by Will Sager
If you own a telescope, you probably looked first at a refractor (Figure 1). It is the quintessential telescope and if you see a telescope in a cartoon, it is probably one of these. This is first telescope invented, often attributed to Galileo Galilei in 1609 although opticians in the Netherlands probably made similar instruments a few years before. But Galileo pointed his telescope skyward, extensively documenting his observations, and became the first telescopic astronomer. Galileo’s telescope used an objective lens to focus light on an eyepiece lens, which is the basic description of this type of scope. There are many different refractor telescopes, so a beginner can get confused without some background. The goal here is to provide the reader with some details to help understand refractor telescopes and their designs.
Figure 1. A refractor telescope (aka “yard cannon”). (source: Opticalmechanics.com)
By the Numbers
Any telescope description comes with a bunch of numbers, so let’s first consider some important numbers that tell you about a refractor and its capabilities. Some important numbers are aperture, focal length of the objective, f-ratio, and eyepiece focal length (Figure 2).
Figure 2. Simplified diagram of a refractor telescope. Dashed lines represent light rays entering the edges of the objective lens. (author figure)
The aperture is the width of the objective lens, which determines how much light the scope can capture and guide into your eyeball. Bigger is better. The amount of light collected depends on the objective area, which is pr2, where r is the lens radius. If you double the diameter, say from 2 inches to 4 inches, you increase the light gathered by a factor of 4. The focal length is the distance between the center of the objective and the point at which the light going through the lens comes into focus. Focal length is important for two different properties: f-ratio and magnification. The f-ratio is the focal length divided by the aperture and it is a measure of image brightness. This is the same number that you find on your camera lens, where f-ratios <2 are considered “fast”. In photography, fast means that the brighter image requires a shorter exposure to capture an image. Common refractor telescope f-ratios are about f-7 to f-15. A 102 mm (4 inch) aperture with a focal length of 714 mm (28.1 inches) has an f-ratio of 7. At f-15, the focal length is 1530 mm (60 inches). That is a long scope. Why not have lower f-ratios? Because very fast lenses are difficult to make so that the image is sharp across the whole lens (i.e., expensive). Moreover, if the f-ratio is very low, not all of the light will go in your eye (see below). What is the benefit of a “slow” refractor with a high f-ratio? It is easier to make a lens that is sharp across the field. Another benefit is magnification.
Magnification is determined by the focal length of the primary lens divided by the focal length of the eyepiece. Eyepieces come in many focal lengths, but most are between about 30 mm (1.2 inches) for low power and 5 mm (0.2 inches) for high power. For example, our 714 mm focal length refractor yields 24x (this means the image is magnified by a factor of 24) for the 30 mm eyepiece (714/30 = 23.8) and 143x (714/5 = 142.8) for the 5 mm eyepiece. The former is good for low power sweeping across the Milky Way and the latter will give decent views of craters on the Moon, but the power is not very high for discerning details, for example, on planets. Thus, many planetary scopes have longer focal lengths. By comparison, the 1530 mm f-15 scope produces 51x and 306x for the 30 mm and 5 mm eyepieces, respectively. This seems great, but there is a catch. Telescopes will give a maximum useful magnification of about 50x times the aperture in inches. Above that magnification, the image becomes dimmer and fuzzier, but no additional detail can be discerned. Thus, your 102 mm aperture refractor can get up to 205x before it is maxed out. You need a bigger objective to go higher. (But don’t despair – high power is overrated and most of your viewing will be done at low power)
As mentioned above, refractors that have very low f-ratios won’t put all of the light in your eyeball. Why not? The answer is exit pupil diameter. The exit pupil diameter is the width of the light column coming out of the eyepiece into your eyeball. When fully dilated (night adapted) in the dark, most people have pupil diameters of about 7 mm. As people age, this maximum dilation is a bit less. If the exit pupil is larger than the diameter of your pupil, the light around the edges does not go in your eye (i.e., it is wasted). To calculate the exit pupil diameter, divide the aperture by the magnification. For example, 7x binoculars never have objective lenses >50 mm because 50/7 is 7.1. Any bigger objectives and the exit pupil is too large. Considering the 102 mm refractor once again, the 30 mm eyepiece at 24x produces an exit pupil of 4.3 mm. No problem. What if that scope were much faster, say f-4? Then the focal length would be 408 mm and the 30 mm eyepiece would yield only 13.6x and the exit pupil would be 7.5 mm. Whoops, too wide for your eyeball. Such a lens would be great for photography because it is fast and astro cameras don’t have narrow pupils.
Another consideration for high f-ratio refractors is scope length. Remember that the 102 mm aperture f-15 scope has a length of 60 inches. This is the proverbial “yard cannon” that may cause your neighbors to call the police when you bring it out. Refractors are usually mounted by a clamp around the middle. This means that the focuser with the eyepiece sticks out about 30 inches from the mount attachment point. When you turn the focus knob, vibrations are magnified by this lever arm, which makes it difficult to see when the image is in focus. Poorly mounted long refractors can jiggle for many seconds after being touched. As a result, long refractors require heavy, sturdy mounts.
