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▪ ** **CONTENTS
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10. CATADIOPTRIC TELESCOPES
▐
10.1.2. Field flattener
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Systems with sub-aperture correctors are
relatively infrequent and, in the commercial telescope arena, often come with
second-grade products. This doesn't mean that high-quality catadioptric
systems with sub-aperture lens elements can't be built. One example is *hyperbolic
astrograph*, consisting of a hyperbolic primary and either two (**Rosin**),
three (**Wynne**) or four element (a
pair of doublets) sub-aperture lens corrector. Sub-aperture **
Schmidt corrector** can also be used to
enhance off-axis performance of a telescope (for instance, to reduce or
cancel astigmatism in the Ritchey-Chrιtien), but it is seldom used for
this purpose in amateur telescopes.
Due to simplicity and popularity of
Newtonian reflectors, among the most frequently encountered sub-aperture
corrector forms are coma corrector for paraboloidal mirror, and
spherical aberration corrector for a sphere. The goal of such correctors
is to minimize or eliminate the dominant aberration without introducing
significant other significant aberrations. In the case of spherical
mirror, it is desirable to correct both, axial aberration and coma. For
visual use, these tasks often can be accomplished with relatively simple
sub-aperture correctors.
Even a single-element lens corrector
in the form of equal or near-equal radii meniscus,
can significantly improve field performance of a fast paraboloidal mirror (**FIG.
153, left**), or even make possible to use fast spherical mirror (**FIG.
153,
right**).
Since paraboloid forms good near-axis image on its own, the former is a
hybrid catadioptric. The latter is a true catadioptric, since fast
spherical mirrors alone are pretty much useless for astronomical use. In both instances the
corrector is placed in front of the diagonal flat.
**FIGURE 153**: (**A**) Ray spot plot for a fast
paraboloid with meniscus-type coma corrector placed in front of the
diagonal flat. With the coma nearly
corrected, dominant aberration is astigmatism, limiting
diffraction-limited field to 0.18° radius, over three times that of the
paraboloid alone; since the astigmatism offsets with that of the
eyepiece, actual visual field is larger, limited by eyepiece
astigmatism. (**B**) Ray spot plot for a fast sphere with
sub-aperture meniscus corrector in front of the diagonal. This one has slightly different radii,
which is needed to generate sufficient corrective spherical aberration
at a reasonable lens thickness (mirror alone has 1.4 wave P-V of spherical
aberration). Both correctors offer similar diffraction-limited field
(angular), and near perfect longitudinal chromatic correction. Lateral
chromatism is somewhat greater in the latter, due to the thicker
meniscus, but still within tolerable. Neither corrector is fully
optimized, but should illustrate most of their potential. While
appearing quite simple to make, they require very high surface radius
accuracy for given meniscus thickness, which has nearly as tight
tolerance itself. This is partly offset by greater simplicity of
mounting and collimating a single element. The black circle represents
e-line (546nm) Airy disc.
SPEC'S
Main priority with the meniscus corrector in combination with spherical
mirror is correction of spherical aberration, without introducing
significant aberrations of other types and, then, to reduce mirror's
coma. Meniscus orientation is concave toward primary; the reverse
orientation wouldn't work due to significantly less spherical aberration
generated, and unfavorable aberration distribution between the two
surfaces (the corrective front surface generates much less of the
aberration than the rear surface, unless it is made much more strongly
curved, which would make chromatism unacceptable). This is also viable
orientation for coma-corrector in a paraboloid, since a meniscus of
equal radii in this form doesn't introduce appreciable amount of
spherical aberration but, if properly designed, can reduce or nearly
cancel mirror's coma.
Sub-aperture meniscus corrector for a single mirror can be also placed
closer to the focal plane, at the bottom of the focuser. Off-axis
correction
is nearly as good as with the corrector placed in front of the diagonal
flat, while offering advantages of smaller meniscus and lighter, smaller
diagonal flat assembly. It is described in more detail toward page
bottom.
