Wave Errors: Getting
to the Root
AMATEURS have learned to pay attention not
just to the wave
rating of a telescope but to how that number was measured.
Late in the 19th century,
when Lord Rayleigh established his 1/4-wave tolerance
as a criterion of telescope performance, he meant there
should be no more than a 1/4-wave difference between
the extreme "peak" and "valley"
in the wavefront converging toward focus.
An alternative measure, the root-mean-square (r.m.s.)
error, has gotten lots of bad press among amateurs because
of a concern that manufacturers might use it to make
their wares seems better than they really are. In reality,
an r.m.s. error, when identified as such, offers a better
"figure of merit" for comparing instruments
because it takes into account both the amount and area
covered by any defects. It is simply the square root
of the sum of the squares of the error values sampled
at hundreds of random points in the wavefront. Just
keep in mind that the r.m.s. value is numerically 30
percent as large as the peak-to-valley number when a
telescope suffers from pure spherical aberration. Such
an instrument meets the Rayleigh criterion only if the
r.m.s. value is 0.075 wave or less. It is easy to convert
either measure of wavefront error
(peak-to-valley or r.m.s.) to its equivalent on the
glass surface. For a mirror, divide by 2. For a lens,
divide by (n - 1), where n is the refractive index of
the glass. Since n is about 1.57 (on average) for the
lenses used in astronomical telescopes, it follows that
a lens may have 3.5 times as much surface error as a
mirror before the same harm is done to the wavefront.
The wavelength is a convenient unit of measure because
it is so small. For the yellow-green light to which
the human eye is most sensitive,
1 wavelength is 0.000022 inch or 0.00056 millimeter.
with permission from Sky Publishing Corporation as excerpted
from the September 1993 issue of Sky & Telescope,
pages 83-87. Featured in Telescope Making edited by
Roger W. Sinnott under the article titled "Rules
of Thumb for Planetary Scopes --- II" authored
by William P. Zmek.