by Yu. A. Klevtsov
(Submitted December 7, 1998) Opticheskij Zhurnal 67, 104-109 (February 2000)
The deficiencies of the popular mass-produced telescopes
of the Schmidt-Cassegrain design include their low aperture
ratio and narrow spectral range. The novel systems for Cassegrain
telescopes with a meniscus corrector proposed here are free
of these deficiencies. Two such systems are described: a
system with corrector lenses made from the same material
and a system with corrector lenses made from different materials.
The systems are technologically convenient (all the surfaces
are spherical) and are distinguished by small lens diameters
(down to 1/3 of the effective aperture), compactness, a
high aperture ratio (up to 1:6.5-1:7), high-quality aberration
correction, and a broad spectral range (400-900 nm), which
is sufficient for working with modern photographic materials
and CCD arrays. © 2000 The Optical Society of America. [S1070-9762(00)02002-9]
More than 20 years ago, the leading American manufacturers Celestron
and Bausch & Lomb and, somewhat later on, Meade
mastered the production of telescopes of the Schmidt-Cassegrain
design with an effective aperture diameter equal to 8-16 inches.
These companies strenuously advertised their development, but
virtually did not provide customers with information regarding
the features and possibilities of the optical systems in the telescopes
produced by them. In this context, we turn the reader's attention
to the difficulties in obtaining a high image quality in a Schmidt-Cassegrain
system with a relative aperture greater than 1:10.
First, the spherochromatic aberration, which cannot, in principle,
be eliminated in this scheme, precludes covering the spectral
range from 400 to 900 nm, which is sufficient for work with modern
isopanchromatic photographic materials and CCD arrays. Second,
the systems of decentration tolerances of the aspherical elements,
which are prohibitively narrow for mass production with a high
aperture ratio, preclude transportability of the instrument without
impairing its optical quality.
Probably for just these reasons, manufacturers increase the diameter
of the secondary mirror in models with a large relative aperture,
thereby reducing the asphericity of the plate and the spherochromatic
aberration introduced by it, as well as expanding the decentration
tolerances of its elements. However, significant central shadowing
is then introduced, which leads to a drop in contrast when fine
details of celestial objects are observed. We point out that in
the 8- and 10-inch models of Schmidt-Cassegrain telescopes recently
introduced by Meade with a relative aperture of 1:6.3 the central
shadowing reaches 18.5% of the area of the effective aperture
of the system, as opposed to the 12% allowed by diffraction theory.
Such telescopes are unsuitable for observing the fine structure
of nebulae and small low-contrast details on the surface of the
Moon and planets.
We also note that the relative aperture of 1:10 adopted in most
models of this system is insufficient for photographing weak diffuse
objects, for which the exposure time can reach several hours,
especially on modern color films. The relative aperture indicated
is also insufficient for achieving the limiting penetrating power
of a telescope with a reasonable delay time (1-1.5 h) in work
with modern black-and-white photographic materials having elevated
sensitivity at prolonged exposures.
Apparently endeavoring to overcome this restriction, manufacturers
have taken the route of equipping their telescopes with focal-distance
converters, which increase the relative aperture of the telescope
from 1:10 to 1:6.3 and consist of positive and negative components
placed after the primary mirror of the telescope in front of the
Cassegrain focus. In turn, each component is assembled from two
lenses. Such a focal converter corrects the curvature of the image
surface, thereby providing an angular field of view up to 1.4-
1.7°, of which more than half can be used for visual observations.
However, such a converter restricts the spectral range of operation
of the telescope, introduces additional scattering and light absorption,
and can create a parasitic background.
In order to explore the possibilities for eliminating the deficiencies
indicated, attention was focused in the present work on the scarcely
studied class of Argunov-Acme optical systems. These systems,
which were designed according to the Cassegrain scheme, have several
design advantages: small dimensions, an absence of aspherical
surfaces that complicate mass production, and correcting lenses
of small diameter (close to 1/3 of the effective aperture of the
Without going into a discussion of the design features of Argunov's
systems, we only point out that the deficiency of his first system
 with an achromatic two-lens corrector
is its large secondary spectrum, and the deficiency of the system
with a three-lens corrector is the complexity of its fabrication
and the narrow correction range for the residual chromatism. In
his second system  with an afocal corrector
placed at a short distance from the secondary mirror, it was not
possible to eliminate the parasitic background to the required
extent, despite the good correction of aberrations. The same deficiencies
also plague Acme's system , which is an
analog of Argunov's system. For these reasons,
Argunov's telescopes have not become widely used.
