[mmaimcal] Quadripod Calculations

[Mark Holdaway]

Primary beam differences for a Heterogeneous Array

OK, I ran the beams for the actual feedleg shadowing profiles given to me
by Robrt Lucas, 12 dB taper in the PB at the edge of the dish, and a 
perfect surface.
I formed the three primary beams and looked at the RMS difference 
between the
beams divided among primary beam regions of similar PBlevel.  The fact the
the Vertex - EIE  rms  is essentially twice the Vertex-Cross RMS means 
that these
errors are systematic, but they are still very small.   Still the 
largest error is at the
0.3% level -- a factor of 20 below the 6% specification.

These rms differences are larger than my previous uninformed calculation 
-- the
actual feed leg shadows are larger than what I had started out assuming.

The beams have been normalized to have a peak of 1.0, yet the
integral of the Vertex and EIE beams differ by 0.4% -- if left uncorrected,
this would translate into something like a 0.4% flux scale error -- 
hardly something
to get too excited about.

PBLev    Vert-EIE  Vert-Cross   EIE-Cross
0.025   0.000306  0.000158  0.000158
0.05    0.001798  0.000893  0.000905
0.1     0.003080  0.001519  0.001560
0.2     0.001435  0.000715  0.000719
0.3     0.002300  0.001146  0.001154
0.4     0.001272  0.000636  0.000636
0.6     0.001974  0.000986  0.000988
0.8     0.000710  0.000355  0.000355
1       0.000501  0.000250  0.000250


While it is a pitty that we have two different array designs, mostly
for those scientists who will have to figure this stuff out and the 
technicians
and engineers who will have to turn the bolts, I cannot say anything too 
bad
about the two antenna designs from the point of view of the primary beam 
differences.


     -Mark