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3D Printing a Spherometer - Does it need adjustable legs?

ATM Mirror Making
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#1 Noobulosity

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Posted 04 November 2021 - 05:59 PM

I'm just about to embark on my first-ever mirror-grinding experience.  To help ensure I get a solid start, I'm planning to 3D print a spherometer and fit a dial indicator into it.  However, I was planning to epoxy 3/8" steel ball bearings into dimples, and I'm seeing other people using bolts instead.  Are these bolts recommended if I'm printing my own base?  Does it need adjustable legs?  Or will it be just fine to use the ball bearings as they are?

 

For reference, here are shots containing a couple of initial designs.  I'm not set on the full circle on the smaller one.  I don't know that it's really necessary there, but it may help with holding and moving it around.  The larger one is a 6" base and the smaller one is 3".  They'll fit a Mitutoyo dial gauge, if all goes well, and allow for about 3/8" of depth measurement.  Should be plenty on a small mirror.

 

51655457988_1be00eda4a_c.jpg

 

51654421747_91f409b1b4_c.jpg



#2 geovermont

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Posted 04 November 2021 - 06:32 PM

I wouldn't bother to make such a device for your first mirror. All you need is a straight edge and either a set of feeler gauges or a set of drill bits to slip under. That and using the sun to make an image on the wetted disk will get the job done. See the mirror-making guide at the Springfield Telescope Makers website or any of the standard books.



#3 BGRE

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Posted 04 November 2021 - 06:43 PM

If you only use it the measure concave surfaces adjustable length legs shouldn't be required.
If measuring short RoC convex surfaces then longer legs will be required.
For smaller diameter surfaces legs closer to the centre will be necessary.

https://trioptics.co...#technical-data

Illustrates the geometric details of several Trioptics spherometers.

Edited by BGRE, 04 November 2021 - 06:53 PM.

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#4 Noobulosity

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Posted 04 November 2021 - 07:09 PM

I wouldn't bother to make such a device for your first mirror. All you need is a straight edge and either a set of feeler gauges or a set of drill bits to slip under. That and using the sun to make an image on the wetted disk will get the job done. See the mirror-making guide at the Springfield Telescope Makers website or any of the standard books.

I already read through a lot of the Stellafane material, including all of the grinding and polishing information.  I wish they had more on parabolizing...  But, I have on loan a copy of "How to Make a Telescope" by Texereau and purchased a copy of "Build Your Own Telescope" by Berry, so those are what I'm working through now.  I decided to go with a spherometer because, well...  I'm an engineer.  And everyone knows engineers tend to over-complicate things on the first go.  I don't see why having a spherometer to check the curvature is a bad thing.  I have a straight edge and feeler gauges, but a spherometer is easy to use and accurate, plus I have a 3D printer.  So, why not?

 

If you only use it the measure concave surfaces adjustable length legs shouldn't be required.
If measuring short RoC convex surfaces then longer legs will be required.
For smaller diameter surfaces legs closer to the centre will be necessary.

https://trioptics.co...#technical-data

Illustrates the geometric details of several Trioptics spherometers.

I was thinking there must be a reason for the longer legs, and measuring convex lenses makes a lot of sense.  Thanks!

 

I was considering the smaller version to check for uniformity and zones requiring some correction around the mirror blank when I verify my rough/fine grinding.  Probably overkill for a beginner, but it's easy enough to print one and give it a shot.



#5 MKV

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Posted 05 November 2021 - 02:07 AM

For reference, here are shots containing a couple of initial designs.  I'm not set on the full circle on the smaller one.  I don't know that it's really necessary there, but it may help with holding and moving it around.  The larger one is a 6" base and the smaller one is 3".  They'll fit a Mitutoyo dial gauge, if all goes well, and allow for about 3/8" of depth measurement.  Should be plenty on a small mirror.

 

Calculate the deepest sagitta (depth or height of a mirror surface) you're likely to encounter with your spherometer and then make the legs adequate for that. You'll be able to measure smaller depths/heights easily with that.

