L2S3

3. SENSITIVITY OF OPTICAL TELESCOPES

If your eyes are excellent (and you eat plenty of carrots), the faintest star you can see on a very dark night has brightness of 5th magnitude (the higher the magnitude, the fainter the star). The Hubble Space Telescope can detect stars of brightness 32nd magnitude -- approximately 10¹¹ (100 billion) times fainter!

There are four main factors that limit the sensitivity of your eye, or a telescope. The first is the aperture of the telescope primary mirror (in your eye, the pupil). The area of the aperture, given by A = p D²/4, where D is the diameter of the telescope, determines the number of photons per second that are focused on the detector. The increased aperture is the main reason that a telescope is more sensitive to faint sources than your eye. For example, the ratio of areas of the Keck 10-meter telescope to your eye (pupil diameter = 3 mm), is [10/(3 ´ 10^-3)]² = 1.1 ´ 10⁷, i.e., more than 10 million.

The second factor that determines the sensitivity of a telescope is the sensitivity of the detector. This sensitivity has an important name: quantum efficiency (Q.E.). When a photon strikes the detector, it does not necessarily record a signal (i.e., send an impulse through the optic nerve, expose a grain on photographic film, or send an electronic signal from the CCD to the computer). The quantum efficiency is given by the formula Q.E. = (photons that record a signal)/(photons that strike the detector).

The quantum efficiency of your eye (when fully dark-adapted) is a few percent. That is, for every 100 photons that hit the retina, two or three of these photons will actually cause your retina to send a signal to your brain. It's about the same for fast film. But CCDs have much better Q.E. -- often 90% or better, i.e., more than 30 times better than the eye or film. When astronomers replaced film with CCDs on telescopes, the telescopes immediately became more sensitive by a factor of about 30. That means that a 1 meter telescope equipped with a CCD is as sensitive as a 5.5 meter telescope with film.

The third factor is exposure time. Anybody who has used a camera knows that you can compensate for low lighting with a longer exposure time. The retina of your eye takes a new exposure about 10 times a second or faster, so the exposure time of your eye is about 0.1 seconds. Exposure times in astronomy range from seconds to days. The deepest exposure I know of took 10 days with the Hubble Space Telescope. That image, called the Hubble Deep Field, contains the faintest objects ever observed by astronomers.

The fourth limiting factor is background light. A familiar example is the sky in daytime. Although your eyes are sensitive enough to see thousands of stars on a dark night, you can't observe any stars during daytime because of the bright blue sky (caused by air molecules scattering the blue photons in sunlight). For the same reason, you (and telescopes) can see many more stars on a mountain top far from cities than you can in Boulder. But even on the darkest mountaintop, airglow at night is a limitation for telescopes -- it is about 1/3 as bright as the Milky Way. In space, the sky (away from the Milky Way) is about 100 times darker.

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