The MultiDrizzle Handbook
3.5 Photometric Accuracy After Drizzling
The HST instrument optics geometrically distort the images formed on the detectors: pixels at the corner of each CCD subtend less area on the sky than those near the center. Flatfields for the HST instruments are defined such that, after application of the flat-field, a source of uniform surface brightness on the sky produces uniform counts in each pixel across the CCD. Unfortunately, because of the changing pixel scale across the field, this definition of the flat-field causes point sources near the corners of the chip to be artificially brightened compared to those in the center. For example, in the WFPC2 chips, a star in the corner becomes ~4% brighter than it would have been in the center of the chip.
Fruchter and Hook (1997) carried out a set of tests to study the ability of drizzle to remove the photometric effects of geometric distortion. This involved first creating a grid of 19x19 artificial stellar PSFs, subsampled by a factor of four, using the TinyTIM WFPC PSF modeling code. The stars were convolved with a narrow Gaussian to approximate the smearing caused by cross-talk between neighboring pixels. This image was then shifted and down-sampled onto four simulated WFPC2/WF2 frames, each with the original WF2 pixel sampling, and dithered in a 2x2 pattern of half-pixel shifts. This process also included multiplying each image by the Jacobian of the WF2 camera geometric distortion, thereby adjusting the counts to reflect the effects of geometric distortion. The amount of data and dithering patterns, therefore, resemble ones that a typical observer might produce (in contrast, the HDF-N contained 11 different pointings.) These four images were then combined using drizzle with typical parameters (output pixel 1/2 of the original WF2 pixels, and a drop size with pixfrac=0.6). The geometric distortion of the chip was removed during drizzling using the polynomial model of Trauger et al. (1995).
Aperture photometry was then obtained on the stars in one of the four simulated input images, and on the stars in the output drizzled image. The results are shown in Figure 3.6, where the photometric measurements of the 19x19 stars are represented by a 19x19 pixel image. The effect of the distortion on the photometry of the input image is very clear - the stars in the corners are up to ~4% brighter than those in the center of the chip. Figure 3.6 shows the results of aperture photometry on the 19x19 grid of stars after drizzling. The effect of geometric distortion on the photometry is dramatically reduced: the r.m.s. photometric variation in the output drizzled image is 0.004 mags. Thus, the removal of the geometric distortion by drizzle can be sufficiently effective to enable aperture photometry to be carried out successfully on resulting images, without the need to correct independently for the geometric distortion by other means.Figure 3.6: Photometric Results of Drizzling
The figure on the left shows the stars (all of equal intrinsic brightness) as they would appear in a flat-fielded WF image. In order to compensate for the smaller area on the sky of the pixels near the edge of the chip, the flatfield has artificially brightened the stars near the edges and the corners. The image on the right shows the photometric results for these stars after drizzling, which corrects for the geometric distortion.
In practice, observers may not have four relatively well interlaced images but rather a number of almost random dithers, with each dithered image suffering from cosmic ray hits. Therefore another test was carried out, using the shifts actually obtained in the WF2 images of the HDF-N as an example of the nearly random sub-pixel phase that large dithers may produce on HST. In addition, each image was associated with a pixel mask corresponding to cosmic ray hits from one of the deep HST WFPC2 images. When these simulated images were drizzled together, the r.m.s. noise in the final photometry (which does not include any errors that could occur because of missed or incorrectly identified cosmic rays) was less than 0.015 mags.
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