 

For instance, say that for now you'll most likely see a mirror that's a 10-inch clear diameter D, with a radius of curvature R of 60 inches (f/3). Your sagitta even with a spherometer spanning 8 inches will be less than 3/16". Most people, especially less experienced ones, are unlikely to make a 10-inch f/3 mirror. If you're 3D printing your spherometers, it's just as easy to make one with larger ball contacts, in case you decide to make something with deeper surfaces, like a Maksutov corrector. :o)

 

One thing to keep in mind is to make the spherometer body as robust as and stiff as possible to avoid flexure, and from the looks of your illustrations, you're already doing that, so  waytogo.gif!

 

For parabolic mirrors used in Newtonians a precise radius of curvature is not critical, however for Cassegrains and compound configurations, the radii of curvature have to match meet tight tolerances. Also, if possible, calibrate your spherometer against a certified surface.of a known radius of curvature

 

Every spherometer has two internal errors. One error is the in the distance between the ball contact. This distance is measured mechanically (usually with calipers) with an uncertainty of anywhere from 0.005 o 0.01 mm, depending on the model used. 3D printers operate at an accuracy of 0.1 mm, possibly more. The second source of error is your depth gauge/dial indicator.

 

In order to calculate your internal (repeating) spherometer error you need to take the error of the spherometer radius (dr) and that of  your dial indicator into account (ds). The latter is usually found in the indicator's manufacturer's literature and is typically of the order of ±02 to 0.002 mm); again more expensive gauges may do better than that..

 

The error fraction contribution to the radius of curvature by the radius of the spherometer contact points Δr = (r/s)*dr, and of the dial indicator spindle, Δs = ((s/r)² − 1)*ds/2. The total reading error contribution of your spherometer then equals Δr + Δs. *(see reference below)

 

This then is your uncertainty factor in calculating the radius of curvature of a test mirror/lens measured by the spherometer.

 

Let's say that your spherometer r = 50 mm, dr = 0.1 mm, sagitta depth s = 1.25 mm, and sagitta error contribution ds = 0.002 mm.

 

Then Δr = (r/s)dr = 4, and your Δs = 0.5((s/r)² − 1)ds = 1.599, hence the total spherometer error contribution is 4 + 1.599 = ± 5.599 ≈ ± 5.6 mm.

 

Based on the sagitta of 1.250 mm and spherometer radius of 50, your radius of curvature R = (r² + s²)/2s  = 1000.625±5.6 mm. The true R is somewhere between 995.025 and 1005.6 mm.

 

The actual R is 1,000 mm, but the reason you are getting 1000.625 is because your measurements have inherent errors in them even if your measuring techniques are flawless. In order for your R to read 1,000 your sagitta should have been known down to six decimal places -- 1.250782 mm! Still your results are very much in the acceptable tolerance envelope: (1000/1000.625)*100 = 99.94% accuracy.

 

I don't know what kind of thermal expansion and contraction is expected from 3D printed objects. That should have to be taken into account by recalibrating the spherometer before each use. The same is true of precision machined metal spherometers.

 

Mladen

 

*Ref: William M. Browne, Advanced Telescope Making Techniques, Mechanical, Willmann-Bell, 1986, p.109

______________

 

Edit: typos


Edited by MKV, 05 November 2021 - 11:00 AM.

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#6 Noobulosity

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Posted 05 November 2021 - 12:49 PM

.....[lots of info].....

Thank you for all of that information!  This will be quite helpful in properly measuring and understanding readings as I go.  Obviously, I won't be measuring down to microns with a relatively-inexpensive dial indicator.  However, the one I purchased is a calibrated Mitutoyo 2416S with the included factory calibration specifying an error of approximately 0.00025" over a full revolution of the needle on the dial, so quite good at this price range.  The dial only indicates measurements down to 0.001".

 

As you noted, I am shooting for high rigidity in my printed designs to avoid flexure throwing off the measurements.  As the dial indicator moves fairly freely, I suspect it shouldn't flex very much at all.

 

For ball contacts, I went with steel ball bearings for a nice, spherical surface.  Obviously, there's still some error in the spherical shape, but this should be quite a bit better than printing a ball as part of the frame.  I saw one video where ruby spheres were attached to the legs.  Seems a bit overkill for my current application...  if I get into this as a larger hobby, I may consider buying better measuring and testing equipment down the road.

 

As for calibrating the spherometer, I have a granite plate I use for sharpening.  This is ground flat and calibrated, though I don't know if I still have the calibration sheet for the plate anymore.  It should be flat to within 0.0001" or better across the plate, according to the specs on the item page.

