Grating frequency (lines per unit of measurement) =
Grating offsets from radius of curvature =
I use the matching Ronchigram test along with the star test on my
mirrors. I’ve successfully figured many dozens of mirrors from 4 inches
to 30 inches, from f/8 to f/3 with the Ronchi test. This test is
particularly useful in mirror making classes where the mirrors come off
of short figuring spells and must be tested quickly lest a bottleneck
builds. It’s common to have several mirrors waiting to be tested at any
one time.
The matching Ronchigram test shows very small changes in the mirror’s
figure such as zones and differences in correction from one part of the
mirror to the other. With care, I have observed defects down to 1/30
wave. Turned edges and overall smoothness are easy to detect.
Overall correction, that is, is the mirror 100% corrected or is it ever
so slightly under or overcorrected, is harder to see. That’s where the
star test jumps into the fray. The star test, comparing the inside of
focus star pattern to the outside of focus star pattern, is exquisitely
sensitive to overall correction. There is every expectation that a
mirror can be figured to a standard of ‘indistinguishable from perfect’
when using matching Ronchi test in combination with the star test.
I like a grating of about 100 lines per inch [4 lines per millimeter].
It gives enough sensitivity without being overwhelmed with diffraction
effects on large fast mirrors.
A spherical mirror returns light emanating from the radius of curvature
to its origin. The radius of curvature is twice the focal length, the
focal length is the mirror diameter times the focal ratio. Light coming
from astronomical objects is essentially parallel. This light requires
the mirror surface to be shaped in the form of a paraboloid in order to
bring the reflected light to perfect focus. A paraboloid compared to a
sphere has an ever so slightly deeper center and edge. The result is
that the light is deformed as it returns from the mirror and passes
through the grating to the eye. This deformation is what we judge,
comparing the mirror’s Ronchi bands to a computer generated series of
Ronchigrams.
It’s important to compare at several positions just inside of and just
outside of the radius of curvature. Moving inside the radius of
curvature is a negative offset; outside the radius of curvature is a
positive offset. Inside of the radius of curvature, the bands bow
outward as you center your attention to the middle of the mirror.
Outside of the radius of curvature, the bands bow outward as you move
your eye towards the edge of the mirror. The Ronchi test is sometimes
inappropriately applied by eyeing the curvature of the bands. But this
will not work because the curvature can look very similar for a whole
series of situations. For instance, a 10" f/5, fully parabolized at
0.3" outside radius of curvature will look very similar to the bands of
a 10" f/5, only half parablized, at 0.2" outside radius of curvature.
So we must match bands at precise distances from the radius of
curvature.
As the figure takes shape and errors are no longer obvious, take the
time and care to judge the bands very critically. Be discriminating to
a deviation of one-tenth the thickness of a band. Position the tester
to a hundredth of an inch (1/4 millimeter) using an engineering ruler.
Testing in the final stages can take many minutes.
