Evolution of the Astronomical Eyepiece - Brayebrook Observatory

EVOLUTION of the ASTRONOMICAL EYEPIECE
The apparent field of view is governed
by the eyepiece design, and is given by:
where:
θ = 6 π sin−1 e
2
e = Ed
Fe
where Ed is the field
stop diameter, provided angular magnification
distortion and rectilinear distortion
are fully corrected. In the pres -
ence of either, i.e. where the condition
of orthoscopy is not met, then e is mod -
ified by:
e = Ed (
Fe 1+ E.tan 3 θ )
where E is the coefficient of distortion
and ϑ the apparent field. In some wide
angle designs, such as the Erfle and
the Na gler, rectilinear dist ortion
exceeds 25% (E=0.25+), a lthough
a ngul ar m agni fica tion d istortion is
suppressed (E=0.05-). It is not possible
to suppress both angular magnification
distortion and rectilinear distor -
tion simultaneously at the same field
radius because the former is proportional
to the tangent of the angular
field radius, and the latter the field
radius in radians. In mili tary eyepieces,
and binocular eyepieces,
wher e terrestrial objects are viewed,
rectilinear distortion is undesirable,
and it is suppressed at the expense of
astigmatism. The real field is given by:
θ ′ = 2 tan −1 . Fe
F .tanθ 2
and is limited by the diameter of the
drawtube, hence:
and
θ ′ = 2 tan −1 . Ed
2F
θ max
′ =
48
π.D mm ( )
.sin −1 Ed
16. f / no.
hence for a given aperture, the widest
real field increases with the focal ratio.
The eye relief or eye clearance is also
governed by the design, and can very
from zero to over 1.0Fe. Having too
great an eye clearance can prove as
bothersome as having none at all.
Values between 0.6Fe to 0.9Fe are to
be desired in medium focal lengths
(10mm to 25mm), the latter enabling
spectacle wearers to observe without
having to remove them.
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