G.I. Popov was apparently the first who proposed correcting
the aberrations of a prefocal system of spherical mirrors by a
meniscus placed near the secondary mirror in the double ray path
. However, his investigations showed that
the meniscus parameters are insufficient for eliminating positional
chromatism and ensuring aplanatic correction of the system, and
the alternative solutions proposed by him had a coma that, in
principle, could not be eliminated.
Fig. 1. Optical system of a telescope with a meniscus
corrector: 1-primary spherical mirror, 2-quasi-afocal meniscus,
3-negative lens with a reflecting surface.
In 1974 I was engaged in investigating a similar system, but
did not have information on Popov's work. A quasi-afocal meniscus
lens placed in the double ray path near the secondary mirror has
two free parameters when the thickness is assigned: the curvature
and the difference between radii. For this reason the correction
of two aberrations, viz., the spherical aberrations and coma,
can be provided. Because the difference between radii is small,
such a lens introduces only very small positional and magnification
chromatism into the system. Since the free parameters of the meniscus
are already set in the system, compensation of the positional
chromatism is clearly possibly only at the cost of dispensing
with complete correction of the coma. Endeavoring to overcome
this restriction, in 1975 I proposed  using
a Mangin mirror 3 made from the same material as the meniscus
2 instead of a secondary mirror in the system (see Fig.1).
Such a reflecting element makes it possible to introduce compensating
positional chromatism of either sign, depending on the relationship
between its radii, into the system. Since the value of the positional
chromatism needed for compensation is small, the difference between
the curvatures of the surfaces is also small. Thus, the Mangin
mirror should not introduce monochromatic aberrations differing
significantly from the aberrations of a convex spherical mirror
into the system, and the conditions for aplanatic correction can
clearly be satisfied in the system. The theory of the aberrations
in this system gives four possible alternatives for designing
a corrector, of which the most optimal with respect to the residual
aberrations is the alternative in which the shape of the lens
in Fig.1 is characterized by the following
features: meniscus 2 is quasi-afocal and negative and is turned
with its concave side toward the object of observation; lens 3
with a reflecting surface is negative. It should be stressed that
because of the identical dispersion of the material of the corrector
lenses, the secondary spectrum of the system is extremely small:
in the spectral range from 486.1 (F) to 656.3 (C) nm it is 170
times smaller than in a achromat refractor and roughly 100 times
smaller than in Argunov's system with a two-lens corrector .
Thus, it was possible not only to successfully solve the problem
of correcting the three principal aberrations, but also to avoid
the principal deficiency of Argunov's system, which is associated
with the employment of different types of glass in the corrector,
viz., a large secondary spectrum. Subsequent investigations of
this system with corrector lenses having a diameter as small as
1/3 of the diameter of the effective aperture showed that the
residual axial aberrations in the spectral range from F to C allow
a relative aperture up to 1:8, if a glass with a refractive index
equal to 1.46-1.52 (fused quartz, light crown glasses, and crown
glasses) is employed as the lens material. If glass with a refractive
index equal to 1.66-1.76 is used (for example, TK21 glass or super
heavy crown glasses) is employed, a relative aperture up to 1:7
can be attained in the spectral range indicated, although the
secondary spectrum and the magnification chromatism increase slightly
in that case.
Fig. 2. Secondary spectrum of alternative optical systems
with a meniscus corrector made from glasses of the following
types: 1-STK12. 2-K8, 3-STK12/SKF6, 4-STK10/TK21.
