Bandshape Calibration

In this case too, a bright, unresolved source is used as a calibrator but the nearness requirement (as in the gain calibration) is not essential. On the other hand, the calibrator should not have any spectral features in the band of interest. The measured visibilities from the calibrator across the band of interest can once again (like in the earlier gain calibration) be used to estimate the antenna bandshapes. The observed spectrum from the source is divided by the bandshapes to obtain the true spectrum. The bandshape should have a signal-to-noise ratio (snr) significantly greater than that of the observed spectrum so that the snr in the corrected spectrum is not degraded. For e.g., if the bandshape and the observed spectrum have equal snr, then the corrected spectrum will have an snr which is square root of 2 worse (assuming gaussian statistics of noise). Ideally, one wouldn't want the corrected spectrum to degrade in its snr by more than $\sim$ 10%. This can be used as a criterion to judge if a given calibrator is bright enough and to decide the amount of integration time required for the source and for the calibrator.

There are two methods of bandshape calibration.

(1) Position Switching : In this method, the telescope cycles through the source and a bandshape calibrator but observing both at the same frequency and bandwidth. Depending on the accuracy to which the corrected bandshape is required, and the stability of the receiver, the frequency of bandshape calibration can vary from once in $\sim$20 minutes to once in a few hours.

(2) Frequency Switching : There are situations when position switching is not a suitable scheme to do the bandshape calibration. This can happen due to (at least) two reasons : (a) the band of interest covers the Galactic HI. In this situation, all calibrators will also have some spectral feature within this band due to the ubiquitous presence of Galactic HI. No calibrator is suitable for bandshape calibration. (b) The band is outside the Galactic HI but the source of interest is a bright unresolved source. In this case one might end up observing any other calibrator much longer ($\sim$ 10 times) than the source in order to achieve the desired signal-to-noise ratio on the bandshape. In either of these situations position switching is not desirable. An alternative scheme is employed.

If a spectral feature covers a bandwidth of $\delta\nu$ centered at $\nu$, quite often it is possible to find line-free regions in the bands centered at $\nu \pm \delta\nu$. The bandshapes at these adjacent frequencies can be used to calibrate the observed spectrum. This works well because the bandshape is largely decided by the narrowest band in the signal path through the telescope. This is usually decided by the baseband filter. The bandwidth of this filter is selected to be the same while observing at frequencies $\nu-\delta\nu$, $\nu$, and $\nu+\delta\nu$. It is important to keep in mind that frequency switching works as long as $\delta\nu$ is small compared with the bandwidth of the front-end devices, and feeds. This is usually the case. For e.g., at the GMRT, the 21-cm feeds have a wide-band response, over 500 MHz. This is divided into 4 sub-bands each of 120 MHz width. If the amount by which the frequency is switched is small compared to 120 MHz this technique should work quite satisfactorily. A typical frequency switching observation would thus have an ``off1'', ``on'', and an ``off2'' setting. The ``on'' setting centers the band at the spectral feature of interest (at $\nu$) with a bandwidth of $\delta\nu$ while the ``off1'' and ``off2'' settings will be centered at $\nu-\delta\nu$ and $\nu+\delta\nu$ respectively. The three settings will be cycled through with appropriate integration times. The average of the ``off1'' and ``off2'' bandshapes can be the effective bandshape to calibrate the ``on'' spectrum. In this situation, equal amounts of time are spent ``off'' the line and ``on'' the line to achieve the optimum signal-to-noise ratio in the final spectrum. However, the switching frequency itself will depend on the receiver stability, and the flatness of the corrected bandshape required. This could vary from once in $\sim$20 minutes to once in a few hours.

There are situations when one might to do both frequency and position switching. If one is observing Galactic HI absorption towards a weak continuum source, it is advantageous to obtain bandshape calibration by observing a brighter continuum source with frequency switching.