[ATM] Elliptical mirror

[mdholm@telerama.com]

The conic constant is, as I recall, -e^2 where e is the eccentricity given in
analytic geometry textbooks in the formula for an ellipse.  The conic constant
for an ellipse should be between 0 and -1.

It is possible to go from an equation based on the two foci to an equation using
e, though I do not recall how.  It should be in an analytic geometry text.  That
would allow you to go from the planned dimensions of the Gregorian to e to conic
constant.

Figuring an ellipse should be very similar to figuring a parabola, except that
you don't go quite as far with the aspherical correction.  The form of the
deformation away from a sphere is exactly the same as for a parabola, it is just
the degree that is different.

You can make a null test for the ellipse in a fairly straight forward way.  At
the place where the primary focus is to end up, make a spider, similar to the
spider for a secondary mirror.  Mount the light source (pinhole or a small
Ronchi grating) on the spider facing the mirror.  Put your knife edge or a
second Ronchi grating at the place where the final focus is planned (actually,
you have to put it where the light actually focusses, hoping that is near your
plan).  Figure for a null.

With modern small and light light sources (an LED is ideal here) that give off
little heat, it is easy to make one compact and cool enough for this job.  To
minimize heat generated in the light path, wire the dropping resistor for the
LED remote from the LED and make sure it is outside, and not under the light
path.  You can't do anything about the heat generated in the LED itself, but
hopefully it will be little enough not to disturb the test unduly.

Mark Holm
mdholm@telerama.com
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