Project Cyclops, A Design... - Department of Earth and Planetary ...

APPENDIX
N
SYSTEM
CALIBRATION
The phase of the signal from a given antenna, as it
reaches the data processing center, depends on (1) the
geometrical time delay caused by the orientation of the
array with respect to the source, and (2) several other
effects that may be regarded as errors, including unequal
amounts of refraction in the atmosphere above the
various antenna and unequal phase shifts in the various
amplifiers, transmission lines, and other components.
These errors must be eliminated, insofar as possible,
which means that each antenna channel must be
phase-calibrated at regular intervals.
The most practical method of phase calibration
would appear to involve well-known cosmic radio sources.
One of the several antennas in the array is chosen as the
reference, with which all others are compared. A
correlator, that is, a multiplier capable of accommodating
the IF bandwidth, is connected between the reference
antenna and each antenna to be calibrated. The
output of this correlator is given by
in
D
),o
8
d
H
F --
which
27rD
)[O
[_ - sin 6 sin d - cos 8 cos d cos (H-
= distance between antennas
= wavelength at the center of the RF passband
= incidental phase shift in the electronic system, in
fractional
wavelength
= declination of the cosmic radio source
= declination at which the baseline interests the
celestial
sphere
= hour-angle of the cosmic source
h)]
= hour-angle at which the baseline interests the
celestial
sphere
Presumably H and 5 are known precisely; H increases
uniformly with time; therefore, the "fringe function"F
oscillates with time as the source moves with respect to
the baseline between the antennas.
The calibration procedure would be to observe the
source for several minutes and to store th_ output of the
correlator. From assumed values of the parameters in the
above formula a synthetic fringe function is computed
and compared with the observed function. The unknown
parameters, say _, h and d, are varied until the
mean-square difference between the observed and the
computed fringe function is minimized. The resulting
values of the parameters constitute the calibration
factors of the system. Atmospheric refraction effects
will be included in the parameter _j.
Five minutes of observation would probably be
required to calibrate one channel. A number of channels
could be calibrated simultaneously if a sufficient computing
capacity were available. The permissible interval
between calibrations will depend on the mechanical and
electronic stability of the system, but will probably be
on the order of days.
Atmospheric effects will probably vary much more
rapidly than outlined here; except under unusual circumstances,
however, it is not expected that atmospheric
refraction will degrade the array performance seriously.
Small-scale atmospheric inhomogeneity will increase the
RMS phase error and will therefore decrease the gain of
the array, while large-scale inhomogeneity will cause
beam-steering errors. Experience with current radio-astronomical
interferometers suggests that phase errors as
large as 30 ° may occasionally occur over baselines of a
few km at 10-cm wavelength. This effect varies strongly
with weather and with season at a given site, and it is
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