Up until now we have concentrated on discovering the basic properties of heterodyne instruments. In order to see more clearly how a heterodyne system can be used to make precise measurements we can now look at a specific example. The example chosen shows some of the strengths of the heterodyne method and demonstrates how a real system can be calibrated and operated.
Millimetre-wave and Terahertz astronomy is concerned with measuring the radiation from distant sources in a frequency range extending from around 60 GHz to above 1 THz. Because these sources are far away the signal levels astronomers can collect are very low. The combination of the high signal frequency and low power level makes the application a demanding one. The main reason for selecting this example was because it shows the power of heterodyne methods to provide a level of frequency resolution and power (or source temperature) sensitivity which would otherwise be virtually unobtainable. Before examining the receiver system it's useful to outline the application it is designed to suit.
Figure 3.1 illustrates a typical astronomical arrangement. Here a mm-wave receiving antenna (i.e. a telescope) is pointed at a distant cloud of molecules. Each type of molecule in the cloud will tend to radiate energy at a set of Line Frequencies which are characteristic of that molecular species. For example, one of the most common molecules in space is CO (carbon monoxide). This can emit radiation at 115 GHz and its harmonics, 230 GHz, 345 GHz, etc. As a result, by measuring the amount of power radiated by a cloud at these frequencies we can hope to measure how much CO it contains. Given a large enough antenna it is also possible to ‘map’ the distribution of CO in the cloud by measuring how its brightness at these frequencies varies across its apparent surface.
The precise line frequency of a molecule can be measured (or sometimes theoretically predicted) very accurately. However, radiation which has been emitted from molecules moving towards (or away) from us will have its frequency Doppler shifted. As a result, if we accurately measure the frequency distribution of radiation around each line's rest frequency we can learn something about the dynamics of the molecules being observed. This can provide information about the cloud's overall velocity towards or away from us along the line of sight. It can also tell us whether the cloud is expanding, rotating or has regions with differing properties. Since this isn't a book on astronomy we needn't spend any time thinking about the scientific value of such measurements. Instead, we can consider how measurements of this kind are made.
For the sake of example let's consider a system observing the radiation arriving from the CO molecules in a cloud at frequencies around 345 GHz. Molecules which are moving at a velocity, v, in the line of sight will produce an observed frequency
where c is the velocity of light. (Here we define a positive velocity as being one which decreases the observed frequency — i.e. a movement away from the observer.) For a line rest frequency, = 345 GHz , a velocity in the line of sight of 1 km/s will shift the observed frequency by 1·15 MHz. This means that if we want to measure the velocity of moving molecules with an accuracy of 1 km/s we have to be able to resolve spectral details of the 345 GHz radiation it emits with a precision of about 1 MHz. This requires us to be able to determine the signal's frequency spectrum with an accuracy and resolution of one part in 3×10.
Figure 3.2 represents a ‘typical’ spectrum astronomers might obtain from such a cloud given a heterodyne system which can measure the received spectrum with an accuracy of 100 kHz. The spectrum shows that this particular cloud is moving towards the observer and seems to consist of three distinct ‘lumps’ producing frequencies which have been Doppler shifted upwards by 900, 2000, and 3000 kHz. This implies that these three sections of the cloud are approaching with velocities of 0·78, 1·74, and 2·6 km/s. The frequency resolution of this spectrum, 100 kHz, corresponds to a nominal velocity resolution of just under 0·1 m/s ( 0·045 miles/hour). Astronomical spectra of this type are often plotted in terms of nominal line of sight velocities (i.e. in km/s) instead of frequencies since this is of more interest to astronomers.
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