A simple doublet corrector of **
Jones-Bird** type can also achieve good overall correction level
in combination with spherical mirror (**FIG.
154**). Even simpler version, a split meniscus concave toward mirror,
with the front surface somewhat stronger (intermediate form toward the
above meniscus corrector) , also corrects for spherical
aberration and coma, while introducing strong astigmatism and field
curvature. It offers better control of secondary spectrum, but has some
lateral color.
Another more recent
sub-aperture corrector type for spherical mirror, incorporated in the
Cape Newise telescope, consists of a pair of widely separated
doublets (one in front of the diagonal, the other at the bottom
of the
focuser tube). It seems to be capable of very good performance. However, its specifications are not available.
**
FIGURE
154**: LEFT: Ray spot diagram for 200mm /5.9 system with
/4 spherical
primary and Jones-Bird type corrector (*Telescope Optics, *Rutten/Venrooij),
placed in front of the flat. Black circle is the e-line Airy disc. The
corrector is a single-glass lens doublet: bi-concave front lens and positive meniscus. Its strong astigmatism
can be advantageous for visual use, to partly offset strong astigmatism in conventional eyepieces
(which also relaxes the effective field curvature, which is as strong as
70mm for the objective's image). Chromatic correction of the Jones-Bird
is approximately at 4"
/30 achromat level -
but with excessive chromatism in the violet. As the LA graph shows, it is
mostly due to chromatic defocus (secondary spectrum).
Two-glass J-B corrector
gives better
results; replacing F2 with SSK3 reduces the** h**/**r** error six
fold, tenfold using PFCB19-61 and FN11).
RIGHT: Same corrector type, slightly modified (the front lens becomes
negative meniscus) with paraboloid. Level of correction is
similar, except for traces of spherical aberration and coma. Chromatic
correction is noticeably improved due to the use of two different
glasses, BK7 and SSK2. It also resulted in significantly lower corrector
magnification (f/4.6 effective system). Correction of all aberrations
can be further improved by use of low dispersion glasses (orange frame).
SPEC'S
For imaging applications, strong field curvature is undesirable. Thus
correctors intended for imaging (or all-purpose) have one more
requirement to fulfill, nearly flat image field which, in turn, requires
good correction of astigmatism as well. With simple two-lens corrector,
it either results in relatively significant residual spherical
aberration, which can only be remedied by hyperbolizing primary.
As a result, flat-field two-element coma correctors for paraboloid
induce spherical aberration; the larger, faster mirror, the more so. The
basic corrector form here is the Ross corrector, originally a negative
meniscus followed by biconvex lens. According to Bratislav Čurćić, the
MPCC coma corrector is of this type, while the former Lumicon coma
corrector is modified by replacing biconvex lens with positive meniscus.
Examples of these two corrector types, as well as of the split meniscus
form are given in **FIG. 155**.
FIGURE 155: Three types of a flat field coma corrector with BK7
lenses. Modified
Ross, which is actually Rosin-type corrector, has best color correction,
although not significantly in practical terms. All three correctors
induce spherical undercorrection, particularly split meniscus, which would require
slower parabola for acceptable performance. The P-V wavefront errors
with 200mm f/4 paraboloid are 0.73, 0.76 and 1.07 wave, respectively
(note that the axial blurs for paraboloid are in reduced proportion).
Since the error scales with DF3, a quarter-wave 200mm paraboloid for the
three would be f/5.7, f/5.8 and f/6.5, respectively (for given aperture,
needed mirror conic for cancelled spherical remains unchanged, due to
the offset between the increased corrector's and mirror's aberrations).
SPEC'S
For complete correction of a paraboloid, more complex correctors are
required. In general, they need to have three (or more) single lenses,
or two or more achromatized doublets. The lenses are more widely separated,
creating more degrees of freedom, so that
combined aberrations can be brought to a negligible minimum (for
instance, the Paracorr-like corrector corrects coma with the front
achromat without inducing spherical aberration, but it does come at a
cost of inducing enormous astigmatism, then corrected with the rear
achromat - something that cannot be done without widening lens
separation). Examples of
this advanced corrector type are TeleVue's Paracorr and
Wynne triplet.
