By Joshua N. Winn, Princeton University
Most people tend to think that we build telescopes to magnify or to make distant objects seem closer, which they do. It is great, if one is a birdwatcher. But for professional astronomers, magnification is one of the least important reasons to build a big telescope. Why?
A Tarsier and an Astronomer
Magnification is the least important function of a telescope for an astronomer. In order to understand why, let’s talk about a tarsier, a primate from Southeast Asia. Even if a person hasn’t ever heard of a tarsier before, one might guess right away that it must be nocturnal, just by looking at it. Why else would it have such enormous eyes? Tarsiers work at night, so they need to make the most of the faint light from the moon and the stars.
What a tarsier has in common with astronomers is that they both work at night. Thus, they too would require big eyes, even bigger than a tarsier’s.
More Sensitive to Photons
Collecting more light improves our ability to detect faint sources, and to measure their properties with greater precision. In addition to having bigger eyes, nocturnal mammals have better eyes. A tarsier’s retina—the light-sensitive layer of cells at the back of the eye—has more rod cells than cone cells, compared to our eyes. That makes their eyes more sensitive to photons.
Likewise, astronomers use sensitive digital cameras instead of relying on our retinas. For every hundred photons that hit our retina, no more than 5 or 10 actually get registered and contribute to the signal that gets to our brain. We say the ‘quantum efficiency’ of the human eye is less than 10%. But a digital camera optimized for astronomy can have a quantum efficiency of 90%. And, of course, a camera can make quantitative objective records, so one can count the number of photons that hits each pixel, instead of relying on subjective visual impressions.
Telescopes and Cameras
There are lots of other reasons to love telescopes and cameras. They give us better angular resolution than our eyes: the ability to resolve fine details. They give us better spectral resolution: the ability to distinguish different wavelengths. Better time resolution: the ability to discern changes in brightness or color. And, we can detect radiation that’s invisible to our eyes, like radio waves, and X-rays.
Out of all of these, the number one reason would be to collect more light. One can think of the light from distant sources as a gentle rain of photons, falling onto the Earth’s surface. When we look up, our eyes collect the rain that happens to fall through our pupils. When we’re using a telescope, we’re using a bigger bucket to collect the rain.
This article comes directly from content in the video series Introduction to Astrophysics. Watch it now, on Wondrium.
Proxima Centauri
Let’s consider Proxima Centauri, the closest star to the Sun. The light coming from Proxima Centauri amounts to about 100 photons per square centimeter per second. That might sound like a lot, but the pupils of our eyes are only a 5th of a square centimeter, and our retinas don’t respond to 90% of the photons that get in. Even worse, we only have about a 10th of a second to detect a signal. Our visual system can’t accumulate signals for longer than that. It’s like a camera, but with a hard-wired shutter speed.
Putting all that together, the average number of photons from Proxima Centauri that enter our eyes and get detected during a 10th of a second is 0.2. That’s less than one. Which is why Proxima Centauri is invisible to the naked eye.
Photon Fluctuations
With a telescope and a digital camera, though, we can boost all the factors in this calculation. We can increase the collecting area. We can detect nearly all the photons. And we can use whatever shutter speed we want. This is important because the rain of photons is not completely steady. There are fluctuations. Often these fluctuations prevent us from measuring the star’s brightness as precisely as we might want.
Another important factor is the Poisson distribution. Whenever we’re dealing with events that occur at random times, but with a well-defined average rate—like radioactive decays, earthquakes, or, the arrival of photons from a distant star—the relevant piece of mathematics is the Poisson distribution.
Poisson Distribution
Presuming that N is the average number of events that we expect to occur in some time interval, then the probability we will actually observe k events is N to the kth power, divided by k factorial, times e to the minus N. That’s the Poisson distribution.
To add to this, if we plot for the case of N equals 100 photons, it would mean that the standard deviation is 10. Which means there’s about a 68% chance that the number of photons in our image will be between 90 and 110. Another way to put it is that the signal-to-noise ratio of the measurement is 10. The ‘signal’ is the average flux of the star, and the ‘noise’ refers to the random deviations from the average.
Light from a star is often blended together with other sources of light, from other nearby stars in the sky that we can’t resolve with our telescope, or from the faint glow of the Earth’s atmosphere. The photons from those other sources contribute to the fluctuations, too. We call that ‘sky noise’.
To conclude, the inevitable fluctuations in the photon count, the Poisson noise, is an unforgiving fact of life in astronomy. There are lots of ways a measurement can be wrong, but even if one has perfect equipment and makes no mistakes, they can’t eliminate the Poisson noise.
Common Questions about Telescopes
What a tarsier has in common with an astronomer is that they both work at night. Thus, they too would require big eyes, even bigger than a tarsier’s.
The average number of photons from Proxima Centauri that enter our eyes and get detected during a 10th of a second is 0.2.
Light from a star is often blended together with other sources of light, from other nearby stars in the sky that we can’t resolve with our telescope.
