The limits for adaptive-optics-assisted and space-based astronomical imaging at high contrast and high resolution are typically determined by residual phase errors due to non-common-path aberrations not sensed by the wavefront sensor. These impose quasi-static speckles on the image, which are difficult to calibrate as they vary in time and with telescope orientation. Typical approaches require phase diversity of some sort,1 which requires many iterations and is accordingly time-consuming. This is especially true of integral field spectrographs, where use of standard phase diversity based techniques is additionally complicated by the presence of the image slicer/integral field unit. We present the first application of the kernel phase based ‘asymmetric pupil Fourier wavefront sensing’ scheme to ground-based AO-corrected integral field spectroscopy, whereby an asymmetric pupil mask and a single image are sufficient to map aberrations up to high order, including non-common-path error. This method is closely connected with kernel phase interferometry, already applied to space-based and AO-assisted imaging, in which a phase transfer matrix formalism partitions focal plane Fourier phases into a kernel space which is self- calibrating with respect to pupil aberrations, and a row space which can be used to determine those aberrations via a matrix pseudo-inverse. This requires two key conditions be satisfied: the first, that phase errors are < 1 radian in magnitude. These conditions are typically satisfied for space-based telescopes such as the HST, or AO-corrected ground-based telescopes in the near-infrared. The second requirement is that the telescope pupil is not centro-symmetric; this can be achieved simply by placing an asymmetric mask in the optical path. The row phase reconstruction then provides a phase map which can be applied directly to a deformable mirror as a static offset. While in our approach we have iteratively applied corrections, we have deliberately damped correction steps, and in principle this can be done in a single step. We push toward internally diffraction-limited performance with the Oxford-SWIFT integral field spectrograph coupled with the PALM-3000 extreme AO system on the Palomar 200-inch telescope. This represents the first observation in which the PALM3000 + SWIFT internal point-spread-function has closely approached the Airy pattern. While this can only be used on SWIFT with an internal stimulus source, as at short wavelengths the uncorrected atmospheric wavefront errors are still < 1 radian, this nevertheless demonstrates the feasibility of detecting non-common-path errors with this method as an active optics paradigm for near-infrared, AO-corrected instruments on Palomar such as PHARO or Project 1640 (P1640), or other instruments such as VLT-SPHERE or the Gemini Planet Imager (GPI). We note that this is a particularly promising approach for correcting integral field spectrographs, as the diversity of many narrowband images provides strong constraints on the wavefront error estimate, and the average of reconstructions from many narrow bands can be used to improve overall reconstruction quality.