Applied Signal Processing

1. Aperture Synthesis using The Westerbork Synthesis Radio Telescope.

The Westerbork Synthesis Radio Telescope (WSRT) in Drenthe is one of the most important radio telescopes in the world. It is an interferometer, working in the radio regime, consisting of 14 radio telescopes. The 14 telescopes sample the spatial Fourier Transform of the brightness distribution of radio emission in the sky using the 91 possible combinations of the 14 telescopes as samplers. Each telescope pair (interferometer) samples certain spatial frequencies of the sky brightness distribution. The larger the telescope separation the smaller the angular scale in the sky. The distribution of telescope separations (baselines) is such that all spatial frequencies from the smalles to the longest baseline are covered. Since the number of baseline lengths is limited and discrete (in practice the lenghts run from 36m to 2844m in steps of 72 meter) and hence the telescope response to a unit source (the point spread function or impulse response funtion, usually called: the beam) exhibits sidelobes and the observed image is the convolution of the sky brighness distribution (the input signal) with the beam (impulse response). Before proper analysis of the radio image is possible one needs to deconvolve the observed image and correct for the telescope response.

The aim of this project is to study the most commonly used deconvolution method CLEAN. This is an iterative method which decomposes a radio image into a series of delta functions representing the sky brightness distribution. A mathematical description of this method can be found in papers by J. Hogbom and U.J.Schwarz .
More information about the CLEAN algorithm can be found at http://www.cv.nrao.edu/~abridle/deconvol/node7.html

There are two images, one with only neutral hydrogen line emission and one with neutral hydrogen line plus continuum emission. Use the CLEAN routine in GIPSY or MIRIAD to deconvolve the images (alternatively you may consider writing your own CLEAN algorithm in python or c; this actually will be more instructive as you have to understand the CLEAN algorithm and make it work, so it will earn you some bonus points). Describe the CLEAN method and study how the results depends on the specification of the area within which the delta functions are found and the so-called loop gain, i.e. the fraction of each delta function that is subtracted from the input image (the observed image) in each iteration. In the case of the line plus continuum image multiple areas can be used. Compare and discuss the effect of single versus multiple areas.

Radio images in FITS format can be downloaded following these links:

n4565.bm.fits.gz (the beam),
n4565.ch83.fits.gz (the line image),
n4565.ch83.cs.fits.gz (the line + continuum image),

Information about interferometry can be found at: Astronomical Optical Interferometry, http://en.wikipedia.org/wiki/Astronomical_interferometer, which also contains a list of useful references.
See also the principles of synthesis imaging:   http://scienceworld.wolfram.com/physics/SynthesisImaging.html
and the article by D. Gary:  http://web.njit.edu/~gary/728/Lecture6.html