A small telescope is often described as a rather simple device. By place two lenses in a tube at the right distance, Galileo changed our understanding of the universe. But in fact the interaction of light and glass is extraordinarily complex, as you can see in the video above. 

The video simulates a pulse of light striking a series of lenses. You can see how some of the light reflects off the surface of the lenses rather than simply passing through and how the effective speed of the light slows down while passing through the glass. You can also see how the colors of the light begin to spread apart, which is a process known as chromatic aberration. It’s a subtle dance we can’t see directly, but the effects of this dance makes telescope design challenging.

While it is fairly easy to make a basic telescope, making a truly good one is a big challenge. It’s forced us to learn how to make lenses and mirrors with precision, and even to use computer modeling to create more useful telescope designs. We’ve come a long way, but we are still learning about the ways light interacts with material, and how we can use that dance of light to better see the cosmos.

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The history of astronomy is in many ways a history of building ever more powerful telescopes. Since Galileo first pointed a telescope at the night sky, we’ve strived to peer deeper into the night. Of course one of the downsides of ever more powerful telescopes is that with higher magnification generally comes a smaller field of view. 

Technically, a field of view is measured in an angular area known as steradians, but since a telescopes field of view is generally circular, it’s often simply measured in terms of the width of the circular field. For example, a modern 8-meter telescope has a width of about 0.2 degrees, or a bit less than half the apparent width of the Moon. By comparison, the faint-object camera on the Hubble space telescope has a field width of about 0.001 degrees. Modern telescopes aren’t nearly as bad as Galileo’s telescopes, which had a magnification of only 10 and a field of view only a quarter the width of the Moon, but it is still an issue for many telescopes. At high magnification, it is often like looking at the night sky through a narrow straw.

Mirror design of the LSST. Credit: LSST

This isn’t a problem if you want to look at faint objects with a small apparent size, but it is terrible for doing large sky surveys. For that you’d like to have both high magnification and a wide field of view. Fortunately with computer designed lenses and modern manufacturing techniques we are starting to achieve that goal. Perhaps the clearest example is the Large Synoptic Survey Telescope (LSST) currently under construction. It’s 8-meter design will have a field width of about 7 Moons. It does this through a complex three mirror system. Since the primary mirror is more ring-shaped than disk-shaped, it loses some of the light gathering power than more traditional 8-meter telescopes have, but the wide field more than makes up for it.

The goal of telescopes like LSST is to scan the sky in a matter of days. In this way we can observe how the sky changes on a scale of months and weeks, and we’ll have a better chance of observing transient objects such as supernovae in their early stages. This wouldn’t be possible without a wide field of view.

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Glass has the useful feature of being transparent at optical wavelengths. That, and the fact that light can refract (change direction) when it passes through curved glass is what made it useful as lenses, and eventually telescopes.

We usually think of Galileo as the inventor of the telescope, but this isn’t the case. Glass lenses have existed in Europe since the 1200s, and by the mid 1300s basic eyeglasses had appeared. These early lenses were pretty basic convex lenses. Convex means that they were thicker in the middle than at the edges, and as a result light passing through them would refract closer together. A magnifying class is a good example of a convex lens, and if you’ve ever let sunlight pass through one to make a concentrated point of light that can set things on fire (kids, don’t try this at home), then you’ve seen its effect.

In the mid 1400s a different type of lens known as a concave lens appeared. These are thicker on their edge than in their middle, and causes light passing through it to spread apart. If you are nearsighted and wear glasses, these are the type of lenses they use.

The first astronomer to use lenses seems to have been Leonard Digges. In the 1570 book Pantometria his son Thomas describes a “proportional glass” that might have been a telescope, though the description is vague. The first true telescope dates to at least 1608, when Hans Lipperhey applied for a patent for the device in the Netherlands. The device used a larger convex lens and a smaller concave lens place along either end of a tube. Light passing through the convex lens would be focused together, and would then pass through the concave lens, which spread the light into its original orientation. The net effect was to magnify the image entering the device.

In July of 1609 Thomas Harriot used such a telescope to look at the Moon. His telescope only had a magnification of 3, which isn’t much at all, so Harriot wasn’t able to determine the nature of the lunar features. That same year Galileo had a similar telescope constructed. Galileo’s first telescope had a magnification of about 9, which was powerful enough to distinguish features of the moon. Galileo’s later telescopes had magnifications of up to 30. So it is Galileo whom we now associate with the telescope.

Refracting telescopes such as Galileo’s are still used today, though they are less popular than reflecting telescopes which are easier to construct at larger sizes. But even reflecting telescopes require an eyepiece, which is typically a glass lens. So even when we aim a mirror to the night sky, we still raise a glass.

