Visual Wavelength Telescopes

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By far, the most common conception of a telescope is one that works in the visual wavelength region of the electromagnetic spectrum. As you will see, there are two basic kinds of visual wavelength telescopes - refracting and reflecting with a host of "variant" forms of each. In this section you will learn about visual wavelength telescopes, how they work and their fundamental limitations.

Reflecting, Refracting and "Hybrid" Telescopes

Regardless of the kind of telescope, all astronomical telescopes can be "defined" in the following way:

The applet provided below in Figure 5.6 provides an illustration of some of the key ideas concerning reflecting telescopes.

Figure 5.6 Click on image to launch applet showing how a curved mirror reflects light.

A concave mirror will reflect and converge an incoming beam of light to a focus. A lens will do a similar thing by refracting or bending the light. In either case, the mirror or lens that collects the incoming light and focuses it is called the objective or primary optical element. This is the most important optical component in a telescope - but it is not the only component.

Example 5.3 Does the concave mirror simulated in the applet in Figure 5.6 form a "perfect" focus? How does the quality of the focus change if you change the curvature of the mirror (by adjusting the slider on the bottom of the applet)?

Solution: The concave mirror shown in the applet does not produce a"perfect" focus. This is an example of a spherical mirror which, though relatively easy to make, suffers from a serious optical defect called spherical aberration. Inexpensive "department store" reflecting telescopes would use a mirror like this. In this aberration point sources like stars appear to be "smeared out" into fuzzy "blobs". If the aberration is not too great then a useful image can still be formed. It is easy to see that in Figure 5.7a a strongly curved mirror does not concentrate the light in a single point but spreads out. In Figure 5.7b the focus is better but still not perfect. The only way to achieve a "perfect" focus is to use a parabolic shape rather than a spherical one and even then the focus will only be perfect for rays that travel parallel to the horizontal axis (called the optical axis) of the mirror. In general, forming sharp images is a major task for astronomers and optical designers. We will explore some of the ingenious methods that have are being used in the quest for sharp images. We can't go too deeply into this subject however - it is a field of study in itself. The point at which light from the objective mirror or lens is concentrated is called the prime focus of the telescope.
	Figure 5.7a Deeply curved mirror
	Figure 5.7b Shallowly curved mirror

Example 5.3 addresses one of the main concerns that astronomers have when designing and using telescopes. The light must be concentrated in as tightly focused beam as possible. In many instruments the prime focus is where an electronic detector (similar to your digital camera) would be placed. In some configurations this is not possible and a small secondary mirror is used to direct the beam out of the telescope to from a focus at a more convenient location. Table 5.5 shows some of the possible configurations for optical telescopes.

Prime Focus This is the simplest configuration in which light from the objective mirror is brought to a focus for further analysis.
Newtonian Focus In this configuration the converging light from the primary mirror is reflected by a flat secondary mirror and directed out of the telescope. This is the most common configuration for amateur reflecting telescopes.
Cassegrain Focus In the Cassegrain focus configuration a convex secondary mirror redirects the converging beam back along the optical axis and through a small central hole in the primary. This a very common configuration and has the advantage of making the telescope much more compact.
Schmidt-Cassegrain The Cassegrain telescope, while compact, suffers from a number of optical defects introduced by the convex spherical mirror. To offset this a corrector lens is placed in front of the secondary to significantly improve image quality. This is the Schmidt-Cassegrain configuration and is a very popular design for small telescopes. Many "upper-end" amateur telescopes use this design (or close variants of this).
Singlet - Refractor The simplest refracting telescope uses a single objective lens. This was Galileo's telescope design and what you would likely purchase today at a "dollar store". This design suffers from a very serious optical defect called Chromatic Aberration. Lens disperse light (just as prisms) into the colours of the spectrum. Different colours focus at slightly different points. Star images appear fuzzy and surrounded by a halo of light.
Achromatic doublet The effects of chromatic aberration can be reduced greatly (but not removed entirely) by introducing a second "correcting" lens directly behind the first. This is the achromatic doublet configuration and is the most common configuration for refracting telescopes.
Table 5.5 Examples of some of the reflector and refractor optical designs.

