Before considering the variety of techniques used to detect the radiation collected by telescopes and analysed with spectrographs or polarimeters, we need to establish what we must do to detect radiation. Most astronomical objects are very faint; they are ob¬served in the presence of a considerable amount of unwanted radiation, such as that from the night sky. When we set out to observe a celestial object it is convenient to think of the radiation as having two components. One is the radiation from the object itself; this is called the SIGNAL. The second component is the sum of the radiations from all the other sources, including spurious signals from the detector. This component is what we would detect if the object was not there at all, and is called the NOISE. The quality of any observation can be expressed in terms of the ratio of these two components, that is, the SIGNAL-TO-NOISE RATIO. In order to establish the quality of an observation we must determine the noise level present in the signal.

At any one instant the signal-to-noise ratio of an astronomical observation may be very poor indeed. However if we add up the signal as it comes in (integrate the signal), it builds up in direct proportion to the time, whereas the noise only builds up in pro¬portion to the square-root of the time. This difference occurs because the noise is a sequence of random fluctuations whereas the signal is not. The effect of integrating a signal is, therefore, that the signal-to-noise ratio, and hence the quality of measurement, increases in proportion to the square-root of the time. Another way of improving a signal-to-noise ratio is to increase the bandwidth of the detector (the wavelength range across which the detector is sensitive). This lets through more signal and more noise; but the signal-to-noise ratio is improved by the square-root of the increase in relative bandwidth.

In the above we have assumed that the noise is independent of the signal. However, there are situations in which the noise level is determined primarily by a low signal level. This may happen at wavelengths shorter than 1 Jim where detectors can be built which are able to register individual photons, so that the signal simply consists of a stream of photons. The (arrival time of successive photons is entirely random. In a series of short identical exposures, the exact number of photons detected varies from exposure to exposure in a way governed by the laws of statistics. These tell us that if we have collected n photons on average, the number we will actually collect in any one exposure will be different from n by an amount n1/2 on average. This uncertainty is equivalent to a noise contribution to the signal of n1/2 and is known as PHOTON NOISE. This means that any observation which gathers n photons cannot have a signal-to-noise ratio better than n1/2. In practice it can also happen that some of the photons detected are themselves not from the object but from other sources which count as noise. This will further reduce the overall signal-to-noise ratio of the observation.

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