We present the result of calculations to optimize the search for molecular oxygen (O2) in Earth analogs transiting around nearby, low-mass stars using ground-based, high-resolution, Doppler shift techniques. We investigate a series of parameters, namely spectral resolution, wavelength coverage of the observations, and sky coordinates and systemic velocity of the exoplanetary systems, to find the values that optimize detectability of O2. We find that increasing the spectral resolution of observations to R = 300,000 - 400,000 from the typical R ~ 100,000, more than doubles the average depth of O2 lines in planets with atmospheres similar to Earths. Resolutions higher than about 500,000 do not produce significant gains in the depths of the O2 lines. We confirm that observations in the O2 A-band are the most efficient except for M9V host stars, for which observations in the O2 NIR-band are more efficient. Combining observations in the O2 A, B, and NIR -bands can reduce the number of transits needed to produce a detection of O2 by about 1/3 in the case of white noise limited observations. However, that advantage disappears in the presence of typical levels of red noise. Therefore, combining observations in more than one band produces no significant gains versus observing only in the A-band, unless red-noise can be significantly reduced. Blending between the exoplanets O2 lines and telluric O2 lines is a known problem. We find that problem can be alleviated by increasing the resolution of the observations, and by giving preference to targets near the ecliptic.
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