Introduction: Grind and Polish a Dobsonian/Newtonian Telescope Mirror With Hand Tools
Author's note: This Instructable was written and published by our Making and Tinkering Programs Manager, who's personal Instructable account we co-opted. He is now publishing personal Instructables over at member ID MechaNickW.
Making a telescope about 10 years ago was one of the most rewarding projects I've ever undertaken. I ground the mirror and made every other component out of recycled materials as much as possible. This Instructable will cover how to grind a mirror for your telescope - I'll link to other sources for building the other aspects of a telescope. I'm entering this into the Hand Tools Only Contest, so be sure to vote if you get inspiration or good info from this!
This style of reflecting telescope was actually invented by Isaac Newton, so the optical system is called a Newtonian telescope. The mount style that I used is sort of like a cannon mount, and was originally designed by John Dobson, so called a Dobsonian. It's a dead simple mount to build and I highly recommend it if you are looking to build a telescope.
The process for grinding telescope mirrors at home actually doesn't look too much different than when Isaac Newton first developed it, and he didn't have any power tools. John Dobson was a monk and did much of his work in secret from his brotherhood. Both of these individuals were very interesting characters, google them on Wikipedia if you want some interesting bits of history!
Anyway, it's amazing the precision you can achieve simply with some glass, grit, pine pitch and a lot of work. I've heard that this is literally the highest amount of precision a human can achieve with simple hand tools! Just grinding the telescope mirror probably took 80-100 hours for me, but I was learning a lot and taking my time. I'm entering this into the Hand Tools Only Contest because when I did this project that's all I had!
- 2 pieces of glass - one will be the mirror, the other is the tool you will use to grind it. Mine were plate glass 6.25" in diameter for the mirror and 5.75" in diameter for the tool, 3/4" thick. You can buy glass blanks online, in addition to other telescope making supplies at First Hand Discovery.
- A variety of grinding grits and polish grits, also available at the supplier linked above. It is best and easiest and cheapest to get a kit that is for your diameter of telescope mirror, 6", 8", 10", 12" etc. are common sizes and each will need different amounts of grit.
- Pine pitch, should come in your kit of grits and such.
- A work surface to grind on - I used some old dresser thing I found on the curb and weighted the bottom with bricks, a 50 gallon barrel is a very common surface.
- Some scrap wood or plastic and a couple of screws.
- A knife sharpening stone (also called a carborundum stone).
- A good toothbrush or bristle brush.
- 5 gallon bucket.
- Soap and water
- Old newspaper, cardboard or carpet.
- A chunk of window screen (NOT metal, the plastic kind)
- A squirt bottle or two
- A small paint brush
- A ruler and measuring tape
- Small drill bit set or feeler gauge
- A light (I used an old bike light, almost anything like a flashlight or your phone light is good)
- A magnifying glass or telescope eyepiece
- A razor blade
- Turpentine, acetone, mineral spirits or another solvent and a towel
- An old soup can
- Sterno can or stove
- For testing, you'll need to build a focault tester. I built mine with hand tools out of things from my recycle bin, here's a great Instructable for making one of these.
Step 1: Determine Your Mirror's Focal Length and Sagitta
You'll want to first determine the shape of your mirror and the focal length that it will eventually have. When designing a telescope of this style, there is a very, very handy tool called Newt for the Web. You can put in your mirror diameters for the one we'll be making (primary mirror) and the secondary mirror, as well as the focal length of the primary mirror, and it will give you a lot of other parameters for your telescope that are necessary to consider as you grind your telescope mirror.
Really we want two things here to calculate what we need to know - the focal length and the focal ratio. The focal length is simply the length from the surface of your mirror to where the image will focus. I was shooting for about 48". The focal ratio is the ratio between this length and the diameter of your mirror, a very common one is f/8 (48" divided by 6"). Mine ended up being about f/7.6, this is not super critical to hit on the nose. What we want in this step is just to determine what your end result should be so we can calculate how much glass we're going to remove from the flat surface of your mirror.
To get this measurement, you need to use the formula r^2/2R. That's the radius of the mirror squared over 2 times the radius of curvature. I know it sounds confusing, but the radius of curvature is twice the focal length (96") - I like to think of this as a big invisible sphere to which the mirror is attached, and the sphere is taking a chunk out of the surface of the mirror. Here, it's 3 squared over 192, which is 0.0459 inches, round it to 0.046. To take the headache out of this and a lot of other measurements, use this handy calculator from Stellafane. You won't need to do any math, just enter the measurements and you're good!
