A Raytrace Analysis of Various Telescope Systems

by Bob Jones

February 16, 1997

[Planetarium director's note: This is an advanced page on telescope design. If you are just begining in astronomy and are interested in buying a telescope, this is NOT the page for you. I suggest that you start with the Ott Planetarium's "Buying your First Telescope" page or the slightly more advanced "Telescope Buying - Advanced Information" page.]

It has been brought to my attention that only a few people in the astronomy hobby really know how to choose a telescope design based on its merits. This is from talking to various members of our astronomy club and some of my customers over the course of the last two years. Therefore, I will try to explain what the merits of various systems are as well as discuss what their disadvantages are based primarily on raytrace analysis and experience. To keep comparisons the same, I will use the same size and focal ratio (a 12.5" f/8 system) except when discussing Schmidt-Cassegrains (using an 8" f/10).

Refractor

The refractor is probably one of the best telescope designs for small apertures as it has no inherent spherical aberration when the lenses are properly ground. This leads to a telescope system free from coma and related effects. However, to get a good telescope with reasonable aperture and fairly free from color problems (known as chromatic aberration), one need to spend a small fortune for a 4"-5" triplet design. An example would be a Takahashi or Astrophysics 6" f/6 refractor used for a lot of the images found in the gallery section of Sky & Telescope and Astronomy. Optical tube assemblies run an average of about $5000 from what I have heard. So, as most members already know, refractors become cost prohibitive over 4" to 5" aperture depending on what you can spend.

To give an example, I recently debated making 5"-8" refractor doublets for sale and spent close to 3 months designing a system using various glasses. When I settled on a pair that gave near-triplet performance, I got a quote from Schott Glass Works for the two blanks (8.25" diameter by 1" thick flat both sides rather than molded). The cost was $7000 for the pair in quantities of 1000 pairs. The cost for 5" blanks was $4500 per pair. Obviously this places the finished optics out of the reach of almost all amateurs.

Reflector

A non-spherical mirror is not exactly trivial to make, which is why costs are what they are. When making a non-spherical mirror, one first grinds and polishes the blank to the desired focal length or more accurately, the radius of curvature (twice the focal length). This leaves you with a spherical mirror regardless of whether its done by hand or machine. To make a mirror non-spherical, you need to "figure" which is further polishing in select regions. For a mirror larger than 8" this is usually accomplished by polishing more at the edge than the center. This hard part to figuring is getting the curve smooth without turning or over correcting the edge.

The system most amateurs own is the Newtonian design (Figure 1). This design uses a paraboloidal primary mirror and a flat secondary mirror tilted 45⁰ to the optical axis. The main advantage of this design is the reflective nature meaning that this type of system is free from color unlike the refractor. Also, by being reflective, a larger aperture can be had because the glass used does not have to optically perfect (i.e. no bubbles, striae or severe internal stress). This cost effectiveness per aperture is true for all reflector designs. To compare costs, a 12.5" fine annealed Pyrex blank purchased in quantity is $170, an 8" is $32 (compared to $7000). So the main advantages to a Newtonian are low cost and a simple design.

When a Newtonian system is raytraced, there is an effect out from the optical axis known as coma. This causes star images to be spread out into a cone shape. For a 12.5" f/8 Newtonian, this spot, when located at the edge of the field of view (which is 0.93^o for a 2" field) measures 71 x 50 microns. The Airy disk under perfect conditions is 10 microns. This gives a spot-to-Airy disk ratio (S-A ratio) of 7.1

The next system in level of complexity of manufacture, and also one that has gotten

an unfair bad reputation in my opinion, is the Dall-Kirkham style Cassegrain. For members who frequent the Astromart ads, this is the system used for the Takahashi Mewlon series Cassegrains which get good reviews. The Dall-Kirkham or D-K design uses a spherical secondary mirror mated to an ~80% corrected primary (oblate ellipsoid). This design, in a 12.5" f/8 configuration gives a spot size of 248 x 170 microns for an S-A ratio of 24.8 which is roughly 3.5 times that of the equivalent Newtonian. However, this really is not very fair to the design. The D-K design is really excellent when made longer than f/12 and used for planetary viewing (an f/12 has a 0.62^o field of view at 2" and a spot size of 129 x 86 microns to an Airy disk of 16 microns for an S-A ratio of 8.1).

Also, the D-K design would be excellent for use with CCD cameras, even a fast system like this f/8. An example would be using a 12.5" f/8 D-K system and a ST-8 camera (1024 pixels at 9 microns per pixel in long direction). This camera chip has a width of about .3628" for an offset of .1814" or .0844^o. This leads to a spot size of 73 x 48 microns and an Airy disk of 16 microns. The ST-8's pixels are 9 microns wide making the Airy disk about 2x2 pixels and a star at the extreme edge of the chip would be 8x5 pixels. However, atmospheric blurring and even minor tracking errors or mount vibrations would be of at least the same magnitude, so the stars would still appear round in the CCD image. This is even more true for older cameras with larger pixels and/or a smaller chip size.

