A Drizzle Coadder for WIRE

1. Overview

The WIRE focal plane is badly undersampled with 15.5" pixels sampling a diffraction-limited beam 8-17" FWHM. This is a situation similar to that encountered with HST/WFPC2. Even with the PC, at short wavelengths a single PC pixel is considerably larger than the FWHM of the expected PSF. In order to combat this, Andy Fruchter and other at STScI have developed the "Drizzle" method of coadding images, taking advantage of the additional spatial information contained in individual frames which have been dithered by fractional number of pixels.

The inherent problem with a shift-and-add coadder like that implemented by the data pipeline is that it convolves the PSF with a top-hat function of the original pixel size, which in the case of WIRE is similar to the expected telescope performance. Drizzle eliminates this problem by reconstructing the data onto an arbitrarily fine spatial grid. Rather than shifting and adding the original pixels with interpolation, drizzle shrinks each pixel into a smaller footprint (called a "drop") and then places them onto the finely sampled reconstruction grid (hence the name "drizzle"). When the drop size is equal to the original pixel size, this is equivalent to shift-and-add. When the drop size is made extremely small, this reduces to interlacing. Drizzle has the added advantage that it can be used to coadd frames with any geometric relation, i.e. they can be shifted, rotated, or of different sizes and pixel scales. With the regularity of the WIRE data, however, this may not be particularly useful. Also, drizzle is known to be flux conserving.

2. Implementation

I have written a Drizzle coadder for use with WIRE data. It is a series of csh scripts that borrow heavily from Fruchter's code, pieces of IRAF, and several bits of homegrown IPAC software. Currently, the software

1. Scans the current directory for all WIRE data.
2. Derives approximate shifts from the image headers.
3. Computes more accurate shifts using cross-correlation and the initial shift values.
4. Drizzles the data onto a new grid whose shape is user-specified.

There is currently no cosmic-ray rejection.

3. Results

On the right is a simulated pipeline coadd of 40 data frames at 12um. On the left is the same data coadded with Drizzle using a 9.3" drop size and reconstructed onto a 5"/pixel grid.

Drizzle Coadder Pipeline Coadder

Fortunately the two look very similar! In practice one wants to minimize the "drop" size, since this minimizes image degradation due to convolution with the drop size. However, the minimum size of the drop is dictated by the diversity of sub-pixel image shifts available - a drop size smaller than a typical shift will result in data gaps in the reconstructed image. In reality the drop size must be made still larger in order to ensure a sufficiently high amount of data coverage. Similar arguments hold for the reconstructed pixel size. For 40 frames with the current dither pattern, drop sizes between 6-9" seem to provide adequate coverage. Given the achieved spatial resolution, the 5" pixel size seems to provide adequate sampling. Smaller drops may be used in the future with different dither patterns or more frames.

Results have not been as encouraging as I had hoped. The achieved FWHM at 12um is typically 18-19", which is larger by a factor of 2 than the diffraction limit, and only slightly better than the pipeline coadder. The apparent improvement in image resolution is mostly a result of resampling to a 5" grid; the resulting image is not as badly aliased as that produced by the pipeline. The mottled appearance of the background is a result of the actual noise being related to the spatial sampling of the dithered frames and the noise in the original pixels, which are now mostly decoupled from the physical pixels in the regridded image. The interpolation and large pixels used by the pipeline coadder smear this noise.

Update: I have now been working with Andy at STScI, and it appears that drizzle with sub-pixel dithering will not acheive much more than 19.5" at 12um. However, the images do look quite a bit better, with less correlated noise in the drizzle image. It now appears that a 7.73" pixel size and a small (0.01) pixel fraction is the best approach.

4. Performance

In order to test the performance of the source extractor on a drizzled image, I used 40 frames of simulated data at 12 microns. The pipeline coadder was used to generate a grand coadd, and the source extractor was applied in order to generate a basis for comparison.

The frames were then drizzled using a 7.73" pixel size and a 0.01 pixel fraction. The standalone version of DAOPHOT II was used to generate a new PSF for use in the source extraction. Wiredao was then run using the same input parameters as the original source extraction, only using the new PSF and estimate of the fwhm. The resulting source list was then matched against the truth list used to create the simuklated frames using the "match4" program.

As was anticipated from looking at the images, the results are nearly identical. This is not too surprising given then the coadder works in nearly the same manner as drizzle, but with a pixel fraction of 1. The postscript file linked immediately above gives detailed information on the completeness, reliability, and other interesting indicators of performance. The "600" frame is the drizzle coadd, while the "500" is the survey coadder. Ignore the 12 and 25 micron labels, they are placed there automatically by the "stplot2" program that generated this output.