Azimuths and horizontalTrue system

As the 30m telescope has an alt-azimuth mount, the equatorial (or galactic) astronomical coordinates are converted to the azimuth-elevation system of coordinates to (or in) the mecanichal system, and the encoders return the actual telescope position in this system (e.g. actual position, tracking errors, etc). However, because this system is spherical, azimuths are not suited to measure distances on the sky. At the interface of the user and the telescope, the horizontalTrue system is defined to address this issue: horizontalTrue offsets in IMBFITS files (when duly indicated) and trueHorizon values in some PAKO options.

Figure: Illustration of azimuth-elevation effects on coordinates and distances. All plots show the celestial sphere with the horizon ($0^{\circ}$ elevation) and an arbitrary azimuth of observations in red. We display here the effect at $0^{\circ}$, $40^{\circ}$, and $80^{\circ}$ elevations. Left: a $10^{\circ}$ arc along azimuth is represented at the three elevations. Center: three sources are tracked in wobbler-switching mode at the same azimuth but different elevations, with their pair of off-positions apart. Right: the same map (same size, in grey) is observed at the same azimuth but different elevations, with an illustration of the telescope jittering at its center.

The Figure  illustrates the effects on the coordinates we can find in the IMBFITS files.

• Left: the same arc ($10^{\circ}$ horizontalTrue here) on the sky covers different ranges of azimuth coordinates from horizon to zenith ( $10^{\circ} / cos(\mathrm{el})$).
• Center: for wobbler-switching scans, the secondary mirror wobbles along the azimuth, resulting in offsets about $4'$ apart from the source; their corresponding azimuths depend on the elevation.
• Right: the tracking errors of the main dish result as jittering around the desired position. See subsection for details.