[ATM] Re: Aplantic Gregorian

[vladimir sacek <vladis.2@juno.com>]

Richard Snashall wrote: 

> S = f2 / f1 = r2 / r1
     T = D2 / D1
     M = f / f1
     B = b / f
     P = d / f

where:
f1 and f2 are the primary and secondary focal lengths
r1 and r2 are the primary and secondary radii of curvature
D1 and D2 are the primary and secondary diameters
f is the focal length of the system
d is the separation between the primary and secondary
b is distance of the final focal surface behind the primary<

I find it helpful to keep parameters consistent with the sign convention
(left to right "positive", right to left "negative"; above the axis
"positive", 
bellow the axis "negative).

Consequently, T should be defined as the "height of the marginal ray at
the secondary".
It determines what amounts to a minimum secondary diameter - not
necessarily
actual secondary diameter (which is somewhat optional, and usually larger
than
secondary's minimum size). It is precisely given by T=1-d/f1, giving
positive value for the Cassegrain,
negative for Gregorian.

Also, there is no logical basis to consider primary's f.l. (or diameter)
as being of different 
sign for the two systems. It would probably be better to write that f/f1
gives absolute value 
for secondary magnification, |M|=f/f1. This would be only correct, since
the simplified relation 
f/f1 doesn't give secondary  magnification itself, only the proportion of
its magnification.

Vlad
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