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The MultiDrizzle Handbook

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3.1 Theory


While much high spatial frequency information in the image is permanently lost by smearing with response of the detector pixels, the quality of the image can be greatly improved by combining sub-pixel dithered images. Each of the pixels from the different exposures can be thought of as sampling a final, higher-resolution image, which is the "true image" of the sky convolved with the optical PSF and the pixel-response function of the CCD. The effect of undersampling is illustrated by a set of four different examples (Figure 3.1). In the upper left hand corner one sees the "true" image, as it would be seen by a telescope of infinite aperture. In the upper right, the image has been convolved with the PSF of the HST/WFPC2 and in the lower left it has been subsequently sampled by the WF2 CCD. The loss of spatial information is immediately obvious.

Figure 3.1: The Effects of Image Convolution and Subsampling


 
Representation of the effects of image convolution and subsampling; In the upper left hand corner one sees the "true" image, as it would be seen by a telescope of infinite aperture. In the upper right, the image has been convolved with the PSF of the HST/WFPC2 and in the lower left it has been subsequently sampled by the WF2 CCD. The loss of spatial information is immediately obvious. On the lower right the image has been reconstructed using the Drizzle algorithm.
 

Much of the information lost to undersampling can be recovered. This is shown in Figure 3.1, which displays the image recovered using one of the family of techniques referred to as "linear reconstruction". However, the simple implementations of these techniques generally introduces 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. 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 3.2: How Drizzle Maps Input Pixels to Output Pixels


 
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 3.2. The drop size is controlled by the parameter pixfrac (Section 5.5.6), which is simply 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 (or psize in PyDrizzle) (Section 5.5.6), allows the user to specify the size of the output pixels. In the case of the Hubble Deep Field North (HDF-N), the drops had linear dimensions one-half that of the input pixel (i.e., pixfrac=0.5) - slightly larger than the dimensions of the output subsampled pixels. 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.


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