In this report I investigate the possibilities of ``Fast (or undersampled)
On-The-Fly Mapping'' at the Heinrich-Hertz-Telescope, using the MPIfR 19-channel
bolometer array. This Fast OTF Mapping is based on the idea that, when observing
with a multichannel array, not every channel needs to produce a fully sampled
map, as long as the co-added map resulting from all channels is fully sampled.
The region that can be mapped in the conventional way using a bolometer array is limited by the requirement of full sampling (as a function of beam size) and the time scale of changing atmospheric conditions. Individual maps should be kept short also because of the parallactic rotation of the objects on the sky with hour angle. Assuming a maximum mapping time of 100 minutes to account for the latter two requirements, and the standard mapping parameters at the HHT (subscan distance of 8'' and a scanning velocity of 8''/sec (to keep azimuthal smearing small), the region which is covered by all 19 channels of the array is limited to about 36'2, i.e. or equivalent area, with a wobbler throw of and an array extent of 200'' in Azimuth and Elevation. The mapping of larger areas can be performed in a mosaicing mode, if the object of interest is only extended in one direction. However, for objects which are extended in two dimensions, new observing techniques are required.
The idea behind Fast OTF Mapping is to drop the requirement that every of the 19 individual maps obtained during one mapping observation has to be completely sampled. One can instead obtain a sufficient sampling by adding up all 19 channel maps, with the sky positions of the data points observed in one channel falling in between those observed with the other channel maps. However, the exact location of the individual channels (and therefore the obtained sampling) strongly depends on the actual relative positions of the individual channels. These depend on the number of channels, the channel offsets, and - because of the rotation of the array - on the elevation of the source.
A group of people (Teyssier & Sievers 1999, 2000) discussed this method for its use at the 30-m telescope. Their discussion, however, was based on the argumentation that ``by jumping a row of pixels between each scanline plus a small distance, consecutive rows of bolometer pixels just nicely fill in the gaps''. In addition, most bolometer arrays in use at the 30-m telescope have more channels (i.e. more pixels which can fill in sampling gaps), and even for the 19-channel array at the 30-m, the ratio of channel separation to beamwidth is about 20'' / 11'' = 1.82 and therefore much smaller than for the 19-channel array at the HHT ( 50'' / 22'' = 2.27). As a consequence it is more difficult to find a usable subscan separation for each elevation at the HHT, and a more sophisticated approach needs to be found.
Instead of taking the rather intuitive approach of Teyssier & Sievers, the situation at the HHT makes it necessary to obtain a clear statement if Fast OTF Mapping is possible for each point in the parameter space given by elevation and subscan separation. In order to achieve this goal, I developed a program (actually a NIC macro) that calculates for every pair of the above mentioned parameters the maximum pixel distance d. For , Fast OTF Mapping can be used without problems, for it can be used for a short time period, when field distortions in the equatorial frame due to changing parallactic angles are negligible.
The calculations were performed using a field size of 10' in elevation, and the maximum subscan separation was calculated in the elevation range between and . I should further note that the real (measured) channel offsets were used during these calculation.
Fig. 1 shows the calculated maximum pixel distance (or sampling interval) d for various elevations and values of SINT. The rotation of the bolometer array with elevation leads to a symmetry pattern around elevations of and . At these elevations, some subscan separations, which are multiples of the channel elevation distance, cause ``islands of undersampling''. This occurs in particular for and around , and for and around , where is the rotation symmetry angle of a hexagonal packed array, 50'' the channel distance in the array, and n an integer number.
More important than array symmetries and the beauty of Fig. 1 are, however, the results as far as observations are concerned. The contour levels correspond to d = 8'' and d = 11''. When choosing the right subscan separation for a given elevation we have to keep in mind that a) we want to observe with the largest possible subscan separation, in order to keep mapping times short, and b) we don't observe at one fixed elevation, but the source is moving in elevation during the mapping. Even if the decision must also be based on the elevation variation with time, which depends on the source coordinates, a few rules of thumb can be given (note that the elevation is that during the map, not that at the start of the map):
The main advantage of Fast OTF Mapping is that a map of a given size can be
observed in shorter time, or a larger map in a given time. The time available
for an individual map is limited by atmospheric stability (i.e. the time between
two skydip observations) and map distortion due to changing parallactic angles.
Thus Fast OTF mapping, compared to normal OTF Mapping, yields
As shown above, Fast OTF Mapping can be used over the the whole elevation range of the HHT. When starting an observation, the observer has to make sure that the source stays during the duration of the map in an elevation range where full sampling is given for the chosen subscan separation. To give an example: If the source is currently at an elevation of and still rising (i.e. before transit), and an area of should be mapped, a reasonable command would be (for a wobbler throw of )
The following text refers to the old SMT control system. Similar map parameters can now be set using the RAMBO interface.
OBST> cmap /mapsize 800 8 756 54 /time 101 OBST> start
For very large fields to be mapped it is also possible to increase the scanning speed. While the recommended value is 8''/second (as above), the map is fully sampled in Azimuth for scanning speeds of up to 16''/second for a wobbler frequency of 2Hz.
Copyright Arizona Radio Observatory.