Wynne-type corrector offers excellent correction level
with either paraboloidal or hyperboloidal mirrors (it is also used in
two-mirror systems), both in regard to monochromatic aberrations and
chromatism. However, while one of the three lens elements is a simple
near plano-convex or PCX, the other two are strongly curved, thin
menisci, very demanding in both, fabrication and positioning/centering.
Still, the Wynne corrector is not out of reach for advanced amateur
telescope makers and designers. Large, fast amateur mirrors
in particular benefit from a corrector of this type (**FIG. 156**).
**
**
**
FIGURE 156**:
TOP - Paracorr-like coma
corrector for paraboloid - which also flattens the field - consists of a
pair of achromats, negative in front. It has a negative net power,
extending focal length for 10-20% (approx.). At left is design published
in Smith, Ceragioli and Berry (Telescopes, eyepieces, astrographs),
scaled to 250mm f/4.5 mirror. It uses four different non-ED glasses. In
the middle is a similar arrangement using only two simple glasses
(BK7/F2), and at right is arrangement using perhaps best glass
combinations possible - or close to - including ED glass, designed by
Mike I. Jones (also scaled to 250mm f/4.5 mirror). Expectedly, the
latter has the best correction, except near edge, where higher order
astigmatism starts exploding (it is still of little consequence
visually, not only for the corrector's astigmatism being likely
dominated and offset by that of the eyepiece, but also for being still
angularly small for the eye - even in a f=24mm 80°
AFOV eyepiece, which would have field stop radius about 20mm, the Airy
disc is 4.6F/f=0.96 arc minutes, so at F=5 the blur size where the eye
just begins to recognize shape is about five times the Airy disc
diameter; in a 50mm 40° AFOV even the edge
blur would still appear as a point). Visually, the 2-glass corrector is
not significantly inferior to the 4-glass at left, and photographically
is only marginally inferior. In practical terms, the two are not
significantly inferior to the better corrected ED arrangement. Note that
the lenses are limited to 48mm in diameter, resulting in a significant
vignetting of the edge beams at the rear element.
BOTTOM - Wynne corrector
in its original form consists of a three or four singlets (doubling the
middle lens in the standard 4-lens arrangement does not significantly
improve performance). In addition to correcting for coma, it also
flattens the field. Similarly to the Paracorr-like corrector, it has a
negative net power, extending focal length by little more than 10%. All
three designs use a single crown glass (BK7); they are scaled to 250mm
f/4.5 mirror to make the performance comparable to that of the Paracorr-like
correctors; Wynne correctors are normally used for larger, faster
mirrors, and the plots are illustrative of why. At left is one of the
original Wynne's designs (*A new wide-field triple lens paraboloid
corrector*, Wynne 1974), scaled down from a much larger and faster
aperture, and slightly tweaked to correct for some residual lateral
color (possibly due to the large scale of downsizing). It features the
typical thin lenses (in large telescopes, it is desired to minimize
short-wave absorption, but is not a performance requirement). It hasn't
been design for fields significantly wider than about 1°
in diameter, and it shows in the size of the edge blur (reduced
fourfold); the rear lens had to be nearly doubled in the thickness to
make possible for it to cover this 1.86 degree field; mid lens is also
thicker by a third, but neither appreciably affected the performance.
