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 system).

Without going into a discussion of the design features of Argunov's systems, we only point out that the deficiency of his first system [1] 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 [2] 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 [3], which is an analog of Argunov's system.[1] 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 [4]. 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 [5] 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 [1]. 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:

where , , 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 converter).

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 [6]. 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:

where is 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 glasses can be expressed as

where is 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 1.3".

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 is applied.

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 design. 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 [7]. 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, February 2000