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▪ ** **CONTENTS
#
**10.2.3.3.
MAKSUTOV-CASSEGRAIN TELESCOPE**
Full-aperture meniscus corrector can be also used in various
arrangements, including two-mirror systems, as described in Maksutov's
extensive writings between 1941 and 1946. Nowadays, it is most
often used in the
Cassegrain configuration (**FIG.
186**), hence these systems are known as *Maksutov-Cassegrain
telescopes* (MCT). The benefit of such an arrangement is - similarly to that in
combination with the Schmidt corrector - greater flexibility in
correcting primary aberrations than in an all-reflecting system.
The usual meniscus orientation is concave to outside, when its coma is of opposite sign
to that of the primary. It also generates more of higher-order spherical,
but negligibly so unless the radii are strongly curved (in the Maksutov-Gregorian,
where the secondary contribution for both, spherical and coma, is of opposite sign,
both are a disadvantage, and it works better with the meniscus convex to outside;
still, even with f/3 primary, a 200mm aperture has unappealing 1/20 wave RMS design limit
for spherical aberration, and the reduction in it by aspherizing primary coming at a
price of added coma).
As it will be illustrated in this text, an MCT with separate secondary can be
made corrected for all aberrations (correcting field curvature requires
large secondary mirror) in an all-spherical arrangement. In addition,
corrector's chromatism can be made nearly non-existent.
However, in compact systems with fast
primary mirrors, strongly curved surfaces of Maksutov corrector quickly
begins to generate higher-order spherical aberration, which changes in
proportion to the aperture and, approximately, with the fourth power of
primary's relative aperture. It can only be corrected by applying
aspheric surface term to either mirrors or the corrector - something too
complex to be viable for amateur telescopes. While it varies somewhat
with the specifics of corrector, acceptable optical quality in this
respect doesn't extend significantly beyond a 6" f/3 primary level.
Another option is to have the primary aspherised, which allows for
weaker corrector, with reduced higher-order spherical aberration.
**FIGURE 186**: Maksutov-Cassegrain
telescope optical elements. Meniscus corrector, which induces not
only spherical, but also off-axis aberrations, offers greater
flexibility in correcting system aberrations. As a result,
Maksutov-Cassegrain can be made free from coma and astigmatism in a
compact all-spherical arrangement. The weak point is strong
higher-order spherical aberration with fast primary mirrors that
require strongly curved corrector surfaces. It can not be corrected
in an all-spherical arrangement. Secondary mirror can be either an
aluminized spot on the rear of corrector, or a separate surface,
which generally allows for better field quality.
First published telescope arrangements in
the U.S. that followed the
1941 introduction of a full-aperture meniscus corrector for spherical
mirror was a pair of two-mirror Cassegrain systems - f/15 and f/23 - and
Maksutov-type corrector by John Gregory in 1957. In it, the secondary
was an aluminized spot at the back surface of the corrector. At the
time, Lawrence Braymer was already producing his
famous-to-be Questar Maksutov-Cassegrain,
a design very similar to
Gregory's (in order to avoid patent infringement, Questars had - for
about a decade - the aluminized spot placed at the front meniscus
surface). As a later development, an arrangement with separate secondary
was introduced. Nowadays, both Gregory-type and the arrangement with
separated secondary are being used in various forms. In general,
separate secondary is preferred, since it gives additional degrees of
freedom for correction of
aberrations (**FIG. 187**).
**FIGURE 187**: Two basic
Maksutov-Cassegrain arrangements: **(a)** all-spherical with an
aluminized spot on the back of corrector for the secondary
(Gregory-style), and **(b)** with separated secondary. Due to
design limitations imposed by the two surfaces of identical radius
of curvature, the former has noticeably inferior off-axis
performance: at 0.5° off-axis the wavefront error (best surface) is
0.24 wave RMS, mostly due to the coma, but also astigmatism. The
design with separated secondary is highly corrected, with less than
0.025 wave RMS wavefront error at 0.5° off-axis. It is also better
corrected axially (1/43 vs. 1/33 wave RMS), with lower field
curvature due to both, lower astigmatism and larger secondary. Some
lateral color (**LC**) is noticeable. Both systems have very low chromatism:
0.09 and 0.075 wave RMS combined **h**- and **r**-line on
axis.
SPEC'S
Although known as all-spherical design, Maksutov-Cassegrain can also be made with
aspheric surfaces. While either of the two main types above can have aspherized surface(s),
in the amateur telescopes' arena it is usually the Gregory-style MCT, and it is usually the
primary that is aspherized. The reason can be either making possible more compact, somewhat
faster systems, or minimizing the higher-order spherical residual (or both, in larger apertures,
such as Astro-Physics 10" MCT). Meade had its well known 7" f/15 version, and nowadays they are fairly
common in the 4-8" aperture range, usually at about f/12.
