Frequency switched

In frequency switched observations, the switching happens as the telescope is slewed. This is correct as long as the switching time is much smaller than the time needed to slew a significant fraction of the telescope beam.

It is easy to understand that

$$\ensuremath{t_\ensuremath{\mathrm{onoff}}}= \ensuremath{\en... ...emath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{tot}}},$$ (18)

$$\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensure... ...{\mathrm{onoff}}}}{\ensuremath{n_\ensuremath{\mathrm{beam}}}},$$ (19)

$$\ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensur... ...\mathrm{onoff}}}}{2\ensuremath{n_\ensuremath{\mathrm{beam}}}},$$ (20)

and

$$\ensuremath{\sigma_\ensuremath{\mathrm{fsw}}} = \frac{\sqrt... ...th{\mathrm{tel}}}\,\ensuremath{t_\ensuremath{\mathrm{tel}}}}}.$$ (21)

The velocity check can then be written as

$$\frac{\ensuremath{A_\ensuremath{\mathrm{map}}}}{\ensuremath... ...emath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}.$$ (22)