LWS spectra of off-axis point sources or of extended sources show fringing.
In wave-
number space, these fringes are cosinusoidal with a fixed phase and a constant
period
of 3.6 cm
, independent of the detector channel. This leads us to
suppose
that they arise from within the instrument and are caused by the interference
of two
beams arriving at the detectors along paths which have a fixed difference in
length.
Some examples of fringing are show in figure 3.
If our interpretation of the origin of fringing is correct, the output
spectrum 
of a single extended or off-centre source is a
modulation of the input spectrum 
:
where 
is a function of the extent of the source or the amount by
which it is off-axis, and 
is unity. The process of de-fringing
consists of estimating the modulating term and dividing the observed
spectrum by it. A more complicated case consists of a point (or very modestly
extended) source with spectrum 
embedded in a field of
extended emission with spectrum 
. In this case, the
output spectrum is of the form:
In ths case, although there are fringes in the spectrum, the spectrum of the source of interest is not itself intrinsically fringed. The procedure for de-fringing in this case is to subtract the spectrum of the extended source, estimated from the off-source measurement. More generally, it may be possible to subtract the off-source spectrum and then remove remaining fringes intrinsic to the source of interest.
At the shortest wavelengths, the period of the fringe in wavelength space is comparable with the grating resolution element, making the detection of lines more difficult. Fringing of significant amplitude in these detectors only occurs in the case of bright sources off axis, however.
Note that the effect of fringing is present in both grating and Fabry-Perot spectra of extended or off-axis sources.
