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Up: 2. The interferometer principles
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Figure 2.4:
2-element heterodyne interferometer with delay tracking
after frequency conversion
![\resizebox{12.0cm}{!}{\includegraphics[angle=270]{sg1f4.eps}}](img228.gif) |
To compensate for the geometrical delay variations, delay lines
with mirrors (as in optics...) would be completely impractical given
the required size of the mirrors. The compensating delay is thus performed
electronically after one (or several) frequency
conversion(s), as illustrated in Fig.2.4. This can be implemented
either by switching cables with different lengths, or in a more sophisticated
way, by using shift memories after digital sampling of the signal in the
correlator. Apart for a few details (see R.Lucas lecture), the principle
remains identical.
In the case presented in Fig.2.4, for USB conversion, the
phase changes of the input signals before reaching the correlator are
Introducing
as the delay tracking error,
the correlator output is
|
r = |
![$\displaystyle A_o \vert V\vert \cos(\Phi_1 - \Phi_2 - \Phi_V)$](img234.gif) |
|
USB |
r = |
![$\displaystyle A_o \vert V\vert \cos(2\pi(\nu_{LO}\tau_g + \nu_{IF}\Delta\tau) - \Phi_V -\Phi_{LO})$](img235.gif) |
|
LSB |
r = |
![$\displaystyle A_o \vert V\vert \cos(2\pi(\nu_{LO}\tau_g - \nu_{IF}\Delta\tau) - \Phi_V -\Phi_{LO})$](img236.gif) |
(2.25) |
When the two sidebands are superposed,
DSB |
r = |
![$\displaystyle 2 A_o \vert V\vert \cos(2\pi(\nu_{LO}\tau_g - \Phi_V - \Phi_{LO}))
\cos(2\pi\nu_{IF}\Delta\tau)$](img237.gif) |
(2.26) |
i.e. the amplitude is modulated by the delay tracking error. The tolerance can
be exceedingly small. For example, at Plateau de Bure, the IF frequency
is 3 GHz, and a 1 % loss is obtained as soon as the delay tracking error would
be 7.5 picoseconds, i.e. a geometrical shift of 2.2 mm only. Due to Earth rotation,
the geometrical delay changes by such an amount in 0.1 s for a 300 m baseline.
Hence, delay tracking would have to be done quite fast to avoid sensitivity losses.
To avoid this problem, it is common to use sideband separation.
The delay tracking error should then be kept small compared to the bandwidth
of each spectral channel,
, and the delay can then
be adjusted much less frequently.
Next: 2.4 Fringe Stopping and
Up: 2. The interferometer principles
Previous: 2.2.2 Finite Bandwidth
S.Guilloteau
2000-01-19