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The Atmospheric Infrared Sounder (AIRS) is a high-resolution infrared sounder launched aboard the National Aeronautics and Space Administration's Aqua satellite on May 4, 2002. AIRS is a grating spectrometer with 2378 channels located between 15 and 3.8 μm, with nominal resolving powers of ν/Δν=1200. As the first of a new generation of upcoming infrared instruments with similar spectral coverage and resolution, there will be much interest in the performance of AIRS. The ability to retrieve good atmospheric profiles from AIRS observations will depend in part upon our knowledge of the spectral response of AIRS to the upwelling radiance. This paper discusses the spectral calibration of AIRS based upon an extensive set of laboratory test data generated by the instruments prime contractor, BAE. In particular, we describe the calibration of the AIRS spectral response functions, showing that our requirement for accuracies of "1% of a width" have been achieved.