All of the available dither patterns were chosen pre-flight to enable different types of observations. For the full array mode there were two types of dithering available, fixed and cycling. The five fixed patterns, described below in more detail, performed identically at each mapping position. The cycling pattern performed a different subset of dither points at each map position.
Two fixed patterns were available for the subarray mode, as the fields of view covered by the arrays in the subarray mode were much smaller than in the full array mode.
The characteristics of the available dither patterns are given in Table 3.1.
· The Reuleaux Triangle patterns were designed with the idea of optimizing the Figure of Merit of Arendt et al. (2000), based on their usefulness for allowing calibration on all spatial scales. They thus sample a wide range of spatial frequencies in a fairly uniform manner, and were well suited to the Fixsen et al. (2000) least-squares flat-fielding technique.
· The 9-point and 16-point patterns were designed to have the optimum dither steps for 1/3 and 1/4 subpixel dithering, respectively.
· The random 9 pattern was based on a uniform random distribution.
· The spiral 16 pattern was designed by R. Arendt to provide a pattern which was both compact and had a good figure of merit for self-calibration.
· The cycling patterns were designed for observations (AORs) having many mapping/dithering pointings. The large and medium patterns were Gaussian distributions of offsets with dithers larger than 128 pixels removed. The small pattern was specifically designed for mapping, where only a few dithers were taken at each map position. It was also based on a Gaussian distribution, but the center was downweighted to decrease the fraction of small dithers in the pattern, and it was truncated at a maximum dither size of 11 pixels to ensure that maps with up to 280 arcsecond spacing have no holes, even if there was only one dither per map point.
All the patterns were constrained to have no pair of dithers closer than three pixels in any run of four consecutive points. The cycling dither table wraps around once the final (311th) element was reached. This pattern had a 1/2 sub-pixel sampling pattern superposed on it, starting with point 1 and repeating continuously every four points (at point 311, the final cycle was simply truncated early, thus patterns which wrapped around the table missed a sub-pixel dither point). The 5-point Gaussian pattern was a general use pattern suitable for shallow observations where the exact sub-pixel sampling was unimportant. It had a 1/2 sub-pixel pattern, with the fifth point at sub-pixel (1/4,1/4). Figure 3.2 shows the dither patterns at the default (large) scale. Figure 3.2 shows the cycling dither patterns and the distribution of both the dithers and of the separation between the dithers for each scale. The dither offsets are also available online at IRSA’s Spitzer documentation website:
Table 3.1: Characteristics of the dither patterns.
Dither Pattern
Scale
Max dither (pixels from (0,0))
Median dither separation (pixels)
Sub-pixel dither
pattern (pixels)
Cycling
Small
11
10.5
1/2
Medium
119
53
1/2
Large
161
97
1/2
5-point Gaussian
Small
26
23
1/2
Medium
52
46
1/2
Large
105
92
1/2
9-point random
Small
16
14
1/3
Medium
34
28
1/3
Large
69
59
1/3
12-point Reuleaux
Small
13
15
1/2
Medium
27
30
1/2
Large
55
59
1/2
16-point spiral
Small
16
12
1/4
Medium
32
23
1/4
Large
64
45
1/4
36-point Reuleaux
Small
17
19
1/4
Medium
34
39
1/4
Large
67
78
1/4
Each of the IRAC dither patterns was available in three sizes, large (default), medium, and small. For most of the patterns, the scaling of the large, medium, and small patterns was approximately in the ratio 4:2:1. Exceptions were the small cycling pattern, which was about 1/5 of the size of the large cycling pattern and had a lower-weighted inner region to reduce the numbers of small separation dithers, and the 4-point subarray pattern, where the scaling was 4:3:1.5. For all the patterns, the sub-pixel dithering was maintained, independent of scale.
Sub-pixel dithering, combined with the drizzle technique (Fruchter & Hook 2002) to reconstruct the images, could improve the sampling of the mosaics that are obtained from IRAC (or any other) observations. Such strategies have been used for the WFPC2, NICMOS, ACS, and WFC3 instruments on the HST for some time (for details, see the HST Multidrizzle Handbook). Dithering was also needed to calibrate the intrapixel sensitivity variations, and for programs requiring accurate photometry and astrometry (Anderson & King 2000). To be effective, however, accurate pointing and low image distortion were required. The offsetting accuracy of Spitzer was in the range 0.1 - 0.4 arcseconds. This, combined with the image distortion in the IRAC arrays, placed a limit of about 1/4 pixel on the sub-sampling that was likely to prove useful in practice. For example, the distortion of the IRAC camera was < 1% (see Figure 2.5). Thus, for the largest dither patterns, which typically offset up to ±64 pixels from the starting point, the offsets were up to ±0.6 pixels from the nominal values. Only in the small-scale patterns, where the offsets were less than ±16 pixels, would the sub-pixel sampling work well, though even on the larger scales some improvement of the images would probably be noticeable.
Figure 3.2: IRAC dither patterns for the “large” scale factor. The x- and y-axes are in pixels.
Figure 3.3: Characteristics of the cycling dither pattern. The x- and y-axes are in pixels in the left column plot. The histogram x-axis (separation) is in units of pixels (middle and right plots).
