Combination by drizzling

In most cases resampling and mosaicing should be done using TRANNDF and MAKEMOS, but for certain specialised applications the

• DRIZZLE

program may be superior. It combines resampling and mosaicing in one task and the resampling is done using the Variable-Pixel Linear Reconstruction (or informally ``drizzling'') algorithm.

This algorithm was originally developed for the Hubble Deep Field, a project whose purpose was to image an otherwise unexceptional region of the sky to depths beyond those of previous astronomical images. Its primary application is to provide a method for the linear reconstruction of an image from a set of undersampled dithered data; it preserves photometry and resolution, and can weight input images according to the statistical weight of each pixel.

The input grid is mapped onto an output grid which is normally finer; where many dithered input images are being combined this allows subsampling of the input data. Before the pixels are resampled onto the output grid however, they are shrunk into smaller pixels, now referred to as ``drops'', which rain down onto the output grid. Each drop affects the pixels in the output grid which it covers in proportion to the area of overlap; if an output pixel is not touched by any of the drops it receives no data from the image. This is shown schematically in the figure.

Figure: A schematic representation of Drizzling. The input pixel grid (shown left) is mapped onto a finer output grid (shown right). Each input image only affects the output pixels under the drops, so that here the central output pixel recieves no information from that image (Fruchter & Hook, ADASS VI, ASP Conf. Series, Vol. 125, 1997, G. Hunt and H.E. Payne, eds., pp. 147-150).

The transformation of input grid to output grid is basically the transformation between the pixel coordinates and Current coordinates of the image file; however an additional shrinking factor can for convenience be given using the MULTI parameter of DRIZZLE. The ratio of the linear size of the drop to the size of the input pixel is controlled by the parameter PIXFRAC. The default values for these parameters are 1.5 and 0.9 respectively.

The algorithm has a number of advantages over the resampling and combination methods provided by TRANNDF and MAKEMOS. Since the area of the pixels scales with the Jacobian of the geometric transformation, the algorithm preserves surface and absolute photometry. Flux can therefore be measured using an aperture whose size is independent of position on the output frame. As the algorithm anticipates that output pixels may not receive data from a given input pixel, bad pixels do not cause significant problems, so long as the stack of input images is sufficient to fill in the gaps caused by these zero-weight input pixels. Shifts of a few pixels between input images therefore allow the user to remove small scale defects such as hot pixels, bad columns and cosmic ray hits. Additionally, non-integral drizzling allows the user to recover some information lost to undersampling of the point spread function by the CCD pixels.

However due to the nature of the algorithm, it is computationally intensive, and it is important to consider whether any advantage will be gained from its use. It has been primarily designed to combine undersampled image data in an attempt to reconstruct dithered CCD images. Unlike the resampling methods used by the TRANNDF routine, drizzling requires the forward rather than the inverse mapping for the geometric transformation.

If you intend to make use of DRIZZLE it is recommended that you read the paper A.S. Fruchter and R.N. Hook, 1998, ``A Method for the Linear Reconstruction of Undersampled Images'' (PASP, in press) which discusses the algorithm in depth. Further information can also be found on the web at http://www.stsci.edu/%7Efruchter/dither/drizzle.html where the authors of the algorithm discuss its use in reconstructing the Hubble Deep Field.

The DRIZZLE program supports the full range of normalisation capabilities described above for MAKEMOS, however it also allows you to supply scaling and zero-point factors via a plain text input file. If you wish the DRIZZLE program to carry out scaling and/or zero-point corrections this is controlled via the SCALE and ZERO parameters (as for MAKEMOS) and, additionally, the CORRECT parameter. So:

% drizzle in='*' out=mosaic scale zero correct='!'

would determine (and apply) both scale and zero-point corrections. However, DRIZZLE also has the capability to read scale and zero-point corrections in from a (correctly) formatted file by setting the CORRECT parameter to point to the file. So:

% drizzle in='*' out=mosaic scale zero correct='drizzle.dat'

would read the corrections in from the file drizzle.dat. MAKEMOS has the ability to generate this file, although it should be noted that it does so in the same manner as DRIZZLE finds the corrections, so there is no advantage in doing it in two steps like this; the facility is provided for users who wish to normalise their frames very accurately.

A full description of DRIZZLE is given in appendix §. Since it does its own resampling, the remarks about the units of the Current coordinate systems made about TRANNDF apply here -- see the section on resampling.