 

Despite the apparent simplicity of the grinding process, there's an amazing amount of technical depth to get sucked into if you start looking!



#7 chantepierre

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Posted 05 November 2021 - 02:04 PM

Coating the mirror with oil or glycerine and measuring ROC with a foucault tester is handy when you feel you are in your spherometer's error margin territory.

I now know this because I trusted my spherometer too far in the process of grinding my 153mm f/10 and it came at 1380mm of focal length. Other people use shoe wax I think.

Edited by chantepierre, 05 November 2021 - 02:06 PM.


#8 Noobulosity

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Posted 05 November 2021 - 03:36 PM

Coating the mirror with oil or glycerine and measuring ROC with a foucault tester is handy when you feel you are in your spherometer's error margin territory.

I now know this because I trusted my spherometer too far in the process of grinding my 153mm f/10 and it came at 1380mm of focal length. Other people use shoe wax I think.

So, you do this after rough grinding to test for the radius?  Also, did you use a full-diameter spherometer?  Or was yours sub-diameter?  For testing, I have a piece of Ronchi screen that I'll use.  I need to figure out if I want to build a Foucault tester.

 

While you ground a little too far, the upside is a faster focal ratio.  :)



#9 MKV

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Posted 05 November 2021 - 06:57 PM

For ball contacts, I went with steel ball bearings for a nice, spherical surface.  

Steel ball feet you find in a hardware store are fine for your purposes. Be aware that the steel balls will rust, and rust will scratch your glass surface. On a regular basis, ether keep the spherical contacts very lightly oiled (a touch of oil on a lint-less napkin and then wipe it off, to prevent rust, or replace them with stainless steel ball feet (preferably), and regularly wipe them with a mciro fiber cloth before use.

 

Glycerine is one of many ways to accomplish the task for a Newtonian mirror curvature. Using a spherometer is more versatile for all stages of mirror making. Otherwise, a simple straightedge and a drill bit will give you a good idea what sagitta you have. 


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#10 Noobulosity

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Posted 05 November 2021 - 07:07 PM

Steel ball feet you find in a hardware store are fine for your purposes. Be aware that the steel balls will rust, and rust will scratch your glass surface. On a regular basis, ether keep the spherical contacts very lightly oiled (a touch of oil on a lint-less napkin and then wipe it off, to prevent rust, or replace them with stainless steel ball feet (preferably), and regularly wipe them with a mciro fiber cloth before use.

 

Glycerine is one of many ways to accomplish the task for a Newtonian mirror curvature. Using a spherometer is more versatile for all stages of mirror making. Otherwise, a simple straightedge and a drill bit will give you a good idea what sagitta you have. 

The bearings I have are chrome steel and will likely rust if left exposed.  I'll make sure to coat them in something.  Thanks for reminding me to do this.

 

As for glycerine, I'm confident I have some in the medicine cabinet.  I bought a small bottle for enhancing wet-shaving creams and soaps with a drop or two.  Should be plenty left.



#11 MKV

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Posted 05 November 2021 - 10:05 PM

As for glycerine, I'm confident I have some in the medicine cabinet.  I bought a small bottle for enhancing wet-shaving creams and soaps with a drop or two.  Should be plenty left.

I find a drill bit very convenient -- and clean. :o)

 

sag drill bit.jpg

 

With fractional drill sizes you can sneak up to 99% of the design value in most cases.

 

Mladen



#12 Noobulosity

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Posted 06 November 2021 - 02:16 AM

I find a drill bit very convenient -- and clean. :o)

 

attachicon.gifsag drill bit.jpg

 

With fractional drill sizes you can sneak up to 99% of the design value in most cases.

 

Mladen

Now I'm a bit confused.  What's the glycerine for, exactly?



#13 MKV

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Posted 06 November 2021 - 05:26 AM

Now I'm a bit confused.  What's the glycerine for, exactly?

Glycerin makes the ground surface somewhat shiny so it eflects light. People use it to "wet" the surface and point their ground blank to the sun and measure the rough image distance they get from the reflection. Others use a Foucault tester to estimate where the radius of curvature is. 



