Polar Responses

9008-019

9008-019a

The polar response of an antenna or telescope determines its directional characteristics.  The graphs for the microwave and optical telescopes show how the transmitted beams and received responses changes with angle. Note that the Microwave Telescope (9008-016) is plotted on the basis of an angle in degrees, the Infrared Telescope (9008-017) on the basis of an angle in arc minutes, and the Visible Telescope (9008-018) on the basis of an angle in arc seconds.  Thus, factors of 60 exist in the horizontal scaling between each of the graphs.  The latter two graphs are logarithmic plots.

The normalized polar power responses (PR) are plotted according to the following relationship for diffraction at a circular aperture:

     [2J1{(pi.d/Wl)sin Theta}]2
PR = --------------------------
        [(pi.d/Wl)sin Theta]2

where:

J₁ = Bessel function of the first kind,
d = diameter (aperture) of telescope,
Wl = wavelength,
Theta = half-angle.

9008-019b

The half-angle of diffraction, is given by:

         90.Wl
Theta = ------  degrees
         pi.d

The graphs plotted are of the normalized signal power response, and hence the beamwidth is defined as being between the half-power (3 dB) points, i.e., between points on the central lobe that equal 0.5. The half-power radiation angle is 2 , approximately corresponding to the Rayleigh criterion for angular resolution.   For an ideal circular aperture, the first side-lobes are 18 dB down on the maximum response.  The Sun's disk (diameter = 1.39 x 10⁹ m) subtends an angle of 0.53^o at the Earth (range = 1 A.U. = 1.50 x 10¹¹ m).   The beamwidth of the 300 meter diameter Arecibo telescope at 1.5 GHz is seen from (9008-016) to be 0.038^o.  Hence this telescope can just resolve the Sun's disk at 10 A.U.  Because the beamwidth is slightly smaller than the angle subtended by the Sun's disk at this distance, the solar radiation at 1.5 GHz received by such an antenna located near Saturn and pointing at the Sun, is reduced by a factor of approximately (0.038/0.051)², i.e., by 2.6 dB.