  It is known that spectral properties of the Fabry - Perot interferometer
(FPI) depend on the spatial characteristics of the incident radiation. This
paper proposes a general method for taking this dependence into account, based
on the decomposition of the incident field into the angular spectrum of plane
waves, which are the FPI eigenfunctions. In the scalar approximation, the
angular-frequency transfer function and the point-spread function (Green
function) of the FPI are calculated, which enables to relate the spatial
coherence functions of the incident and transmitted radiation and to derive an
expression for the output intensity I(r, k) and for the integral transmittance
P(k) depending on the wavenumber of the incident monochromatic radiation k. In
the resulting expressions, I(r, k) is completely determined by the Fourier
transform of the input coherence function, and P(k) is determined by the
angular power spectrum (APS) of the incident radiation. For beams of small
divergence and high-quality FPIs, simplified formulas have been obtained that
allow, in the first approximation, for the dependence of the FPI parameters on
the angle of incidence and on the radiation wavelength. Analysis of the
expressions obtained makes it possible to clarify an exact meaning of the
well-known regularities in the distortions of the FPI transmission band
associated with the incident beam deviation from the plane wave (shift to the
shortwave region, broadening, reduction of the maximum transmittance and the
appearance of asymmetry). As examples, calculations of the integral
transmittance for three types of APS, corresponding to Gaussian and conical
beams, and the output intensity distribution I(r, k) for the input beam with a
Gaussian APS are performed. Results are consistent with other theoretical and
experimental works.