Mid design is a scaled version of the design published in Smith,
Ceragioli and Berry (no mention of the designer of this particular
corrector). At right is a monster-Wynne, designed by an ATM who posted
it at atmlist.net. It has perfect correction all the way to the edge,
which can be credited to the elimination of higher-order aberrations due
to less strongly curved, larger elements (this is why, in general, wider
corrected fields require longer Wynne corrector). The rear lens is about
48mm in diameter (a bit larger in the design at right), showing little
or no vignetting; the front lens, however, wouldn't fit into 2-inch
barrel without reduction resulting in some moderate vignetting; the long
design would require nearly twice wider barrel just to accommodate the
axial cone. This type of corrector can also be used to correct hyperboloidal
mirror, with similar results (it is also used to correct prime focus image of large
observatory Ritchey-Chrιtien telescopes). While the
correction level achievable with Wynne corrector is impressive, these lenses pack large
amounts of aberrations - astigmatism, coma and chromatism - thus may require
very tight fabrication and mounting standards.
As mentioned, this wide corrected fields do not result in practical benefit to
the visual observer
(even
without considering much greater magnitude of the seeing error), but can
be advantageous for imaging.
With smaller mirrors, it is easier to achieve high level
of correction by combining sub-aperture corrector and hyperboloidal
mirror. This is due to simple coma correctors generating
under-correction, thus introducing one aberration while correcting for
the other. Having the mirror
hyperboloidal practically takes spherical aberration out of the equation,
allowing corrector design to be optimized for correcting other
aberrations. For that reason, hyperbolic astrographs can be designed to
a high level of correction with quite simple doublets in place of the
correcting element (**FIG.****
157**).
FIGURE 157: Ray spot plot for 10"
/4
hyperbolic astrograph with Rosin-type corrector designed by Mike I. Jones
(black circles represent the e-line Airy disc).
The corrector consists of a positive and negative meniscus, placed at
the bottom of the focuser base. The primary is a hyperboloid with the
conic K=-1.408. Evidently, image quality is excellent across the flat
1o field. The LA graph shows most colors focusing tightly together. Only
the violet end departs somewhat, resulting in the violet h-line blur of
approximately 12 microns in diameter (~0.2 wave RMS error), also
exhibiting some lateral color error. However,
it is still quite small, and can easily be remedied by using slightly
different glasses, for instance LAF9 for the front element. Low level of
aberrations allows upscaling to significantly
larger apertures while preserving high correction level. The two
corrector lens elements are relatively easy to fabricate; main
fabrication difficulty is aspherizing the
primary. Needed in-focus distance for the corrector is relatively
small, allowing it to be mounted below the focuser
base. The final focus to corrector separation, on the other hand,
is large enough to accommodate use of various accessories, if desired. A
very good example of how successful can be combining
hyperboloidal mirror and relatively simple two-element sub-aperture
corrector in creating near-perfect photo-visual telescope/astrograph.
SPEC'S
Follow a few examples of less sophisticated, but
potentially useful sub-aperture correctors for a single mirror:
**EXAMPLE 1: Close meniscus corrector - **As
illustrated on the top, meniscus corrector can be used for both,
spherical and paraboloidal mirror. While single meniscus can always
correct for coma, the amount of residual astigmatism depends on its
location. In general, the closer it is to the focal plane, the higher
residual astigmatism. Still, meniscus corrector closer to the image
plane can significantly improve field definition, and may be preferred
for being smaller and easier to mount and dismount. Follows an example
of such a corrector.
The starting point for either type of meniscus
corrector is a form with the front radius transforming the incident
converging cone into near-collimated pencil. This requires front surface
radius R1~(n-1)L,
with **n** being the glass refractive index and **L** being the
surface-to-mirror-focus separation. Having ray heights at the two
meniscus surfaces similar roughly minimize/balances 4th and 6th order
spherical aberration, so that they can be combined to optimize for a
minimum total aberration. The 4th order aberration total is given by a
sum of the three 4th order peak aberration coefficients (equaling the
P-V wavefront error at paraxial focus). For the mirror, object is at
infinity, stop at the surface, and, from
TABLE 2, peak aberration
coefficient for primary spherical alone (equaling the P-V wavefront
error at paraxial focus) is **S****m**=W**P-V**=(K+1)D4/64R3
(for **K**,** D**,** R **
the mirror conic,** **
aperture diameter and radius of curvature,
respectively).
