Exploring calibration algorithms to maximize the null depth in KPIC's vortex fiber nulling mode

Vortex fiber nulling (VFN) is a new interferometric technique with the potential to unlock the ability to detect and spectroscopically characterize exoplanets at angular separations smaller than the conventional diffraction limit of $\lambda$/D. In early 2022, a VFN mode was added to the Keck Planet Imager and Characterizer (KPIC) instrument suite on Keck II. VFN operates by adding an azimuthal phase ramp to the incident wavefront so that light from the star at the center of the field is prevented from coupling into a single-mode fiber. One of the key performance goals of VFN is to minimize the ratio of on-axis starlight coupling to off-axis planet coupling, which requires minimizing the wavefront aberrations of light being injected into the fiber. Non-common path aberrations can be calibrated during the daytime and compensated for with the KPIC deformable mirror during nighttime observing. By applying different amplitudes of low-order Zernike modes, we determine which combinations maximize the system performance. Here we present our work developing and testing different procedures to estimate the incident aberrations, both in simulation and on the Keck bench. The current iteration of this calibration algorithm has been used successfully for VFN observing, and there are several avenues for improvement.