#14 GLS

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Posted 06 November 2021 - 06:25 AM

Don't sell short the age old compass technique of making a template by scribing a line on cardboard with a wooden batten with a nail holding it to a wooden surface and a sharp pencil affixed at the ROC distance from the nail allowing the batten to sweep the prescribed arc.  Carefully cut out the template with sharp scissors.  A glass cutter can also scribe a line on a pane of window glass which can be precisely broken along the scribe.  I've used glass window pane as well as shirt cardboard cut with an Xacto blade affixed to the batten's end.  Using this method combined with the sun's image measurements to hit ROC.  Another trick is to put the wet mirror on a stand and hold a flashlight even with your dominant  and move the flashlight right and left. If the image moves in the same direction as your head moved side to side, you are inside ROC; if movement is opposite head movement, you are outside target ROC.  Gil


Edited by GLS, 06 November 2021 - 06:26 AM.

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#15 Arjan

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Posted 06 November 2021 - 09:52 AM

I find a drill bit very convenient -- and clean. :o)

Indeed, a spherometer only gives accurate results when you measure a sphere. As long as you are digging the hole to get your mirror in the ballpark of the required RoC, the curve is rarely a sphere.

Better to measure sagitta directly using a drill bit and a straight edge. When you're at the target sagitta, first approach a spherical curve with finer grit and interchanging ToT and MoT. When you have good overall contact it is time to use a spherometer or wet the surface and do a flashlight test.

 

I built a spherometer once, used it once and then never more.



#16 MKV

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Posted 06 November 2021 - 12:21 PM

I built a spherometer once, used it once and then never more.

For compound and specialized configuration and certain occasions (Maksutovs, Houghtons, Cassegrains, glass objectives, polished mirrors etc.) you need a spherometer. For rough ground mirrors, a drill bit or a wet surface is all you need, but it doesn't hurt to use a spherometer. For Newtonian mirrors the RoC can be half an inch or even more longer or shorter, so any method will work.

 

Unless the actual figure is very, very fast, sagitta difference between a sphere and a parabola is negligible. For example the difference in sagitta between a 10-inch f/4 parabola and a sphere is 3.8 microns. Most home-made spherometers have a total reading error much bigger than that. To read focal lengths and radii of curvature to a micron accuracy, an autostigmatic microscope is the tool of choice. And that's hardly something you'll commonly find in an ATM's toolbox.

 

Edit: typos


Edited by MKV, 06 November 2021 - 02:43 PM.

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#17 Noobulosity

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Posted 06 November 2021 - 06:07 PM

For compound and specialized configuration and certain occasions (Maksutovs, Houghtons, Cassegrains, glass objectives, polished mirrors etc.) you need a spherometer. For rough ground mirrors, a drill bit or a wet surface is all you need, but it doesn't hurt to use a spherometer. For Newtonian mirrors the RoC can be half an inch or even more longer or shorter, so any method will work.

 

Unless the actual figure is very, very fast, sagitta difference between a sphere and a parabola is negligible. For example the difference in sagitta between a 10-inch f/4 parabola and a sphere is 3.8 microns. Most home-made spherometers have a total reading error much bigger than that. To read focal lengths and radii of curvature to a micron accuracy, an autostigmatic microscope is the tool of choice. And that's hardly something you'll commonly find in an ATM's toolbox.

 

Edit: typos

Yep, as I've been reading more on mirror-making, figuring a parabaloidal mirror is basically just a very, very small difference from a spherical shape.  I realize my spherometer is likely overkill for my own use.  My dial indicator will in no way be useful for final figuring.  But, I have a 3D printer and it's easy to make.  Why not?  Plus, it seems less fiddly than sliding feeler gauges around or picking out various drill bits.  .........  and I just like making and printing stuff, lol.

 

When you say the RoC can be plus or minus half an inch, are you just referring to getting close to the focal ratio you intended to grind?  Or is there more to that statement?  My intent with the 6" mirror is to shoot for maybe f/6 or f/8.  I haven't really decided, yet.  For the 10" blank I have, I was considering f/5 or so to avoid a really long OTA.



