Wilkinson Microwave Anisotropy Probe

The main and near-sidelobe response of each of the 20 WMAP antenna feeds has been mapped in-flight using observations of Jupiter. The 7-year release is comprised of 13 Jupiter observing seasons:

Oct/Nov 2001 Feb/Mar 2002 Nov/Dec 2002 Mar/Apr 2003

Dec 2003/Jan 2004 Apr/May 2004 Jan/Feb 2005

May/Jun 2005 Feb/Mar 2006 Jun/Jul 2006

Mar/Apr 2007 Jul/Aug 2007 Apr/May 2008

As a prelude to beam analysis, an archive of calibrated time-ordered observations is constructed, consisting of Jupiter passages within roughly 7.0, 5.5, 5.0, 4.0 and 3.5 degrees of either the A- or B-side beam center for K, Ka, Q, V and W bands respectively. The time-ordered observations are corrected to a fiducial Jupiter distance of 5.2 AU, background subtracted and corrected for aberration. To constrain low signal-to-noise beam pedestals, a hybrid TOD archive is then constructed in which model predictions (Hill et al. 2008) are substituted for data at the 3,4,6,7 and 10 dBi levels of K,Ka,Q,V and W respectively. This hybrid beam archive serves as the basis for beam map and window function analysis.

For purposes of constructing beam maps, the data in the hybrid beam TOD archive are assigned to 2.4 arcminute bins on a coordinate grid centered on either the A or B-side focal plane axis. The beam response for each feed is computed from the average temperature in each bin. No correction has been made for the side-A vs. side-B input transmission imbalance. These beam maps are convenient for some applications, but are not used in the computation of the flight beam transfer functions. The 2.4 arcminute binning acts as a smoothing kernel which filters high frequency spatial content. The pixelization transfer function may be estimated from the Legendre transform of the symmetrized radial profile of the binning kernel. Assuming a square pixel of 0.04 degrees on a side centered on the origin, the symmetrized radial profile of the binning function may be represented as

f(r)	= 1.0	for r < R
	= 1.0 - (4/pi)*acos(R/r)	for R <= r <= R*sqrt2

where R = 0.02 deg. Both the pixelization profile and pixelization transfer function are provided as a useful reminder of the limitations of the 2.4 arcminute binning.

Beam maps are provided in 10 FITS image format files, one file for each differencing assembly. Each file contains:

• the beam map for the A side, in mK (antenna temperature)
• the statistical error of each bin of the A side beam map, in mK (antenna temperature). The statistical error is based on the number of observations in each bin. Model points are assigned 100% error.
• the beam map for the B side, in mK (antenna temperature)
• the statistical error of each pixel of the B side beam map, in mK (antenna temperature) Model points are assigned 100% error.

The beam coordinates form an equal area rectangular coordinate system centered on the optic axis of the spacecraft. They are related to coordinates theta (elevation from optic axis) and phi (azimuth about optic axis) as follows:

• X_beam = 2*sin(theta/2) * cos(phi)
• Y_beam = 2*sin(theta/2) * sin(phi)

The "optic axis" of the spacecraft is elevated by 19.5 degrees from the S/C XY plane and lies within the S/C YZ plane. Although this vector is close to the S/C Y axis (+ or - depending on A or B side), it becomes the Z axis of the focal plane coordinate system.

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For each differencing assembly, an azimuthally symmetrized radial beam profile is computed by binning the ensemble of individual A- and B- side hybridized Jupiter observations. A constant bin size of 0.25 arcmin is used, and the straight mean of all hybrid samples within a radial bin represents the value for that bin.

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Beam transfer functions are computed from the Legendre transform of the binned hybrid radial beam profile. The window function applicable to power spectra is the square of the beam transfer function.

Beam transfer functions are presented as ASCII tables, with the first column being multipole moment l and the second column the transfer function (amplitude) normalized to 1.0 at l=1.

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Additional Information

• WMAP Seven Year Explanatory Supplement