Beam Widths vs lambda. All rcvrs, 2004
The Half Power Beam Width (hpbw) is determined
by the size of the dish and the wavelength:
hpbw=K * lambda/Diameter
K is a constant that varies with the edge taper.
For uniform illumination on a spherical dish K=1.02. The AO dish optics
is 213m by 237 m (700 by 776 feet). It has a geometric taper of about 9
When measuring the gain of the telescope, there can
be errors in the cal values used and the flux of the sources. The beam
width is not sensitive to errors in the cal or the source flux. It is affected
by collimation errors, surface errors, and the size of the source (it should
be small compared to the beam).
Calibration data taken mar04 thru feb05 was used
to plot the
hpbw versus wavelength (.ps) (.pdf)
for all receivers. The value plotted is the average hpbw (the average of
the major and minor axis). The zenith angle has been limited to 5 <
za < 14 degrees.
The illumination pattern is elliptical. The gregorian optics is designed
for a 700 x 776 feet (213 x 237 meters) illumination. The geometrical
mean of this is 225 meters. The hpbw of the measured receivers fall
close to this value. Those receivers that are larger are over illuminating
while those that are below this may be under illuminating the optics. The
tertiary skirt will be placed around the tertiary so that the tertiary
spill over will see the sky rather than the 250+K of the radiation inside
the dome. When this is installed we could open up the illumination of the
sbn/cbh receivers without drastically affecting the system temperature.
It should also help some of the receivers that over illuminate (although
no so much with the lower frequencies since the sky temperature is picking
Fig 1: The hpbw/lambda. This should be a constant. Colors differentiate
receivers. The scatter at the higher frequencies is partly coming from
the source sizes. Many of the sources are 15 to 20 asecs which can add
15 to 20% to the hpbw at xband. The alfa hpbw's include all of the pixels
(central pixel and outer 6) so there is more scatter in the hpbw than lbw.
Fig 2: The hpbw is converted to diameter using diam=1.02*lambda/hpbw
(1.02 is the constant for uniform illumination). The median value from
each frequency in fig 1 was used for these plots. The dashed line is a
diameter of 225 meters. The 50cm (green 610 rcvr) and 90 cm (black 327
rcvr) sit above the other receivers. These two receivers use dipole feeds.
The other receivers have horns.
Fig 3: Blowup showing xband thru lband. The curvature in a receiver
is caused by the horns illumination pattern of the tertiary vs frequency.
The light blue sbn and red cbh both have smaller diameters. This is because
these two receivers are under illuminating the tertiary. This gives them
the lowest system temperatures while sacrificing some gain from the under
Fig 4: Blowup showing xband thru cband. The cband hi receiver has
a horn illumination that is falling off with frequency. This causes the
diameter to decrease at lower wavelengths. The xband horn has a flat response
over the 8500-9200 Mhz of the measurements.