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10.2.3.2. Maksutov-Newtonian   ▐   10.2.3.4. Maksutov-Cassegrain aberrations
 

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. 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 begin 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" /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 full-aperture meniscus corrector for spherical mirror was a pair of two-mirror Cassegrain systems - /15 and /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

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 (F1') farther away than without corrector in place (F1). 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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