#18 Noobulosity

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Posted 06 November 2021 - 11:36 PM

Initial designs are printed.  I may redo or try to refit the smaller one to get a tighter fit on the dial indicator, but it should stay put just fine anyway as long as I don't turn it upside-down.  The ball bearings are held in with hot glue.  It sticks surprisingly-well to PLA. So much so that it can be a bit challenging to pull it back off cleanly.  Those bearings are not coming out on their own.  The dial indicator is just held in place with friction.

 

3in spherometer:

51661296170_73d2195421_z.jpg

 

51661098509_7b2c3dcf39_z.jpg

 

6in spherometer:

51660420211_c06eed326f_z.jpg

 

51659616697_2a40685fff_z.jpg


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#19 MKV

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Posted 07 November 2021 - 02:08 AM

Yep, as I've been reading more on mirror-making, figuring a parabaloidal mirror is basically just a very, very small difference from a spherical shape.  I realize my spherometer is likely overkill for my own use.  My dial indicator will in no way be useful for final figuring.  But, I have a 3D printer and it's easy to make.  Why not?  Plus, it seems less fiddly than sliding feeler gauges around or picking out various drill bits.  .........  and I just like making and printing stuff, lol.

I agree with you 100%! 

 

 

When you say the RoC can be plus or minus half an inch, are you just referring to getting close to the focal ratio you intended to grind?

Yes.


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#20 MKV

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Posted 07 November 2021 - 02:26 AM

The dial indicator is just held in place with friction.

 

No, you need to drill and tap a hole for a machine screw to hold it. Alternatively, just drill a hole and use a self-tapping machine screw. The dial indicator must be secure in its housing lest you get false reading. Otherwise, you can reduce the 3D print file dimension for the dial indicator housing diameter by a small amount to get a slightly tighter fit. However, you'll still need a side screw to hold it securely. In fact you can add a hole that will be  big enough for the self-tapping screw in the new file (saves you from drilling a hole!) and print a new spherometer housing. 


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#21 BGRE

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Posted 07 November 2021 - 06:00 AM

Either that or print an integral flexure clamp for the stem of the dial indicator.

#22 MKV

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Posted 07 November 2021 - 02:26 PM

Either that or print an integral flexure clamp for the stem of the dial indicator.

Yes, that would be ideal, but if the fit is sufficiently tight with no perceptible play, then a simple side tension screw is all you need. Another thing to consider is whether integral flexure claps are good for the plastic material used in 3D printing.



#23 Noobulosity

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Posted 07 November 2021 - 10:31 PM

At least with the larger 6" version, the fit is quite snug with zero noticeable wobble.  The black version is a little looser, but still fairly snug.  It does wobble just a touch, so I may reprint that one with the slightly smaller hole I used on the blue version to get the same tight fit.

 

Once again, I'm a little bit confused by the information here.  Initially, it seemed that a spherometer was overkill and that a simple metal ruler and drill bits or feeler gauges was fine.  Wouldn't I get a less-accurate reading from that method than these spherometers with a dial indicator?  I thought with making the spherical figure that it wasn't super critical to get really precise readings everywhere.  That's what the Foucault tester and Ronchi screen are for, right?



#24 MKV

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Posted 07 November 2021 - 11:43 PM

Once again, I'm a little bit confused by the information here.  Initially, it seemed that a spherometer was overkill and that a simple metal ruler and drill bits or feeler gauges was fine.  Wouldn't I get a less-accurate reading from that method than these spherometers with a dial indicator?  I thought with making the spherical figure that it wasn't super critical to get really precise readings everywhere.  That's what the Foucault tester and Ronchi screen are for, right?

It makes little sense to make a spherometer and then make it intentionally less accurate than it can be. For rough ground surfaces a spherometer is an overkill, but hopefully you'll use it on fine ground and finished surfaces as well. Otherwise just use glycerine, as someone suggested.

 

Your Foucault tester and and your Ronchi screen can also test the radius of curvature -- of a polished and finished concave surface. A spherometer can test the RoC of any surface, including the convex ones. With a spherometer. you also find a replacement for a cracked piece of optics.


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#25 Oregon-raybender

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Posted 08 November 2021 - 10:46 PM

You can set the sphereometer to the the value you want by using gage blocks under the 3 points raising the unit. This will allow you to set it to indicator to zero. This is one way to improve the measurement. The indicator does not travel it's length which increases the errors. If you a .0001" dial it really improves.

Just a thought.

 

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