For the meniscus, the object is relatively close
(virtual image formed by mirror for the first surface, and the image of
the mirror's image for the second), and appropriate
stop-shift relations
apply (note that all relations are for the aberration at the Gaussian
focus, thus for any non-zero sum the actual P-V wavefront error for
primary spherical is four
times smaller).
Despite this being a single-lens corrector, it is not simple to formulate required specifications.
One reason is that it is not a thin lens, and relatively simple thin
lens aberration relations do not apply. Instead, aberrations are to be
calculated for each of the two surfaces, with the object for the first
lens surface being the (virtual) image formed by the mirror, and for the
second lens surface the (virtual) image formed by the first surface.
Both lens surfaces have displaced stop: for the first, it is at the
mirror, and for the second it is the image of the stop (mirror) formed
by the first surface. All these elements need to be calculated in order
to obtain parameter values for the stop-shift relation applicable to the
surface, which is fairly complex in its form.
In addition, strongly curved surfaces tend to
generate significant higher-order aberration terms, requiring
additional, more complex calculations for determining design
specifications accurately. Keeping it simple, details of parameter
calculation for sub-aperture correctors will be only outlined in general
terms.
With **R** being numerically negative, and both
**R****1**
and **R****2**
positive, spherical aberration of the meniscus is cancelled in the first
approximation for R1=R2,
if the ray height differential on its two surfaces is negligible.
Chromatic correction is also at the optimization level. For **
paraboloid**, all that is needed is to
find out the appropriate thickness that will correct for mirror's coma.
Since it typically involves balancing lower- and higher-order coma, it
is best done with ray-tracing software, such as OSLO (it is also needed
to optimize higher- and lower-order spherical aberrations, as well as
chromatic correction). First approximation for the needed thickness is ~1/14
of the corrector-to-original-focus separation.
For instance, BK7 coma corrector for 200mm
/4 paraboloid
located (front surface) at 100mm in front of the mirror focus has,
in the first approximation R1,2=52mm
and 7mm center thickness.
With these parameters, the optimum location is found
at 95mm in front of the original mirror focus (shown to the left).
Diffraction limited field is 0.27 degrees in diameter, set by
astigmatism, about four times stronger than mirror's own. That makes
corrected field nearly 5 times larger, linearly, than the original
coma-limited field, and expectedly larger in visual use, due to the
offset with (stronger to much stronger) eyepiece astigmatism of opposite
sign. Chromatic correction is nearly perfect with respect to secondary
spectrum, with the RMS error 1/130 wave at the blue F-line, and 1/116
wave at the red C-line. Center-field correction is 1/160 wave RMS.
Lateral color is present, but low, approximately at a level found in
eyepieces
(significantly lower than in the typical Kellner). Since meniscus
generates coma according to the f-ratio, it works for any aperture size,
as long as it is at the same distance from mirror's focus (slight axial
adjustments may be necessary to optimize color correction). Tolerances
are fairly forgiving: up to 2-3% deviation in axial displacement,
thickness deviation, or radius (it needs to be near equal on both sides)
will not result in appreciable error. If suitable lenses are available,
corrector can be made out of a PCX/PCV pair.
Correcting spherical aberration of a **
spherical mirror** requires slightly
weakening rear corrector radius relative to the front. Since the
aberration contribution of either surface of the corrector is several
times larger than that of the mirror, and the aberration contribution
changes with the 3rd power of the radius, the rear radius is typically
~5% weaker. Due to the change in the powers, chromatic correction is
compromised, and typically requires reduction in both radii by 20-30% to
arrive at a near-minimum level. Astigmatism and field curvature increase
significantly. In order to minimize coma, the meniscus needs to be 2-3
times thicker (roughly) than with a paraboloid.
**EXAMPLE 2**: **Sphere with sub-aperture doublet lens corrector**
- Simple doublet corrector for spherical mirror, made of two
equal-radius plano-convex and plano-concave K11 lenses (n**e**=1.5)
in near contact. The simplest way to keep them achromatic is to have the
two powers near equal and of opposite signs. To simplify the
calculation, only correction for spherical aberration will be sought.
