RADIO ASTRONOMY AND COMMUNICATION THEORY : Absolute gain calibration with an interferometer

The need for absolutely calibrated antennas in order to establish a set of calibrator sources on the sky which will then be used to obtain calibrated observations of other objects without the need for a telescope with known gain. Radio astronomers have made good use of the small number of relatively large horn antennas for this purpose, but often the signal to noise ratio is insufficient for accurate results. A powerful method is to observe a source with an interferometer consisting of a relatively small standard gain horn and a large reflector antenna. The gain of the horn can be accurately calculated (Schelkunoff, 1943). The easiest and most accurate way is offered by the existence of an interferometer array with two or more element antennas. The horn antenna is attached to the side of one of the antennas and the receiver is switchable between the horn and the antenna feed.

Observing a strong radio source we then measure the output of the interferometer in two situations; one with the horn and the other with the antenna. The second antenna delivers a constant and strong reference signal. After allowing for any difference in loss between the horn and feed output ports (which will have to be measured separately) the ratio of the interferometer output signals is equal to the voltage ratio of the horn and the antenna gains. The gain of the main antenna is then equal to the sum of the output ratio, expressed in dB, and the known gain of the horn. The gain of the horn will typically be some 40 dB less than that of the antenna. While in a total power measurement the horn gain would be too low for an accurate measurement, in the interferometer the output signal will be one percent of that of the two antenna interferometer and still amenable to accurate measurement. With a realistic accuracy of one percent for the gain of the horn, the gain of the antenna can thus be measured to 1-2 percent without the need to know the precise flux density of the source. This procedure can be repeated for the other interferometer element and in principle be extended to the remaining antennas of a multi element array. Alternatively, the measured antenna temperature due to the source can be measured accurately with a careful thermal calibration method of the receiver system and hence the source flux density can be determined from the known gain of the antenna. This absolutely known flux density can now be used to determine the gain of other antennas without the need for the horn comparison measurement.

If only one antenna is available, the gain of which needs to be determined, one can form an interferometer between it and the standard gain horn and measure the correlated output. The source is also observed with the antenna under test alone. As before, we need to make an accurate calibration of the sensitivity of the receiver systems with the aid of matched loads at different and known temperature to express the output voltage in equivalent antenna temperature at the input of the receiver. Now we have the following relations:

where S is the (unknown) flux density of the source, Ar and Ah the absorption areas of the reflector (to be determined) and the horn (known), respectively. From this follows

The proportionality sign hides some terms related to the electronic gains of the two different systems, which can however be accurately determined in the laboratory. These methods have been applied by Welch and colleagues to calibrate the antennas of the BIMA array (Welch et al., 1996) and to establish some absolute planetary brightness temperatures at 11 and 3 mm wavelength to an accuracy of 1-2 percent (Gibson et al., 2005; Gibson and Welch, pers. com., Sep. 2005). This is a great step forward in the calibration quality in the millimeter wavelength domain. The goal of a five percent flux calibration for the ALMA submillimeter array may be reached by applying these methods.