# Optical Telescopes

#### The two basic designs

Optical telescopes have undergone several changes since their invention in the late sixteenth century. All telescopes gather light from a large area and bring it to a common focus. But the way they focus the light varies with design.

The earliest and simplest telescopes are refractors. They consist of a long, narrow tube with a lens at the front end. Light which passes through the lens is bent, so that initially parallel rays meet near the bottom of the tube.

Refractors are easy to make and, when small, relatively inexpensive. Large telescopes of this sort become unwieldy. The largest refractor ever put to practical use is the Yerkes 40-inch instrument; its aperture (front lens) is 40 inches in diameter. The tube is a bit longer ...

There are several drawbacks to this design:

1. the lens is supported only around the edges
2. light of different wavelengths comes to a focus in different places

Isaac Newton realized that mirrors would solve the second problem: they can bring light of ALL wavelengths to a common focus. He designed a telescope which used mirrors to reflect light; hence, this type is called a reflector.

The mirror in a reflector can be supported not only around the edges, but also all over the back surface. That means that very large mirrors can be placed into telescopes. The Subaru Telescope has a primary mirror over 8 meters in diameter.

Why build large telescopes? It's not to magnify objects -- the Earth's atmosphere blurs everything to a minimum resolution of about 1 arcsecond. In order to see really fine detail in the optical, you have to move your telescope above the atmosphere:

The real reason astronomers want big telescopes is to detect fainter and fainter objects. The faintest object visible in a telescope depends on the amount of light the telescope can gather ... which in turn depends on its collecting area:

```                              2
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Note that the collecting area increases as the square of the radius (or diameter).

```   Q:   The pupil in your eye has a diameter of about 5 mm.
The little telescope at the front of the class has a

What is the ratio of collecting area of the telescope
to collecting area of the eye?

How many times fainter are the faintest objects you can see
in the telescope, compared to the faintest object you can
```

At some point, however, even though you can support your big mirror across its entire back surface, the mirror becomes so big and so heavy that it starts to sag. Even worse, as you move your telescope to point to different regions of the sky, your mirror will sag in different ways. The mirror will no longer bring all the light rays to a single focus. Our current technology has just about reached that point with mirrors of diameter 8 meters.

What can you do if you want to see even fainter objects?

Answer: use an array of smaller mirrors.

The Keck Telescopes:

The Hobby-Ebberly Telescope:

#### Modern use of refractors

In the late 1800s, the refractor was King: the largest telescopes in the world were the 36-inch at Lick Observatory and the 40-inch at Yerkes.

But around the turn of the century, astronomers decided that they needed as much light-gathering power as possible in order to measure spectra and detect faint stars and galaxies on photographic plates. Reflectors could be made larger than refractors, so the tide turned, and mirrors with larger and larger diameters took over. George Ellery Hale was the driving force behind the construction of a series of very influential instruments:

For most of the twentieth century, refractors fell out of the mainstream of professional astronomical research.

But in the past 20 years, they made a strong resurgence, as a result of three factors:

exoplanets
You've heard about exoplanets, right? They have been a pretty hot commodity in the astronomical community since the first exoplanet was found in 1995.

One of the cheapest and most efficient ways to find (and characterize) exoplanets is via the transit method. All it takes is the ability to measure the light from a star to a tenth of a percent or so (in other words, to the millimag level). But since there are so many stars in the sky, in order to find the rare transit events, one must measure thousands or tens of thousands of stars at a time. Which brings us to ...

(automated) wide-area surveys
There are a LOT of stars in the sky: in rough numbers,
 Mag Approx. Number of stars 5 2000 6 6000 7 18,000 8 52,000 9 190,000 10 450,000 11 1,300,000

In order to check them all for exoplanets -- or for other interesting properties -- it makes sense to use an instrument which has a wide field of view, so that you can measure hundreds or thousands of stars in a single image.

The same is true if one is searching for rare transient events, such as GRBs, SNe, or the optical counterparts to gravitational wave sources. Starting in the late 1980s, astronomers started to combine wide-field telescopes, electronic cameras, and computer-controlled motors in order to carry out surveys of large sections of the sky in an automated manner. I enjoyed dabbling in the early days of automating telescopes myself ...

professional sports

A connection between football and astronomy?

Yes! Photographers who cover sports need lenses with two key properties:

• long focal length (to bring the action close)
• small focal ratio (to put lots of light in each pixel and enable short exposure times)

Well, these are exactly the same major concerns of astronomers. But since there are many more professional sports photographers than astronomers, and since their newspapers and magazines and websites will pay them well to get good pictures, some of the major lens makers have created lenses which meet these needs and are not too expensive. This article might give you some idea for the lenses commericially available -- go to the section labelled "Professional Lenses for Sports Photography."

Let's go through one example to see how this works. We begin with a lens, of diameter D and focal length L.

The focal ratio of the lens is

On the other end of the camera is a detector with pixels.

The relationship between a pixel's physical size p and its angular size α on the image plane is simply

Now, some typical numbers for astronomical instruments of interest, as you will see eventually, are

• CCD pixel size is typically p = 10 microns
• telescope diameter might be D = 4 inches = 100 mm

That might sound like a small telescope, but it's a pretty darn big lens.

Your turn: fill in the columns of this table.

