National Radio
Astronomy Observatory

5.5 Combined Single Dish and Interferometric Imaging (feather)

The term “feathering” is used in radio imaging to describe how to combine or “feather” two images together by forming a weighted sum of their Fourier transforms in the (gridded) uv-plane. Intermediate size scales are down-weighted to give interferometer resolution while preserving single-dish total flux density.

The feathering technique does the following:

1. The single-dish and interferometer images are Fourier transformed.
2. The beam from the single-dish image is Fourier transformed (FTSDB(u,v)), (alternatively, one can specify some smaller portion of the single dish aperture, which corresponds to a wider beam).
3. The Fourier transform of the interferometer image is multiplied by (1 -FTSDB(u,v)). This basically down weights the shorter spacing data from the interferometer image.
4. The Fourier transform of the single-dish image is scaled by the volume ratio of the interferometer restoring beam to the single dish beam.
5. The results from 3 and 4 are added and Fourier transformed back to the image plane.

The term feathering derives from the tapering or down-weighting of the data in this technique; the overlapping, shorter spacing data from the deconvolved interferometer image is weighted down compared to the single dish image while the overlapping, longer spacing data from the single-dish are weighted down compared to the interferometer image.

The tapering uses the transform of the low resolution point spread function. This can be specified as an input image or the appropriate telescope beam for the single-dish. The point spread function for a single dish image may also be calculated using clean.

Advice: Note that if you are feathering large images, be advised to have the number of pixels along the X and Y axes to be composite numbers and definitely not prime numbers. In general FFTs work much faster on even and composite numbers. You may use subimage function of the image tool to trim the number of pixels to something desirable.

The inputs for feather are:

The single-dish data cube is specified by the lowres and the interferometric data cube by the highres keyword. The combined, feathered output cube name is given by the imagename parameter. sdfactor can be used to adjust the flux calibration of the images. Since single-dish processing typically involves the fit of a baseline level, it might be the one with the most uncertain calibration and sdfactor will multiply with the single-dish image values for any needed correction.

When showplot=True, a GUI pops up that displays the single dish and interferometric weighting functions in the uv-domain as a function of uv-distance.

Note that the only inputs are for images and feather will attempt to regrid the images to a common shape, ie. pixel size, pixel numbers, and spectral channels. feather does not do any deconvolution but combines presumably deconvolved images after the fact. This implies that the short spacings extrapolated by the deconvolution process will be those that are down-weighted the most. The single dish image must have a well-defined beam shape and the correct flux units for a model image (Jy/beam instead of Jy/pixel) so use the tasks imhead and immath first to convert if needed.

Starting with a cleaned synthesis image and a low resolution image from a single dish telescope, the following example shows how they can be feathered:

More information about CASA may be found at the CASA web page

Copyright © 2010 Associated Universities Inc., Washington, D.C.

This code is available under the terms of the GNU General Public Lincense