Diffraction-limited observations play an essential role in the study of extrasolar planets. In this talk, I will describe two new programs that exploit the benefits of adaptive optics when operating in tandem with the Doppler radial velocity method:
(1) The TRENDS high-contrast imaging survey is a dedicated follow-up program that targets stars known to exhibit long-term Doppler accelerations. We have detected numerous companions that are responsible for systematically "tugging" on their parent star. These objects promise to yield three-dimensional orbit information and precise dynamical masses. When combined with direct imaging spectroscopy, they may be used to explicitly calibrate theoretical atmospheric models. I will present recent results from TRENDS including: the discovery of a new benchmark brown-dwarf companion; and the first model-independent determination of the gas giant
(1 < m/M_J < 13) planet occurrence rate around M-stars from 0-20 AU.
(2) We are building the world's first diffraction-limited Doppler spectrometer at the University of Notre Dame astrophysics lab. "iLocater" will operate at near-infrared wavelengths and receive a well-corrected beam from the Large Binocular Telescope "extreme" AO system. The practical benefits of a compact, fiber-fed radial velocity instrument are many-fold. iLocater will: discovery planets orbiting in the habitable zone around nearby red-dwarf stars; perform the first systematic study of planets in close-separation binary star systems; and provide essential follow-up observations for TESS.