Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.
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 to 30 years, they have made a strong resurgence, as a result of three factors:
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 ...
| 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 |
Q: Where can one find these numbers?
A: Try the "Search" tab at the Gaia Archive
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 ...
A connection between football and astronomy?
Sports Illustrated cover for Jan 24, 2011
Yes! Photographers who cover sports need lenses with two key properties:
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.
Q: What are the typical prices for these lenses?
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
That might sound like a small telescope, but it's a pretty darn big lens.
One can use this information to compute the angle subtended by pixels in a telescope, and the solid angle covered by each pixel.
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
----------------------------------------------------------------------------
Here's the filled-in version.
Lens Diam D focal ratio focal length pix ang size pix ang area
(mm) f L (mm) (arcsec) (sq. arcsec)
----------------------------------------------------------------------------
100 2.5 250 8.25 68.07
100 5 500 4.12 17.02
100 10 1000 2.06 4.25
100 15 1500 1.38 1.89
----------------------------------------------------------------------------
So, in general,
Q: Which is better: a short focal length, or a long focal length?
Well, the only real answer is "It depends on what you are trying to do." For example, suppose you are trying to make the best measurements possible of the BRIGHTNESS of some stars. We'll discuss this in a future lecture, but one way to compute the signal-to-noise ratio in the measurement of a star with an electronic detector looks like this:
where
N(star) is the number of electrons from the star
which fall within the aperture
N(backpp) is the number of electrons Per Pixel
due to the sky background
N(thermpp) is the number of electrons Per Pixel
due to thermal effects
R is the readout noise per pixel, in electrons
npix is the number of pixels in the aperture
In certain situations, the limiting factor in the measurements becomes the noise due to background or thermal effects in the detector. In such cases, spreading the light from a star over a large number of pixels will lead to a larger amount of noise.
So, in SOME situations, a larger focal ratio, and longer focal length, creates much smaller pixels, spreading out the light from an object over many 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, in SOME situations, 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?
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?
The scientists running Evryscope recently published a paper describing the results of one small region of the southern sky, after only about 8 months of observations:
The very first few results from the TESS project have started to appear in the technical literature:
Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.