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Processing Dithered Data

Contents

Dithering: The Basics

The STSDAS Dither Package

Drizzle Code Release

The Dither II Package

Further Sources of Information

Drizzle: The Poster Paper

Dithering: The Basics

The Problem

Although the optics of WFPC2 now provide a superb PSF, the detectors at the focal plane severely undersample the image. This problem is most severe on the three WF chips, where the width of a pixel equals the FWHM of the optics in the the near-infrared, and greatly exceeds it in the blue. While much high spatial frequency information in the image is permanently destroyed by smearing with the response of the "fat" pixels, the quality of the image can nevertheless be greatly improved by combining sub-pixel dithered images. In sub-pixel dithering, the pointing of the telescope is moved by small, non-integral pixel amounts between exposures. Each of the pixels from the different exposures can then 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. If the dithers are particularly well-placed, one can simply interlace the pixels from the images on a finer grid, but in practice imperfect offsets, and the effect of the geometric distortion on offsets as small as one arcsecond, can make interlacing impossible.

Earlier Solutions

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 on a finer grid. However, it is difficult to use shift-and-add in the presence of missing data (e.g. from cosmic-rays) and geometric distortion. Furthermore, shift-and-add again convolves the image with the "fat" pixel, causing an additional loss of resolution. In the presence of small shifts, where geometric distortion is not significant, one can also use Richardson-Lucy Bayesian image reconstruction, which is incorporated in STSDAS through the task acoadd, written by Richard Hook and Leon Lucy. However, in addition to being unable to handle large dithers, the present implementation of this technique is limited by typical computing capabilities to combining either small regions of many images, or the entire image of only a few dithers. Furthermore, the present task cannot accomodate either geometric distortion or the changing shape of the PSF across the WFPC field of view. And this technique, like all non-linear techniques, produces final images whose noise properties are difficult to quantify.

Drizzle

For purposes of combining the dithered images of the Hubble Deep Field, Richard Hook and I developed a new technique for the linear combination of images known formally as variable-pixel linear reconstruction and informally as drizzling. Drizzling can be thought of as a continuous set of linear functions that vary smoothly from the optimum linear combination technique -- interlacing -- to the old-standby, shift-and-add. The degree to which one must depart from interlacing and move towards shift-and-add is determined by the nature of the input data. Drizzling naturally handles both missing data and geometric distortion, and can largely remove the effect on photometry produced by the geometric distortion of the WFPC camera. Drizzle runs under the NOAO image processing software IRAF. It is available directly from this site, or now as part of the IRAF package for HST image reduction, STSDAS.

Release of Drizzle1.2

A new version of Drizzle is being made available to users as of late-March 1998. Drizzle 1.2 (and the corresponding version of Blot, v0.6) contain several minor changes from previous versions. In particular, the handling of the input and output counts normalization (i.e. whether the images are in counts or counts per second) is now simplified, and the World Coordinate System transormation is now somewhat more general, in preparation for the incorporation of geometric distortion removal from NICMOS images. However, Drizzle v1.1 and Blot v0.6 are now also available in the Dither package of STSDAS 2.0.1, which was released in late March of 1998. You may therefore wish to have your system administrator install this new version of STSDAS rather than retrieving Drizzle separately.

We expect to soon release some beta test versions of IRAF CL scripts which can be used in conjunction with blot to remove cosmic rays from dithered images. In the longer term, we plan to release a new version of Drizzle that will make the drizzling of large mosaics simpler, faster and less memory intensive.

Figure: On the left a single 2400s F814W WF2 image taken from the HST archive. On the right, the drizzled combination of twelve such images, each taken at a different dither position.

The STSDAS Dither Package

The Drizzle task has been incorporated into a larger package of STSDAS tasks related to dithering. The package is called "dither". In addition to Drizzle, the dither package contains tasks designed to help one align images taken at different pointings or rotation angles. A paper on the dither package can be found in the Proceedings of the 1997 HST Calibration Workshop . Both a postscript and a PDF version are available. The PDF (Portable Document Format) file is far smaller than the postscript version, and so is preferable for transfer over the web. If your computer does not have a PDF reader, you can download Adobe Acrobat from the inventors of PDF, Adobe .

Drizzle Code Release

The Drizzle code is now publicly available. To obtain a copy of Drizzle you must register (don't worry: it's quick, easy and kids love it). However, Drizzle and Blot are now incorporated int STSDAS V2.0, as part of the Dither package (discussed in the Calibration Workshop article described in the previous section. As users are likely to find the entire dither package useful, we encourage you to obtain STSDAS 2.0.1 from the STSDAS homepage.

The Dither II Package

A "beta" release of new tasks to remove cosmic rays from dithered data is now available. These tasks, which are in a new IRAF package called Dither II, can be obtained by using the Drizzle registration described in the section above (if you have already registered for Drizzle you should have received an email with instructions for retrieving Dither II). A draft paper describing the use of the tasks in the Dither and DitherII packages to remove cosmic rays from singly dithered data is included in the release. However, those wishing to first examine the paper can click here.

Further Documention

A paper on Drizzle has been submitted to the PASP. It can be electronically retrieved from the astro-ph archives. You can also read an on-line poster paper on drizzling. Although we refer to this as an "on-line poster paper", it contains much of the contents of the full paper. A older conference proceedings version, written for the SPIE, is also available from astro-ph. A discussion of drizzling is also avalailable on the Hubble Deep Field web pages. While this may be of interest to people examining the HDF images, it is quite dated in its description of Drizzle.

Additional information on the analysis of dithered data is provided by the HST Data Handbook. Answers to many common questions about dithering can be found on the WFPC2 FAQ page.

Much useful information on the theory behind dithering and on dithering strategies can also be found in articles written by Hans-Martin Adorf and Richard Hook for the ST-ECF newsletter. The articles are formatted for A4 paper; therefore, if you decide to print out the articles, and are using standard American 8.5x11 paper, be sure to use the "shrink to fit" option of Acrobat Reader when printing.

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