Step 2: Build Your Work Surface and Start Hogging Out Glass
Once you have your sagitta calculated so you know when to stop grinding, it's time to roll up your sleeves and dig in (get it, cuz you're digging into the glass?! oh, nevermind). I took this old dresser thing I found for free on the curb and filled the bottom with bricks - again, a 50 gallon barrel is great, add water inside to weight it or sand or rocks, etc. You'll create some cleats on the top - glue a piece of plywood down if you're using a barrel and screw the cleats to that. These cleats need to be shorter than the thickness of the mirror so you don't hit them, and they should be placed so that the mirror and tool both can fit in there. They keep your mirror and tool in place as you are grinding. My mirror was bigger than my tool so I made another wedge piece that fit in there to keep the tool in place when it's on the bottom. I used some crappy plywood, I would recommend a chunk of thick plastic or nicer wood - you need to clean these a lot and all the little cracks and such were a pain to get cleaned out. Put down some newspaper on the bottom or cardboard or a chunk of old carpet to help keep the mirror from slipping around.
Before you start and as you go along, take a carborundum stone (I just bought the cheapest knife sharpening stone I could find at the hardware store) and bevel the edge of your tool and mirror. This will get ground away so just check it periodically as you work and keep a slight 45 degree bevel to it. This prevents the edge of both pieces from getting too sharp then chipping.
When people ask, "How do you make a telescope mirror?" my answer is usually, "You take two circles of glass and rub them together for a long time with sandpaper grit in between." That is what you will be doing. For a while. When the tool is on top (usually abbreviated TOT), the curve in the mirror becomes deeper. When the mirror is on top (MOT), the curve becomes shallower. Take your roughest grit, typically #60 or #80, and put a spoonful on the mirror, which will be on the bottom for the first part. Add some water, use a spray bottle or a squirt bottle. ALWAYS WORK WET - if you don't add water, you can make a bunch of silica dust from the mirror which is terrible for your lungs and health.
There are a couple of different strokes we'll be using for this process, to start use a chordal stroke, as shown here. It's a large amount of overhang that you reduce as you create the curve in your mirror. You'll do the chordal stroke, then take a step around the barrel, then do the stroke, then take a step, etc. What we want here is randomness with regard to the orientation of the mirror and tool - the more random the better. Don't "spin" the tool over the surface of the mirror, but pull it back off and put back on in random ways.
This part is loud. As the grit wears away, runs off, and works the mirror it will get quieter. Grab your 5 gallon bucket and fill it part way with water. When the grit wears down, rinse it off in the bucket, put it back on the work stand, and add another spoonful of grit. Literally, rinse and repeat. This is called one wet. You'll need to do a number of wets to get through rough grinding. What we are doing here is simply shaping the mirror to the desired sagitta, then the rest of the work will be progressively making the surface of the mirror smoother and smoother.
The video shows about 30 minutes of this process on another mirror that I'm making for my nephew.
Step 3: Measure Sagitta and Focal Length and Finish Hogging
You should do a number of wets and start to see the surface of the mirror get kind of frosty from the sanding you are doing. Once it frosts all the way to the edge, take a quick measurement of your sagitta. There are a number of ways to do this. When I made my first mirror I had little money and access to tools. You can buy a feeler gauge set, which is just a bunch of strips of metal of predetermined and indicated thickness. Or you can make or buy a spherometer, a tool that measures the sagitta with high precision with a dial gauge - for a telescope I'm making now, I 3D printed this one.
BUT, you don't have to use these fancy tools, and I certainly didn't. Neither did Newton or Dobson. If you have a set of very small drill bits (which are useful for a lot of other things anyway), take a pair of calipers and measure them. Find one that is closest to the measurement of your sagitta that you calculated, and hog out the glass until it fits in between a straight edge (I used a metal ruler but a wooden one or nice piece of wood is fine) and the center of your mirror. I was a bicycle mechanic at the time, and happened to discover that a bicycle derailleur cable was exactly the diameter that I needed, 1.2mm or 0.045 inches. This is all I used to keep tabs on this measurement.
Keep using the tool on top and grinding away until you can fit your cable, drill bit or feeler gauge between the straight edge and the center of the mirror then stop. You'll hog out the glass with the roughest grit until you reach the desired sagitta.If you overshoot, that's okay! Just put the tool on the bottom and the mirror on top, then grind until the sagitta decreases. As you do this, sometimes the mirror and tool won't fit together perfectly and there will be bubbles in there - that's okay at this step, as you work through fine grinding though, seeing these can be a sign of a problem.