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When stars are portrayed in media, they are often shown with long spikes emanating from them. Perhaps the most common example is that of the “star of Bethlehem” which, according to the story, led the wise men to baby Jesus. Of course when we look at stars in the night sky, we don’t see any such spikes. Stars twinkle due to atmospheric disturbances, but that’s about it. In photographs, however, bright stars often have such long spikes. So what causes them? It all has to do with an interesting bit of optics.

The Craig lens-based telescope was 85ft long.
Credit: Wakefield Collection

In astronomy, they are known as diffraction spikes, and they appear with certain types of telescopes. Optical telescopes broadly fall into two types: lens-based and mirror-based. Lens-based telescopes were the first to be developed, and are basically a long tube with two or more lenses. Starlight is refracted by the lenses to produce a magnified image. Since the light goes straight through the telescope unimpeded, you don’t get any spikes on stars. The big disadvantage of lens telescopes is that they tend to get be fairly long for large magnifications, and large lenses are difficult to make well.

The mirror supports on my telescope.

Mirror-based telescopes are easier to make, and because they reflect light they can be made shorter. Light can be focused from a large back mirror to a smaller mirror, which then focuses the light onto an eyepiece or camera for viewing. One downside of this type of design is that starlight has to pass the smaller mirror before reaching the large back mirror. As it does, the supports for the mirror cause the light diffract. It’s the diffraction pattern that causes stars to appear spiky, hence the term diffraction spikes.

Normally diffraction spikes aren’t noticeable. When viewing objects directly you won’t typically notice them. But with long photographic exposures they generally show up.  Even professional telescopes have them in many of their images. They generally aren’t a problem for research, and the advantages of mirror telescopes vastly outweigh the minor inconvenience of diffraction spikes.

But the main reason we see diffraction spikes so often is that astrophotographers often use them to artistic effect. They transform a bright point of light into a wondrous stellar image.

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If you’ve ever looked up in the night sky you’ve seen the twinkling of the stars. This twinkle is not due to the stars themselves, but to the turbulent motion of the Earth’s atmosphere. As starlight enters our atmosphere, the variations in density in turbulent air cause the light wave fronts to distort. So instead of reaching the telescope evenly like even rows of a band on parade, the wave fronts come in uneven and wobbly. This wobbly behavior is why stars appear to twinkle.

One way to overcome this problem is to simply put your telescope in space. This not only eliminates the twinkle effect, but also allows you to make observations at wavelengths our atmosphere absorbs, such as most of the infrared. The big downside is that space telescopes are very expensive, and their size is fairly limited. The Hubble telescope, for example, has a mirror diameter of about 8 feet. In contrast the Keck telescopes have a diameter of about 32 feet, which means their mirrors have about 16 times the area of the Hubble. Because of the cost, there are also only a handful of optical space telescopes, while there are dozens of large ground-based telescopes.

There is a way that you can minimize the twinkling effect for ground-based telescopes, and it’s known as adaptive optics. The basic idea is to correct for the wave distortion by adjusting the mirror in real time to account for it. The main way this is done is by using a tip-tilt mirror to realign the image, or if the mirror is segmented (as many modern large telescopes are), adjust each segment to correct for the distortion.

Of course to make this correction you have to be able to distinguish between distortion caused by the air and any real variance in what you are observing. There are a couple of ways this can be done. If what you are observing has a fairly bright star in your field of view, then you can adjust the mirrors to keep that particular star in perfect focus. By accounting for the distortion of the bright star you account for the distortion in your image.

But often what you are observing doesn’t have a sufficiently bright star in your field of view. In this case you can use a laser to simulate a star. You can see this trick being used with a sodium laser in the image above. The laser itself is not particularly bright, but there are small amounts of sodium atoms about 60 miles up, and the laser excites them, causing them to glow. Since the glowing atoms are in the telescope’s field of view, it looks like a star. And since 60 miles is higher than most of the Earth’s atmosphere, the distortion of the sodium’s glow is about the same as the distortion of star light. So by keeping your artificial star in focus you can keep your image in focus.

With adaptive optics and a simulated star ground-based telescopes can obtain images that rival those of a space telescope.

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Launched in 2009, Kepler was intended as a “planet hunter” telescope. It finds planets by observing stars for long periods of time. To make long observations, Kepler needs to be able to point in the same direction very precisely, and it must be able to adjust its direction if it starts to drift. So how do you keep a telescope oriented?

On Earth, a telescope can be mounted to the ground, and any change in direction can be made by orienting the telescope relative to its mount on the ground. But for a space telescope there is nothing to mount it to. This means there are only two ways to adjust the orientation of a space telescope: thrusters and gyroscopes.

Thrusters are basically small rockets. They release a small amount of propellent, and the telescope moves a bit in the opposite direction. It’s Newton’s third law of motion in action. With multiple thrusters you can adjust the orientation of the telescope. But there are two disadvantages to this method. The first is that every time you make a thrust you lose a bit of fuel. The second is that it is difficult to make thrusts with the precision necessary for Kepler.