Sometimes Size Does Matter!

The single most important consideration for an astronomical telescope is its "light-gathering" power or the diameter of its objective lens or mirror. In its crudest form a telescope is a "light bucket" whose job is to collect as much light as possible from a star or faint object. Figure 5.8 shows two telescope primary mirrors, mirror "A" is twice as big mirror "B". Since it is the area that determines how much light a telescope objective will collect we can conclude that telescope A will be able to collect 4 times as much light as telescope B. This means that telescope A will be able to see fainter objects than telescope B. How much fainter? We will consider this question in Example 5.4. The applet provided in Figure 5.10 allows you to investigate how the size of the objective lens or mirror for a telescope will affect the faintest magnitude you could see by looking through the telescope.

Figure 5.8 Light gathering power increases with the area of the objective or the square of its diameter.

Example 5.4 How much fainter (in magnitudes) can a 1.0 m reflecting telescope "see" when compared to a 0.2 m telescope?

Solution: First compare the size of the objective mirrors:Let telescope A have a diameter of 1.0 m and telescope B have a diameter for 0.2 m. The ratio of their diameters is (1.0 m)/(0.2 m) = 5. Since area goes with the square of the diameter this means that telescope A collects (5)² = 25 times as much light as telescope B. Another way to understand this is that stars since in telescope A will be brighter by a factor of 25 times. In Chapter 2.1 you learned about the connection between brightness factors and magnitude. As you recall, a 1 magnitude difference is the same as a 2.5 times difference in brightness, 2 magnitude difference = (2.5 X 2.5) = 6.3 times etc. You can use the following applet (click to launch) to show that a factor of 25 in brightness corresponds to a magnitude difference of 3.5 magnitudes. You will be able to detect stars 3.5 magnitudes fainter with telescope A than with telescope B.

Diffraction and Limits to Resolution

After light gathering power, the next important factor to consider in assessing performance of a telescope is the resolution or "sharpness of view" provided by the telescope. Although the mathematics is very complex, you can quantify resolution. This is because of the wave nature of light and how light (and any wave) behaves when a small part of a wavefront passes through a opening. Figure 5.9 illustrates how you can think about light reaching a telescope. Because of the wave nature of light it comes as a wavefront - in this case drawn as a series of sheets.

When light enters a telescope only a small amount of the wavefront is intercepted - the telescope acts as a disturbance in the incoming wavefront and creates "ripples" that affect what the star images will look like. Rather than appearing as points of light the stars will appear as a series of concentric rings. The bigger the mirror, the more light is intercepted and the smaller the ripples. The ripples are produced by a process called diffraction and are called diffraction rings. The resolution of a lens or mirror is ultimately limited by the process of diffraction. "Perfect" optics are said to be diffraction limited - you can't do better than this. (Note: in low quality optical telescopes other aberration such as spherical or chromatic aberration will degrade resolution much more than diffraction will.)

Figure 5.9 Telescope mirror only intercepts a small part of a wavefront.

So how do astronomers "quantify" resolution? The answer is to consider how close two stars can be to one another and still be seen as separate stars. For example, a visual binary star system consists of two stars, usually very close together.

They may be orbiting each other or they may just happen to appear to be close together. Regardless, the distance between them is measured in seconds of arc (recall that 1 second of arc is 1/3600 th of a degree). For example, Figure 5.10 shows a summertime favourite - the visual binary Albireo or Beta Cygni. This is a pair of stars separated by 35" (quite large by telescopic standards but still less than 1/100th of a degree). The best you can expect for resolution of a completely dark adapted human eye is about 180". So - your eye would not be able to resolve Albireo - the two stars would appear blended together. If, however, you used a good quality, small telescope of only 10 cm diameter you would have little trouble resolving the stars.

Figure 5.10 The binary star Albireo.

