Optimizing dielectric mirrors for scanning Fabry Perot interferometers with constant spectral resolution

Both the spectral resolution and the free spectral range of a scanning Fabry-Perot interferometer at any particular wavelength are functions of the interference order, the reflectance and the phase-dispersion of the cavity's mirrors. It is generally desirable to design the mirror coatings to minimize the phase dispersion. This approach reduces the number of blocking-filters required to suppress multiple orders. It also avoids undesirable order overlap. However, there will always be some phase-dispersion present in the mirror coating design. In an instrument where a constant spectral resolution is required over the tuning range, it is desirable to optimize the combination of reflectance and the remaining phase dispersion to produce the required spectral resolution value. This paper describes a suitable optimization method and provides some numerical results.