drizzle 2.0.0

Requirements

• Python 3.10 or later

• Numpy

• Astropy

The Drizzle Algorithm

This section has been extracted from Chapter 2 of The DrizzlePac Handbook [Driz2012]

There are a family of linear reconstruction techniques that, at two opposite extremes, are represented by the interlacing and shift-and-add techniques, with the Drizzle algorithm representing a continuum between these two extremes.

If the dithers are particularly well-placed, one can simply interlace the pixels from the images onto a finer grid. In the interlacing method, pixels from the independent input images are placed in alternate pixels on the output image according to the alignment of the pixel centers in the original images. However, due to occasional small positioning errors by the telescope, and non-uniform shifts in pixel space across the detector caused by geometric distortion of the optics, true interlacing of images is generally not feasible.

Another standard simple linear technique for combining shifted images, descriptively named “shift-and-add”, has been used for many years to combine dithered infrared data onto finer grids. Each input pixel is block-replicated onto a finer subsampled grid, shifted into place, and added to the output image. Shift-and-add has the advantage of being able to easily handle arbitrary dither positions. However, it convolves the image yet again with the original pixel, thus adding to the blurring of the image and to the correlation of noise in the image. Furthermore, it is difficult to use shift-and-add in the presence of missing data (e.g., from cosmic rays) and geometric distortion.

In response to the limitations of the two techniques described above, an improved method known formally as variable-pixel linear reconstruction, and more commonly referred to as Drizzle, was developed by Andy Fruchter and Richard Hook, initially for the purposes of combining dithered images of the Hubble Deep Field North (HDF-N). This algorithm can be thought of as a continuous set of linear functions that vary smoothly between the optimum linear combination technique (interlacing) and shift-and-add. This often allows an improvement in resolution and a reduction in correlated noise, compared with images produced by only using shift-and-add.

The degree to which the algorithm departs from interlacing and moves towards shift-and-add depends upon how well the PSF is subsampled by the shifts in the input images. In practice, the behavior of the Drizzle algorithm is controlled through the use of a parameter called pixfrac, which can be set to values ranging from 0 to 1, that represents the amount by which input pixels are shrunk before being mapped onto the output image plane.

A key to understanding the use of pixfrac is to realize that a CCD image can be thought of as the true image convolved first by the optics, then by the pixel response function (ideally a square the size of a pixel), and then sampled by a delta-function at the center of each pixel. A CCD image is thus a set of point samples of a continuous two-dimensional function. Hence the natural value of pixfrac is 0, which corresponds to pure interlacing. Setting pixfrac to values greater than 0 causes additional broadening of the output PSF by convolving the original PSF with pixels of non-zero size. Thus, setting pixfrac to its maximum value of 1 is equivalent to shift-and-add, the other extreme of linear combination, in which the output image PSF has been smeared by a convolution with the full size of the original input pixels.

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.

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.

When images are combined using Drizzle, a weight map can be specified for each input image. The weight image contains information about bad pixels in the image (in that bad pixels result in lower weight values). When the final output science image is generated, an output weight map which combines information from all the input weight images, is also saved.

Drizzle has a number of advantages over standard linear reconstruction methods. Since the pixel area can be scaled by the Jacobian of the geometric distortion, it is preserved for surface and absolute photometry. Therefore, the flux in the drizzled image, that was corrected for geometric distortion, can be measured with an aperture size that’s not dependent of its position on the image. Since the Drizzle code anticipates that a given output pixel might not receive any information from an input pixel, missing data does not cause a substantial problem as long as the observer has taken enough dither samples to fill in the missing information.

The blot methods perform the inverse operation of drizzle. That is, blotting performs the inverse mapping to transform the dithered median image back into the coordinate system of the original input image. Blotting is primarily used for identifying cosmic rays in the original image. Blot requires the user to provide the world coordinate system (WCS)-based transformations in the form of a pixel map array as input.