[ATM] testing convex surfaces by reflection - a thought experiment

[David Weinshenker <daze39@earthlink.net>]

Suppose we set up a telescope objective (e.g. a refractor lens) with
a test device (slit source/knife edge etc.) at the nominal focus - if
we place a flat mirror in front of the lens, we have the familiar
"autocollimation" null test for the lens, in which the light from
the entire aperture comes to focus at the same axial setting of the
tester (i.e., the "uniform gray null appearance" of the shadow).

Now suppose we replace the flat with a second lens mounted face-to-face
with the first one, and at the focus of the second lens place a spherical
convex reflector with its radius of curvature at the focus. If the lenses
and the spherical mirror are all perfect, the system ought to null at a
common focal distance across the aperture, as before... and if the convex
reflector has an aspheric shape (e.g. a hyperbolic secondary for a Cass or
RC configuration), it should be possible to calculate the axial movement
of the test setup to focus the various zones on the convex mirror.

It may be argued that using this method to test a convex surface
requires the availability of a pair of "known good" telescope lenses,
just as the basic autocollimation test requires a "known good" flat
mirror... although the test could easily be conducted in monochromatic
light - at which point the lenses do not need to be achromatic, though
they should be free of spherical aberration.

-dave w
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