Figure 2 presents plots of the secondary spectrum of this system
for the spectral range from 365 (i) to 1530 nm. The corrector
lenses were made from K8 and STK12 glass. As follows from the
data in Ref.5, when the relative aperture is 1:8, a system operating
in the spectral range from F to C with a corrector made from K8
glass can have an effective aperture of 750 mm. A detailed investigation
of the residual axial aberrations of systems of this type showed
that they are determined by the lens diameters (the latter should
not be less than 1/3 of the diameter of the effective aperture
of the system) and by the corrector magnification, i.e., by the
ratio of the equivalent focal distance of the system to the focal
distance of the primary mirror, which should be assigned in the
range from -3 to -4 because of design considerations. In addition,
the residual aberrations of the system decrease with increasing
refractive index of the material from which the lenses are made,
as well as with increasing thickness of the meniscus. Excessively
thick menisci are undesirable, since they introduce considerable
magnification chromatism and absorb too much light. The magnification
chromatism is given by the following approximate relation:
, and )
are the refractive indices of the lenses for the edges and middle
of the spectral range; d2 is the relative thickness
of the meniscus (for
= 1); h3 and
are the Lange parameters, which are calculated with normalization
to h1 = 1 and
= 1 and express, respectively, the relative diameter of the internal
surface of the meniscus and the magnification of the corrector.
The performance of calculations in practice showed that alternative
solutions in the form of compromises with respect to the residual
axial aberrations and the magnification chromatism lie in the
range of values of d2 from -0.006 to -0.012. As for
the kind of glass, the relation (1) confirms that it is best to
use glasses with small dispersion (
- ) and
a large refractive index
for the corrector and that, as a rule, the magnification chromatism
does not exceed 0.04-0.08% in the ranges of values of the free
parameters of the system cited above and the spectral range from
F to C.
The residual coma is corrected fairly well and does not exceed
0.6" on a 30' field for an effective aperture of the system
equal to 200 mm (1:7) and compromise values of the free parameters.
When the relative aperture of the system is 1:8- 1:10, such values
of the residual coma can be obtained already in a field up to
1° with a corrector made from K8 glass or fluxed quartz.
The distortion in the systems under consideration does not exceed
0.01-0.02% on an angular field up to 1°.
The astigmatism' and curvature of field are, in principle, not
correctable in the range of variation of the free parameters of
the system indicated, but they are fairly small5 and permit the
use of a 30' - 40' field for photographic work. We note that because
of the curvature it is also not possible to use a larger field
in telescopes of the Schmidt-Cassegrain design (without a focus
One deficiency of the system considered is the comparatively
narrow operating spectral range (434.1-656.3 nm). This deficiency
is especially noticeable when the relative aperture is increased
to 1:8 - 1:7. The residual spherical aberration can also be detected
in that case. However, the main causes of difficulty in expanding
the spectral range to 400 - 900 nm are the residual spherochromatism
and, to a lesser degree, the secondary spectrum.
Fig. 3. Residual axial aberrations (a-longitudinal,
b-wave) of a system with a corrector made from the STK12/KF6
pair of glasses (200 mm, 1:7).
Significant expansion of the possibilities of the system is achieved
when glasses of different types, which are similar in dispersion,
but differ significantly in refractive index, are used .
An investigation of the possibilities provided by this scheme
showed that a decrease in the refractive index of the reflecting
lens along with correction of the residual spherical aberration
also makes it possible to correct the spherochromatic aberration
over a very broad spectral range. It was found for a meniscus
refractive index equal to about 1.7 (a superheavy crown glass)
that highly perfect correction of the residual axial aberrations
is achieved in the spectral range 365-1530 nm when the refractive
index of the reflecting lens is about 1.5 [see Fig.3a].
A decrease in the refractive index of the meniscus from the value
indicated leads to a decrease in the refractive index of the reflecting
lens to unrealistic values or narrows the range of possible types
of glass so much that it no longer includes glasses capable of
providing for compensation of the secondary spectrum on the edges
of the range indicated. An increase in the refractive index of
the meniscus to 1.74- 1.76 leads to an increase in the refractive
index of the reflecting lens to 1.66- 1.67. However, although
the assortment of glasses having suitable dispersion is fairly
small, it is possible to select glasses which provide a decrease
in the secondary spectrum in the range 436-852 nm. Therefore,
the optimal value of the refractive index of the meniscus glass
is apparently confined to the range 1.7 - 1.73. In the Russian
catalog of optical glass there is only one glass with a refractive
index in this range and a high dispersion coefficient, which,
incidentally, has suitable technological parameters, viz.. STK12
glass. A system of the preceding design with an effective aperture
diameter equal to 200 mm (1:7) was calculated from this glass
for comparison. The secondary spectrum of this system (see curves
1 and 2 in Fig.2) in the range from F to C
is approximately twice as strong as in the system with a corrector
made from K8 glass and reaches an already quite perceptible value
of - 10-4f' on the edges of the range 365-1530 nm.
