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Spherometer


FraserClarke
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Hi All,

I thought I'd put up some pictures of my spherometer, which might be useful to other mirror makers out there. A spherometer is used to, well, measure spheres as the name suggests! You use it to measure the radius of curvature of a mirror during grinding, which is useful if you're aiming for a specific focal length.

As you can see from the first image, this spherometer is nothing much fancier than a plate holding a dial indicator. Here it's sitting on a long forgotten 6" mirror which is almost (but not quite) polished out. For future reference the mirror is 35" (890mm) focal length, measured optically.

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Edited by FraserClarke
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Next image shows the base of the spherometer, and you can see that there are three ball bearings (1/4" in this case) which form the three contact points with the mirror surface. The ball bearings are set in small holes at 120 degree separation on a 100mm diameter circle, which I scribed out with a compass. The holes were just drilled with a 4mm (I think?) bit in a drill press, so that the balls sit on the edge of the hole, not the bottom. The balls are then held in with a spot of epoxy.

You can also see the tip of the dial indicator sticking through the central hole.

The baseplate was cut from a scrap of 1/4-inch aluminium plate. I edged it round in a lathe, but that's just a nicety and doesn't affect the operation at all.

post-18754-13387743813_thumb.jpg

Edited by FraserClarke
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This image shows a close up of the spigot I made to hold the neck of the dial indicator (via an M3 'grub' screw)

The dial indicator I had has a ~15mm 'tip', and a ~15mm neck to clamp on to. To avoid using too thick a bit of plate, I made a separate piece to hold the dial indicator. This was turned on the lathe from a bit of 1-inch bar. I drilled a hole through the middle which was a tight fit to the dial indicator neck, and turned down a step at the bottom to fit into the central hole in the base plate (you can see it in the previous image). I then drilled and tapped a hole through the side of the spigot for a M3 screw which locks the dial indicator in place. The spigot is epoxied into the baseplate.

Unfortunately I didn't take a picture of the spigot pre-assembly... hopefully my description is understandable?

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So, spherometer assembled. How to use... :)

First we sit the spherometer on a 'flat' surface and zero the dial indicator. Here I'm using a piece of ceramic tile, which isn't actually that flat (if you more the spherometer around, you can see the radius change) -- but it's good enough for demonstration purposes. Ideally you would want to do this on an optical reference flat. A surface plate would probably be good enough though.

If you look closely, you'll see the dial indicator is reading 3.00mm

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Now we move the spherometer onto the mirror, and see how the dial indicator changes. Now the indicator is reading 2.27mm. This is a concave mirror, so the middle is deeper than a flat surface, so the dial indicator is less 'pushed in'. So the middle of this mirror is 3.00-2.27 = 0.73mm deeper than at the position of the ball bearings. To turn this into a radius of curvature, we need some maths. I'll leave the details as an exercise for the reader :p -- but the result is;

ROC ~ r^2 / 2e

where 'r' is the radius of the circle the ball bearings sit on, and 'e' is the depth reading from the dial indicator (that equation is an approximation, but unless you need to control ROC to more than ~1cm it's good enough).

For my spherometer, the ball bearings are on a 100mm diameter circle, so r=50 (I could measure the actual radius to get a more accurate result). The dial indicator gave a depth of e=0.73mm. So the equation above gives us a ROC of

50^2 / 2*0.73 = 2500 / 1.46 = 1712 mm

For a spherical mirror, ROC = 2 * focal length, so focal length from this method is 856mm.

That's ~30mm different from the optical value, but I've only used approximate values. Measuring the actual manufactured radius of the circle the ball bearings sit on would improve that (an error of only 1mm in r would give the discrepancy in ROC we measure here). Still it's only out by 4%, which is more than good enough for most applications :)

post-18754-133877438146_thumb.jpg

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Hi Andy,

I can't remember where I got that dial indicator from; probably somewhere similar to the links billy points out. It was only ~10 quid. You don't anything very fancy. 10mm of travel and 0.01mm resolution is perfectly adequate for most situations.

EDIT -- remembered... I think it was 'DG2' from here; http://www.chronos.ltd.uk/acatalog/Chronos_Catalogue_Dial_Gauges___Dial_Indicators____Magnetic_Bases_73.html

Edited by FraserClarke
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Thanks for that link Teadwarf. Unfortunately it looks like there out of stock. Just found this at machine mart Clarke CM220 Dial Test Indicator - Machine Mart

Its more expensive, but not much, and the with the added bonus of they having a store at the end of the road. Saves having to wait for it to arrive in the post atleast. lol

Andy

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If you want a good quality surface plate ie a flat plate (to engineering, not optical, tolerances) go to Tesco and buy a granite worktop protector for around £10. It is as good as an engineers "proper" one that will set you back over £100. If you want a small one buy granite "coasters".

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bought my inch/0.001" dti off ebay on tuesday for £9.95 delivered. arrived today , looks great , next project, spherometer this sat avo, probably in steel triangle format with hard plastic feet /balls,

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