In an infrared (IR) single-mode fibre-linked optical telescope array,
not only the spatial but also the spectral resolution of a star can be
simultaneously obtained as long as the fibre arms are stretched to ge
nerate the optical path difference (OPD) modulation. This imaging tech
nique is called IR single-mode (SM) all-fibre optic (AFO) double Fouri
er interferometry (DFI). The fibre-stretching operation will inevitabl
y introduce a chromatic dispersion problem and make the OPD wavelength
dependent. In this paper, a point source response expression for the
IR SM AFO DFI is first established. Accordingly, the recovered mutual
spectral density (MSD) is deduced. One of the dispersion effects on MS
D is a wavenumber shift; this and other effects on MSD are discussed.
Then, we establish the final map expression for a point source and dis
cuss the dispersion effects on it. One of these effects is a shift of
the image position. Finally, we discuss the effects of the first-order
approximation of the OPD. To reduce these effects, a method of dividi
ng the whole spectral band into subbands is pointed out and discussed.