| Zusammenfassung: | <p>The discovery and characterization of extrasolar planets is a leading frontier of science, which is limited by our ability to extract real astrophysical signals masked by systematic noise. In this Thesis I develop techniques for self-calibration in optical astronomy, in both imaging and photometry, applicable both to observations from the ground and for space telescopes, and apply these to searching for exoplanets. </p> <p>Kernel phase interferometry is a method for improving high angular resolution astronomical imaging by cancelling out the effects of the turbulent atmosphere. I derive a generalization, kernel amplitude, to correct also for the effects of scintillation, or twinkling. I go on to demonstrate kernel phase for the first time from the ground using the Palomar Hale 200-Inch Telescope, as a test case for the extreme adaptive optics instruments SPHERE and GPI.</p> <p>The <em>Kepler</em> satellite and its successor, the <em>K2</em> mission, have been crucial to our understanding both of exoplanets, and via asteroseismology, of stellar physics. The success of <em>K2</em> depends on correcting for its unstable pointing. Using semi-parametric Bayesian statistical models to overcome this issue, I report the discovery of 145 new transiting planet candidates in data from Campaigns 5 and 6 of the <em>K2</em> mission. Furthermore, with two novel techniques, 'smear' and 'halo' photometry, which dramatically extend the dynamic range of <em>Kepler</em> and <em>K2</em>, I recover light curves of bright stars that were previously too saturated to study, and definitively detect variability in the seven naked-eye stars in the Pleiades cluster. These new data analysis approaches enable the <em>K2</em> and TESS space missions to discover planets transiting the nearest and brightest stars, which will be ideal targets for the coming era of exoplanet characterization.</p>
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