Stockton Astronomical Society
Valley Skies - September 2000 Issue
The Telescope Nut
by Jeff Baldwin
The Caustic Test
The standard test for figuring telescope mirrors is the Foucault test. When mirrors are of moderate aperture and mild f ratios, it is an outstanding test. When the apertures increase and the f ratios decrease, the Foucalt test becomes less able to leave the mirror with an acceptable figure. A more precise test is the caustic test.
The optician thinks that the Foucault test shows where the center of curvature is for each zone of the mirror. In fact this is incorrect; it actually shows where rays from these zones cross the optical axis. The centers of curvature for these zones don't even exist on the optical axis where the optician is examining the light. With slow, small mirrors it gives the appearance that the optical axis is where the centers of curvature exist, but with fast mirrors you can see that the shadows cross the zones on the Foucault test from the side of the razor rather than the zones darkening all over at once, implying that the razor isnít really at the center of curvature for the zone. The Foucault test is pretty good to around l/8 error peak-to-valley on the mirror, which is acceptable for moderately sized mirrors, so we use it. Itís a no-go with the big dudes, so a more precise examination is required.
The caustic test actually locates the center of curvature for each zone examined. These centers are not on the optical axis but rather back and to the side of the center of curvature of the center zone. For this reason a two dimensional test stand is required rather than the one dimensional Foucalt tester. The optician needs to know how far back he is from the center of curvature of the center zone, then from there he needs to move right to the center of curvature of the left zone and left for the center of curvature of the right zone, then measure the distance between the two. This measurement must be very close, the usual standard being 1.5 ten-thousandths of an inch. The testís precision is 1/400 the accuracy of this tolerance, which gives us a precision of .00015/400 inches, or 3/8 of a millionth of an inch, or 1/50 wave peak-to-valley error. If your test rig is accurate to 0.0001", then weíre talking 1/4,000,000 inch, or 1/80 wave peak-to-valley error. It is unreasonable to think that the mirror is in fact this accurate, especially since thermal contractions and atmospheric errors are far greater than this, but the test is theoretically much better than the Foucault test. Generally we end up with precision conclusions of 1/32 wave peak-to-valley and then claim 1/20 wave to keep us honest. The mirrors are then star tested before coating, and touch up work is never needed when these results occur. Proof: check out Ericís mirror.
What is a caustic? The caustic of a concave surface is the collection of points all of which are centers of curvature of the surface. For a circle, it is its center. For a sphere, the center of curvature of the sphere. For a parabola, it is a cardioid starting at the center of curvature of the vertex of the parabola and spreading away from the parabola. For a paraboloid, just revolve that cardioid about the optical axis. The three-dimensional cardioid looks like a trumpet horn, where the horn is pointing away from the vertex of the mirror. Prolate ellipsoids, oblate ellipsoids, hyperboloids and other aspheric mirrors have different caustics.
The test is so sensitive that precautions must be taken to get accurate data. All it takes to throw it all off is temperature changes in the shop, bringing the precision down to that of the Foucault test. An observer standing in the room on a concrete floor, then changing positions to another part of the room, may actually bend the floor enough to mess up the test. Flipping masks off zones from one zone setting to another may bump the mirror more than 1,000,000th of an inch, ruining the test. For this reason we use string attached to playing cards in front of the zones to open and close zones without touching the mirror. We avoid moving across the room. In Washington, we caustic tested in basements so that we could keep a constant temperature in the shop. Here in California basements are scarce, so garages must do. The temperature changes hourly in garages, so results are questionable. This is tough because the mirror needs to spend about a day equilibrating to the ambient temperature, then the setup for the test rig takes a couple of hours, then the test takes about an hour to do if nothing goes wrong. This is one of the reasons why more opticians donít do the caustic test. It is difficult and takes a lot of time. Other reasons are not knowing how to do it; not knowing what to do with the data; the Foucault test being accurate enough for moderate size mirrors; and star testing for qualitative results rather than quantitative results. All good reasons.
Why do the caustic test? Itís nice to have a high order test that can be done in a shop. Star testing is great, but there might be three months of adverse weather keeping you from star testing (I lived in Washington...this is a reality). Large, fast mirrors must have a test of higher order than the Foucault test. The caustic test is a reasonably easy test that yields results to nearly the same order as interferometry, Ross null test and autocollimation, all of which are either tricky, expensive or difficult.
As in the Foucault test, the caustic test doesnít address a couple of items: astigmatism and T.D.E. This means that the caustic test alone doesnít make the mirror perfect and, as in any test, it should not stand alone to confirm a mirrorís condition. Ronchi testing and star testing will test T.D.E., stig testing and star testing will test astigmatism, and star testing and knife-edge examination will confirm smoothness.
The Foucault test and the caustic test are similar and different when done. The Foucault test is done by masking the mirror with a couder mask with zones open on both right and left sides. Same with the caustic test, only you open two opposing zones at a time. Both can be used with a moving or stationary slit, both can be used with a wire or knife-edge, both move forward and back on a micrometer-based slider. The caustic test also has a transverse micrometer slider (X-Y stage). When doing the Foucault test you move the knife-edge to the place where the right and left zones black out simultaneously, write down the numbers, then move on to the next zone. On the caustic test you need to start out by finding the outermost zoneís X-reading, which is the distance between the centers of curvature of the two zone holes. You simply move to some location, measure how far apart the CoCs are, and adjust the longitudinal micrometer until that distance is within 1.5 ten-thousandths of an inch from perfect. Once this location is established, the routine is to move forward to the next zoneís longitudinal position, then measure the X-reading there, and repeat this for all the zones. If the numbers are too large, that zone is over-corrected; too small implies under-corrected. You simply work the mirror until the numbers are without error. When this happens, the precision of the mirror is OUTSTANDING.
There is a lot more to caustic testing than what I just outlined, and I have shown you no proofs. This is just the Readerís Digest Condensed Version. If you are interested in an in-depth discussion, or the mathematical proofs, you know where to find me.
As in the Foucault test, the errors found in the caustic test can be Root Mean Squared (RMS). During the figuring stages where the mirror is still not finished, you will have errors, and these errors can be RMSed to get an idea of how smooth the mirror is in addition to what its peak-to-valley error is. If the mirror has a peak-to-valley error of less than 1/4 wave and the RMS is less than 1/14 wave, it has met both the Raleigh and Dujon criteria of being diffraction limited. When the mirror has been caustic tested without error, then it is impossible to do an RMS because there will be no errors to average and square. This does not mean there is no RMS error, just that it is too small to be calculated by the caustic test. An interferometric examination will determine an RMS error. If it passes the caustic test, then you know the RMS is going to be remarkably small.
The caustic test is my favorite test. I have not gone
into enough detail to fully describe itósorry, but itís too much for this
forum. Hopefully someday there will be other members in our ATM group who
will be active caustic testers.
Clear Glass...Jeff Baldwin
Copyright © 2000 by Jeff Baldwin
For more information on Telescope making jump to the ATM page.
Lasted Updated: 12/10/2000
Clear Glass...Jeff Baldwin
Copyright © 2000 by Jeff Baldwin