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...arch 18, 2002
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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.
I present some calculations, based on the offsets of the individual bolometer channels, showing that Fast OTF Mapping is possible and can be easily performed at the HHT. However, some combinations of current elevation and subscan separation should be avoided.
Some instructions for observers who want to map large regions (e.g. $10' \times 10'$ or larger) are given.

1. Introduction

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. $6' \times 6'$ or equivalent area, with a wobbler throw of $\pm 60''$ 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.

2. Fast On-The-Fly Mapping

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.

3. Calculations

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 $d \le 8''$, Fast OTF Mapping can be used without problems, for $d \le 11'' = 0.5 \times HPBW$ 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 $- 0.5\,{\rm field size} + 100''$ and $+ 0.5\,{\rm field size} -100''$. I should further note that the real (measured) channel offsets were used during these calculation.


  \resizebox{12cm}{!}{\includegraphics*[angle = 270]
{plototf.eps}} 10#1
Fig. 1 The calculated sampling interval (in arcsec) as a function of elevation and the subscan separation during observations (SINT). Contour levels correspond to 8'' and 11''


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 $30^{\circ}$ and $60^{\circ}$. At these elevations, some subscan separations, which are multiples of the channel elevation distance, cause ``islands of undersampling''. This occurs in particular for $30^{\circ}$ and $90^{\circ}$ around $SINT = {\rm n}\,\cos(60^{\circ}) \times 50''$, and for $0^{\circ}$ and $60^{\circ}$ around $SINT = {\rm n}\,\sin(60^{\circ}) \times 50''$, where $60^{\circ}$ is the rotation symmetry angle of a hexagonal packed array, 50'' the channel distance in the array, and n an integer number.

4. Results

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):

Elevation possible SINT
$ El < 12^{\circ}$ $ \sim 35''$
$ 4^{\circ} < EL < 24^{\circ}$ $ \sim 54''$
$ 12^{\circ} < EL < 48^{\circ}$ $\sim 44''$
$ 24^{\circ} < EL < 36^{\circ}$ $ \sim 57''$ or $\sim 44''$
$ 36^{\circ} < El < 56^{\circ}$ $ \sim 54''$
$ 48^{\circ} < EL < 72^{\circ}$ $ \sim 35''$
$ 64^{\circ} < El < 84^{\circ}$ $ \sim 54''$
$ 72^{\circ} < El $ $\sim 44''$
$ 84^{\circ} < EL $ $ \sim 57''$ or $\sim 44''$

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
$\odot$ smaller field distortion in the equatorial frame
$\odot$ the possibility to map large sources
$\odot$ fast exploration of unknown fields
$\odot$ lower scanning effects due to addition of several maps at different hour angles.

5. Hints for observers

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 $40^{\circ}$ and still rising (i.e. before transit), and an area of $10' \times 10'$ should be mapped, a reasonable command would be (for a wobbler throw of $\pm 100''$)

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

This would perform a map of 15 subscans, going from an elevation offset of - 378'' over 0'' at subscan 8 to + 378'' at subscan 15, with a subscan separation of 54'' and a duration of 101 seconds for each subscan. The whole map can thus be completed in about 26 minutes, compared to the 2 hours and 40 minutes needed for the 96 subscans of a conventional OTF map. The required sensitivity is build up by repeated Fast OTF observations.

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.


6. References


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Last updated: 11/08/11.