The mirror is 200mm with m=1000mm
(/5), with the following lower-order peak
aberration coefficients: Sm=0.003125,
Cm=0.001091,
and Am=-0.000381
for spherical aberration, coma and astigmatism, respectively, with the
last two for 0.5° field angle.
With the two lenses facing the mirror with
their curved side, positive lens in front, the shape factors, from q=(R2+R1)/(R2-R1), are q1=q2=1.
With the front lens to mirror image distance **O****1**,
the lens position factor p1=
(21/O1)-1.
For the second lens, the object is the image formed by the front lens,
which is at half its focal length to the right behind it (obtained from
lensmaker's formula,
which also can be used to calculate the rear lens' stop separation).
That determines position factor for the rear lens as p2=(42/O1)-1
(keep in mind that with the light coming to the mirror from left,
******1**
is numerically negative, while ******2**
and object-to-lens distance O1
are positive).
Substituting **n**, **q****1**
and **q****2**
in Eq. 97 gives
simplified expressions for the aberration coefficients for the front and
rear lens that can be used for calculations (when obtaining peak
aberration coefficient, **D** is the marginal ray height at the lens
surface). With the front corrector lens placed 100mm inside the mirror
focus, spherical aberration of the mirror is corrected with |f1,2|~240mm;
however, the system coma is prohibitive, being over four times that of
the mirror. At the other viable corrector position, about 250mm inside
the mirror focus (in front of the diagonal), with |f1,2|=1000mm,
color correction is still perfect, but the coma is reduced to double
that of the mirror (the wavefront error is effectively appropriate to
that of a mirror with the **F**
number smaller by a factor of 0.8, or
/4
in this case). Astigmatism is comparably negligible, effectively
flattening the field. Note that both lenses use BK7 crown glass (SPEC'S).
Performance of the corrector could be improved by bending the lenses and
using two different glasses. However, in this simple form, any
significant gain in correcting one aberration - in this case coma - can
only be achieved by allowing significant increase in one or more of
other aberrations. For instance, the alternative
Jones-Bird corrector does correct
for coma, but at a price of introducing strong astigmatism/field
curvature. It also requires more complicated lens shapes, with two
different glasses to control chromatism (which remains compromised in
the violet). Nevertheless, it is still advantageous field-wise for
visual observing, not only because it offers some 50% wider diffraction
limited field (linear) in the image of the objective, but also because
its astigmatism partly cancels that of the eyepiece.
Note that aberration calculations using 3rd order thin lens formulas can
be very approximate, due to possibly significant higher order
aberrations, and lens' thickness factor. Final design optimization
requires ray-tracing.
**EXAMPLE 3: Corrective tele-extender lens** - A simple doublet of
negative power placed at the bottom of a focuser in fast Newtonians
would, by extending converging cone, make possible reduction in the
minimum size of the diagonal mirror. It can also be designed to reduce
coma, while inducing low spherical aberration and acceptable
astigmatism. Since even this simple sub-aperture corrector requires
quite involved procedure, the calculation will be only outlined, and the
effect illustrated with a slightly modified (SPECS)
tele-extender from *Telescope Optics*, Rutten and Venrooij.
A few words about **Barlow Lens**. It is
designed to extend the focal length, without introducing significant
aberrations to a telescope. Any Barlow with a single lens group at the
bottom of the barrel has magnification factor M=1-L/B,
with
**L** being the length between the lens and the eyepiece field stop,
and
****B
the Barlow focal length, numerically negative (this means that, for
instance, inserting a diagonal into Barlow appropriately increases its
magnification factor). The focal length can be approximated if the
magnification factor is known from
B~-L/(M-1)
with
**L** being the distance between the lens group and the top of
Barlow's barrel. Also, approximate axial separation of the original
focus from Barlow lens is given by ~L/M.
