Till now we had assumed that the radiation from the source was
monochromatic. Let us now consider the more realistic case of
quasi-monochromatic radiation, i.e. the radiation spectrum^{4.4} contains
all frequencies in a band around , with
small compared to . If the radiation at some frequency arrives
in phase at the two antennas in the interferometer, the radiation at
some adjacent frequencies will arrive out of phase, and if
is large enough, there will be frequencies at which the radiation
is actually 180 degrees out of phase. Intuitively hence one would expect
that averaging over all these frequencies would decrease the amplitude
of the fringe. More rigorously, we have

The quantity in square brackets, the sinc function, decreases
rapidly with increasing bandwidth. Hence as one increases the bandwidth
that is accepted by the telescope, the fringe amplitude decreases sharply.
This is called *fringe washing*. However, since in order to achieve
reasonable signal to noise ratio one would require to accept as wide a
bandwidth as possible^{4.5}, it is
necessary to find a way to average over
bandwidth without losing fringe amplitude. To understand how this could
be done, it is instructive to first look at what the fringe would be for
a spatially extended source.

Let the direction vector to some reference point on the source
be , and further assume that the source is small that it lies
entirely on the tangent plane to the sky at , i.e. that
the direction to any point on the source can be written as
,
.,
..
Then, from the van Cittert-Zernike theorem we have^{4.6}:

where , the complex *visibility* is defined as:

The information on the source size and structure is contained
entirely in , the factor
in
eqn. (4.3.4) only contains the information that the source rises
and sets as the earth rotates. Since this
is trivial and uninteresting, it can safely be suppressed. Conceptually,
the way one could suppress this information is to introduce along the
electrical signal path of antenna an instrumental delay which
is equal to . Then we will have
, i.e. the fast fringe oscillation has been suppressed. One
can then average over frequency and not suffer from fringe washing.
Since changes with time as the source rises
and sets, will also have to be continuously adjusted. This
adjustment of is called *delay tracking*. In most existing
interferometers however, the process of preventing fringe washing
is slightly more complicated than the conceptual scheme described
above. The complication arises because delay tracking is usually
done digitally in the baseband, i.e. after the whole chain of frequency
translation operations described in Chapter 3.
The geometric delay is however suffered by the incoming radiation,
which is at the RF frequency.

- ... spectrum
^{4.4} - Radiation from astrophysical sources is inherently broadband. Radio telescopes however have narrow band filters which accept only a small part of the spectrum of the infalling radiation.
- ... possible
^{4.5} - See Chapter 5
- ... have
^{4.6} - apart from some constant factor related to the gain of the antennas which we have been ignoring throughout.