An advantage for refractor telescopes is that they have rigidly mounted lenses, so that once collimated (i.e., the lens axes are aligned) – usually during manufacture – they tend to stay collimated. In contrast, most telescopes with mirrors require periodic adjustment to collimate the optical axes. This makes refractors good for travel scopes and for astronomers who don’t like to collimate.
Before moving on, note one particular feature of the refractor diagram (Figure1). The light beam coming in on one side of the lens ends up coming out of the other side of the eyepiece. This geometry means that refractor images are upside down and backwards. If you use your scope to look at something terrestrial, this flip will be immediately obvious. When viewing the sky, it is mainly an inconvenience of which the observer should be aware. Binoculars, which are designed to give right-side-up images, have special prisms that turn the image around. For an astronomical telescope, the extra reflections cause slight image dimming, so the erecting prism is usually left out (but you can purchase one if you want).
Achromat and Apochromat, What’s the Diff?
Looking at refractor telescope ads, you will find a huge price range for scopes of similar size. Using the 4 inch refractor for example, Celestron sells a 102 mm refractor OTA (optical tube assembly, i.e., the tube without a mount) for about $300. In contrast, Tele Vue sells a 101 mm OTA for about $4,270. Why the big difference? The Celestron scope is an f-10 with an achromat lens whereas the Tele Vue is a fast f-5.5 with a Petzval lens. The Petzval lens is much more complicated and designed to create fast, sharp images for photography. Mostly the price difference reflects how well the lens focuses the image. Making a lens that produces pinpoint stars across the field of view is difficult.
All lenses suffer from aberrations. Chromatic aberration occurs because a single lens does not focus all wavelengths of light at the same distance from the objective (Figure 3). This divergence occurs because the lens behaves like a prism. This means that a simple lens can only be designed to make a sharp image for some wavelengths. Other wavelengths will appear as out-of-focus halos. Cheap refractors with poorly corrected lenses will show such fringes on bright objects and straight edges. A remedy for chromatic aberration is to put two lenses together with different refractive indices so that the second lens bends the divergent wavelengths more closely into focus. A common inexpensive approach is a two-lens objective (doublet) using one element of crown glass and one element of flint glass. The two glass types have different elements added that change the refractive index. This two-lens design is called an achromat. This is the type of lens used in most inexpensive refractors (Figure 4).
Figure 3. Diagram illustrating chromatic aberration, caused by the glass lens having different indices of refraction for different light wavelengths. The result is that different light wavelengths have different focal distances. (source: Bob Mellish, Wikipedia)
Figure 4. Diagram of a doublet achromat objective lens pair, showing reduced chromatic aberration. (source: Bob Mellish, Wikipedia)
An apochromatic objective (aka “apo”) is one that is designed for better color correction. Such telescopes often have a three-element lens (a triplet, Figure 5), but there are some doublets made with exotic (expensive) glass elements that provide decent correction for chromatic aberration. Doublet apos are often called semi-apochromatic. One can purchase a 4-element objective, called a Petzval, which contains two doublets. More lenses and more expensive glasses give better correction, but the more lenses and more expensive glasses make these objectives expensive to manufacture. This is why high-quality apo refractors have big prices.
Figure 5. Diagram of three-element apochromat objective lens assembly, which further reduces chromatic aberration. (souce: Egmason, Wikipedia)
Multiple-element objectives also help correct other aberrations. Any telescope objective produces spherical aberration, which is caused by the fact that light rays coming through the lens at different distances from the center are not guided to the same focus point (Figure 6). Coma is another imperfection, caused by off axis light rays not focusing at the same point (Figure 7). Well-designed multiple-lens objectives do a better job at correcting these aberrations and that is why they are more desirable, especially for photography, where sharp, pinpoint stars are desirable.
Figure 6. Diagram illustrating spherical aberration, caused by a lens not bringing all light rays (blue lines) to focus at a single point. (source: Mansurov, 2019)
Figure 7. Diagram illustrating coma, which is caused by off-axis light rays not converging to a single focus point. (source: Edmondoptics.com)
Which Refractor Scope for Me?
If you want a refractor, which scope is the right one for you? It depends on what you want to do with it. If you will primarily use the scope for visual observations, a good achromat will probably be just fine. It should probably have a higher f-ratio (around f-10) so that the aberrations are less and the longer focal length will allow you to get up to the maximum effective magnification. You might get some color fringes on bright objects, but the cost will be affordable. If the fringes bother you, consider getting a semi-apo doublet. It will be more expensive, but will be more pleasing to your discerning eye. If you want get into astrophotography, you probably want an three or four element apo with excellent color correction.
As you scan telescope ads, you find that size and cost go hand-in-hand. You want a larger objective to collect more light and allow more magnification. Common consumer refractors max out at about 6-inches objective diameter. You can get a decent 6-inch Celestron achromat OTA for about $1,000. Apo refractor OTA will be a factor of 4-8 times more expensive. Larger refractor scopes are too expensive to manufacture at prices that many people will pay and larger objectives also translate it large, long tubes that require sturdy mounts, often a pier fixed in an observatory. As a result, one rarely encounters a refractor with a larger objective unless you visit a professional observatory.
Reference:
Mansurov, N., 2019. What is spherical aberration? Photoraphylife.com
Lens design primer: https://www.pencilofrays.com/lens-design-forms/