The first step in designing corrective tele-extender is determining the
doublet focal length ** **D.
From
Eq. 100, it is
approximated from
D=(1-t)/(1-),
where
****1
is the mirror focal length,
**t** the mirror-to-doublet separation and
**** the desired final focal length (the
value for ** **D
is approximate mainly due to it being relatively close to the image for
lenses to fit tightly into a thin lens definition). Once the doublet
focal length ** **D
is known, the needed focal lengths of its two elements needed to
achromatize are, from
Eq. 43, fD1=(V1-V2)/V1
and
D2=(V2-V1)/V1,
with **V**1
and **V**2
being the respective glass Abbe numbers.
The next step is determining needed lens shape for corrected spherical
aberration. With the glasses and lens location known, after substituting
index of refraction and position factor for the two lenses in
Eq. 97, it can be reduced to quadratic equation; then, deciding for
the initial shape factor of one of the lens elements, the other can be
solved for its shape factor **q**. This gives the frame within which
the lenses can be bent in order to optimize for off-axis aberrations.
Off-axis aberrations can be calculated either surface by surface, as
the example of a single-lens field flattener, or using lens relations,
Eq. 98-99.1. First two
or three outcomes usually outline direction and limitations within given
set of parameters.
Such
procedure would have lead into designing corrective tele-extender for a
fast Newtonian. Although originally designed as a Barlow for
Schmidt-Cassegrain telescope, tele-extender from the Rutten/Venrooij's
book happened to fit for this purpose due to significant negative coma,
needed to offset mirror's coma. The results are quite acceptable, as can
be seen on the ray spot plot (for flat field, best field Rc=-300)
for a catadioptric 200mm
/4/8.4
catadioptric Newtonian with paraboloidal mirror (SPECS).
Other than correcting for the coma, the extender lens, if permanently
mounted, allows for some 20% smaller diagonal mirror.
The doublet consists of a positive flint
(F2) front element, and negative crown (BK7) element, with very small
spacing (lenses are nearly touching). Center field correction is 0.025
wave RMS, with diffraction-limited (0.80 Strehl) flat field diameter,
set by the lens' astigmatism, of ~0.3°. Being opposite in sign to
that of most conventional eyepieces, astigmatism induced by this doublet
is likely to have small positive effect on the visual field quality. At
0.074 wave RMS, the system is at the diffraction-limited level in the
blue F-line (486nm), and still better in the red C line, at 0.039 wave
RMS. This is roughly the chromatism level of a 100mm /70 doublet
achromat, and nearly as good as an apochromat.
Sub-aperture correctors can also be used
with two-mirror telescopes, usually with the goal of improving field
quality. As with the above examples of the Newtonian telescopes corrector, they can be either
integral part of a system, or an optional add-on. Typical sub-aperture
correctors in two-mirror systems are coma-corrector in Dall-Kirkham, or
astigmatism/field curvature corrector in aplanatic Cassegrain
(Ritchey-Chrιtien) telescope. But they also can be used in systems with
full-aperture corrector, either to maximize performance, or to allow for
easier fabrication of the full-corrector, or both. One such example is
aplanatic Houghton-Cassegrain with both, full- and sub-aperture being a
plano-convex/concave lens pair (FIG.
138).
In general, aberrations induced by a
sub-aperture corrector are determined by its effective diameter, as well
as the element shape and power. Ideally, its monochromatic aberrations
would nearly balance out with those of the mirror (or mirrors), while
the chromatism it induces should be negligible. It is not always
possible; in principle, axial monochromatic correction is a priority,
followed by acceptable chromatic correction and correction of off-axis
aberrations. While sub-aperture correctors can be very complex, a simple
single-lens doublet, as illustrated with the above examples, can be very
effective. A brief overview of the aberration properties of a
thin-lens-element sub-aperture corrector follows.
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10. CATADIOPTRIC TELESCOPES
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10.1.2. Field flattener
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