SPHEROMETERS.

Page 1.

I made a spherometer over thirty years ago. It was a ring type and is illustrated later (No. 5). I made it out of the outer race of a ball bearing. At slow speed and using a tungsten carbide tool I machined the small radius off one side. This gave a hard sharp edge that would not bruise or wear. I measured the Sagitta on a 6" dia. f/8 mirror I had and calculated the radius of curvature. This was several inches different from the measurement from the centre of the mirror to the knife edge taken on my Focault tester. I pondered this for a while but as I had other hings to do. forgot about it.

Now all these years later after a break in telescope making, I decided to make Cassegrain optics and maybe iater try my hand at a Maksutov corrector. For this I would need a spherometer. I referred to articles on the subject in the following books I have.

There are three main designs; the ring type, two leg and three leg using pins or balls. A micrometer or dial indicator can be used. It would appear that the micrometer is the more accurate. On a dial gauge reading to. 01 mm. with a 35mm. dial 1 mm. travel of the plunger is multiplied 110 times by gearing. Thre could be tooth errors causing periodic error. Fillmore says he checked his with Gauge blocks and noted the errors. D. Everett Taylor in ATM Book 2 prefers a dial gauge as there is not the problem of feel when using a micrometer. Horne says that measurements of .00001" are possible with a micrometer. This would be a .0001' direct reading type (no Vernier) with a 2" diameter thimble. I believe that with a magnifier I could read to. 00001". But I doubt I would have much feel on a thimble that size. With the 9/16" dia. thimble on my micrometer I would have some feel and could read to .00005'.

I decided to do some calculations to see how accurate a reading was necessary for what I had in mind. As I wanted to use the same tooling for making the optics for the Maksutov as the Cassegrain, I selected a f/15 design of John Gregory. This was the same that Fillmore made. In the following calculations I shall use Fillmores dimensions and his Spherometer. In the grinding specifications for the primary and corrector he gives a tolerance of plus and minus .005". Can diamond milling be done to this degree of accuracy? I don't know. How was the radius measured? With a spherometer? John Gregory puts a tolerance of plus and minus .500" on the primary and .070" on the secondary. More practical. Let us now investigate this. Below is a drawing of a mirror blank showing the three dimensions we are interested in. Also the equations I used for all my calculations. I used a caiculater giving answers to ten decimal places.

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