Investigating the differential limb coupling effect for diffraction-limited spectrographs with PARVI

A promising new architecture for extreme-precision radial velocity (EPRV) spectrographs, hunting for small-amplitude stellar Doppler shifts induced by orbiting planets, is to build diffraction-limited instruments by using single-mode fibers fed by an adaptive optics system. However, the target stars are partially resolved when observing at the diffraction limit, and the resulting RVs are expected to be affected by differential limb coupling (DLC), an effect where the red- and blue-shifted sides of the stellar disk are coupled unequally into the spectrograph, producing an RV error term on the order of m/s for nearby EPRV target stars for the upcoming HISPEC spectrograph for Keck II. We present our efforts to directly measure the RV shifts resulting from DLC for the first time, using the diffraction-limited spectrograph PARVI, in order to verify the expected behavior of DLC and subsequently develop mitigation strategies for HISPEC and other future instruments. We outline an observing strategy designed to produce DLC-induced RV shifts of hundreds of m/s, and describe the execution of this experiment with PARVI. We use these data to characterize the PARVI tip-tilt guide camera and its performance, and have begun analysis of the derived RVs, though this investigation has proven complicated since the RVs are deeply entangled with other instrumental and algorithmic effects.