Space Telescope Science Institute
DrizzlePac 2012 Handbook
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The DrizzlePac Handbook > Chapter 2: Description of the Drizzle Algorithm > 2.2 Drizzle Concept

High spatial frequency information in an image that is permanently smeared out by the detector pixel response can be partly recovered by combining subpixel dithered images. Each dithered image can be thought of as sampling a final higher resolution image–a “true image” of the sky. But the images are also convolved with the optical PSF and pixel response function of the detector. The effect of undersampling is illustrated in a set of four eye chart image examples shown below Figure 2.1. The upper left image represents a “true” image, as seen by a telescope of infinite aperture. The upper right image has been convolved with the HST/WFPC2 PSF. In the lower left of the set, the previously-mentioned image has been sampled by the WF2 CCD. The loss of spatial information is immediately obvious.
Figure 2.1: The Drizzle ‘Eye Chart’ Illustrating Convolution and Sub-Sampling
The effects of image convolution and subsampling The upper left image represents a “true” image, as seen by a telescope of infinite aperture. The upper right image has been convolved with the HST/WFPC2 PSF. The effect of sampling it with the WF2 CCD, as seen in the lower left image, shows even more loss of spatial information. The lower right image has been reconstructed using the Drizzle algorithm.
Much of the information lost to undersampling can be recovered. This is shown in the lower right of Figure 2.1, where the image has been recovered using a method from a family of techniques known as “linear reconstruction.” However, simple implementations of these techniques generally introduce additional blurring due to convolution with the pixel shape. This effect can be seen directly in the present example by comparing the upper and lower right-hand images: the deterioration in image quality between these two images is due entirely to convolution of the image with the pixel.
The Drizzle algorithm is conceptually straightforward, as shown in Figure 2.2. Pixels in the original input images are mapped into pixels in the subsampled output image, taking into account shifts and rotations between images and the optical distortion of the camera. However, in order to avoid convolving the image with the large pixel “footprint” of the camera, Drizzle allows the user to shrink the pixel before it is averaged into the output image through the pixfrac parameter.
Figure 2.2: Schematic Representation of how Drizzle Maps Input Pixels onto the Output Image
The new shrunken pixels, or “drops,” rain down (or “drizzle”) upon the subsampled output image, as shown in Figure 2.2. The “drop” size is controlled by the parameter pixfrac, the ratio of the linear size of the “drop” to the input pixel (before any adjustment due to the geometric distortion of the camera). The size of the drop is further adjusted internally by the Drizzle code to take into account the camera geometric distortion, before the overlap of the drop with pixels in the output image is determined. A second parameter, ­­­­­scale, allows the user to specify the size of the output pixels in arcseconds1.
The flux value of each input pixel is divided up into the output pixels with weights proportional to the area of overlap between the “drop” and each output pixel. If the drop size is too small, not all output pixels have data added to them from each of the input images. One should therefore choose a drop size that is small enough to avoid convolving the image with too large an input pixel footprint, yet sufficiently large to ensure that there is not too much variation in the number of input pixels contributing to each output pixel.

In the case of the Hubble Deep Field North (HDF-N), the drop size linear dimensions were one-half of the input pixel (i.e., pixfrac=0.5). This drop size was slightly larger than the dimensions of the output subsampled pixels which were four-tenths (0.4) the size of WFC pixel (scale=0.04, units in arcseconds).

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