Frequency dispersion of a Fabry — Perot interferometer with a small distance between the mirrors

A study is reported of the influence of the frequency instability of a light source on a Fabry — Perot interferometer designed for measuring small displacements. A reduction in the interferometer base l reduces the dispersion, but only up to a certain limit corresponding to l ≈ (0.5 — 1)λ. For dielectric mirrors this limit is related to the intrinsic dispersion of the mirrors, which is independent of l and which corresponds approximately to l_mirr ≈ 0.3λ. Silver mirrors are characterised by l_mirr ≈ 0, but the useful working range begins from l ≥ 0.4λ. The cases of a metal mirror used in combination with a ‘detuned’ dielectric mirror and of resonant mirrors in a dispersion-free Fabry — Perot interferometer are discussed.