An investigation of the secondary spectrum of systems with glasses
similar in dispersion shows that it is specified to fairly good
accuracy by the following empirical dependence:
the secondary spectrum of the system,
is the secondary spectrum of an equivalent system with a reflecting
lens made from the meniscus material,
is the difference between the relative partial dispersions of
the glasses, and k is a coefficient, which depends
on the design parameters of the system. An equivalent system is
understood to be one in which the focal distance of the primary
mirror and the entire system as a whole, as well as all the lens
thicknesses and air gaps, are identical. If spectral line e
(546.07 nm) is taken as the peak of the curve of the secondary
spectrum, the difference between the partial dispersions of the
can be expressed as
the current wavelength. The single and double primes label the
refractive indices of the meniscus and the reflecting lens, respectively.
It should unavoidably be concluded from Eq.(2)
and Fig.2 that reduction of the secondary
spectrum within the entire working range of wavelengths calls
for as smooth as possible a difference function of the relative
partial dispersions of the glasses, which is proportional on the
edges of the spectral range being compensated to the corresponding
values of the secondary spectrum of the equivalent system.
An analysis of the relative partial dispersions of Russian glasses
having a refractive index close to 1.5 showed that KF6 glass is
best suited to the STK12 meniscus glass for making the reflecting
lens. A plot of the secondary spectrum of a system consisting
of these glasses is presented in Fig.2 (curve
3), whence it is seen that the secondary spectrum was reduced
by a factor of 4.8 relative to the equivalent system in the near-ultraviolet
region and by a factor of 3.2 in the infrared region.
A further increase in the refractive index of the meniscus permits
a further increase in the aperture ratio of the system, but the
spectral range narrows. I obtained a relative aperture of 1:6.2
(with an effective aperture of 234 mm) for the STK10/TK21 combination
of glasses. Unfortunately, for reasons following from the foregoing,
in this system the residual axial aberrations could be corrected
only in the spectral range 436-852 nm (see curve 4 in Fig.2,
which is the secondary spectrum for this combination of glasses).
The residual axial aberrations of the system with a corrector
made from the STK12/KF6 pair of glasses with an effective aperture
of 200 mm (1:7) in the spectral range 365-1530 nm are presented
in Figs.3a and 3b. A double correction takes
place on the axis of the system: within the effective aperture
there are two crossings of the longitudinal aberration curves,
one on the edge of the pupil and one approximately at 0.55D/2.
This leads to a roughly twofold decrease in the wave aberrations
in the visible region of the spectrum and to a more than sixfold
decrease on the edges of the range 365-1530 nm in comparison to
the equivalent system with lenses made from a single material
(STK12). It is understood that the latter decrease is also associated
with weakening of the secondary spectrum.
As can be seen from Fig.3b, work can be performed
on the axis of the system without refocusing over the extremely
broad spectral range 365-1530 nm. Work can be performed in a field
up to 30' over the very broad spectral range 405-768 nm, which
is quite sufficient for work with modern photographic materials
and CCD arrays, and in this case the magnification chromatism
does not exceed 0.18%, which amounts to 1.6". The residual
coma in the same spectral region and angular field does not exceed
As for the astigmatism and curvature of field, the system just
described does not differ in this respect from the system with
corrector lenses made from a single material: on the surface of
the best images of a 30' field the scattering spot diameter does
not exceed 2".
Where necessary, the astigmatism and curvature of field can be
corrected by introducing a focal distance converter into the system,
as is done in the mass-produced telescopes of the Schmidt-Cassegrain
design from Meade. The converter can have a very simple three-lens
design, the field of view increases on the average to 1.5°, and
the relative aperture increases to 1:5.
Rigorous estimation of the image quality provided by the system
under consideration with an effective aperture of 200 mm (1:7)
and an STK12/KF6 pair of corrector lenses on the basis of a ray
analysis with allowance for the shadowing and diffraction in the
pupil allows drawing a conclusion that even without a focus converter
in the plane of best orientation in a 30' field in the spectral
region 405-768 nm the diameter of the scattering spot, which contains
80% of the energy of the light collected by the system, does not
exceed 28 µm.
While the relative aperture is 1:7, the proposed telescope system
is exceptionally compact, i.e., the distance between the primary
mirror and the corrector only slightly exceeds the diameter of
the effective aperture.
