We have carried out a systematic analysis of a relatively unused method to point a radiotelescope, generally known as conical scan technique. It consists of moving the phase center of the feed along the circumference of a circle which is centered on the optical axis. The modulation of the signal returned from a point source that is off axis leads to an estimate of the pointing error.
This pointing technique has major advantages in the case of large radiotelescopes, such as the 305-m dish at Arecibo, where the feed turret and tertiary that will be used to move the feed in a circular path around the optical axis, are of very low mass compared with the 200-ton feed arm and 75-ton Gregorian enclosure. Also noticeable is the absence of tracking problems near zenith.
Three different methods have been discussed to retrieve the pointing corrections from a conical scan: (i) the standard fitting technique to the antenna signal; (ii) a fit to the normalised signal difference; and (iii) the dot-product method. The first one is a numerical technique that can be linearized and speeded up under the approximations of small pointing errors, in which case it becomes a very convenient analytical method. The other two are also analytical methods, and the dot-product technique, though less precise, can be implemented in hardware alone.
The results obtained with a Gaussian
antenna beam indicate that during simulated
observations of high SNR all methods are roughly equivalent, although
at small (
) pointing errors the linearised standard method
is likely to give a better performance if the conical scan is repeated at least
twice, in a consecutive way. Furthermore, the linearised
standard method performs better at low SNRs, especially when conical scan is
repeated more than once.
We have also carried out simulations with a sinc2 beam, to reproduce
a situation where the (symmetric) antenna beam is not exactly known and some
sidelobes may be present. In these cases
the method fitting the signal difference and the dot-product method
give a better performance at high SNRs and large pointing errors,
whereas as usual the standard method gives better performance at small target
displacements, although a general degradation is observed. However,
contrary to the case of a Gaussian antenna beam, the standard method
can now show some unwanted "ripples'' in the distribution of the residual
pointing error when the radius of the conical scan, 
, is progressively
increased. The method fitting the signal difference and the dot-product method
are also deteriorated by the increased 's and the presence of the
sidelobes.