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This information is in the category of general knowledge at a layman level. It aims to introduce 3 key ideas involved in radio interferometry cross-correlation for achieving better visibility. Though the info is not for specialists, some mathematical background is needed to understand the concepts involved.
Angular Resolution
The aim is to improve angular resolution Ó¨ of antenna detection for a specific wavelength λ (or frequency) of signals from the sky. The equations show that we can reduce Ó¨ easily by 1220 times by placing a 2nd antenna at a distance (B = 1000D) apart from the 1st antenna.
o For a single antenna of diameter D, Ó¨ ~ 1.22 λ / D
o For a pair of antennas of baseline B apart, Ó¨ ~ λ / B
Noise to Signal Ratio
The aim is to reduce noise so that the signal measured becomes more accurate. This is achieved by multiplying the signals from an antenna pair because signal will correlate whereas noise will not.
o Conjugate has the same real part but reversed sign of the imaginary part. Taking the conjugate of f (the symbol is f *) ensures that aligned peaks or aligned troughs with imaginary components will contribute positively to the integral. Tau is time and t is time delay of wave reaching the other antenna.
o Do the same for other pairs (cross-correlation) and integrate within a time period for exposure before rotation of the Earth introduces smearing.
Convert Signal Visibility to Human Brightness Perception
This is a Fast Fourier Transform: I (l,m) = ∫ V (u,v) e i2π(ul+vm) du dv where
o I is brightness intensity & l, m are angular coordinates of brightness
o V is visibility in wavelength units, and u, v are spatial coordinates of wave
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