have been doing this for many years now: https://www.edmundoptics.com/resources/application-notes/opt...

Yes, that is considered a 'solved' problem, but the costs and market for such devices limits their wide-spread use. Typically they are used for nanoscopes and telescopes. There are a few purveyors, but add 2 0s to the end of whatever you think the cost should be.

The limiting factor is the light coming in and having a 'known' value to measure your noise against. In telescopes, this is typically a 'guide' star that has a very well calibrated light spectrum and positions that you can measure the noise values against.

Also, another cool thing youmay want to look into is electro-wetting lenses, basically a digital lens: https://en.wikipedia.org/wiki/Electrowetting

I don't know if it's exactly what you're thinking but many modern research scopes use adaptive optics which is both software and hardware


I'm a software engineer working in the precision optical fabrication and metrology industry since the late 80's. I've written a lot of software advancing the art in interferometry and computer controlled optical fabrication. It's always a thrill to visit optical shops all over the world and see my software still running on machines I helped build 20 years ago. I really have appreciated the opportunity to build software of enduring value, and to work on the enabling technologies for fab and test of microlithographic, aerospace, medical, research, and photographic optics.

From one of Jon Bentley's Programming Pearls books, the "Bumper sticker computer science" chapter:

[Thompson's Rule for First-Time Telescope Makers] It is faster to make a four-inch mirror and then a six-inch mirror than to make a six-inch mirror.

    Bill McKeenan
    Wang Institute
This is offered as wisdom for software development..

I work in optics at my day job. For me, one of my secret pleasures of optics is learning the ancient technologies, techniques, and measurements, that remain viable even in modern times. It's a pleasurable counterbalance to the "new framework of the month" syndrome, and helps keep me sane.

I interned at a great company (https://qedmrf.com/) that engineers magnetorheological fluid and machines for polishing / analyzing optics. I can't imagine doing it by hand. Fascinating stuff.

If you live in the SF East Bay, there's a free workshop that meets every Friday night at the Chabot Space Center:


How is the curvature of the mirror measured during manufacturing? It's obvious that the mirrors require extreme precision in order to function correctly.

Spherometers are only used during the initial stages. Towards the end you switch to optical testing.

Needs the same for lenses. I'm very eager to try optics.

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