To help give you some insight into how diffraction affects star images please experiment with the applet provided in Figure 5.11. (Note: this require rather extensive numerical computation so be patient - it will take a bit longer than most applets to run. To improve performance you may wish to set the number of stars at 1.)

Figure 5.11 Applet illustrating how diffraction affects telescope resolution. Click to launch applet.

Example 5.5 Investigate how diffraction affects depend on the wavelength of light as well as the diameter of the telescope. What combination of the two will give the "best" resolution?

Solution: If you experiment with the applet in Figure 5.11 you will discover that diffraction effects become worse with either longer wavelengths or smaller diameter telescopes. For example, compare the following 3 images:

			The results can be summarized this way: Diffraction effects are more severe with longer wavelengths and with smaller telescopes. Equivalently you can say that resolution of a telescope improves with size and with smaller wavelengths.
Diffraction around star image produced with a 0.4 m telescope and 500 nm wavelength	Diffraction around star image produced with a 1.2 m telescope and 500 nm wavelength	Diffraction around star image produced with a 1.2 m telescope and 700 nm wavelength

The calculator in Figure 5.12 allows you to investigate how telescope size and wavelength affect telescope resolution.

Location! Location! Location!

Location is not just the concern of real estate agents! Astronomers are acutely interested in where they build major observatories. With perfect optics (ie - only limited by diffraction) a 1.0 m telescope should be able to resolve down to about 0.12 seconds of arc. However, it is rare for a telescope to be able to resolve details less than about 1 second of arc across. In fact, in urban areas (where many small observatories are located) the situation is considerably worse. The problem, of course, is Earth's atmosphere. The tall, billowing cumulus clouds of an Alberta summer or the rapidly twinkling stars seen some evenings are hints that the atmosphere is highly turbulent. What this does to incoming starlight is to distort the wavefronts and resulting images that the telescope forms. Instead of seeing tiny points of light surrounded by fainter rings (Airy diffraction rings), stars get smeared out into irregular, quivering blobs. This phenomenon is called atmospheric seeing or just "seeing".

To get around the problems of seeing astronomers are willing to go to great lengths - literally. Extensive searches are made of regions on the globe that have very good seeing. These are most often found on mountain tops along coastal areas. The combination of altitude and geography place the telescope above much of the atmosphere and in locations that normally have steady skies. Figure 5.13 shows one of the very best sites on Earth - the top of Mauna Kea in Hawaii.

Figure 5.13 Aerial view at sunrise on Mauna Kea with Gemini North (large silver dome) on the foreground ridge.  Part of the shadow of Mauna Kea can be seen in the background as well as many other observatories that include from left to right:  24" (very small dome on left), University of Hawaii 88", Gemini 8-meter, Canada-France Hawaii Telescope (CFHT), James Clerk Maxwell Telescope (dimly lit in shadow behind CFHT), NASA Infrared Telescope Facility (silver dome in front of twin Keck domes), Keck I&II (large twin white domes), Subaru (silver structure with Keck I shadow). "Copyright 1999, Neelon Crawford - Polar Fine Arts, courtesy of Gemini Observatory and National Science Foundation"

At an altitude of 4200 m the telescopes in this picture are already above a significant fraction of the Earth's atmosphere. In fact most of the "weather" is trapped by an tropical inversion layer well below the mountain summit leaving an observing site that is usually cloud free, dry (important for Infrared Astronomy) and have seeing often between than 1 second of arc.

Cerro-Tololo Inter-American Observatory This major observatory is located in central Chile, the largest telescope is the 4.0 m Victor M. Blanco telescope. This world class facility has extremely dark skies but there is growing concern that the site is being threatened by encroaching light pollution from a rapidly growing population.
Paranal Observatory This observatory is situated on the summit of Cerro Paranal, Chile at an altitude of 2,635 m. It hosts 4, 8 m class telescopes situated so that they can be linked to form the VLTI, Very Large Telescope Interferometer.
La Palma - Roque de los Muchachos Observatory Located on the Canary Islands, this is Europe's premier observatory and home of the Isaac Newton group of telescopes.
Kitt Peak National Observatories This is the major continental-US observatory located southwest of Tucson, Arizona on the Tohono O'odham Nation. Strict light pollution control in Tucson allows Kitt Peak to remain one of the world's major observatories.
Table 5.6 Some of the world's leading observatories.

