When recording spectra from the ground, atmospheric turbulence causes degradation of the spatial resolution. We present a data reduction method that restores the spatial resolution of the spectra to their undegraded state. By assuming that the point spread function (PSF) estimated from a strictly synchronized, broadband slit-jaw camera is the same as the PSF that spatially degraded the spectra, we can quantify what linear combination of undegraded spectra is present in each degraded data point. The set of equations obtained in this way is found to be generally well-conditioned and sufficiently diagonal to be solved using an iterative linear solver. The resulting solution has regained a spatial resolution comparable to that of the restored slit-jaw images.
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