An unsuitable choice of the IF bandwidth 
may lead
(a) to irrecoverable distortion of the image by chromatic aberration
if the bandwidth is too great or (b) to unacceptably low
sensitivity if it is too small.
As discussed in detail by Bridle & Schwab
(1989), images made with finite bandwidth are
degraded away from the delay tracking center in a way that can be
described as a radial smearing by a position-dependent distortion
function. The width of the distortion function grows with distance
from the delay tracking center. The effect can be thought of as a
reduction in amplitude, and a simultaneous broadening, of the apparent
point source response.
Bridle & Schwab
derive expressions for the amplitude reduction
(where I is the observed amplitude and 
is the amplitude in the small-bandwidth limit) for three combinations
of bandpass shapes and u-v tapering. All three are functions of the
simple dimensionless parameter 
, i.e. of the fractional bandwidth times the angle from
the delay tracking center measured in synthesized half-power
beamwidths:
for a square bandpass and u-v
coverage with no tapering, Si being the standard sine integral,
( 
),
for a square bandpass with circular Gaussian u-v
tapering, erf being the error function, and
The first step in choosing the IF bandwidth for continuum work is to
ask over what field radius 
(arcsec) you want to limit
chromatic aberration to a given reduction of amplitude 
of the point source response. Then find the corresponding maximum
value 
of the normalized parameter 
from whichever
expression for best approximates your instrument. The
maximum allowable IF bandwidth 
(MHz) consistent with these
constraints is then given by
where 
is your observing frequency in MHz and 
is the
half-power beamwidth in arcsec at which you expect to make your
images. Unless you are prepared to relax your smearing/attenuation
criterion slightly, select the closest allowed bandwidth that is
narrower than . If you are prepared to relax it, choose the
closest wider bandwidth.
Your choice of may be determined by the need to image
an extended structure with minimal distortion, or by the need to
include a strong confusing source in the minimally-distorted field of
view. The latter need arises because you may wish to subtract or
deconvolve a confusing source's sidelobes from the interesting region.
The value of will always be greater than, or about equal to,
the value of 
used earlier when selecting the range of
baselines. In general, choose the delay and pointing center to
minimize the required for your observations. When using a
wide field to include a confusing source, consider displacing the
delay center away from the target towards the confusing source. This
will avoid the use of unnecessarily narrow bandwidths (and thus of
unnecessarily low sensitivity). If the field is dominated by
a strong point source (more than ten times brighter than other
structure), this source should be placed near the delay center
and pointing center when high dynamic range is required. This
strategy will minimize the total distortion of the image resulting
from bandwidth, pointing, averaging time and computational effects
(such as u-v truncation) involving the strong source (for more
details, see Clark 1981).
For point source detection experiments the above criteria will
normally select the widest available bandwidth, unless the search
position is exceptionally inaccurate or the field is known to be highly
confused. Chromatic aberration affects observing strategy less
critically at higher frequencies for several practical
reasons--fractional bandwidths ( 
) are often smaller;
the usable field of view is limited by the primary HPBW of the antennas
for the narrower fractional bandwidths; receiving systems are noisier
and antennas are less efficient (so sensitivity, not distortion, limits
image quality).
When deciding on the value of that is appropriate for
an image of an extended source, consider the detectability of the
extended emission at the resolution you will be using for your
images (see Resolution, Baseline Range and Observing
Frequency and
Total Integration Time). There
is no point ensuring that extended structure is not smeared radially
by the bandwidth effect if low signal-to-noise on the same structure
introduces uncertainties larger than the bandwidth distortions. As
the signal-to-noise on extended emission itself depends on the choice
of IF bandwidth, this calculation may need to be iterated until a
suitable compromise is reached.
