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.