High Resolution Spectroscopy using Fabry Perot Intereferometer Arrays: An Application to Searches for O${}_2$ in Exoplanetary Atmospheres

We present a novel implementation for extremely high resolution spectroscopy using custom-designed Fabry Perot Interferometer (FPI) arrays. For a given telescope aperture at the seeing limited case, these arrays can achieve resolutions well in excess of $\mathrm{R}\sim {10}^5$ using optical elements orders of magnitude smaller in size than standard echelle spectrographs of similar resolution. We apply this method specifically to the search for molecular oxygen in exoplanetary atmospheres using the ${\mathrm{O}}_2$ A-band at 0.76 ${\rm \mu m}$,andshowhowaFPIarraycomposedof$\sim10$ etalons with parameters optimized for this science case can record $\mathrm{R}=3-5\cdot {10}^5$ spectra covering the full ${\mathrm{O}}_2$ A-band. Using simulated observations of the atmosphere of a transiting nearby Earth-like planet, we show how observations with a FPI array coupled to a long-slit spectrograph can reduce the number of transit observations needed to produce a $3\sigma$ detection of ${\rm O_2}$by$\sim30%$comparedtoobservationswitha${\rm R=10^5}$ echelle spectrograph. This, in turn, leads to a decrease in an observing program duration of several years. The number of transits needed for a $3\sigma$ detection can be further reduced by increasing the efficiency of FPI arrays using dualons (an etalon with a buried reflective layer), and by coupling the FPI array to a dedicated spectrograph optimized for the ${\mathrm{O}}_2$ A-band.