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ATM An Old TMs Simple Query



Guy's n Gals,
 
I have asked a few of the guys, on the side, this question...Well, now I'm putting it before the board. (Gulp), Here goes...
 
I have been building small Schmidt systems for many years now, configured as prime focus cameras, visual Newtonians, and  photo/visual Cassegrains.   Primarily, I've been using Everhart's variation of "Grandpa" Bernard's vacuum pan method for producing the corrector plates, with very good results.  His math was, and still is, quite easy for me to understand and relate to the actual physical, quantifiable, and mechanical functions necessary to produce the desired optical effect upon the system as a whole.   However, in all the years of walkin' around the bench and holding my eye precariously close to a very sharp object, peering earnestly, hour upon hour, past a little spot of light, I have never been able to grasp the basics of the polynomial equations necessary to describe the specific profile on a specific corrector plate and how it actually relates to the plate.  You know, the old

 a*rho^2+b*rho^+b*rho^4...

 The coefficients of the even aspheric I think is what it's called.  How does this become the 3 expressions that are used  when referring to a specific plate, AND WHAT ARE *THEY* WITH REFERENCE TO THE PLATE?  Call me dense... Call me 'tupid... But over my head it goes...     In any case, these and other related equations plum stump the ol' Coyote.  I can create the proper curves on the glass at the bench, but I'll be damned if I can figure it out mathematically so I can enter it into a computer program.  Chuckle, chuckle,
 chuckle!

 Any help you all can lend would be GREATLY appreciated! "
 
 
Talk with you soon,
Coyoté