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Arecibo Observatory Technical Memo AOTM 2000­01
THE LBW FEED: THE MUELLER MATRIX IN 1999 AND 2000
Carl Heiles
ABSTRACT
We present measurements of the Mueller matrix and associated quantities at two
epochs for 1420.4 MHz (February­March 1999 and March 2000) and one for 1665.3
MHz (March 2000).
1. SUMMARY AND RESULTS
In AOTM 99­01, we presented the theory and practice of deriving the Mueller matrix for the
LBW system. We also presented the result we derived during Feb­Mar99. We repeated these
measurements in March 2000, using much less integration time and only three sources (P0736+01,
3C454.3, 3C286); consequently, the more recent results have larger uncertainties. Nevertheless,
the agreement between the two years at 1420.4 MHz, and for the second year between the two
frequencies, is good. This provides confidence that our measurements are meaningful.
All quantities are as defined in AOTM 99­01 as the elements of MA+F ; there are only six
independent elements. We present five below; the sixth element mQU represents the mechanical
rotational offset of the dipoles from their nominal position angles, which translates directly into
an error of the measured position angles; it is zero by assumption. One of the remaining is forced
to zero by adjusting the cal values TCAL xx and TCAL yy , and one more is forced to zero by
correcting for the phase difference between sky and cal, denoted in the table by \Delta\Phi.
This work was supported in part by NSF grant AST 95­30590.

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Table 1. MUELLER MATRIX ELEMENTS AND ASSOCIATED QUANTITIES:
TWO YEARS, TWO FREQUENCIES
Quantity Mar99, 1420.4 Mar00, 1420.4 Mar00, 1665.3
mQI 0 \Sigma 0:0004 0 \Sigma 0:0007 0 \Sigma 0:0005
mUI 0:0112 \Sigma 0:0002 0:0065 \Sigma 0:0007 0:0044 \Sigma 0:0006
mV I \Gamma:0055 \Sigma 0:0002 \Gamma0:0032 \Sigma 0:0002 \Gamma0:0022 \Sigma 0:0004
mVQ \Gamma0:0088 \Sigma 0:0024 \Gamma0:0061 \Sigma 0:0039 \Gamma0:0095 \Sigma 0:0067
mVU 0 \Sigma 0:0021 0 \Sigma 0:0038 0 \Sigma 0:0049
TCALxx 10.33 10.14 10.21
TCALyy 9.62 9.80 9.73
\Delta\Phi 2:37 ffi \Sigma 0:12 ffi 3:19 ffi \Sigma 0:22 ffi 3:37 ffi \Sigma 0:28 ffi
Note. --- The TCAL's are in Kelvins and are the values required to force mQI = 0: The ``official'' values at
1420.4 MHz are 10.76 and 9.25 K; we adjusted our values so as to keep the sum constant.
Note. --- \Delta\Phi = \Phi XY;SKY \Gamma \Phi XY;CAL as defined in x2.1 of AOTM 99­01. It is the value required to force
mVU = 0.