# Map Smearing Due to Azimuth Pointing Uncertainty

This applies to flight 2 only, where we have a residual uncertainty in the azimuth of all radio beams.  This uncertainty comes from the fact that we did not have CCD star lock during our Cas A calibration, and had to use the magnetometer to transfer the azimuth.

### Magnetometer Error

How do we know the magnetometer error?  We have two ways to determine the offset/scale constants (for the model AZ = atan[(x+a)/((y+b)*c)]): via CCD locks at various azimuths and via a global scale/offset determination.  Here are the fit results and the (generous) estimate of the uncertainty that comes from the comparison of the two fits:

   CCD locks     global offset/scale     uncertainty estimate a +0.5 +0.42 0.01 b -0.17 -0.166 0.01 c 1.0 0.9983 0.002

These uncertainties result in the following uncertainty in the magnetometer azimuth as a function of azimuth:

From this calculation, the azimuth error has been set at 0.5 degrees.

### Azimuth Shift of Data

The effects of this shift are easily explored - just apply an additional azimuth shift to the data and recalculate the power spectrum.  This has been done, and has shown no major changes in the results.  Another way to characterize the effect of this uncertainty is to calculate the beam broadening experienced by various regions of the map.  The results of this are below and are very encouraging.

Here are details on the shift of Ka1/2 by -0.5 degrees in azimuth (click on images for full-size versions):

 beam broadening number of samples coverage mean shift shift direction

Here is what the beam broadening looks like in the other channels.  Remember, channel pairs (e.g. Ka1/2) are identical.  Also, a positive or negative shift makes almost no difference in the map of total beam broadening.  The pictures below use a shift of -0.5 degrees in azimuth.

 Ka1/2 Q1/2 Q3/4

Finally, here are plots of the number of samples (weighted) or pixels (unweighted) above a certain threshold in beam broadening.  The pixel size is 0.1 degrees, so in large pixels, the few pixels with the largest broadening would likely be suppressed.  Click on the graphs for a PS version.

The beam sizes are from 0.65 to 0.9 degrees, so the beam broadening due to an azimuth shift of 0.5 degrees in either direction has a significant impact on the maps.