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12.3.
Eyepiece
aberrations II
Eyepiece
distortion
Due to
the eyepiece being working with much larger field
angles than the objective, image distortion becomes significant aberration.
As explained in 2.6. Distortion, it is
caused by wavefront tilt error, shifting Gaussian image point
away from its ideal
position. There is no effect on point-image quality, only its position
in the image space. Distortion has two different forms, linear and angular
(FIG. 212).
 FIGURE
212: Image
distortion in
the eyepiece is a result of large apparent angles it
produces. The difference between relatively large angle (in radians)
and its tangent becomes significant. As a result, if the projected
apparent heights h'1
and h'2 are proportional to the appropriate point-source P1
and P2
heights in the object image plane (IP), then the ocular-produced angles
α'1
and α'2
can't be proportional to the appropriate field angles
α1
and α2
at which the
point-source heights are seen in the object image plane - and the other
way around. When the heights are not proportionally imaged, the
eyepiece suffers from linear distortion, which can be positive (barrel
distortion) or negative (pincushion distortion). Likewise, when the
angles are not proportionally re-imaged, eyepiece suffers from
angular
distortion - also either positive or negative - which manifests itself
by elongating objects, vertically or horizontally, farther out in the field.
Obviously, the two forms of field distortion can't be both cancelled
at the same time. In amateur astronomy, the preference is, in
general, minimized linear distortion, for esthetic reasons. In
professional astronomy, angular precision is more important.
Most eyepieces exhibit both forms of
distortion, although one is usually dominant. In astronomy, angular
attributes are more important than linear, although in amateur astronomy
the aesthetic quality of low linear distortion is usually more of a
priority. Manufacturers seldom
give the specs on eyepiece distortion; linear distortion, expressed as a
percent, %ld=100(1-tanα'/tanα'),
with α'
being the actual angle, and
α
the ideal (zero distortion) angle, is considered negligible if up to ~5%
for conventional ~45-degree apparent field of view (AFOV) eyepieces.
However, since it increases with the third power of field angle, it is
hard to control with wide AFOVs. Consequently, wide-field eyepieces can
have it exceeding 20%.
Likewise, the percent of angular distortion can be expressed as
%a.d.=100(1-α'/α).
Eyepiece chromatism
Eyepiece chromatism can be expected to be cancelled longitudinally.
However, lateral chromatism is hard to correct for entirely. In general,
it will be more noticeable in wide-field eyepieces, but ordinary oculars
can have noticeable amounts of it as well (FIG.
213).
 FIGURE
213: Basic forms of conventional eyepiece types in amateur
astronomy, with ray spot diagrams illustrating their typical
aberrations in e (green), F (blue) and C (red) spectral lines. The
spots are given for /10 and /5 focal ratio (except for those that
can't handle satisfactorily the /5 cone), for the field center, 7° and
10° off-axis (black circles are the e-line Airy disc, and RC
is best image curvature). Of
the older types
-
Huygens,
Ramsden, and monocentric -
the last one is standing out for its high overall correction level
(with somewhat limited field, due to higher-order astigmatism).
More recent types, like Kellner,
Abbe (orthoscopic),
König,
Erfle and Plössl have similar
level of correction, with the Kellner being somewhat
inferior. The last two "types" are a pair of either singlet or
achromatic lens. They can have good correction, except for the
excessive lateral color in the singles-pair variety. Axial color
correction is good for all (where it appears to be excessive, it is
due to residual spherical). Lateral color - which increases with
the field angle and doesn't change with -ratio - is acceptable, in
general. Axial image quality is limited by spherical
aberration at fast -ratios (>/5). Off-axis field quality is
limited by
the astigmatism, although coma can also be relatively strong (the
two version of König differ significantly only in two of the radii values).
SPEC'S
It should be noted that the above eyepiece
designs are not fully optimized, but can be considered within their
standard quality range (most of them are down-scaled designs from Rutten
and Venrooij, with some tweaking added in the process). Significant
variations in the amount of specific aberrations is possible within the
same eyepiece type, depending on the design goal and design/fabrication
quality.
The old Nagler wide-field doesn't seem to
be among the top performers neither in regard to spherical aberration
(at fast -ratios), nor color correction. However, its field correction
is roughly half a dozen times better than in conventional eyepieces.
Spherical aberration of the exit
pupil
The
last eyepiece aberration to address is spherical aberration of the exit
pupil. Ideally, telescope ocular will re-image the aperture into a
single plane; in other words, all the bundles of parallel rays exiting
the ocular would merge into a common circle symmetrical around the optical axis
(FIG. 209). In reality, in re-imaging
the entrance pupil (aperture opening), an eyepiece acts as any positive
lens does - in other words, it suffers from under-correction. As a
result, object-image points toward the edge will cross closer to the eye lens (FIG.
214). In effect, exit pupils
for the outer zones are shifted toward the eye lens, away from the eye, and -
depending on the extent of shift - it may result in the outer field
either being not visible from the same eye location as the mid-field (central field
area is always visible), or it being vignetted. If the eye needs to be moved back and forth in
order to view the entire field, it may become decentered , having parts of the field vignetted
or lost from the
FIGURE 214: Exaggerated
illustration of the spherical aberration of exit pupil. The eyepiece
(EP) transforms diverging light cones emerging from the image points
into parallel pencils. Those coming from the points
higher in the image plane are intersecting the axis closer to the
eye lens than those from the lower image points. As a result, exit pupils for the
former are shifted closer to the eyepiece.
Large enough pupil separation will make it difficult or
impossible to hold the entire field in view for any single eye
position. The effect can be noticeable in wide-field and long-focus eyepieces, both
having, in general, greater longitudinal exit pupil aberration.
Point image quality is unaffected, only the axial position of its
exiting pencil.
view (the "kidney bean effect"). Other than that,
spherical aberration of the exit pupil doesn't affect image quality (it
only occurs when the light within the pencil exiting the eyepiece is not collimated). Also, it
can be minimized in any particular design, and not all wide-field or
long-focus eyepieces necessarily suffer from it to a significant degree.
There is a number of eyepiece designs, but
vast majority of those used in astronomy are variations of just a few
basic configurations (FIG. 215). In general, more elements allow better
overall correction, but at the price of increased scatter and absorption
of light. The exit pupil range in the figure below indicates the extent
of the spherical aberration of exit pupil for the few basic eyepiece
types.
FIGURE
215:
Basic forms of astronomical eyepiece, with its front focal point coinciding with the focal plane FP
of the objective.
Ex indicates the extent of spherical aberration of the
exit pupil, normally not troublesome in conventional eyepiece types. The simplest
of them - Kellner
- features 45°-50° apparent field and satisfactory correction for
spherical aberration at ~/5 and slower -ratios. Plössl has better
overall correction, setting quality standards for conventional
eyepieces. Orthoscopic
(Abbe)
usually has somewhat smaller field than Plössl, not due to
inherently inferior field definition, but for its high standards
and customary use for planetary observing.
Conventional wide-fields, König
and Erfle, have better spherical
correction than Kellner, but more intrusive edge astigmatism, due to
their larger, 60°-70° fields. Most of today's standard wide-fields
are variations of these two basic concepts.
Nagler
(Type 1),
whose negative front lens allows for better correction of astigmatism,
offers well corrected fields exceeding 80°. Its wide exit pupil
range indicates more intrusive spherical aberration of the exit
pupil ("kidney bean effect"), better corrected with later types.
Darker color
indicates glass of higher refractive indici. (data from
Telescope Optics, Rutten/Venrooij).
◄
12.2. Eyepiece aberrations I
▐
13. THE EYE
►
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