Ritchey-Chretiens, Dall-Kirkhams, Classical Cassegrains
What does it all mean? And does a curved field really matter?
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Continue Cassegrain Primer
I get a lot of queries regarding the purchase of Cassegrain telescope optics of some form or another. Many of these questions indicate there is a considerable amount of misunderstanding as to what the various types of Cassegrain telescopes are designed to do and what they are capable of doing. Most of the confusion seems to revolve around the true purpose of a Ritchey-Chretien telescope. Other misconceptions surround exactly what a Dall-Kirkham is and its advantages as well as its limitations. And then there is the classical Cassegrain. What makes it classical? And what are its advantages and disadvantages? Hopefully, the following will help clarify some of these questions.
The concept of the two mirror telescope began to emerge
in the mid 1600s with the postulation of both the Gregorian and Cassegrain type
instruments. The two are primarily differentiated by their secondary mirrors,
the Gregorian utilizes a concave mirror placed beyond the focal point of the
primary mirror and the Cassegrain utilizes a convex secondary mirror placed
somewhat inside of the focus of the primary mirror. Both of these mirrors are so
formed as to cause a final focus to take place usually somewhere behind the
primary mirror, which has been perforated so as to allow the light to pass
through. Both the Cassegrain and Gregorian types are extremely useful
instruments. Gregorians were initially the more popular of the two because the
concave secondary allowed primitive 18th century shop testing at the center of
curvature to take place while the convex Cassegrain secondary could not be shop tested at the center of curvature. The Cassegrain telescope
did not assume significant popularity until after the 1850s, and really even later than that, when more sophisticated shop tests were developed. The
testing of a Cassegrain system really requires the use of an autocollimating
flat mirror equal to the size of the primary mirror. Alternative tests have been
devised to test the secondary mirrors separately, but it is almost always best
to test the entire telescope as a completed system. Prior to the use of
autocollimating shop tests the only way to test the telescope was to actually
assemble the optics in a completed instrument and perform a star test; something
that is problematic, being influenced by atmospheric turbulence and weather dependant.
has been the advent of modern shop testing that has allowed the Cassegrain to
assume the role that it has in modern optical astronomy.
The original postulation for the Cassegrain telescope was to have a primary parabolic mirror focusing its rays onto a convex hyperbolic secondary mirror; the classical Cassegrain. This combination of aspheric curves yields excellent correction over moderate fields both for visual and photographic astronomy. The typical Cassegrain was designed to work at focal ratios ranging from f/12 to perhaps f/30. Such geometry results in a fairly small field view, and small fields were readily accepted in early visual and photographic work. It was not until interest in wide field photography that the usefulness of the two mirror system began to be expanded. In 1906 Martin Schwartzchild, a German physicist and optical scientist, published a set of equations that defined the characteristics of two mirror telescopes. Applied to the Cassegrain design these relatively simple formulas began to reveal the fact that by juggling the asphericity between the two mirrors off axis aberrations could be controlled; practically speaking, essentially reduced where possible and appropriate. This was the first time in history that the concept of optimization in the reflecting telescope was understood in a truly scientific sense. Optimization had been developed in the early 1800s by Josef Fraunhofer, and carried forward by Steinheil and Abbe, for aplanatic refractor objectives but it had not been well understood when applied to reflecting systems. Schwartzchild changed all this. History is fuzzy here so there is some speculation to be made, but it is likely that through these equations George Willis Ritchey may have worked out the original designs for what came to be known as the Ritchey-Chretien system. He had established a long distance relationship with the French optical scientist Henry Chretien and Chretien may have made Ritchey aware of these equations and prompted Ritchey to do some exploratory work. All of this is extremely conjectural but the fact is this design emerged just after the publication of Scwartzchild's equations. George Willis Ritchey had a particular interest in astro photography, and a developing interest in the infant area of wide field astro photography.
The fundamental concept of the Ritchey-Chretien is that the off axis aberrations resulting from wide field photography are reduced to a minimum through aspheric optimization. In a classical Cassegrain there are two aberrations that are problematic: astigmatism and coma. The astigmatism component is quite small while the coma component is comparatively large. It turns out that by making the primary mirror slightly more prolate, that is, going beyond a parabola into a hyperbola, and compensating by making the secondary mirror even more hyperbolic, one can correct coma at the expense of astigmatism. But since astigmatism is so small it can be raised considerably before it becomes larger than the coma. The result is a two mirror system optimized over a specific field of view. We now see that the Ritchey-Chretien camera was developed for a specific purpose, wide field photography, not high resolution imaging over a small field. Ritchey-Chretien systems, therefore, are usually made quite fast for a two mirror Cassegrain type system. While classical Cassegrains for visual and high-resolution imaging are in the arena of f/15 to f/25, Ritchey-Chretien systems are usually at about f/8 or f/9 and often as fast as f/6. Such systems have primary mirrors a short as f/2.5 or f/2 and require massive aspherization of their strongly curved primary and secondary mirrors. It must be understood that the final optical performance in terms of wavefront of such fast and highly aspherized systems is usually a lot lower than what is found in slower less aspherized Cassegrain systems. From a practical perspective, extreme aspherization and the desire for a high quality wavefront is never a good combination. As to how much sky area a Ritchey-Chretien can cover it is relatively small when compared to other wide-angle systems such as the Wright, Houghton or Maksutov systems and the ultra-wide-angle Schmidt type systems. While a Schmidt system might cover three or four degrees, a Ritchey-Chretien might cover one degree.
