Map calibration

Figure: Upper panel: Logarithmic contour plots of Uranus beam maps overlaid on grayscale. At 850 $\mu$m we plot ten contours starting from 0.25% of the peak intensity, while the 450 $\mu$m beam map goes from 1% of the peak intensity. One can see a diffraction like ring in the 850 $\mu$m map at a radius of $\sim$ 47'', but the amplitude is $<$ 1% of the peak. At 450 $\mu$m the ring is at $\sim$ 25'' and has an average amplitude of $\sim$ 2% of the peak intensity. This is seen more clearly in the lower panels, which show radially averaged beam profiles plotted in a logarithmic scale

Until now we have deliberately avoided the issue of calibrating your data. This means that your reduced data, up until this stage, are in units of volts. Since the calibration varies from night to night and even within a single night, one should generally calibrate individual maps before coadding to achieve the best result. So how does one convert instrumental units into a physical measure of luminosity or surface brightness? The solution as in most astronomy is to look at a source of known brightness in exactly the same way, i.e. using the same mode of observing for your target as well as for your calibrator(s).

In the optical and infra-red the standard sources are almost always point sources, standard stars, and the point spread function is well defined. In the submillimetre things are more complicated. Our primary calibrators, Mars and Uranus, are not point sources, and the point spread function is very extended and strongly wavelength dependent. The JCMT beam at 450 $\mu$m is actually much worse than the ill-fabled Hubble before the mirror was corrected.

The way we calibrate may differ depending on whether we observe point sources or extended sources. For point sources we can ignore the error beam and do simple aperture photometry, for extended sources we normally have to calibrate in Jy/beam and characterize our beam profile. In the following we first go through how to characterize the beam profile, then the case of calibrating in Jy/aperture and finally we proceed to the more general case of calibrating in Jy/beam, which is valid for all cases.