Re:ATM An Old TMs Simple Query

[Jerry Hudson <hudsonjk@pacbell.net>]

To ol' Coyote -

Your formula,
>  a*rho^2+b*rho^+b*rho^4...
giving the shape of the Schmidt plate, is
exactly opposite in sign to the wavefront
aberration describing an uncorrected spherical
mirror.  The glass introduces just enough extra
path length where it is thicker to compensate.

A straightforward way to see how this all works
out, if you have the patience and either a
good calculator or BASIC, is to start
at the desired focal point of the sphere and
trace a ray, bouncing it off the sphere, and
taking it out to where it intersects a plane
positioned where you want the plate to go.
Figure out the path distance along that ray,
and subtract off the path distance for the
central ray.  THat's your "wavefront aberration."
If you plot this against radial distance of
the ray from the axis, you will get a 4th order
looking curve.

Note that adding the rho^2 term simply re-focuses
the wavefront - you have this degree of freedom
to try to make the overall power of the plate
to be zero (avoiding all but a trace of color).

I hope this helps.

BTW, I'd enjoy a direct off-list exchange with
you about Schmidts - an interest of mine.  I've
only made one: a Wright-type Newtonian.  And, yes,
Edgar Everhart's articles were a great help to me!
He was a smart guy and a great glass-pusher!

- Jerry Hudson