How to obtain efficiencies at desired wavelengths

Aperture efficiency

Wavelength dependence of aperture efficiencies () is generally expressed by the following formula containing the accuracy of the parabola surface ():
(1)
The obtained efficiencies at the 100 GHz region show some differences between S100 and S80. These differences seem to be due to some loss of power in S80. We fitted all the aperture efficiencies except those of S80. The obtained results are shown below and in Figure 1:
(2)
The errors correspond to one sigma. Aperture efficiencies at desired wavelengths can be estimated with this formula except those of S80.

In addition, ratios of the aperture efficiencies of S80 and S100 at the same wavelengths were plotted against wavelength as shown in Figure 2 to estimate aperture efficiencies of S80 at desired wavelengths. It is difficult to fit these data points with error bars by a polynomial because of the limited number of points. One example of the fitting by a second order polynomial is shown below and in Figure 2:
(3)
Please note that this formula is appropriate among the three data points. It is possible to use this formula to estimate aperture efficiencies of S80 at your desired wavelengths between 2.6 and 3.5 mm.

Fig. 1: Wavelength vs. Aperture Efficiency

Fig. 2: Wavelength vs. Aperture Efficiency Ratio (S80/S100)

Main beam efficiency

From the formulae used to calculate efficiencies for the 45m telescope
and
,
it is possible to obtain a formula to express a relation between and :
(4)
Using this formula can be calculated from . For this calculation a beam size at the desired frequency is necessary, and it can be estimated from the formula of wavelength dependence of beam size already available in our home page (see Fig. 3).

Fig. 3: Wavelength vs. Beam size

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