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When observing in the infrared one frequently uses dithering patterns
to be able to subtract the bright sky from a median stack of several
science frames. However if one uses a grid with uniform spacing, one
may get artefacts in the skyframe, and hence the reduced science data,
e.g. since objects in the field will start to overlap. Hence, for deep
imaging of faint sources, it is a good idea to have a non uniform grid.

Ideally as few as possible of the n*(n-1)/2 offset vectors connecting 
the points in the grid should have the same length and position angle.
A problem is however that when the gridpoints are many, it is difficult
and time consuming to check this by hand.

Based on a proposed grid (supplied as a file with x- and y-coordinates
of the grid positions), the program 'checkpattern' calculates all the 
offset vectors, the distance to the nearest vector (the absolute distance
between the head of two vectors when placed in the same origin) and
warn about duplicated vectors. By identifying the responsible grid point,
one may adjust it slightly to try to get around the duplication. One should
also look at the distance to the nearest offset vector; if this is smaller
than 2-3 seeing disks one may still get artefacts. The program also
calculates the relative offsets from point to point in the grid, i.e.
the 'teloffset' commands you should give in the bias-program macro.
Note however that any offset you want to apply to the 1st position, eg to
get your arbitrary defined pattern box in the centre of the image, is
not accounted for.

When n is large and one wants to obtain a duplication free pattern, one
may try the program 'createpattern' which start from a uniform grid with
approximately the spacing you want to use (e.g. based on the size of the
largest object in your field) and randomises around these points, and tries
to find patterns that have no duplications within a tolerance given in
arcsec, e.g. 2 seing discs or typically 1.4 arcsec. However, there exist
many more bad patterns than good ones and the program may have to make 
many attempts before (if ever) finding a solution. Especially for compact
grids with many positions it may be very hard to find a good solution.

It is probably overkill to fight very hard to try to get around every
single duplication of offset vectors, but it is probably a good idea
to check the pattern you have in mind.

An expample of a 16 position grid with approximate dimension 36x36 arcsec
and random offsets of up to 3.5 arcsec around these grid points that get
no offset vector closer than 1.4 arcsec to any other is provided by the
pattern with grid positions (units in arcsec):

     x	    y	
   14.65   14.36	pos1
   -1.06   -0.20	pos2
    8.51   -3.08	...
   23.12    0.41
   35.67   -1.11
   -2.36    9.95
   20.69    8.72
   38.14   10.82
   -1.07   23.02
   11.73   26.97
   21.62   27.06
   32.84   26.75
   -1.87   35.22
   12.61   36.74
   27.21   34.76
   33.35   33.73	pos16

Of course, one may wish to take the positions in a different order
(this does not affect the offset vectors)  but for the order given above
the teloffset commands would be:

teloffset   0.0     0.0		(pos1)
          -15.7   -14.6	 	(pos2)
            9.6    -2.9	 	...
           14.6     3.5
           12.5    -1.5
          -38.0    11.1
           23.1    -1.2
           17.4     2.1
          -39.2    12.2
           12.8     3.9
            9.9     0.1
           11.2    -0.3
          -34.7     8.5
           14.5     1.5
           14.6    -2.0
            6.1    -1.0	 	(pos16)

And in order to get back to the initial position: teloffset   -18.7   -19.4

This grid is stored in the file: 	pattern16x16_random.dat
The offset sequence can be found in: 	pattern16x16_random.off
The offset vectors can be found in:	pattern16x16_random.ou


Goran Ostlin 2002-04-05
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