Mapping speed and throughput

In order to map areas of the sky that are much larger than the array size, the mapping speed is proportional to the size of the array until the accessible focal plane area is covered. For large area surveys the aim must therefore be to fill the focal plane with detectors. The number of pixels is not a good measure of success toward this goal, because this number does not take into account the size and sky acceptance angle of each pixel. A more useful characteristic is the throughput (etendue) of the array, i.e., the product of its area and the acceptance solid angle. For a roughly circular array with diameter $D$, half acceptance angle $r$ the throughput is $(\pi r D/2)^2$. This number provides a basis of comparison between arrays, even if they operate on different telescopes. The throughput of an array can also be compared with the maximum throughput of the telescope. In this case $D$ is the telescope diameter and $r$ its angular field radius. Throughput is also some measure of the difficulty of producing a particular array: the thermal load from the ambient infrared background that has to be kept from the ultra-cold bolometer array by means of filters, is proportional to the throughput. APEX will have a field radius of 0.253 degree, resulting in a maximum throughput of 69.3 cm$^2$ sterad. The Nasmyth mirrors of the IRAM 30 m telescope limit the throughput to 11.93 cm$^2$ sterad. If the throughput were only limited by the vertex hole, and if the focus were located close to that position, the 30 m would have the enormous throughput of 1124 cm$^2$ sterad. Although, because of spatial restrictions, not all of that can be used, the 30 m is potentially a high throughput telescope, but only if it were converted into a Cassegrain system. The 117-element MAMBO array has an effective throughput of 7.64 cm$^2$ sterad, which is 64% of the Nasmyth field, filling 80% of the diameter of the Nasmyth mirrors. LABOCA will have a throughput of 12.1 cm$^2$ sterad, which is only 17% of that available, or 42% of the maximum field diameter of the APEX focal plane. We see from these numbers that bolometer arrays are reaching the limitation imposed by the Nasmyth configuration at the 30 m. For sparsely sampled arrays, the limit at 1.2 mm would be $\approx 144$ channels. Should a conversion of the 30 m to a Cassegrain (with optional Nasmyth) be seriously considered, more information on the technical options is needed before the scientific and instrumental consequences can be considered. A minimum requirement would be a convenient change of secondary between Nasmyth and Cassegrain operation, which would seem relatively easy given the existence of the subreflector platform. However, the telescope would need to remain in a specific state for some time, limiting its flexibility in pooled bolometer/heterodyne observations.