Gyroscopes use a different approach. A gyroscope is basically a spinning wheel. When the wheel is spinning, it resists changing direction (a property known as conservation of angular momentum). You can see this effect in the video. With three gyroscopes you can orient a telescope in any direction, and you can keep it in a specific direction very precisely.

The Kepler spacecraft has 4 gyroscopes (called reaction wheels), but about two years ago one of them started acting wonky and was shut down. This wasn’t a huge deal, since the telescope can get along just fine with 3 gyroscopes. But last year a second reaction wheel malfunctioned, and that put the mission at risk.

So what could be done? They basically tried two options. The first was to start up the first reaction wheel in the hope that it would function well enough to be used. The second was to use a combination of thrusters and the two remaining gyroscopes. But neither of these solutions were successful.

So it was feared that Kepler’s planet hunting days were over. There are other projects the telescope could be used on, but its orientation simply wouldn’t be precise enough to detect planets. This would have been really disappointing, but it wouldn’t mean a failure of the mission. Kepler completed its mission in 2012, and then entered an extended mission phase because it was still functioning well. It has gathered tons of data that has yet to be fully analyzed, so there is plenty to keep astronomers busy.

But it turned out the failure of the reaction wheels wasn’t the death of Kepler. Using some clever tricks, a new project known as K2 was devised.  But that’s a story for another time.

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Our eyes see color through cones in our retina, where the three different types (S, M, and L) each have a slightly different range of wavelengths to which they are light sensitive. Through the response of these different cones our brains are able to distinguish different wavelengths of light, which we interpret as color. Telescope detectors typically have a much wider range of light sensitivity, which is good if you want to detect a great deal of light, but not so good if you want to observe a particular color range. So many telescopes have filters that block light outside a particular range.  

Credit: NASA, ESA

As a case in point, consider the Hubble space telescope. Hubble has a camera that mainly looks at visible light (the Advanced Camera for Surveys, or ACS) and another that mainly gathers infrared light (the Wide Field Camera 3, or WFC3).  Since the sensitivity range of each of these cameras is so wide, each has several filters that block all but a narrower region, known as a band.  The colors in the figure don’t correspond to the colors we see.  Our visible spectrum is roughly the V band, while B is violet to ultraviolet, i is red to near infrared, and all the others are infrared.  You can see how the different bands overlap, and how the amount of light each filter lets through can vary. In order to look at the broad spectrum of light from an object (which is not the same as the spectral lines), Hubble images an object through different filters.  These images can be combined to create a “color” image.  Though often it is a false-color image with different visible colors assigned to each band.

The figure shows another interesting aspect of the spectra, which deals with redshift. The wavelengths of light we observe from an object are not always the wavelengths that object emits.  The light from an object can be redshifted or blueshifted due to the motion of the object relative to us, and things like cosmic expansion.  For distant objects, the redshift due to cosmic expansion can be pretty severe, pushing visible and even ultraviolet light well into the infrared.  The white line in the figure shows the light typically emitted by a distant galaxy at different redshifts (known as z).  You can see that by the time you get to about z = 12, most of a galaxy’s light is so far to the infrared that Hubble can only detect a small portion of it.  This means for the Hubble telescope, z = 12 is about the largest redshift it can detect.

Still, there’s quite a bit that Hubble can see simply by reading the rainbow.

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In astronomy we rely upon telescopes and other optical devices, and that means we have to deal with the complexities of how light behaves.  In many ways light can behave in fairly simple ways, but this simple behavior is not perfect.  As a result, telescopes can have optical aberrations.  Dealing with these aberrations can sometimes pose quite a challenge.

Chromatic aberration in a simple lens. Credit: Bob Mellish

One type of difficulty is known as chromatic aberration.  It is most commonly seen in simple telescopes.  Lenses focus light by using the fact that light will bend when it enters a material such as glass.  The amount of bending the light does depends on the index of refraction of the material.  But the index of refraction varies slightly for different wavelengths.  As a result, red light focuses at one point, but blue light focuses at a different point.  This means a simple telescope can’t focus all colors in the same way.  When a star or planet is in focus for blue, for example, the other colors appear slightly blurry.

One way to overcome chromatic aberration is to add an extra lens with a different refractive index.  This can help bring the focal points of different colors closer together.  This isn’t a perfect solution, however.

