A New Method for reconstructing Visibilities

One of the ways to do this involves fitting sinusoids to each cycle of the modulation profile, and shifting them by 90°, and this is done by hsi_calib_ev2vis.pro in the HESSI) SSW library. However, this program has certain drawbacks of its own, and it is important to create other methods which may mitigate these drawbacks. (Or at least move the perhaps inevitable failings to a different region of parameter space)..

A new method for reconstructing visibilities from modulation profiles is based on a surprising relationship between the Fourier transforms of the real and imaginary parts of the visibility due to a point source. For a point source, the Fourier components (I_n) of the imaginary part of the visibility are simple linear combinations of the two neighboring Fourier components (R_n) of the real part of the visibility:

Since an arbitrary source may be represented as a superposition of point sources, if the source is sufficiently compact (i.e. its extent is much less than the distance to the spin axis), the linear relationship still holds.

The plan of the new method is as follows:

• Perform an FFT on a suitably normalized count profile;
• Apply the linear filter derived from the above equation;
• Perform an inverse FFT, and return the imaginary part of the visibility.

The mathematics of this new technique is contained in the .ps or .pdf files:
new_vis_method.ps
new_vis_method.pdf