If your desires lie in the visual or 35mm photography realm, your might consider a Classical Cassegrain, this is the system used on the 200 inch at Mt. Palomar. This design uses a parabolic primary and a slight hyperboloidal secondary. This type of system is made by first making and figuring the secondary mirror (using what's called a Hindle test to properly figure) and then matching the primary to it. This manufacturing technique is also used on the more difficult and costly Ritchey-Cretien design. (Ritchey worked on the 200-inch design, and had conceived the R-C design, but it was an untested idea and they chose not to try it on the, then new, 200-inch.)

For doing 35mm film photography or visual use, a moderate to long f/ratio Cassegrain is hard to beat. For our 12.5" f/8 test system a star at the extreme edge of the field of view would have a spot size of 78 x 60 micron with a 10 micron Airy disk. This is almost the same size as that in the Newtonian above but with a tube length of about 36" instead of 9' for the Newtonian. This feature makes all of the Cassegrain types easier to handle than an equivalent Newtonian.

One problem with all of the Cassegrain types is the secondary size; for these Cassegrain type systems, the secondary would be 5" diameter versus using a 1.52" flat for the Newtonian. This would give more energy to the rings of the focused star's Airy disk pattern. Having bright diffraction rings may be a problem for some people who like ultra-high magnifications.

For people who do LARGE format photography such as 70mm, 110mm, or even 220mm formats, then the only real choice would be the Ritchey-Cretien design. This design uses hyperboloidal surfaces on both mirrors and is the design used on large observatory telescopes such as the 4m at Kitt Peak, the Kecks in Hawaii, and even the Hubble Space Telescope.

When tested at the same point as the other test systems, the Ritchey gives a spot that is 30 x 27 microns and is almost perfectly round. However, since the Ritchey design is best suited for large format work, lets try a spot at the edge of a 70mm and 110mm picture. For the 70mm film this spot is 48 x 48 microns, and for the 110mm (3 x 4 inch roughly) film, this is 114 x 116 microns. However, due to the cost of buying a 12.5" Ritchey ( a tube assembly from Optical Guidance Systems currently runs for about $6000 - $8000), most amateurs will never own one. For any potential customers of mine who are interested in a Ritchey, I usually dissuade unless they are using 70mm or larger film, or place a 35mm camera off-axis.

Lets now compare these 12.5" f/8 raytrace results with a couple of more common telescopes, say a 10" f/4.5 Newtonian (similar to a Coulter) and an 8" f/10 Schmidt-Cassegrain (like the venerable C-8). A 10" f/4.5 Newtonian's spot at 1^o from the center (the full field being 2.07^o) is 205 x 149 microns with an Airy disk of 6 micron. Amazingly, I can barely make out this amount of coma in a Coulter. Now, with a C-8, the spot is 756 x 690 microns and the Airy disk is 13 microns, a fairly significant amount of coma and readily seen at medium magnifications.

The Schmidt Cassegrain uses spherical mirrors making it easier and cheaper to mass produce than any of the previous systems except the refractor is small sizes. This, coupled with its short tube length, are the primary advantages to the S-C design.

Summary

In summary, if you should want a very portable telescope with fair optics and many standard accessories, or want a readily available computerized mount, then a Schmidt-Cassegrain like a Celestron C-8 or a Meade LX-200 8" would probably be preferable. If money is no problem, then a Takahashi or Astrophysics refractor would also be a good choice for portability.

Should money be tight, like it is for the majority of us, then an inexpensive Newtonian would be the better choice; especially when coupled with an alt-az mount known as the Dobsonian mount. The Newtonian design also lends itself to equatorial mounts like the split ring and German style also.

Should the majority of your telescope use be for planetary work where a long focal length is desired, then you have 3 excellent designs to choose from, a long refractor, a Dall-Kirkham, and a Classical Cassegrain. For focal ratios longer than about f/12, the Dall-Kirkham design would be the better choice due to cost. If you wanted a short tube with a focal ratio between f/8 and f/12 or so, then the Classical Cassegrain would be the better choice. Should a long tube and high cost for a moderate aperture be acceptable, then a 6" to 8" refractor would be suitable.

Photographic use of a telescope really falls into 3 categories; CCD, 35mm, and large format. Should CCD work be your main interest, then any design would work exceptionally well. If most of our work is 35mm and visual use, then a well made Classical Cassegrain would be preferred. For those who want to do only large format photography, with the high cost of camera equipment, then the Rithey-Cretien is the only viable option.

A few last notes. One, I get a lot of inquiries about Ritchey sets from people who want a visual or 35mm photography platform. For these people, I recommend a Classical Cassegrain instead as it will work just as well a Ritchey for them for less money. A Ritchey should only be used if you are doing 70mm and larger film work. Also, all of the spot diagrams in this article were done using Ultra Trace written by Steve Dodds at Nova Optical. All of these spot diagrams except for the 10" f/4.5 are to the same scale with the exception being 2/3 scale.

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