MAP Main Beam Ellipticity Simulations at UCLA

The main beam ellipticity has been represented using several copies of the symmetrized main beam. The first attempt using two half-weight copies did not give a good iteration result, so the results I am reporting here use a quad of low amplitudes copies in the following pattern: 

              -0.085

     +0.085    1.0      +0.085

              -0.085
For sidebeams with amplitude ± &eps, spaced d &sigma away from the main beam, the second moment in the wide direction is sigma^2*(1+2(d/sigma)^2*eps) while in the narrow direction it is sigma^2*(1-2(d/sigma)^2*eps). If the spacing is set at the HWHM of a Gaussian [d/sigma = 1.18] these amplitudes produce a 27% difference between the major and minor axes of the elliptical beam. For the simulations reported here the spacing d=0.46o to match the HWHM of the K band beam.

In these simulations the time-ordered data is generated by looking up the appropriate pixels in a res=9 simulated map of the K band sky. This is the "gpc" map that included both CMB fluctuations and the simulated galaxy.


The iterative solutions were done on res=8 maps, so in regions of high gradient there will be errors. There will also be errors in the reference regions which are 135o away from regions of high gradient. The iterative solution did not use data taken with the reference beam close to the Galactic Plane, but Orion A and B are far enough from the plane to cause trouble.

Two TOD streams were generated. One just had the main beams, while the second stream had the quad of sidelobe beams. The map generated from this second stream shows the error made by not allowing for the ellipticity of the main beam.

The graph below shows the simulated signal in the main beams:


while the graph below shows the difference produced by the beam asymmetry.

Since this signal is 10 microK, one would expect fairly large effects in the map, but the actual map produced from the ellipticity effect is quite flat over most of the sky: 95% of the sky is in a ± 1.2 microK range.

The green curves in the map show the reference arcs which are 135o away from the bright sources Orion A (l,b)=(209.0,-19.5), Orion B (206.5,-16.3) and Sco-Oph (353.0,17.1) which are the three brightest sources outside of the sin|b| < 0.1 region. The map-making algorithm was set to ignore data taken with the Milky Way in the reference beam [sin|b| < 0.1] so these galactic sources that fall outside of this band should be added to reference beam exclusion region.

The map below shows the residuals after 30 iterations on the signal just from the main beam. One sees the usual slowly converging ell=4 residual plus the granular errors generated by high gradients.


These high frequency errors are due to non-uniform coverage of the 4 res=9 pixels within each res=8 pixel.

Future Work

The iteration scheme should be modified to explicitly allow for these Gaussians. But in some sense this effort is unnecessary, because the magnitude of this effect is small enough to ignore.

The technique used here can easily be extended to handle the four-fold symmetric sidebeams introduced by the reflector distortion in the W-band beams. Eight sidebeams with alternating amplitudes would be used to model the deviation from a symmetric beam.

MAP@UCLA Index

Edward L. Wright, 12 March 2001г
..:: Перевел с английского В.Г. Мисовец
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