The National Astronomy and Ionospheric Center (NAIC
) is currently completing
the second Upgrade of the 305-m Arecibo Observatory (AO) radiotelescope.
This includes the construction of a 26-m Gregorian enclosure on the feed arm
137-m above the reflector. 19.8-m secondary and 7.6-m tertiary subreflectors
have been installed inside this aerodynamic enclosure. This system replaces one
of the previous two carriage houses, and provides correction for spherical
aberration. One of the main achievements of the Gregorian upgrade will
thus be to extend the frequency coverage of the Arecibo telescope to the
highest practicable frequencies limited by the accuracy of the primary
reflector (
GHz), with considerable
advantages for both molecular spectroscopy and pulsar astronomy (see
Kildal et al. 1994 and Olmi & Baan 1997).
The goal of the upgrade is to have a 305-m telescope which performs well at
radio wavelengths as short as 3 cm. As the main beam width of large diameter
antennas becomes very narrow with increasing operating frequency,
the highest pointing accuracy is required.
In the case of Arecibo, positioning the 
beam at
10 GHz will require a pointing accuracy of 5'' or better.
The conical scan method described below can be used as a fast, precise alternative to the widely-used cross-scan or five-point map techniques to measure pointing errors. Conical scanning is also known as sequential-lobe comparison, and is a technique widely used in tracking-radar systems (Skolnik 1970). It locates the center of the image through, e.g., mechanical nutation of a single feed that is displaced from the axis. The phase center of the feed is moved along the circumference of a circle which is centered on the optical axis (for a definition of the latter see below). A constant return occurs for a target on the boresight, and a modulated signal return occurs for a target that is off axis. This modulation, when properly compared in phase with the reference signal generated by the nutating mechanism, leads to the vectorial pointing error: the modulation amplitude gives the size of the correction, and its phase angle gives the direction.
Continuous beam scanning can be accomplished by mechanically moving the feed of an antenna, as the antenna beam will move off axis when the feed is moved off the focal point. The feed is typically moved in a circular path around the focal point, causing a corresponding movement of the antenna beam in a circular path around the target. Conical scanning can also be accomplished by fixing the feed and moving a subreflector. At Arecibo we plan to combine movement of the feed turret in azimuth and the tertiary subreflector in zenith angle.
A very significant advantage arises from the very low mass of the
feed turret and tertiary compared to the 200-ton feed arm and 75-ton
Gregorian enclosure. The latter are used to track the nominal
source location, while the turret and tertiary provide small, rapid
motions, not feasible with their more ponderous counterparts.
In addition, movement of the feed turret by a fixed amount provides
a fixed great circle motion of the beam on the sky, in strong
contrast to motion of the feed-arm, which must increase its offsets
proportional to 
, where z is the zenith angle,
for a fixed great-circle beam motion. Hence, one of the principal
advantages of this method is the absence of tracking problems near the zenith.
An alternative technique to sequential-lobe comparison in radar tracking applications is simultaneous-lobe comparison (or monopulse) which does not require sequential movement of the antenna beam in a path around the "target'', and utilizes two (or more) different beams at the same time. The beams can be obtained either by using an array of physically distinct feeds or generating them electromagnetically, by using a multimode monopulse feed (Skolnik 1970; Sherman 1984). The obvious advantage of the monopulse technique is the ability to obtain complete angle-error information on a single pulse, or integration cycle in the case of astronomical applications, whereas conical scanning operates through a time-dependent scan.
However, in addition to other problems which include linearity in the response and cross-talk in the different output channels, the monopulse technique has some fundamental drawbacks in its radioastronomical use which are: (i) the need of a completely separate feed specifically designed for this purpose; (ii) its use at just one frequency band, and (iii) the need to accomodate this special feed where space is at a premium, as on the rotating platform which hosts the feeds in the upgraded Arecibo telescope. Instead, the use of the actual observing feeds in the sequential-lobe technique guarantees that any offsets peculiar to these feeds are included in the pointing correction. Therefore, in the present work we shall discuss the conical scan technique only.
The conical scan technique has been used for years at the Deep Space Network (DSN) antennas (Abichandani & Ohlson 1981; Ohlson & Abichandani 1982; Abichandani 1983 and Eldred 1994) and at the Parkes radiotelescope (Wark & Wright 1990) for the main purpose of tracking spacecraft. The references cited above give both a general and detailed description of the conical scan method, with respect to the tracking problem, including optimization techniques (Eldred 1994). In this work we want to enhance those aspects of the conical scan technique which are more important to observe normal radio sources, by also using quantities which are familiar to radio astronomers. Furthermore, we compare alternative retrieving methods, including some analytic ones, and also discuss the implications of two important aspects of "real'' antennas: the presence of sidelobes and the ellipticity of the antenna beam.
In Sect. 2 (click here) we thus list our main assumptions and derive the antenna temperature for a conical scan. Then, in Sect. 3 (click here), several retrieving algorithms for the pointing offsets are described, and we discuss their general properties. The results obtained with simulations carried out with these different methods are described in Sect. 4 (click here), where both Gaussian and non-Gaussian antenna-beams are considered. Our conclusions are listed in Sect. 5 (click here) and we include two appendices: Appendix A discusses the effects of a non-circular antenna beam, and a definition of the principal symbols can be found in Appendix B.