II. User's Guide to the WISE Preliminary Data Release

3. Atlas Images

g. Astrometry of Image-derived Source Positions

The magnitude and direction of these biases are fixed in the Level-1 image x,y coordinate frame (Table 1), although they vary with location on the sky in the x,y system of Atlas Images. The latter is brought about by the varying angle between survey scans and Atlas Image footprints, with the variation being strongest as one approaches an ecliptic pole. The biases are also band-dependent and cause source peak emissions to be misaligned when multi-color images are made using the default WCS from each band-specific Atlas Image (e.g., Figure 1). The absolute (radial) differences between source-peaks and "true" astrometric positions anywhere on the sky are no larger than ~0.50, 0.26, 0.26, and 1.4 arcsec in bands 1, 2, 3, and 4 respectively.

We strongly advise using the catalogued source position if available, otherwise, if you would like the equatorial coordinates of a source in an Atlas Image not in the catalog, e.g., because it didn't satisfy the catalog selection criteria, and you desire an accuracy better than that quoted above for a given band, we recommend the following procedure.

i. Methods to correct image-derived coordinates and WCS

1. Query the WISE source catalog for the footprint spanned by your Atlas Image tile. At minimum, you will need ra, dec, wx, wy - the equatorial and Atlas Image based pixel coordinates. You may need to explicitly pre-select the wx, wy fields before submitting your query. These positions will represent your "true" astrometric positions and we relabel them: RA_t, Dec_t, x_t, y_t respectively for use below. Note that in general, you can use any astrometrically calibrated catalog. The only difference is that you won't have immediate access to the pixel positions x_t, y_t for expediting the optional estimation of global/statistical corrections in step 4.


2. Overlay these positions on your Atlas Image using an interactive image viewer, e.g., DS9 or IPAC Skyview to get a sense of the source-peak to astrometric position bias. Note that these biases may be hard to see by eye since they're typically no larger than ~one-third of a co-add pixel for bands 1, 2 and 3 and ~one pixel in band 4 (see measures quoted above). Figure 1 shows an example for bands 1 and 4.


3. If you're interested in the equatorial positions of a few uncatalogued WISE sources in your field (call them RA_u, Dec_u) and the source-peak to astrometric biases are easy to see for the brighter sources, you can measure the peak positions for the latter (RA_p, Dec_p) and corrections therefrom manually:

   δRA = RA_t - RA_p, (Eq. 1)
   δDec = Dec_t - Dec_p,

   then use these to estimate your unknown astrometric positions:

   RA_u = RA_p - δRA, (Eq. 2)
   Dec_u = Dec_p - δDec.

   Caution must be exercised near an equatorial pole due to the strong Dec dependence of the correction along RA. Here you will need to use RA corrections calibrated at approximately the same Dec as your unknown source positions (if available), otherwise we recommend using the more generic pixel-based coordinate method in step 4.



4. We recommend the method below if either:
   1. you'd like to derive the astrometric positions for many uncatalogued sources in your Atlas Images, or
   2. the position biases are too small to enable a manual astrometric calibration as outlined in step 3, or
   3. you'd like to create properly registered multi-color Atlas Image overlays.
   
   First, you'll need to estimate the corrections statistically in the x,y coordinate system of each Atlas Image using all available astrometric positions for a given band, i.e.,

   δx = x_t - x_p [pixels], (Eq. 3)
   δy = y_t - y_p [pixels],

   where x_p, y_p are "source-peak" positions measured as either positions of the maxima of source signals, or intensity-weighted centroids measured within apertures centered on your astrometric priors x_t, y_t. A scatter plot of the corrections for a band 1 Atlas Image is given in Figure 2. After computing the median or trimmed-average correction along each axis, ⟨δx⟩, ⟨δy⟩, these can be applied to the reference-pixel WCS keywords CRPIX1,CRPIX2 (always = 2048, 2048) in Atlas Image headers:

   CRPIX1_new = 2048 - ⟨δx⟩ (Eq. 4)
   CRPIX2_new = 2048 - ⟨δy⟩

   After replacing the CRPIX1,CRPIX2 values in your Atlas Image FITS header with those from Eq. (4), you can re-extract your sources and they will be astrometricaly calibrated. Dangers at the equatorial poles are circumvented if your source-finding/extraction software properly handles WCS transformations when converting from pixels to RA, Dec.

Figure 1 - Atlas Image zoom-in with overlay of bands 1 (blue) & 4 (red) showing misalignments between source centroids (or peak emission) across bands, and with astrometric positions (green crosses). Field measures ~3.6′ x 6′ and was taken from tile 0229p545_aa11. Coordinate grid is equatorial with North up, East to the left.	Figure 2 - Distribution of differences between source (flux-weighted) centroids and astrometric positions (from WISE catalog) for the full band 1 tile in Figure 1. Red dashed lines mark the median corrections on each axis.

ii. Source Position Biases in Level-1 Frames

Table 1 - Source-position biases in x,y system of Level-1 frames

Band	δx [arcsec]	σδx [arcsec]	δy [arcsec]	σδy [arcsec]	δr [arcsec]
1	-0.441	0.009	-0.192	0.010	0.481
2	-0.239	0.008	0.086	0.006	0.254
3	-0.047	0.015	-0.251	0.014	0.255
4	1.211	0.0233	0.664	0.032	1.381

Notes to Table 1

1. δr in last column = √(δx²+δy²).
2. To convert these offsets to approximate native Level-1 frame pixel coordinates, divide by 2.75, 2.75, 2.75, 5.5 arcsec/pixel for bands 1, 2, 3 and 4 respectively.

Last update: 2011 February 14