An example of spherical aberration. Credit: Amazing Space

Of course not all telescopes use lenses.  Many use mirrors, which don’t produce a chromatic aberration.  There is however a different effect known as spherical aberration.  Spherical aberration can also occur with lenses, but it is more common with mirror telescopes.  It turns out that a mirror with a spherical focuses light almost to a point.  This is a good thing, because producing spherical mirrors is much easier than producing non-spherical mirrors.  However a spherical mirror doesn’t focus light to an exact point.  Light reflected from the outer edges is focused slightly closer than light reflected near the center.  For small mirrors this effect is small, and can usually be ignored, but for larger mirrors this effect matters.

You might remember when the Hubble telescope was launched, there was an issue with its mirror that prevented the telescope from focusing properly.  This error was a result of spherical aberration.  To overcome spherical aberration, a mirror must be ground with a parabolic shape.  The Hubble mirror was ground to a more spherical shape, and as a result the outer edge was too shallow by about the width of a human hair.  Of course once it was in space the telescope couldn’t be brought back to Earth, so a corrective lens needed to be put in place to correct for the error.

Modern telescopes are designed to minimize these effects, even small hobby telescopes.  If you happen to have a small telescope at home, you can be proud to own a rather sophisticated optical instrument.

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One of my favorite objects in the night sky is the Orion nebula.  It’s easy to find, just below the belt stars in the constellation Orion, and it is the closest stellar nursery.  It’s also a bit bigger than the Moon.  Actually that’s a bit misleading.  It is actually about 24 light years across, but because it is also about 1300 light years away, its apparent diameter is about a degree, which is about twice the apparent diameter of the Moon.

Credit: The Wondrous Sky.

In astronomy, apparent size is important because it’s one of the factors that determines our ability to observe them in detail.  With any telescope, there is a limit to how close two features can be before they blur together.  This is known as its resolving power.  For a simple telescope, this is a function of the diameter of its main mirror or lens (all other things being equal).  A 4″ telescope, for example, has a resolving power of about 2 arcseconds.  An arcsecond is 1/3600 of a degree, so using such a telescope to look at the Moon would be kind of like looking at an image of the Moon about 900 pixels wide.

Of course there are other factors as well.  The resolution power of telescopes also depends on the wavelength at which you are observing, then there is the issue of how much light pollution you have in your area, whether the air above you is calm or turbulent, and others.  Usually a backyard telescope can’t resolve things to their theoretical limit.

Moon compared to Hubble Extreme Deep Field. Credit: NASA/Hubble

One way to overcome many issues is to put your telescope in space.  The Hubble space telescope is above the atmosphere, so it can resolve things at close to its resolution power, which is about 100 milliarcseconds.  This is one of the reasons we put telescopes in space.

One  way to overcome the resolution limit is to use multiple telescopes.  This process is known as  interferometry.  The light gathered from multiple telescopes can be combined to create a “virtual” telescope.  The greater the virtual size, the more resolution you can have.  This particularly useful with radio telescopes.  The largest of these is the Very Long Baseline Array, which has an effective diameter of over 8,000 kilometers.

When things are billions of light years away, even large objects have a tiny apparent diameter.  This is why we’re always striving for greater resolution in our telescopes.

It’s all a matter of scale.

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In observational astronomy, it’s always good to gather more data.  Sometimes this is achieved by making more observations, but at other times it is achieved by making observations at different wavelengths of light.  You’re probably most familiar with observations made in the visible spectrum.  After all, it is how we observe things with the naked eye, which is how astronomy was done for thousands of years.

In the 1930s, we started building radio telescopes, which opened a whole new realm of observational possibilities.  Expanding observations to even more wavelengths was a bit of a challenge because our atmosphere tends to absorb light in the infrared, at large radio wavelengths, and at wavelengths shorter than visible light.  This is generally a good thing, because things like ultraviolet light and x-rays tend to be harmful to us.  It means, however, that to observe these wavelengths we have to get above the atmosphere.  For this reason, satellites capable of ultraviolet and x-ray astronomy didn’t appear until the 1970s.

X-ray astronomy presents an additional challenge because you not only have to put your x-ray telescope in space, you also have to build your telescope very differently.  A visible or radio telescope typically uses a curved surface that acts as a mirror to reflect light back to your camera or detector.  But the wavelengths of x-rays are so short they act almost like tiny bullets.  If you tried to use a curved surface to reflect x-rays back to your detector, the x-rays would simply pierce through your “mirror.”

To focus x-rays, then, you have to use a series of slightly curved surfaces aligned so that the x-rays glance off the surface at a shallow angle, as you can see in the figure below.

This means x-ray telescopes have to be fairly large.  The Chandra telescope, for example, is more than 40 meters long, compared to the Hubble telescope, which is about 10 meters long.  It also makes it more difficult to make high resolution images.  Chandra’s resolution is about 1/2 an arcsecond, which is roughly the apparent size of the minor planet Ceres as seen from Earth.

The big advantage, of course, it that x-ray astronomy lets us observe many of the phenomena that occur at high energies, such as black holes and supernova.

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