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A formalism is exposed in [Wynne 1979], but an easier derivation is possible.
We have the following wavelength
dependent relationships (according to the notation of Fig. 2):
Basically, the diameter of the Airy disk is :
| |
(3) |
The Lagrange invariant is :
| |
(4) |
The Wynne correctors make the exit pupil chromatic and allow the approximation:
.
a is a constant determined at where the correctors do not have any
effect:
| |
(5) |
is the magnification induced by the achromatic doublets:
| |
(6) |
hence :
| |
(7) |
and:
| |
(8) |
The Airy disk diameter no longer depends on wavelength.
Figure:
Final radial chromatism on the detector (f/976) calculated
from a numerical simulation,
after correction by the Wynne triplets, for 2 different locations in
the field (solid line ,
dashed line ).
|
6/15/1998