Processing Dithered Data
Dithering: The Basics
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.
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
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
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
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
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
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
of the 1997 HST Calibration Workshop .
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 .
The Drizzle code is now publicly available.
To obtain a copy of Drizzle you must
(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
As users are likely to find the entire dither package useful,
we encourage you to obtain STSDAS 2.0.1 from the
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
Drizzle has been submitted to
can be electronically
retrieved from the
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.
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
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
The articles are formatted for
A4 paper; therefore, if you decide to print out the articles, and
standard American 8.5x11 paper, be sure to
use the "shrink to fit" option of Acrobat Reader when printing.
This page accessed
times since September 15, 1996.
fruchter @ stsci.edu