Noise

An antenna absorbs power from the radio waves that fall on it. This power is also usually specified in temperature units, i.e. degrees Kelvin. To motivate these units, consider a resistor placed in a thermal bath at a temperature $T$. The electrons in the resistor undergo random thermal motion, and this random motion causes a current to flow in the resistor. On the average there are as many electrons moving in one direction as in the opposite direction, and the average current is zero. The power in the resistor however depends on the square of the current and is not zero. From the equipartition principle one could compute this power as a function of the temperature, and in the radio regime the power per unit frequency is well approximated by the Nyquist formula:

$$P = kT,$$

where $k$ is the same Boltzmann constant as in the Planck law. In analogy with this, if a power P (per unit frequency) is available at an antenna's terminals the antenna is defined to have an antenna temperature of

$$T_A = {P \over k}$$

Note again that the antenna temperature does not correspond to the physical temperature of the antenna. Similarly the total power available at a radio telescope terminals, referred to the receiver (i.e. the RF amplifier) inputs^3.9 is defined as the system temperature $T_{sys}$, i.e.

$$T_{sys}= {{\rm Total~Power~referred~to~receiver~inputs} \over k}$$

The system temperature when looking at blank sky is a measure of the total random noise in the system and hence it is desirable to make the system temperature as low as possible. Noise from the various sub systems that make up the radio telescope are uncorrelated and hence add up linearly. The system temperature can be very generally written as

$$T_{sys} = T_{sky} + T_{spill} + T_{loss} + T_{rec}$$

$T_{sky}$ is the contribution of the background sky brightness. For example the galaxy is a strong emitter of non thermal^3.10 continum radiation, which at low frequencies usually dominates the system temperature. At all frequencies the sky contributes at least 3K from the cosmic background radiation.^3.11

Figure 3.7: The Arecibo telescope consists of a large ($300$ m) spherical reflector fitted into a naturally occuring valley. The telescope has feeds which are suspended from cables which originate from towers on the surrounding hills. Photo courtesy of NAIC, Arecibo observatory.

The feed antenna is supposed to collect the radiation focused by the reflector. Often the feed antenna also picks up stray radiation from the ground ( which radiates approximately like a black body at 300 K ) around the edge of the reflector. This added noise is called spillover noise, and is a very important contribution to the system temperature at a telescope like Arecibo. In Figure 3.8 is shown (schematically) the system temperature for the (pre-upgrade) Arecibo telescope at 12cm as a function of the zenith angle at which the telescope is pointed. At high zenith angles the feed radiation spills over the edge of the dish and picks up a lot of radiation from the surrounding hills and the system temperature changes from under 40 K to over 80 K. If a reflecting screen were to be placed around the telescope edges, then, the spill over radiation will be sky radiation reflected by the screen, and not thermal radiation from the ground. At cm wavelengths, $T_{sky} << T_{ground}$, so such a ground screen would significantly reduce the system temperature at high zenith angles^3.12.

Any lossy element in the feed path will also contribute noise ($T_{loss}$ ) to the system. This follows from Kirchoff's law which states that good absorbers are also good emitters, and that the ratio of emission to absorption in thermodynamic equilibrium is given by the Planck spectrum at the absorber's physical temperature. This is the reason why there are rarely any uncooled elements between the feed and the first amplifier. Finally, the receiver also adds noise to the system, which is characterized by $T_{rec}$. The noise added after the first few stages of amplification is usually an insignificant fraction of the signal strength and can often be ignored.

Figure 3.8: Schematic of the variation of T$_{sys}$ with zenith angle for the pre-upgrade Arecibo.

The final, increasingly important contributor to the system temperature is terrestrial interference. If the bandwidth of the interference is large compared to the spectral resolution, the interference is called broad band. Steady, broad band interference increases the system temperature, and provided this increase is small its effects are relatively benign. However, typically interference varies on a very rapid time scale, causing a rapid fluctuation in the system temperature. This is considerably more harmful, since such fluctuations could have harmonics which are mistaken for pulsars etc. In aperture synthesis telescopes such time varying effects will also produce artifacts in the resulting image^3.13. Interference whose bandwidth is small compared to the spectral resolution is called narrow band interference. Such interference, provided it is weak enough will corrupt only one spectral channel in the receiver. Provided this spectral channel is not important (i.e. does not coincide with for eg. a spectral line from the source) it can be flagged with little loss of information. However, if the interference is strong enough, the receiver saturates, which has several deleterious effects. Firstly since the receiver is no longer in its linear range, the increase in antenna temperature on looking at a cosmic source is no longer simply related to the source brightness, making it difficult, and usually impossible to derive the actual source brightness. This is called compression. Further if some other spectral feature is present, perhaps even a spectral line from the source, spurious signals are produced at the beat frequencies of the true spectral line and the interference. These are called intermodulation products. Given the increasingly hostile interference environment at low frequencies, it is important to have receivers with large dynamic range, i.e. whose region of linear response is as large as possible. It could often be the case, that it is worth increasing the receiver temperature provided that one gains in dynamic range. For particularly strong and steady sources of interference (such as carriers for nearby TV stations), it is usually the practice to block such signals out using narrow band filters before the first amplifier^3.14.

Footnotes

... inputs^3.9

By `referred to the reciever inputs' we mean the following. Suppose you have a noise power $P$ at the output of the radio telescope. If there is only one stage of amplification with gain $G$, then the power referred to the inputs is $P/G$. If there is more than one stage of amplification, one has to rescale each noise source along the signal path by the gain of all the preceeding amplifiers.

... thermal^3.10

By non thermal radiation one means simply that the source function is not the Planck spectrum.

... radiation.^3.11

Historicaly, this fact was discovered by Penzias and Wilson when they set out to perform the relatively mundane task of calibrating the system temperature of their radio telescope. This excess 3K discovered to come from the sky was identified with the radiation from the Big Bang, and was one of the powerful pieces of evidence in favour of the Big Bang model. The field of Radio Astronomy itself was started by Karl Jansky, who too was engaged in the task of calibrating the system temperature of his antenna (he had been set the task of characterizing the various kinds of noise which radio receivers picked up, this noise was harmful to trans-atlantic communication, and was hence essential to understand). Jansky discovered that one component of the `radio noise' was associated with the Galactic center, the first detection of extra-terrestrial radio waves.

... angles^3.12

As can be seen from Figure 3.7, such a screen has indeed been built, and it has dramatically reduced the system temperature at high zenith angles. The wire mesh for this screen was produced, with the co-ordination of NCRA by the same contractor who fabricated the mesh for the GMRT antennas, and was exported to the USA.

... image^3.13

It is often claimed that interferometers are immune from interference because different antennas ``see'' different interfering sources and these do not correlate with one another. However since the interference is typically varying on timescales faster than the system temperature is calibrated, the resulting variations in the system temperatures of the different antennas cause variations in the observed correlation coefficent (for telescopes which do a continuous normalization by the auto-correlation of each antenna's signal) and hence artifacts in the image plane.

... amplifier^3.14

Recall from the discussion above on the effect of introducing lossy elements in the signal path that the price one pays is precisely an increase in receiver temperature