Fabry–Perot Resonances at Small Fresnel Numbers

A theory of Fabry-Perot resonances designed to be useful at small Fresnel numbers is given. This theory is applied to the case where the interferometer mirrors are of arbitrary curvature and have circular apertures. Asymptotic formulas are derived for the diffraction output and phase shifts in the limit of small Fresnel numbers. These formulas demonstrate the mode discrimination properties of the interferometers when operated in this regime. Numerical results are presented covering a wider range of Fresnel numbers.