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With the Earth rotation, the cosine term of Eq.2.22 modulates
the correlator output quasi-sinusoidaly with a natural fringe rate of
which is of order of 10 Hz for b
m baselines and
GHz. Note that the fringe rate only depends on the
effective angular resolution (
is
the angular resolution,
in the above example).
The fringe rate is somewhat too high for simple digital sampling
of the visibility. An exception is VLBI (because there is no other
choice), although the resolutions are
mas. The usual
technique is to modulate the phase of the local oscillator
such that
at
any given time. Then Eq.2.25 is reduced to
![$\displaystyle r_r = A_o \vert V\vert {\rm cos}(\pm 2 \pi \nu_{IF}\Delta\tau - \Phi_V)$](img355.png) |
(2.28) |
(with the + sign for USB conversion, and the - sign for LSB
conversion), is a slowly varying output, which would be constant
for a point source at the reference position (or delay tracking
center). This process is called Fringe Stopping, since it
stops the fringe pattern modulation.
After fringe stopping, we can no longer measure the amplitude
and the phase
separately, since
is now a constant for a point source. A modulation
of the delay tracking could be used to separate
and
. Instead, it is
more convenient and effective to use a second correlator, with one signal phase
shifted by
. Its output is
![$\displaystyle r_i = A_o \vert V\vert {\rm sin}(\pm 2 \pi \nu_{IF}\Delta\tau - \Phi_V)$](img360.png) |
(2.29) |
With both correlators, we measure directly the real
and
imaginary
parts of the complex visibility
. The device is
thus called a ``complex'' correlator.
Note:
From Eq.2.28, a delay tracking error
appears as
a phase slope as a function of frequency, with
![$\displaystyle \Phi(\nu_{IF}) = \pm 2 \pi \nu_{IF} \Delta\tau$](img363.png) |
(2.30) |
Next: 2.5 Fourier Transform and
Up: 2. Millimetre Interferometers
Previous: 2.3 Delay Tracking and
  Contents
Anne Dutrey