Chapter 10: Detecting Radiation from Space

Artist conception of the James Webb Space Telescope

Electromagnetic transmittance, or opacity, of the Earth's atmosphere.

Why do astronomers continue to build bigger and bigger telescopes? Because the electronic detectors in common use today are nearly perfect; gains can only be made by collecting more light with a larger mirror. The number of photons gathered by a telescope is proportional to the collecting area. So we can compare the light gathering power of two telescopes (A and B) by calculating the ratio of their collecting areas:

 

 

Artist rendering of the Giant Magellan Telescope. A 30-meter class telescope composed of seven 8.4 meter mirrors.

Gain in Light Gathering ∝ (πR_A²) / (πR_B²) = D_A²  / D_B²

 

The proportionality holds whether we use the radius R of the mirror or the diameter D, but astronomers generally quote the entire aperture or diameter. So we see that a 4-meter telescope has (4/1.5)²  = 7 times the collecting area of a 1.5-meter telescope.

SN1987A in the Large Magellanic Cloud.

Since the light from an object in space diminishes with the inverse square of the distance, there is another way of looking at the comparison between two telescopes. If a 1.5-meter telescope can collect a certain number of photons per second – let's say 500 – from a star. Then a 4-meter telescope can collect 500 (4/1.5)²  = 3560 photons per second from that same star. The 4-meter telescope would collect 500 photons per second from that star when it was √(3560/500) = 2.7 times further away. This is of course the ratio of the apertures. A larger telescope allows an object to be detected out to a larger distance in space. So we get the important result that:

 

Gain in Limiting Distance ∝ D_A / D_B

Northern arm of the LIGO interferometer on Hanford Reservation.

The twin Keck telescopes on Mauna Kea, Hawaii

Hubble Space Telescope as seen from the Space Shuttle Atlantis

For another example, the Hubble Space Telescope has a mirror 2.2 meters across – this was the largest structure that could fit in the cargo bay of the Space Shuttle. Each Keck telescope on Mauna Kea has an aperture of 10 meters, so the Keck telescope has (10/2.2)²  = 20.7 times the collecting area of the Hubble Space Telescope.

Light-collecting area is not the entire story of a telescope. The other important attribute is resolution, or the ability to discriminate light arriving at the telescope from slightly different angles on the sky. We might want to distinguish two stars with a small angular separation. Or we might want to discern details on the surface of a planet. In either case, good resolution is required. The fundamental limit to a telescope's ability to resolve small angles is due to diffraction — the slight bending of light as it passes through a telescope. The angular resolution is:

Angular Resolution = 2.5 × 10⁵  × (Wavelength / Diameter)

In this equation, the angular resolution is in seconds of arc and the wavelength of radiation and diameter of the telescope must be in the same units. What is the angular resolution of the eye? The pupil has a diameter of about 2 millimeters or 0.002 meters. Visible light has a mean wavelength of about 5 × 10^-7 meters, so the resolution of the eye is 2.5 × 10⁵  (5 × 10^-7  / 0.002) = 63 arc seconds or about one arc minute. This accounts for the limited accuracy of the measurement of star and planet positions before the invention of the telescope.

Consider a modest-sized telescope that a hobbyist might use. A telescope of aperture 0.2 meters (about 8 inches) gives a resolution of 2.5 × 10⁵  (5 × 10^-7  / 0.2) = 0.6 arc seconds. This is excellent — the angular diameter of a dime seen at a distance of 3 miles! Larger telescopes than this gain in light gathering power but have effectively no gain in resolution because turbulence in the atmosphere jumbles all images to an angular size of about 1 arc second. To do better we must go into space. The Hubble Space Telescope has an aperture of 2.2 meters and an angular resolution of 2.5 × 10⁵  (5 × 10^-7  / 2.2) = 0.05 arc seconds, which is about ten times better than can be done from the ground. Equivalently, the Hubble Space Telescope can distinguish a pair of objects that is ten times further away than the resolution limit of a ground-based telescope.

Angular resolution varies inversely with the telescope diameter — the larger the telescope, the smaller (or better) the resolution. You can also see that the angular diameter varies in proportion to the wavelength of radiation — images made with short waves have better resolution than images made with long waves. The same telescope will make sharper images in blue light than in red light. Interestingly this principle also controls the miniaturization of electronics. Integrated circuits are etched onto silicon wafers using chemicals and light, and the semiconductor industry strives to use shorter or bluer wavelengths for this process so that more components can be packed onto a single wafer. Also, information is stored and read from compact disks using lasers and engineers devote much effort to developing blue or ultraviolet lasers that can pack more data or music or video onto a CD.

What are the diffraction limits in other parts of the electromagnetic spectrum. No waves beyond the blue end of the visible spectrum — shorter than 3 × 10^-7 meters — can penetrate the Earth's atmosphere. So all ultraviolet, X-ray, and gamma-ray astronomy must be done from space. In fact, these very short waves are absorbed by glass so other techniques must be used to focus the waves and the simple equation for angular resolution does not apply. At the opposite end of the electromagnetic spectrum radio waves are gathered and focused in a similar way to light waves. A large radio telescope has a diameter of 100 meters, so if it imaged radio waves with a wavelength of 1 cm or 0.01 meter, the resolution would be 2.5 × 10⁵  (0.01 / 100) = 25 arc seconds. So the much longer waves overcome the benefit of a larger aperture and radio telescopes give a blurry view of the universe.