Another way to measure your mirror is to determine the focal length using a light. This is ultimately the most important thing we're going for here, the sagitta measurement is just a quicker way to do it. But you can take your mirror after it's ground at this stage, spray some water on it, and get it to reflect an image. Where that image focuses most clearly is the radius of curvature, which is twice the focal length. If you want to do it this way or double-check your work, just take a piece of cardboard or a cereal/snack box and poke a small hole in it. Put a flashlight inside. Take a measuring tape and your mirror with wetted, reflective surface and go into a dark room. Hold the mirror at about the distance of your radius of curvature (ROC) and see how clearly the mirror reflects the pinprick of light. Move towards the light or away until the reflection is the clearest - that is your ROC so see what that distance is on your measuring tape, divide by half for your focal length. If it's too short, grind some more with the tool on top. If too long, grind with the mirror on top.
Step 4: Work Through Fine Grinding
Once you've got your sagitta/focal length at the desired measurement, the rest of the work you do on the mirror is really just making the surface of it very, very smooth. Like, the most perfect thing you can do with a set of hand tools and crude measuring tools. Ultimately, when you are done you want the difference between the highest peak on the surface of your mirror and the lowest valley to be about 590 nanometers, the wavelength of sodium emitted light. You read that right. And it's possible to do!
So, take your mirror and the next roughest grit. Hereafter, we don't want to change the shape of the mirror too much, so alternate having the mirror on top for a few wets, then the tool on top, then mirror, etc. I would track mine and the number of wets with each grit with sharpie tallies on the cardboard. For a mirror I'm making now I found this weird counter thing at a garage sale and used it, but marks on piece of paper work just fine.
You'll use a different stroke here, called the Normal Stroke. which is just pushing the tool straight over the center of the mirror. The overhang to which you will push/pull this is important, in this part it's 1/3. That's 1/3 of the mirror diameter in total, so 1/6th forward, 1/6th back. If your mirror is 6" in diameter, push the tool until it overhangs 1", then pull it back until it overhangs 1", and repeat. The Stellafane website has a guide to strokes, and is an invaluable resource for all aspects of this project, I highly recommend you read through it before even starting this project. This is the stroke you'll use through all of fine grinding and most of polishing, so get comfortable with it early on.
Do a few wets (maybe like 10-15) with your grit, and then look at the surface of your mirror. You want all of the pits in the surface to be about the same size - it will be easy to see pits from the previous, rougher grit as they will be larger and sparklier than the ones you are making with a smaller grit. You'll work with a grit until all of the pits from the previous one are gone and the surface is uniform - if you see large pits, keep going! Use a magnifying glass, or alternatively a telescope eyepiece that you look through backwards - you'll need one of those later anyways to look through your telescope. You can also hold it up at an angle to the light and the larger pits will scatter more light than the small ones.
Once you have finished with a grit, clean, clean, clean everything. Take a toothbrush and soap and water, remove your cleats and throw out the cardboard/newspaper, and make sure that Every. Single. Piece. of old grit is washed off the mirror, work surface, etc. Get it out of the screw heads for your cleats, wash the bucket super well, etc. Honestly, this is the most frustrating and annoying part of making a telescope - you have to clean everything very, very well between grits so that a grain of larger grit isn't between your mirror and tool when you are working with a finer one to scratch the mirror. I found that I would spend as much time cleaning up after a grit size as grinding with it, but it's important so take care with it!
As you work through grits, periodically check your sagitta to make sure you're not altering your focal length. If you're drifting too long or short, compensate by putting the mirror on top more or tool on top more. Remember to periodically chamfer the edge of your mirror and tool as you go.
When you get to the very fine grits, having warm water helps a bit for your wets. Also, be very mindful of the fact that you are making these two surfaces fit together almost perfectly, and if you have too little grit or water in between a vacuum can form and they can get stuck together. If this starts to happen, try to push through the stroke during which they stick. If they stick completely, you can soak them in warm (not too hot) water and see if they will dislodge. I also found it easier to make a slurry with the very fine powders towards the end of fine grinding, and paint it on the mirror.
Once you get to your finest grinding grit, we'll move onto polishing and figuring!
