Bath and Ceravolo Interferometry
Foucault testing is adequate for moderate apertures and focal ratios and moderate quality, but to improve quality, increase aperture, and shorten focal ratio, it is highly recommended that the mirror is completed using either a Bath interferometer or a Fizeau interferometer. These use interference fringes to test the mirror’s wave-front to a very high precision.
For the Fizeau [Peter Ceravolo’s design and components], we use a 632.8 nm gas tube laser, which is phase, polarized monochromatic light shining onto and reflecting off of a reference surface and off of the mirror to recombine into interference patterns. The shapes of these interference patterns are rulers comparing the differences between the reference’s and the optic’s wave-fronts. If the wave-fronts are exactly the same, their interference patterns will be straight lines alternating dark and bright. If the reference is a sphere and the optic is a paraboloid, then the fringes will not be straight but will have a specifically-shaped curve. We use Open Fringe, a software written by Dale Eason, to analyze these fringes to determine if the mirror is a paraboloid or of expected quality. Open Fringe shows where the mirror needs correction, and we repair the aberrations and retest the mirror until it is of a minute enough error that we finally declare the mirror complete.
Jeff’s Fizeau interferometer. From the left is the reference lens, the 15mm cube beam-splitter, the GRIN lens, finally the gas tube HeNe laser. Between the GRIN and the laser will be a polarizer. On this side of the cube beam-splitter will be a spatial filter, and then the camera. The whole apparatus is sitting upon an X-Y-Z stage for micro control and positioning. Other than the stage, the lens, beam-splitter, GRIN lens, laser and material cost about $600. Diode lasers supposedly don’t work well on Fizeaus since the coherence is too broad, 1 nm as compared to 0.01 nm. I haven ‘t tried it yet, I’d like to just to see what I get. It would make this so much smaller and easier to use-transport-store, and they would be cheaper to build
Jeff’s Bath interferometer. On the left is a 650 nm diode laser, and on the right is a three-piece unit consisting of a 10mm cube beam splitter, a 5mm plan0-convex lens, and a 45 degree prism. They are all glued together using UV curing glue. They are held to the tripod with an X-Y-Z stage. It takes only about 2 minutes to set up and obtain fringes. Other than the tripod and the stage, the laser, optics, glass, batteries, switch and wires only cost about $50.
The Ceravolo Fizeau interferometer compares the wave-front of the mirror with that of a high quality reference sphere. The Bath interferometer “cheats” a little by not having a reference sphere, but by passing the light through a lens twice, once before striking the mirror and once after striking the mirror, and then recombines these wave-fronts. It is a “common path” interferometer. Since the light is passing through the same lens exactly the same way, then a high quality reference sphere is not needed, and the apparatus can be built with less money or precision. Both offer high precision fringe analysis to be entered into Open Fringe. The Bath also has the light passing through a minute ;piece of optic. Between that and the fact that it is common path, very cheap components can be used. It is an off-axis interferometer, and that has to be accounted for in the software, where the Fizeau is on-axis.
The Raleigh criteria for diffraction-limited mirrors is that the peak to valley error [P-V] does not exceed l/4, and the Root Mean Square standard deviation [RMS] does not exceed l/14. That will place 80% of the light that was supposed to go into the Airy disk into it. However, it is known that higher precision mirrors with higher Strehl ratios perform visually and photographically better if the Strehl ratio is higher, and it is also known that once you get to 94%, a higher quality is not visually or photographically improvable. So at our shop we aim for a Strehl ratio of 94%, which puts the needs of the optic’s wave-front at l/10 P-V and l/26 RMS. Many shops boast about higher RMS values, but those are boasting figures, and may not hold true when side-by-side comparisons are made. If a mirror maker wants to improve their mirror beyond our criteria, we’re not going to hold them back. However, fringe analysis with large-fast mirrors may have resolution issues with Open Fringe and the results may not be true to the interferogram report. For smaller, slow optics with less numerous fringe images, there’s no reason for us to hold you back if your goal is high Strehl ratio numbers. The Bath has an issue in that faster than f/5 the return beam is very difficult to cover the optic. A short focal length lens and a small beam splitter helps a lot, but it is very difficult even with these. The Fizeau is optically good to about f/1.6, but if your mirror is fast and fat the crooked fringes may be difficult to analyze with Open Fringe.
There are two interferometers in our shop, a Bath and a Ceravolo. Three if you count the Newton interferometer we use for testing flats. Some other members have made Baths as well, but Jeff’s is the only Ceravolo unit. There is an excellent Yahoo Group doing interferometry, and we suggest that if you are going to test mirrors this way you subscribe to it where real authorities exist. Dale Eason, David Rowe, Peter Ceravolo and many others on that group are wonderful at this and can share their expertise with you.
Meanwhile, if you want to test your mirrors with this equipment and would like to learn to use and make interferometers, please join us in the shop.
Above is an interferogram of Jeff’s Celestron 6” f/5 paraboloidal mirror with an error of about l/2. We like to shoot three or four images in each of five rotational positions, then average them all together. This cancels out the test stand astigmatism leaving only that which resides in the mirror.
Above is an interferogram of Jeff’s 24” f/3.75 as it appeared as a l/2 mirror. The interferogram has lots of pollution in it to be cleaned up and as a result had 511 unwrap errors in Open Fringe. The Bath in the shop has a 5mm biconvex lens and a 10mm cube beam-splitter, which enables us to do fast mirrors. We’ll use the Ceravolo unit to do faster mirrors than f/3.6. Our plan is for this mirror to finish off at least as good as l/10 P-V, l/26 RMS, with a Strehl of 0.94. Hopefully the Bath will allow this for such a large, fast mirror. This shot was taken 6-20-2013. Additional note: this mirror was completed with the SIT test, which evaluated it as l/25 P-V, 0.995 Strehl.
As a result of the above image and nine others averaged together, the mirror’s condition at this point was about l/2 P-V when you disinclude the lips on the edges, which may be on the mirror or may be from the Open Fringe process. Before working those areas we’ll confirm. With the lips the mirror is about 0.7l. The RMS was 0.099l, and the Strehl was 0.822. Here are some images from Open Fringe, a software written by Dale Eason, to analyze interferograms.
This contour map allows us to program where and how to work a mirror to correct it towards correction. Keep working the high areas until the P-V is at an acceptable difference.
The same image can be represented as a 3D image to see the high and low areas.
Between one and sixteen radii can be represented in a Profile graph. The red components are above or below the quarter wave criteria. You can adjust that criteria to your preferences.
It will also produce a simulated star test. You can adjust the parameters of this as well. There are other features not shown on this page.
There are some excellent instruction manuals for bath interferometry, here are their links.