The current (May 1998) integer dither table looks like this: dithtab.txt . The maximum amplitude is 72 units. The current scale factor is 3.85 arcseconds or 1/4 pixel. An example of a five segment dither simulation file is w0510.dith . The actual dithers used by the simulations are shown in w0510.dithsim .
The dither offsets for 1, 5, 20, and 80 segments is shown in Figure 1-1.
The dither offsets are reduced to pixel phases (or the position within a given pixel) in Figure 1-2. Note that the scale factor of 1/4 pixel shows a pattern in the pixel phase in the 80 segment case. If we reduce the scale factor by 3% the pattern disappears: Figure 1-3.
If the object is radially symmetric, and the sub-pixel response is uniform, then the pixel phases can be reduced to a triangular region with a half pixel width: Figure 1-4. Any pixel phase between 0 and 1 in the x and y directions can be represented by a point within this triangle.
Given the dither pattern, one can construct a coverage image which will show the number of exposures which overlap any given part of the field. If we require a minimum coverage 90%, we can determine the area in the field covered by at least 90% of the exposures. I show the fraction of the nominal area versus the minimum coverage required in Figure 2. The crosses represent the current maximum dither amplitude of 18 pixels (72/4). The stars represent an amplitude of 9 pixels, and the circles 36 pixels. If the source extracted image requires a minimum coverage of 80%, we find that 70% of the area is usable with a 18 pixel dither, and 85% of the area with a 9 pixel dither.
With nine targets we construct an area of about 1.5 degrees on a side. The coverage images for these mosaics are shown in Figure 3. Target offsets of 128, 116, 120, and 124 pixels are shown. The dither pattern is repeated for each target. This means that if the offset between targets is exactly one WIRE field width, the coverage across the center of the image is uniform.
For the 116 pixel offset (about 30 arcminutes), the coverage is 1.9 times larger at the corners between target fields than in the center of the mosaic, and 1.4 times larger at the edges between targets. For the 124 pixel offset (about 32 arcminutes), the coverage is 1.3 times larger at the corners and 1.16 times larger at the edges.
The usable area as a fraction of the nomial mosaic area is computed as a function of required coverage in Figure 4. With mosaicing, 90% of the nominal area is usable with a required coverage of 80% with the current dither amplitude and an target offset of 128 pixels. The area decreases for smaller target offsets as shown in Figure 5. You lose about 2 to 3% of the usable area for each arcminute decrease in the offset.
NEW!
(11 May 1998)
Fan Fang has created a simulation dither patter which includes large dither steps of 57 WIRE pixels every 14 entries. (The standard amplitude is 18 WIRE pixels.) These large steps are intended to improve the gain image derivation over large scales. For a single target field, this creates a 3-4% loss in area for a 80% coverage requirement, as shown in Figure 6. On a mosaic 3x3 area, a smaller loss in area is evident, as shown in Figure 7.
A comparison of the single target coverage image is shown in Figure 8, the stretch is 50% to 100% coverage. The "splotches" seen in both images are due to the bad pixel masks. The mosaic field coverage images are shown in Figure 9, the stretch is 70% to 130%. All cases are for 20 segments.
Comment: even without these large dithers, it may be possible to derive an adequate large scale gain using overlapping exposures from adjacent target fields. With an 18 pixel dither amplitude, one would occasionally get "dithers" of about 90-100 pixels in amplitude between target segments.
NEW!
(11 May 1998)
If there is an error in pointing the telescope, imagine that the offset between targets is actually 34-arcminutes. How would this affect the area coverage? The image shown in Figure 10 compares the coverage between a 32-arcminute offset and a 34-arcminute offset, the stretch is 70% to 130%. In the 34-arcminute offset, the coverage goes as low as 70% in the corners between targets and about 85% in the edges between targets.
