Observing methods to cancel atmospheric fluctuations

The "information" collected by a radio telescope has the characteristic of noise, which is normally not discernible from the inherent thermal noise of the antenna-receiver system. The signal is generally broad-band, continuous radiation. The only exception is the presence of spectral lines of cosmic molecules and atoms, which appear at discrete frequencies, but otherwise are noise-like as well. The signals in communication channels are modulated in a particular fashion and therefore easier to separate from the background noise. In both cases the signal-to-noise-ratio (SNR) must be sufficient to reliably detect the information. While the information in a communication channel continuously changes with time, the radio astronomy signal normally does not vary its character over reasonable time spans. Thus the radio astronomer can increase the SNR of his observation by collecting the signal over a long time.

We omit a detailed treatment of the operation of a radiometer here. Excellent descriptions can be found in, for instance, Kraus (1966) and Tiuri (1964). The important radiometer equation, which determines the SNR can be written as follows

L sys

Vt b

where DTrms is the rms noise fluctuation at the output terminals, expressed in Kelvin, due to a system with total noise temperature Tsys, operating with bandwidth B (Hz) and an integration time t (sec). The factor m is of order one and accounts for the detailed configuration of the receiver system and the observing mode used to collect the signal. For a simple total power receiver m = 1. It is clear that collecting radiation over a long time decreases the noise fluctuation, hence increases the SNR, proportional to the square root of the total integration time. In this equation, the total system noise temperature is the sum of the instrumental (receiver) noise temperature TR and the antenna temperature TA due to the antenna and the source (see Ch. 5.2). If we integrate until D Trms << TA, we can reliably determine TA. This assumes that the receiver system is absolutely stable, i.e. that Tsys and the gain of the electronics Grec are constant over time. Gain stability in an electronic system with active components is difficult to achieve and moreover gain fluctuations cannot be countered by longer integration. Without recourse to special methods, the achievable SNR will normally be determined more by gain fluctuations than system noise. Fortunately gain fluctuations tend to be slow with a frequency spectrum falling off as n-2 or steeper.

It was realised by Dicke (1946) that gain fluctuations could be effectively suppressed if the receiver would be switched between the antenna terminals and a constant reference noise source at a frequency well above that of the dominant gain fluctuations. The difference signal of antenna and reference would thus not suffer from gain fluctuations and the necessary SNR could be achieved by a sufficiently long integration. The cost of this method is a loss in sensitivity of a factor two (m = 2 in Eq. 6.35), because the signal from the sky is only observed half of the time. To achieve the same SNR, the observation will take four times as much time compared to the total power system. Nevertheless, the so-called Dicke-receiver has found wide application in radio astronomy.

The Dicke scheme works best if the reference noise temperature is equal to the antenna temperature, in which case the gain fluctuations cancel perfectly. One way to approach this situation is to use a wide-beam "sky horn", pointing in the general direction of the antenna. A next step is to place two feeds in the focal plane of the antenna, looking with similar beams at adjacent patches of sky, several beamwidths apart. This is a very effective method to observe weak point-like sources. When the telescope is scanned across the direction of the source, the output of the radiometer will show an S-shaped trace of double amplitude as the source first traverses the "signal" beam and then the "negative reference" beam. Actually, this layout was first used in surveys for point sources (Conway et al, 1965, Davis M.M., 1967) to increase the reliability of detections. These observations were carried out at relatively long cm-wavelengths, where the influence of the atmosphere is weak.

It occurred to Conway (1963) that this "dual-beam" method might be effective in the cancellation of the stronger atmospheric fluctuations to be expected at short cm-and mm-wavelengths. The argument is that, while the two beams are well separated in the farfield, they will partially overlap in the nearfield region. At the short wavelengths, this region will extend to well above the height of the tropospheric fluctuations (see Eq. (6.1) and thus the beam overlap will be considerable, resulting in an effective cancellation of tropospheric fluctuations. The author (Baars, 1966, 1970) made a detailed study of the beam overlap and demonstrated the efficacy of the method with observations at several wavelengths. Because this observing method has become an essential aspect of millimeter wavelength radio astronomy, we will summarise the main results now.

Millimeter telescopes are generally of the Cassegrain type. The relatively small size of the secondary reflector, typically between 0.5 and 1 m diameter, makes it possible to attach these to a nutator mechanism, which enables the subreflector to be mechanically moved between different positions. This effectively switches the beam of the antenna between two neighbouring points on the sky, removing the need for a second feed to realise the reference beam. The nutating subreflector had earlier been introduced on infrared telescopes for the same reason.

This method is not restricted to the observation of point sources, which will be seen by only one beam at a time. In an important paper Emerson et al (1979) have demonstrated that a dual-beam mapping of an extended source, which is essentially a differential map of the object, can be restored to deliver a reliable representation of

Fig. 6.23. Dual-beam observation of an extended source (upper plot) and the derived map obtained with the EKH-algorithm (lower plot). The beam separation and size is indicated in the lower left hand corner of the lower plot.

the brightness distribution of the source. This "EKH-algorithm" is now widely used in dual-beam observations of extended objects. We show here an example from their paper (Fig. 6.23); the mapping of a supernova remnant 3C10 of 9 arcminutes size with a dual-beam system of 5.5 arcminute beam separation. The upper plot shows the difference output, where the left and right output overlap. The combined result is shown in the lower plot.

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