Images obtained with single-conjugate adaptive optics (AO) show spatial variation of the point spread function (PSF) due to both atmospheric anisoplanatism and instrumental aberrations. The poor knowledge of the PSF across the field of view strongly impacts the ability to take full advantage of AO capabilities. The AIROPA project aims to model these PSF variations for the NIRC2 imager at the Keck Observatory. Here, we present the characterization of the instrumental phase aberrations over the entire NIRC2 field of view and we present a new metric for quantifying the quality of the calibration, the fraction of variance unexplained (FVU). We used phase diversity measurements obtained on an artificial light source to characterize the variation of the aberrations across the field of view and their evolution with time. We find that there is a daily variation of the wavefront error (RMS of the residuals is 94~nm) common to the whole detector, but the differential aberrations across the field of view are very stable (RMS of the residuals between different epochs is 59~nm). This means that instrumental calibrations need to be monitored often only at the center of the detector, and the much more time-consuming variations across the field of view can be characterized less frequently (most likely when hardware upgrades happen). Furthermore, we tested AIROPA's instrumental model through real data of the fiber images on the detector. We find that modeling the PSF variations across the field of view improves the FVU metric by 60\% and reduces the detection of fake sources by 70\%.
