As described in Chapter 4, the response of an
interferometer to quasi-monochromatic radiation from a point source
located at the phase center is given by

(10.1.1) |

For a source located at an angle
, for small ,
. Since fringe stopping compensates for ,
the response of the interferometer for a source away
from the phase center is
where
. If the phase center is
shifted by equivalent of , the interferometer will pick up
an extra phase of and the response will be sinusoidal instead
of co-sinusoidal. Hence, an interferometer responds to both even and
odd part of the brightness distribution. Interferometer response can
then be written in complex notation as

(10.1.2) |

as the complex response of a two element interferometer for a point source of unit flux located away from the phase center given by the direction .

Usually the phase center coincides with the center of the field being
tracked by all the antennas. Let the normalized power reception
patter of antennas (which are assumed to be identical) at a particular
frequency be
and the surface brightness of an
extended source be represented by
. The response of
the interferometer to a point source located away from
the phase center would then be
. For an
extended source with a continuous surface brightness distribution, the
response is given by

in the above equation is the direction of the elemental source flux relative to the pointing center. then has the interpretation of spatial frequency and represents the 1D spatial frequency spectrum of the source.