Aspherizing primary reduces spherical aberration load on the meniscus, i.e. allows more relaxed
radii. Since aspherizing primary introduces positive coma, and a standard Gregory-Maksutov has
some residual negative (tail down) coma, this type of Gregory-Maksutov usually has residual positive
coma, with the degree of aspherization limited by the level of acceptable coma. System above,
with a -0.3 conic on the f/2.5 primary, has it at the visually negligible level (linear field like f/8.4 paraboloid).
Due to the more relaxed radii and shorter tube, lateral color error is also somewhat lower than in the
Gregory-Maksutov above, despite its slower primary. Balanced higher order spherical has 0.025 wave RMS
design limit (comparable to 1/12 wave P-V of primary spherical). The level of chromatic
correction is well illustrated by the violet g-line error: 0.032 wave RMS (0.96 Strehl). An f/15 system with f/2.8 primary, which
should be close to the Meade's 7" GMT in that respect, with the same -0.3 conic on the primary
would have less than 2/3 of the coma of this system (linear field), and an equivalent of
1/20 wave P-V of primary spherical aberration axial design limit. There would be no need for
significantly more aspherized primary, and it is all but certain that it is nowhere close to
parabolic, as some speculate, since such system can't be made functional.
As described in the
previous section, full-aperture meniscus corrector has properties making
it quite complex optically. Part of it is due to its steeply curved
surfaces, generating significant amount of higher-order
aberrations. It is a thick lens, requiring more complex expressions for
accurate assessment. Also, its relatively strong power makes system
properties - including spherical aberration level - dependant on its
location relative to the mirror. In two-mirror systems, this only
becomes more complicated with the secondary mirror added. As a result,
the path to defining a working system of this kind is fairly
complicated, and can not be expressed with reasonably small set of
equations.
With the arrangement
with an aluminized spot for the secondary, needed secondary curvature
for desired focus location determines back radius of the corrector, thus
the only variable is corrector thickness and, to that extent, the front
radius. The secondary curvature itself is determined by the properties
of primary, which in turn are known only with the corrector properties
specified. However, there is a typical level of the effect of the
corrector on the primary, which can be used to obtain better initial
approximation of needed system properties (**FIG.
188**).
**
**
FIGURE 188:
Effect of placing full-aperture
meniscus corrector in a two-mirror system (dotted blue). Being thicker toward the
edges, meniscus delays outer portions of the flat incoming wavefront
more, changing its form into convex toward the primary. As a result,
the outer rays diverge, as if coming from an object placed at
meniscus' focal point (in terms of lens power, the meniscus is a
negative lens). Due to the aperture stop being displaced from the
primary, ray height at the primary is greater than at the first
corrector surface (aperture opening), making the primary's optical
radius
larger. It also focuses (**F****1**')
farther away than without corrector in place (**F****1**). Ray height on the
secondary also increases from **kd** (**k** being the height
in units of the aperture radius **d**) to (k+Δ)d.
Since the corrector causes primary mirror to form its image farther away from the secondary, it
re-images it at a greater distance from its surface, shifting the
final focus **F'** farther out. Changes in the
ray/wavefront geometry resulting from corrector's power change aberration contributions of the two
mirrors. Typical ray height increase on the primary due to
corrector's power is 4%-5%, and primary's effective
focal ratio **
F** is reduced by nearly 0.1 (which is reflected in the slightly
shorter nominal focal length for the corrector and primary combined). These quantities help in the initial
estimate of needed properties of the secondary and the corrector for
given primary mirror.
Meniscus corrector for
an MCT can be closely approximated based on
Eq. 128-128.1, for
a single mirror system, corrected for spherical aberration induced by
secondary mirror. The correction is determined by
Eq. 154, and implemented by substituting
[1/(1+s')1/3]R
for **R** in Eq. 126.
Since the **s'** value is typically around 1/3 (neglecting the minus
sign, which merely indicates aberration opposite in sign to that of the
primary), the front meniscus radius in an MCT is generally somewhat weaker than for
the meniscus that would correct the aberration of the primary alone; rear
radius is then calculated based on the front radius approximation, as
given with Eq. 128.1.
Adjustment to the corrector in order to minimize
chromatism and spherical aberration are generally as those described
under this last equation.
In the Gregory-Maksutov, the additional
constraint is that the secondary radius coincides with the rear corrector
radius. For all spherical system, corrector radius needed to generate
spherical aberration that will - combined with that of the secondary -
cancel out spherical aberration of the primary is, in general, stronger
than the secondary radius required for usable systems with mid-to-low
secondary magnifications. In
order to have both, corrected spherical aberration and accessible final focus,
Gregory-Maksutove typically requires secondary magnification larger than
~5. Usable systems with lower magnification would require aspherized
primary.
Two-mirror
Maksutov system aberrations are addressed in more details in the
following chapter. While fourth-order coefficients - in particular
for spherical aberration - are not sufficiently accurate for determining
final system properties, they are necessary for understanding
system's properties.
◄
10.2.3.2. Maksutov-Newtonian
▐
10.2.3.4. Maksutov-Cassegrain aberrations
►
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