Polishing Double-curvature Mirrors
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Fabricating a toroidal secondary may sound intimidating, but its
symmetry makes it easy to fabricate. Just remember that eyeglass
manufacturers produce thousands of toroidal lenses every day! -
J.M.Sasian, Sky & Telescope, March 1991
Perhaps the main reason that TMs do not undertake the fabrication
of a Yolo is the belief that producing the secondary double curvature
is very difficult. However, the only way to really know how easy or how
difficult the fabrication of the secondary is, is actually to make one.
Although it can be made to work satisfactorily, the mechanical
"warping" harness proposed by Mr. Leonard to deform the mirror has not
been accepted by amateurs as the ideal solution to produce the shape
necessary to correct on-axis astigmatism.
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A simple method to generate and maintain the surface required for the
secondary mirror is to allow translational polishing movements using a
double four-bar linkage. A double curvature mirror has two mutually
perpendicular planes of symmetry, which is a rather symmetric surface
form.
This shape, if appropriately encouraged by constraining in rotation the
polishing movements, will develope naturally. After all, the professional
opticians have to be very careful to reduce to a minimum the amount of
astigmatism on their optical surfaces because there is not such a thing as
a perfect mirror. TMs will find surprisingly little difficulty generating
the Yolo secondary double curvature using a double four-bar linkage and
polishing principals similar to the ones used in making standard
mirrors. - J.M.Sasian, Telescope Making #37
The linkage is made from seven plastic bars perforated at their ends,
with machine screws serving as pivots. The secondary is held to the
appropriate bar with double-sided tape. The idea is to allow only
translational movements so as to keep the double curvature, which
must be generated by doing long strokes in just one direction.
The long strokes will make the secondary's radius of curvature shorter
in the chosen direction when the mirror is on top of the tool.
After the double curvature has been generated there will be
irregularities on the secondary's surface due to the long, unidirectional
strokes used in the previous step. To smooth the surface, the direction
of the next set of polishing strokes should be varied and their amplitude
reduced; the tool should be rotated 180° once in a while. -
J.M.Sasian, Sky & Telescope, August 1988