Analyzing beam maps

The calibration differs for jiggle maps and scan maps and it is also, although more weakly, dependent on chop throw. The relatively large difference in calibration for scan maps is due to the different chop wave form used for scan maps. The difference between a jiggle map with a 120'' chop throw compared to one with a 60'' chop throw is mostly dictated by duty cycle and to a lesser extent by changes in the beam. The beam is slightly broader with a 120'' chop throw, but the duty cycle (time spent on source) is also slightly lower, both of these factors decrease the efficiency for large chops.

In the following example we are going to look at beam maps of Uranus taken in stable night time conditions during three nights in late May, 2001. These maps have been extinction corrected, we have blanked out bad bolometers and corrected each map for pointing drifts. There are slight calibration differences from night to night, but for this purpose the difference is negligible. The final coadded beam maps were rebinned in az and are shown in Fig. .

A quick way to diagnose that the beam profile looks reasonable is to use KAPPA's psf. The task psf fits a radial profile, $A \times exp(-0.5 \times (r/\sigma)^\gamma)$, where r is calculated from the true radial distance of the source allowing for ellipticity, $\sigma$ is the profile width, and $\gamma$ is the radial fall-off parameter. psf can also fit a standard Gussian profile. However, the JCMT beam is better described by a two or three component Gaussian (main lobe plus inner and outer error lobes) and psf therefore overestimates the Half Power Beam Width (HPBW). If we specify norm=no psf will also return the fitted peak value of the source.

 % psf norm=no
IN - NDF containing star images /@u120_lon_reb/ > 
INCAT - Positions list containing star positions /@coords/ > !
COFILE - File of x-y positions /@coords/ > u120l.psf
     Mean axis ratio =   1.093
   Mean orientation of major axis =   52.96 degrees
     (measured from X through Y)
DEVICE - Name of graphics device /@xwindow/ > 
   FWHM seeing = 14.72    arcsec
   Gamma =  2.153
   Peak value = 0.2477

Figure: The radially averaged gaussian fit produced by psf

This produces the plot shown in Fig. . The value of FWHM is 14.72'' across the minor axis. The geometrical mean is simply $\sqrt{\mbox{mean axis ratio}}$ times 14.72, i.e. the measured FWHM (including the broadening from Uranus) is therefore predicted to be 15.4'' if we use psf. However, if we fit a double Gaussian to the same data set we obtain 15.56'' $\times$ 14.30'' with a position angle of 85 for the main beam, and 55.8'' $\times$ 49.6'' for the inner error lobe. To find the true (HPBW) we need to remove the broadening caused by Uranus being an extended source. Using the program FLUXES (just type fluxes at the command line and answer the prompts) we find out that Uranus had a diameter (W) of 3.54'' that day. We convert the FWHM measured, $\theta_m$, to the true HPBW of the telescope, $\theta_{A}$, using the equation

$$\theta_{A} = \sqrt{{\theta_m}^{2} - \frac{ln2}{2} \times W^{2} }$$ (4)

where W the diameter of the planet. In this case we get 14.5'' for the HPBW and $\sim$ 53'' for the near (inner) error beam. If we do the same for 450 $\mu$m we obtain 7.8'' for the HPBW and 34'' for the near error beam. These agree with nominal values for the telescope.