Step 5: Pour a Pitch Lap for Polishing
Your mirror might look pretty smooth and nicely finished at the end of fine grinding, but in reality it's pretty rough. You'll need to polish it to achieve the ultimate smoothness required to ensure that it reflects all the photons from cool things in space appropriately. To do this, you'll pour what's called a pitch lap. As with everything else, this goes back to Isaac Newton - it's crazy that heating and pouring basically tree sap onto a chunk of rock that you can polish something to be almost imperceptively perfect!
Pitch is an interesting material - when at room temperature, it's technically flowing very slowly (there's a fascinating long-term science experiment called the Pitch Drop Experiment if you have interest). When heated it flows very easily. What it does is conform itself perfectly to the shape of your mirror surface so that it polishes it evenly across without making depressions and scratches. Remember, at the end of polishing we will have a surface that deviates between lowest and highest point on the nanometer scale.
To do this, take your mirror and tool and put them in the sink with some hot water. Not so hot that it's scalding, but pretty warm. If the mirror and tool are too cool here, dunking them in the water will thermally shock them and they can crack so make sure they are at room temp. We're doing this because we'll be adding hot pitch to both, and they need to be similar in temperature to the pitch. Take your pitch container and heat it over a stove, put it in plastic to warm in the microwave, or take a can of sterno or a camping stove and heat it like I did. USE CAUTION WITH FLAME - the pitch is semi-flammable as are the vapors, I used a taller can to ensure they escaped instead of catching fire but be careful here. You can add turpentine if it's too thick (shouldn't be necessary if you bought your pitch in a kit - they ensure that it's the right consistency), and that stuff can catch fire.
Once your pitch is nice and gooey, take your mirror and coat it with your polishing compound and water (usually cerium oxide). Don't coat the tool - in fact, take some alcohol or acetone or turpentine and wipe the surface off - we want the pitch to stick to it very well, finger oils can prevent that. Then, take your pitch and pour it slowly in a circle on your tool, working towards the center. We want to work while this is all warm so you have to work somewhat quickly here. Then, take your mirror and put it on top of your tool and squish it down a bit. You'll want to end up with a layer of pitch that's about 1/8" thick. Funny story here: I was doing this with the guidance of my good friend who's a telescope maker, I was being a little to cautious here squishing them together. He told me to stand back and then just STEPPED on my mirror and tool. And it worked great. It's good to have friends you can trust!
Note that the pitch is very sticky, put some paper down and try not to get it all over the place. Once you have poured the lap, we need to cut some facets in it so that it has a lot of surface area to polish the mirror. Take a box knife/razor blade and cut some channels in it so that you have about 1" squares. NOTE: you do NOT want this to be so that you have a channel at the very center of your tool and mirror, that can mess things up. Offset your center channel from the center about 1/4" or 1/2", then work out from there. Then, dunk your pitch lap tool in some warm water to soften the pitch a bit. Take a bit of nylon (NOT METAL) window screen, and place it in between the mirror and lap. Add some of your polishing compound and water slurry. Squish it down a bit. This will create a bunch of small microfacets in your lap. As you polish, you will need to clean out the big facets as the pitch squishes together and refresh these microfacets.
Between polishing sessions, I'll note that you should store your pitch and tool together with tool or mirror on top so the pitch retains the shape of your mirror's surface, and they should be in an airtight container.
Step 6: Polish and Figure Your Mirror
Now, you'll use the normal stroke as in fine grinding and polishing agent to get the surface of your mirror super smooth. It's best to do these sessions in at least 1ish hour increments - the polish works better after 10-15 min of warming up from the first strokes and the pitch really conforms best after a bit of friction. Don't worry if one or two of the edge pieces of pitch slides off - if they start to crack or something, take a razor blade and remove them completely so they don't end up between your mirror and lap.
As with fine grinding, keep everything CLEAN. No dust, other pieces of grit from previous grinding, etc. This is best done indoors not in a dusty garage. I've heard that getting pet hair in there doesn't seem to matter but I would avoid it. You don't want anything to scratch your mirror at this point, because you'll either have to live with it or go back to grinding and grind out the scratch which would be a huge pain.
After a few hours of polishing you can check the surface. I've heard you can use a laser pointer at a steep angle on the mirror and if it's not polished you can see some scatter. I didn't have one of those, I just kept polishing until I could see no more pits in any way and the mirror looked almost completely clear and perfect on the front face. When you are done with polishing you want zero pits and a completely clear surface.
