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(f) Summary of the Low Frequency Measurements

The terms in the account have been discussed and are assembled in the following two equations. To first order in small quantities, the antenna temperature of the reference is

Equation 12 (12)

where epsilonW, RW, TW are the emissivity, reflectivity, and temperature of the window, epsilonP, TP the emissivity and temperature of the warm parts of the calibrator, epsilonL, TL the emissivity and antenna temperature of the load and Rcal, is the reflectivity of the reference taken as a whole. Trec is an equivalent temperature of the receiver and antenna viewed as an emitter. The terms, when known, are listed in Table 1 for the various experiments.

The antenna temperature, looking at the sky, is

Equation 13 (13)

where epsilonant and Tant, are the emissivity and temperature of the antenna, epsilonatm(theta) and Tatm are the emissivity as a function of elevation angle and temperature of the atmosphere, fant(theta) is the side-lobe response of the antenna at the ground with emissivity and temperature, epsilongrd and Tgrd, TGal is the antenna temperature of the Galaxy, and finally TCBR the antenna temperature of the cosmic background radiation. Equations (12) and (13) apply broadly to all the experiments. However, the analysis of any particular experiment may require modifications of the two equations. For example, if the reference is placed at the input of the antenna, Equation (12) would be multiplied by (1 - epsilonant) and the emission of the antenna, epsilonant Tant, would have to be added.

Table 1 is intended to show the magnitudes and uncertainties of the individual terms. As can be seen from the table many of the systematic error sources could be substantially reduced by operating the entire input end of the receiver and calibrator at cryogenic temperatures. The atmosphere, although a dominant random noise source, can be handled as indicated before. There is therefore a future in performing improved observations of the spectrum at frequencies 1 to 90 GHz from the ground.

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