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Knowledge of the point spread function (PSF) is critical to many astronomical science cases. However, the PSF can be very difficult to estimate for cases where there are many crowded point sources or for observations of extended objects. Additionally, for adaptive optics observations, the PSF can be very complex with both spatial and temporal variability in the PSF. Integral-field spectroscopy behind adaptive optics is especially challenging because the fields of view are typically too small to sample the halo for even a single PSF. Here, we present a method for semi-empirical PSF reconstruction for integral field spectrographs using a combination of point source observations on a parallel imager, instrumental aberration measurements, and atmospheric turbulence profiles. This work builds upon the PSF reconstruction project AIROPA designed for imaging and extending it to IFU work (AIROPA-IFU). By using empirical calibrators from the parallel imager, which has a much larger field of view, and accounting for anisoplantic effects and instrumental aberrations, we can predict the PSF on the spectrograph. An important aspect is being able to predict the PSF at many different wavelengths based on observations from broad-band imaging. Here, we discuss how science cases such as observations of stars at the Galactic center can benefit from this method. We also establish metrics to quantitatively assess the performance of PSF reconstruction. We show that for bright stars, AIROPA-IFU can produce spectra with signal to noise ratio 50% higher than with simple aperture extraction of a data cube.
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