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In the upcoming decades, one of the primary objectives in exoplanet scienceis to search for habitable planets and signs of extraterrestrial life in theuniverse. Signs of life can be indicated by thermal-dynamical imbalance interrestrial planet atmospheres. O$_2$ and CH$_4$ in the modern Earth'satmosphere are such signs, commonly termed biosignatures. These biosignaturesin exoplanetary atmospheres can potentially be detectable through high-contrastimaging instruments on future extremely large telescopes (ELTs). To quantifythe signal-to-noise ($S/N$) ratio with ELTs, we select up to 10 nearby rockyplanets and simulate medium resolution (R $\sim$ 1000) direct imaging of theseplanets using the Mid-infrared ELT Imager and Spectrograph (ELT/METIS, 3-5.6$\mu$m) and the High Angular Resolution Monolithic Optical and Near-infraredIntegral field spectrograph (ELT/HARMONI, 0.5-2.45 $\mu$m). We calculate the$S/N$ for the detection of biosignatures including CH$_4$, O$_2$, H$_2$O, andCO$_2$. Our results show that GJ 887~b has the highest detection $S/N$ forbiosignatures and Proxima Cen b exhibits the only detectable CO$_2$ among thetargets for ELT/METIS direct imaging. We also investigate the TRAPPIST-1system, the archetype of nearby transiting rocky planet systems, and comparethe biosignature detection $S/N$ of transit spectroscopy with JWST versusdirect spectroscopy with ELT/HARMONI. Our findings indicate JWST is moresuitable for detecting and characterizing the atmospheres of transiting planetsystems such as TRAPPIST-1 that are relatively further away and have smallerangular separations than more nearby non-transiting planets.

Detecting Biosignatures in Nearby Rocky Exoplanets using High-Contrast Imaging and Medium-Resolution Spectroscopy with Extremely Large Telescope