From: Jerry Hudson 
To: atm{at}shore.net
Reply-To: Jerry Hudson 


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

--- BBBS/NT v4.00 MP