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Statistics

It is worth noting that while the noise in the real and imaginary parts of the visibilities follows gaussian statistics, with a null expected value, the amplitude and phase do not, especially at low signal-to-noise. The amplitude in particular is by definition positively biased, i.e. has a non-null expected value even in the absence of signal.

Figure 1: Probability distribution for the amplitude (Top) and real part (Middle) of the visibilities for various signal-to-noise ratio (0,1,2,3,5,10). Adapted from Wrobel and Walker (1999). Bottom: Expected value for the amplitude as a function of signal strength (in unit of $ \sigma $ ) for the amplitude (plain curve) and real part (dashed curve).
Figure 1 shows the probability distribution for the amplitude and real part of the visibilities for various signal-to-noise ratios and compares the expected values for both quantities. Figure 2 shows the probability distribution for the phase. It follows that at low signal-to-noise a detection is more easily seen on the phase than on the amplitude.

Figure 2: Probability distribution for the phase of the visibilites for various signal-to-noise ratio (0,1,2,3,5). Adapted from Wrobel and Walker (1999).


next up previous contents index
Next: Averaging Up: Amplitude and phase Previous: Closure relationships   Contents   Index
Gildas manager 2022-01-17