Something else to consider with the Ritchey-Chretien design is that in its original embodiment (Ritchey's specific designs) it would form round stellar images somewhat aberrated (out of focus) rather than optimized asymmetric comatic images (which we tend to like for wide field photography). While this is of no particular interest to the majority of amateur astronomers, early wide field photography interests were often concerned with the science of astrometry, the precise measurements of stars in relation to each other within a given field, not beautiful pictures. As such, the early Ritchey-Chretien systems were optimized (pushed) even further than we would likely do today to the extent of forming perfectly round stellar images, even if they were a little aberrated. The important thing was to define the very exact center of these images, not ogle over their beauty.
When discussing the Ritchey-Chretien it is often mentioned that this type of telescope has a curved field, 'like a Schmidt system', so the phrase usually goes. While it is true that it has a curved field it really is of no practical consequence for amateur size instruments. In the spot diagrams given below I have optimized the systems to a flat field - like you get on your CCD imager. Attempts to optimize to a curve field offered nothing in the way of improvement. For example, a 12.5 inch system working at f/8 as a curvature field of approximately 67 inches radius convex toward the viewer. If one analyzes the sagitta over a focal plane area of 1 inch diameter we find that it has a depth of 0.0075". It should be noted that all Cassegrains of a given geometric design have the same curvature field whether they are a Ritchey-Chretien, classical, Dall-Kirkham or any other aspheric combination.
The last type of commonly encountered Cassegrain to consider is the Dall-Kirkham. This type of Cassegrain appears to have been developed in the 1930s by Horace Dall of Luton, England and uses a spherical secondary mirror combined with a primary mirror aspherized somewhat less than a full paraboloid. To understand exactly what this means, a sphere is defined as having an aspherization constant of 0 while a paraboloid is defined as -1. An ellipsoid is defined as something less than a paraboloid (and greater than a sphere) and an hyperboloid would be defined as something beyond a paraboloid or greater than -1. (The anomaly of referring to, say, -1.2 as greater than -1 and -.80 as less than -1 is accepted for this purpose.) Typically, a Dall-Kirkham might have an aspherization constant somewhere in the area of -.70 to -.80. A Ritchey-Chretien, by contrast, might have an aspherization constant of -1.12. The advantage of the Dall-Kirkham lies in that the spherical secondary is fundamentally easier to accurately construct. Figuring a convex prolate (ellipsoidal, paraboloidal or hypboloidal) surface is one of the more difficult things in optics to accomplish well. Combined with the spherical secondary and lightly aspherized primary, the system be more accurately fabricated than any other compound two mirror design. If properly designed and constructed a Dall-Kirkham can deliver the finest images of any Cassegrain type telescope. The principle problem with the Dall-Kirkham design is that it does not correct for comatic off axis images. The extent to which this is a problem is largely connected with the speed of the primary mirror; the faster the primary mirror, all other things remaining equal, the greater the off axis coma. Realistically, the Dall-Kirkham performs extremely well with primaries of f/4 or slower. Slower primaries, however, increase the physical size of the secondary obstruction. Overall focal ratios are typically not lower than 15 with the best systems at f/18 or above. A Dall-Kirkham is best viewed as a strictly narrow-field lunar, planetary and double star instrument, to which use it is admirably suited.
Now that I have discussed the basics let's look at some spot diagrams produced by various types of Cassegrain systems of various focal ratios. I have arranged these in descending order according to effective focal ratio. All spot diagrams were made assuming a mirror diameter of 12.5 inches and a back focus of 15 inches. The spot diagrams for each equivalent focal ratio were optimized as a classical system, Ritchey-Chretien system and Dall-Kirkham system as appropriate. All diagrams are optimized to so as to form the best image over the field, rather than form the best focus at the center. All of the configurations given here will form precise on-axis images. Not all systems were considered appropriate for optimization has a Ritchey-Chretien system due to their large focal ratio, there being essentially no difference between classical Cassegrain and Ritchey-Chretien spot diagram results. Conversely, the faster systems would fail completely as a Dall-Kirkham. Spots are given for each type: on-axis, 1/8 deg, 1/4 deg, 1/2 deg and (for smaller ratios) 1 deg. All are given for flat fields. (In the accompanying spot diagrams the angles given are half-angles.) In practical terms, the higher focal ratio systems will have only 1/4 and 1/8 degree working fields, but 1/2 degree was used and a standard outside reference.
|Focal Ratio of
|Optimization Type||Physical size and percent
size of Secondary and field covered
3.14" - 25.1% - .5 Deg.
|2||24||4||Classical and Dall-Kirkham||
2.7" - 21.6% - .5 Deg.
|3||18||4.5||Classical and Dall-Kirkham||3.54" - 28.3% - .5 Deg.|
|4||18||4||Classical and Dall-Kirkham||3.4" - 27.2% - .5 Deg.|
|5||15||4||Classical and Dall-Kirkham||3.8" - 30.4% - .5 Deg.|
Classical and R-C
|5.7" - 45% - .5 and 1 Deg.|
|7||9||3||Ritchey-Chretien||4.8" - 38.5% - 1 Deg.|
F/24 (Primary f/5) Dall-Kirkham - 1/2 Deg.
F/24 (Primary f/4) Dall-Kirkham - 1/2 Deg.
F/24 (Primary f/4) Classical Cassegrain - 1/2 Deg.
F/18 (Primary f/4) Dall-Kirkham - 1/2 Deg.
F/18 (Primary f/4) Classical Cassegrain - 1/2 Deg.
F/15 (Primary f/4) Dall-Kirkham - 1/2 Deg.
F/15 (Primary f/4) Classical Cassegrain - 1/2 Deg.
F/15 (Primary f/4) Ritchey-Chretien - 1/2 Deg.
F/12 (Primary f/4) Classical Cassegrain - 1/2 Deg.
F/12 (Primary f/4) Ritchey-Chretien - 1/2 Deg.
F/12 (Primary f/4) Ritchey-Chretien - 1 Deg.
F/9 (Primary f/3) Ritchey-Chretien - 1 Deg.