Hi,
A while ago I decided that (rather than buy an acrylic sphere) I would make one, from an acrylic block. (I want the sphere for photography) This turned out to be much much more difficult, and laborious, than I had expected. I will spare you the details of how I got to where I am now, but it was NOT easy.
At this point I have a nearly round object, and completely transparent. It’s round enough to appear so to the touch and eye, but not to the photographic lens, since the images are lightly distorted. My calipers measure to 1/100th of an inch, and the variation in diameter is a maximum of 1/100th.
I would like to get it rounder, if possible; but most of the equipment for doing this is not worth investing in for one project. In my search for a DIY method I came across this (straightdope) site. An old article, here, refers to several methods that might work, i.e. for making deodorant roll-on balls and billiard balls, but the links were either dead or not informative enough.
Does anyone have a relatively low tech method that I can use here?
Thanks,
… john
How big is the sphere?
If it is the size of a bowling ball, the Cook Sphere Machine (with the right Abralon pads, starting with rougher and moving to smoother and smoother, finishing with polishing) may do the job.
If that’s not the size, something jury-rigged with slow-speed drills and abralon pads, but the same principle as in the video above?
In case you’re not aware, a perfect sphere will naturally form a distorted image, with some “pincushion” distortion or “barrel” distortion. This is because the light rays passing through the edges of the sphere are not focused to the same point as rays passing through the center, a phenomenon known as spherical aberration.
I mention this because it sounds like you think the distortion is caused by your sphere not being perfectly round; but in fact a perfect sphere should form a distorted image. It’s also possible that your images are distorted due to astigmatism of the sphere, which would be caused by it not being perfectly round. Without knowing which type of distortion you have, it’s hard to say what the cause is.
Is there much, if any, run-out? Tell me you didn’t do this on a lathe just using the hand wheels. Though I am very curious how you got to where you are right now…
It’s very hard to construct a really good sphere. Woodworkers do it on lathes using a special jig for the cutting tool and even then there’s going to be small spot that has to be hand-shaped where the object is mounted to the lathe. That usually doesn’t matter for something like an ornamental knob since it’s still going to be attached to something else. I doubt they get to 1/100" precision anyway. Ball bearings are made with a multi-step process of grinding and passing the balls through slots and holes of specific dimensions followed by careful polishing and high precision measurement, so no new ball stamped into a nearly spherical shape to start with necessarily ends up with any particular diameter, and many will be rejected and reformed because they are too far off the shape. Hopefully, as noted above the distortion you get is only from optical properties of the materials.
Also, most plastic materials are going to be subject to distortion in a variety of ways, they may continue to outgas plasticizers over time changing the density at any location, the material may not have consistent density to start with and changes in temperature will distort the shape, and many acrylics will absorb a certain amount of water changing their shape.
Machining an optically correct curve is no trivial job. 1/100 of an inch is literally thousands of times larger than the tolerances aimed at when making, for example a telescope mirror. To be nearly perfect optically, you want your surface to be accurate to 1/4 the wavelength of light, about 100 nanometers, or 4 millionths of an inch. There’s no way to measure that mechanically, you have to use optical instruments. I know how to get a spherical or parabolic mirror or lens to that shape (did it once, what a tedious job), but I don’t know how you would do a complete sphere.
Okrahoma - The Sphere is ~ 2.30 inches in diameter. The block I cut it from was slightly larger. Thanks for the shortcut. Yes, this is probably an excellent method. (I presume one would replace the buffing pads with something a little more cutting.) I was hoping I wouldn’t have to go to such lengths, since I will not likely ever do this again.
MikeS - The barrel distortion and pincushioning are exactly what I want. Using a sphere is a poor man’s way of creating the fisheye effect. Good fisheye lenses are very expensive. I’m beginning to realize why. In general terms the sphere does what I want, but I’m also getting wobbles in what should be smooth curves, i.e. railings, posts etc. These I believe are caused by slight variations in the surface curvature; similar to what one gets if he were to polish a scratch out of a lens.
Monkey Mensch - “run-out”?? No, I didn’t do it on a lathe. if I had, I might have a better result. No, I cut it from a block by first cutting the corners off. Then I hot melted one side to a disk, which allowed me to shave it close to a spherical on the drill press. The remaining steps involved a rotary sander, files, progressively finer sandpapers, and finally polishing with a drill and homemade cup attachment lined with felt, and cerium oxide. The result looks impressive, but it’s still not round enough.
Tripolar - Yes, you could be right. I might be dealing with factors other than the ‘roundness’ of my sphere. However, before I toss in the towel I would like try and get it not measureably out of round, at least by my crude calipers.
markn+ - Yes, it took me a long time, but somewhere along the line I realized that this is a very challenging project. In retrospect, I should have bought a cast sphere for few dollars on ebay, or cast my own. Live and learn.
Is this something that might be easier corrected in post?
If you shoot a calibrated grid through your homemade spherical lens, you can generate a distortion profile for it: http://wwwimages.adobe.com/content/dam/Adobe/en/products/photoshop/pdfs/lensprofile_creator_userguide.pdf (PDF warning) and then just correct the distortion to whatever you want it to be afterward… maybe that’s cheating to you.
That just shows the width of your object is constant within that tolerance. That doesn’t guarantee that it’s a sphere. The Meissner tetrahedron is a regular shape that is one example of a non-spherical solid of constant width. Reuleaux tetrahedron - Wikipedia
For the 2-D case, see Curve of constant width - Wikipedia.
Warning: even perfection can have its downside.
Spoilered to comply with two-click nsfw rule…
Reply - ‘cheating’? … no problem. Thanks for the link. I may have to resort to it, if I can’t get it ‘rounder’.
rowrrbazzle - Yes. I eventually came to a similar conclusion, after sanding and sanding and sanding made little change in the tolerance. So, I eventually put it between two files and kept rotating and reducing the opening until it was a constant 2.30 - 2.31 inches in diameter. I ‘think’ that addressed this issue. But one can only get so much precision doing this. It’s been a real challenge.
kaylasdad - Oh yes. You’re preaching to the choir now ;- )
… john
Some people are purists about that kinda stuff! If you’re not, once you have a lens profile, applying it to new photos is a single click away in Lightroom.
I’m not sure how it works with fisheye or near fisheye lenses, though. I used one with an 11mm lens and it was fine, but if it’s much wider than that, I dunno what would happen…
Hi All,
I have made one last attempt at reducing the tolerance in the diameter of this ball. I used the same method I used to get it to where it was; but this time I used fine sandpaper in lieu of files. What I did is stick sandpaper to the jaws of my vice and constantly rotate (by hand) the ball, in all directions, between the jaws. I did this, while occasionally making the gap smaller, until there were no spots where the vice did not touch both sides. In this way I was able to reduce the maximum diameter variation to less then 1 sheet of paper thickness (<0.003"). My photos now show no wobbles in what are actually straight lines. I want to thank you all for your patience and help with this project. I learned a lot and very much appreciate your suggestions. I do NOT recommend this procedure. It was very laborious and tedious.
Thanks again,
… john
You are a man out of time.
I remember reading a passage where Ernest Rutherford paid a visit to Charles Wilson, and talked to him while Wilson sat on a stool, meticulously polishing the cylinder for his cloud chamber. He came back some six months later, to find Wilson in the same spot, still polishing the same cylinder…