An investigation of the system showed that none of the first-
and second-order specks is focused near the image plane, while
in the Schmidt-Cassegrain system the second-order specks, which
are known to be focused near the focal surface, create a noticeable
halo around bright stars on photographs, which can be suppressed
only partially by aspher-ization and effective antireflection
treatment of both surfaces of the plate. Calculations of the parasitic
illuminance show that specks passing through the system as a scattered
beam are essentially harmless. While the first-order parasitic
spot from the convex surface of the reflecting lens was focused
half-way between the corrector and the image plane in the system
with a corrector made from a single material, it was focused near
the corrector in the system with a corrector made from different
materials. Such a situation undoubtedly creates even more favorable
conditions for its suppression when an antireflection coating
Practical work with experimental telescope models showed that
they are considerably less subject to misalignment than are their
mirror analogs, and quantitative estimates of the decentration
aberrations provide evidence that the permissible error in juxtaposing
the center of curvature of the primary mirror to the optical axis
of the corrector is 1.7-2 times greater than in the Ritchey-Chretien
or Cassegrain design with equivalent parameters owing to the absence
of as-pherical surfaces.
Thus, in comparison to telescopes of the Schmidt-Cassegrain design
and, as an analysis has shown, many other telescope designs, for
example, the Ritchey-Chretien design and D. D. Maksutov's meniscus
cassegrain, the proposed telescope design is capable of providing
a high image quality over a considerably broader spectral operating
range from 400 to 900 nm with a higher relative aperture approaching
values of 1:6.5- 1:7 with all the implied advantages, which have
already been mentioned above. Compactness, technological convenience,
a small corrector lens size, an absence of parasitic light, and
relatively broad centration tolerances of the optics are also
positive qualities of this system, owing to which, in my opinion,
it is an ideal basis for a mass-produced small-size telescope
with an effective aperture diameter equal to 200 mm or more.
Fig 4. Experimental model of a 300 mm
(1:9.6) telescope with a meniscus corrector of original
Fig. 5. Experimental model of a 200
mm (1:8.7) telescope developed under the author's guidance
in the Novosibirsk Instrument-Building Plant.
Fig. 6-7. Klevtsov's USSR Inventor's
Certificate No. 605189.
An experimental model of a telescope with an effective
aperture diameter of 300 mm (1:9.6) was constructed and
tested in 1980 . In 1987 a similar
instrument was given to the Krasnoyarsk National Observatory
(see Fig.4). The work with these instruments
showed that they provide images of exceptional quality without
visibly noticeable traces of a colored halo either in the
center or on the edges of the field of view and permit the
observation of fine low-contrast details in images of the
Moon and planets.
The Novosibirsk Instrument-Building Plant is presently
conducting work on setting up mass production of the system
described in Ref.5 with an effective
aperture diameter of 200 mm (1:8.7). The work on experimental
models of the instruments confirmed that the fabrication
and alignment of the optics of such a system under the conditions
of mass production are significantly easier and cheaper
than the fabrication and alignment of the optics for its
predecessor, i.e., D. D. Maksutov's meniscus cassegrain.
The dimensions of the tube in the experimental model of
the telescope (Fig. 5) together with
the ocular assembly do not exceed twice the value of the
effective aperture, and its weight with all the accessories
(view finder and camera) totals no more than 8.5 kg. The
testing of the experimental model of a telescope of this
design has yielded exceptional results.
- P.P. Argunov,
USSR Inventor's Certificate No. 158697, Byull. Izobret.,
No. 22 (1963).
- P.P. Argunov,
"Isochromatic telescope designs with spherical optics."
Astron. Vestn. 6 (1), 52 (1972).
- L.J. Richter,
"New catadioptnc telescope," Proc. SPIE
288, 33 (1981).
- G.I. Popov, "Isochromatic
mirror-lens designs of the Cassegrain type." Izv.
Krymsk. Astrofiz. Observ. 36, 273 (1967).
- Yu.A. Klevtsov,
USSR Inventor's Certificate No. 605189, Byull. Izobret.,
No. 16 (1978).
- Decision to issue a patent
for the invention described in application No. 96105080
with priority from March 10, 1996.
- Yu.A. Klevtsov,
"Telescope of novel design," Zemlya Vselen.,
No. 5, 92 (1991).
J.Opt.Technol. 67 (2), 176-180,