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We present a novel implementation for extremely high resolution spectroscopyusing custom-designed Fabry Perot Interferometer (FPI) arrays. For a giventelescope aperture at the seeing limited case, these arrays can achieveresolutions well in excess of ${\rm R\sim10^5}$ using optical elements ordersof magnitude smaller in size than standard echelle spectrographs of similarresolution. We apply this method specifically to the search for molecularoxygen in exoplanetary atmospheres using the ${\rm O_2}$ A-band at 0.76 ${\rm\mu m}$, and show how a FPI array composed of $\sim10$ etalons with parametersoptimized for this science case can record ${\rm R=3-5\,\cdot10^5}$ spectracovering the full ${\rm O_2}$ A-band. Using simulated observations of theatmosphere of a transiting nearby Earth-like planet, we show how observationswith a FPI array coupled to a long-slit spectrograph can reduce the number oftransit observations needed to produce a ${\rm 3\sigma}$ detection of ${\rmO_2}$ by $\sim30\%$ compared to observations with a ${\rm R=10^5}$ echellespectrograph. This, in turn, leads to a decrease in an observing programduration of several years. The number of transits needed for a ${\rm 3\sigma}$detection can be further reduced by increasing the efficiency of FPI arraysusing dualons (an etalon with a buried reflective layer), and by coupling theFPI array to a dedicated spectrograph optimized for the ${\rm O_2}$ A-band.

High Resolution Spectroscopy using Fabry Perot Intereferometer Arrays: An Application to Searches for O$_{2}$ in Exoplanetary Atmospheres