Example 5.6 Why are there no new major observatories in Canada?

Solution: A quick inspection of Table 5.6 should provide some answers. Most of the major telescopes are in very remote areas close to the equator, on mountain peaks and either in very dry desert areas or coastal areas with the correct meteorological conditions. Canada has very few such locations. In the 1960's mount Kobau in southern central B.C. had been selected for a major observatory. These plans were changed and led to the creation of the Canada-France-Hawaii telescope. Another major problem for telescopes in high northern or southern latitudes is the lack of dark time during summer months. Finally, Canadian skies are often active with aurora (northern lights) which also means that we do not have access to the darkest skies in the world. All of this argues against the enormous capital investment required to build a major observatory. It is "cheaper" for Canadian astronomers to buy plane tickets!

I Can See Clearly Now!

Even the very best sites in the world cannot escape the effects of atmosphere seeing. Using technologies originally developed in the 1980's, astronomers have developed an amazing technique to "tune-out" the atmosphere. By using mirrors whose shapes can be rapidly distorted, changes can be made in the reflected wavefronts that effectively "undo" the affects of atmospheric turbulence. This technique is known as Adaptive Optics. The video clip shown in Figure 5.14 illustrates how adaptive optics (or AO) systems work.

Figure 5.14 Video clip illustrating the use of adaptive optics to remove the effects of atmospheric turbulence on a star image. Video courtesy of Gemini Observatory with support from the United States National Science Foundation and the University of Hawaii Adaptive Optics Group.

With adaptive optics it is possible to achieve nearly diffraction limited images from large, ground-based telescopes. Figure 5.15 is a video clip show how the image of a sunspot snaps into sharp focus once an adaptive optical system is turned on.

Figure 5.15 Video clip showing how the image of a sunspot is dramatically improved by the use of adaptive optics.

Lucky Imaging

Less sophisticated than Adaptive Optics, Lucky Imaging uses high speed cameras to collect many hundreds to thousands of frames (ie - video) of short duration and then mathematically adds them together to produce extremely sharp images. The idea is to capture moments of exceptional seeing and to reject particularly blurry images. Figure 5.15a gives an example of a lunar image taken at The King's University Observatory #1. The film clip is a short piece of a video stream of several thousand images that were then combined to produce the image seen i Figure 5.15b.

Figure 5.15a Video clip showing how Lucky Imaging is used to create a high resolution lunar image. Image courtesy of The King's University Observatory.

Figure 5.15b. Lucky Imaging image of the Straight Wall (Rupes Recta) and large crater Arzachel. Image courtesy The King's University Observatories.

Image 5.15b shows features on the lunar surface smaller than 1 km across. This means the resolution is better than 0.8" - a level of sharpness far exceeding the typical seeing of 3" in the Edmonton, Canada area.

Example 5.6a How close is Figure 5.15b to the maximum resolution for a 0.34 m telescope?

The Future of Ground-Based Visual Wavelength Observatories

Ground-based observatories will continue to be built into the future. Advances such as adaptive optics have greatly extended what can be accomplished from the ground. One of the most exciting projects on the near horizon is the Thirty Meter Telescope (TMT) project in which Canada is playing a significant role.

The 30 m telescope will be 3 times the size of the largest telescopes currently in operation and will make use of the most sophisticated telescope technologies ever developed. The huge primary mirror will consist of a mosaic of 492 hexagonal mirrors whose individual shapes are warped (via computer control) to help maintain an optimal image. At a cost of over 1 billion dollars this will be the most ambitious ground based observatory ever built. If all goes according to plan the TMT will be in operation before 2020.

Figure 5.16 Artist's conception of the TMT. Note the segmented mirror design for the primary mirror.

To understand the basic principles that govern various kinds of visual wavelength telescopes.