I wanted to get my mirror as perfect as possible, and to do that you need to use a very fine polish. In addition to cerium oxide I used jeweler's rouge, basically a very fine rust powder. All of the warnings about this stuff say that it stains everything, but I wasn't too concerned. I ended up staining my kitchen counter a bit, permanently. Also, my cat jumped up on the polishing table and got some on him, and he was pink for like two weeks. Don't be like me, use caution with the rouge and don't get it on anything you don't want to be pink/red!
I'm going to gloss over the figuring part of the mirror - that is a whole Instructable on its own. Fortunately, there is this great one that talks about how to make a focault tester and test your mirror. I made my Foucault tester out of literal trash and recyclables with nothing more than a hacksaw, hand drill, file and some chunks of a cutting board. Use what you have! If you want to avoid using a focault tester, you can do a Ronchi test instead - that just involves a light and a small transparency with a bunch of lines on it. I ordered my grate transparency at Willman-Bell. You'll need to do some research as to what number of lines you'll need on it. It's not as exhaustive of an optical test as focault testing (or *shudder* caustic testing), but if you are just trying to get a mirror that you are reasonably happy with that you made yourself it's totally acceptable.
You'll need to test your mirror to see how spherical it is and if there are any issues, then polish it to a parabola. Stellafane has good resources on navigating this - it's a tricky thing to do but if you keep a log (recommended) of the process, you can get to a good result. I had help from a seasoned telescope maker, and am grateful for that. It takes patience and perseverance, but if you've come this far through this Instructable you have what it takes to finish it off!
Step 7: Send Off for Coating (optional, Informational Reading Past This Point)
This part and all that follows is all just for informational purposes since I had the fortunate opportunity to visit the coating facility where I had my mirror coated. Normally, you do all of the above steps then mail it to a coating facility where they coat it with aluminum and then send it back. I lived near a coating facility at the time in Iowa. I reached out and explained that I was just some rando who made his own little mirror and wanted to see the process they used to coat them. They graciously allowed me to awkwardly stand around in the facility and pepper the poor technician with questions over two days about how this works, so I thought I'd share that part simply because it's rather interesting.
Reflecting telescopes were originally made of metal, and the mirror was called a speculum. Metal is not as good as glass for a lot of reasons in telescopes, but it was shiny. Once techniques came along to coat glass with silver, metal was no longer used. Today, the mirrors are coated in aluminum - it doesn't tarnish as easily as silver. Mine is coated in aluminum, then a layer of tantalum pentoxide to increase how reflective it is, then a small layer of glass to seal it all.
How this is achieved is cool - they have a huge vacuum chamber that pulls a very strong vacuum. The mirrors are mounted on a big plate with the surface facing downward. They are placed in the top of the chamber and it's closed up, and a vacuum is pulled - this takes several hours. (In fact a day in my case - it was summer and the chamber equipment was overheating periodically, so we had to leave it overnight).
Once the vacuum is pulled, a couple of small pellets of aluminum are heated in a crucible at the bottom of the chamber. The crucible is heated and the aluminum is vaporized - it flows through the chamber and evenly coats the surface of the mirror and everything else in the chamber. There is a complicated quartz sensor that vibrates at a specific resonant frequency, and as the aluminum (or whatever else) is deposited on this sensor, it changes how it vibrates. Using this sensor, the technician can tell how many angstroms (a small, small unit of measurement) of material are deposited. Once the aluminum is done, tantalum pentoxide is then vaporized onto the surface to increase the albedo (reflectivity), then a thin layer of silica glass to seal it all up so that it doesn't tarnish.
After it's all coated, the vacuum is released and they pull the mirrors out all nice and shiny.
Step 8: Install in Telescope and Enjoy!
There are many resources to use when building your telescope. I love the book "All About Telescopes" by Sam Brown/Edmund Scientific (bonus: lots of drawings and interesting facial hair from the 1970s). It's out of print but easy to find used copies. "Build Your Own Telescope" by Richard Berry is very good too - lots of designs and techniques that are great. The books/resources recommended by Stellafane (again, read that website fully if you want a complete picture of this whole process) and here at Willman-Bell are all very useful.
I hope this Instructable demonstrates that making your telescope mirror can be done with a few simple hand tools, some research and a bit of persistence. I've used my telescope extensively since building it, and I learned a lot about how optics work and many things about woodworking and building that I've used since.
If you find this useful or inspirational, please vote for it in the Hand Tools Only Contest. Clear skies!
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