```

Lens Diam D   focal ratio   focal length   pix ang size   pix ang area
(mm)           f              L (mm)        (arcsec)     (sq. arcsec)
----------------------------------------------------------------------------

100            2.5

100            5

100           10

100           15

----------------------------------------------------------------------------

```

Let's pick as a target the planet Jupiter!

Image of Jupiter courtesy of NASA and hubblesite.org

Some representative numbers for Jupiter (which of course changes in size and brightness as it and the Earth move around the Solar System) are

• magnitude approx -2
• angular diameter approx 40 arcsec

We'll need to use these basic facts to figure out a couple of more pertinent parameters: how many photons we can expect to gather from Jupiter, and how those photons will be spread out over our CCD's pixels.

For the first, we'll use the nice and simple approximation that

```

A star of magnitude V = 0 sends through the V-band filter

photons
106  --------------
sq.cm. * sec

```

```

Q:  How many photons per second will enter our camera?

Q:  If we insert a narrow-band filter which transmits only
0.1% of the incident light, how many photons per second
will reach our detector?

```

Okay, now we need to figure out the area on our CCD over which this light will be spread.

```

Q:  What is the angular area of Jupiter's disk

```

Right. With this information, we can continue our table of values to include the number of photons per second striking every pixel:

```

Lens Diam D   focal ratio   pix ang area    Jupiter area    photons per sec
(mm)           f          (sq. arcsec)      (pixels)         per pixel
----------------------------------------------------------------------------

100            2.5           68.1

100            5             17.0

100           10              4.25

100           15              1.89

----------------------------------------------------------------------------

```

Do you see the tradeoff? A larger focal ratio, and longer focal length, creates much smaller pixels ... but that means that the light from any object in the sky will be spread out over many more pixels. If we are fighting against sources of noise -- such as background light or readout noise or dark current -- which affect each pixel independently, then we will lose the signal-to-noise battle as the light of our target is spread out over many pixels.

In other words, a short focal ratio means big pixels, and big pixels mean a higher signal-to-noise ratio in short exposures.

```

Q:  What happens if we make the focal ratio _too_ small,
and the pixels get _too_ big?

```

Yes, if the pixels are so large that they cause neighboring stars to blend together, we won't be able to measure the light of each star properly. That brings up another question: just what is the typical distance between stars? It would be convenient to express this in arcseconds, of course.

Let's choose stars of magnitude 10. There are very roughly 500,000 (half a million) such stars, and let's assume that they are spaced evenly all over the sky. In real life, of course, there are more in certain directions.

```

Q:  How many square degrees does it take to cover
the entire sky?

Q:  How many stars of mag 10 can we expect to find
in each square degree?

Q:  What is the typical distance between mag 10 stars?
(in degrees, and in arcsec)

```

Right. So, armed with this knowledge, we know that wide-field surveys which target hundreds or thousands of stars at a time will want to use a lens with LARGE diameter (and hence large focal length), but SMALL focal ratio. The typical description of a lens in photographic catalogs looks like

```

200 mm              f/4

focal length       focal ratio

```

Can you find prices for lenses which have focal lengths between 150 mm and 300 mm, and focal ratios between f/1.2 and f/6?

In particular, you might check out the Canon 200mm f/1.8, which has been adopted by several astronomical projects.

You might be wondering why I'm spending so much time to talk about surveys of "boring old stars" with magnitudes between 8 and 12. Well, one reason is that I've spent quite a bit of time working on a couple of surveys of this type, so this is stuff I actually understand pretty well.

Here's a picture of one of the Mark III triplets, showing the three telescopes (each a camera lens and CCD) which point at the celestial equator.

Figure 1 taken from Richmond et al., PASP 112, 397 (2000)

The telescopes don't move; instead, they operate in "drift-scan" mode, reading out the CCD at exactly the same rate that stars drift across the field of view. The optics in this system are 135mm f/2.8 lenses.

```

Q:  Why were these lenses chosen for TASS Mark III?

```

#### A few refractor-based sky surveys of the future

The future looks bright for refractors in astronomy, as many people remain fascinated by exoplanets and relatively bright transient sources. If you go to this webpage from my 'Exoplanets' course, you can see a pair of examples:

```

Q:  How much does each of the Evryscope's camera lenses cost?

Q:  How many lenses does the Evryscope have?

```