Whitelight calibration. The whitelight cube was used to map the spatial and spectral shape of the interference filter, which was then removed in the same manner as flatfielding. The whitelight cube was heavily smoothed ( pixels) in the spatial dimension, re-sampled from 0.65Å to 0.99Å steps, to match the etalon gap spacings of the data cubes, then normalized and divided into the corresponding data cubes.
Frame alignment. The frames in each data cube were aligned using two stars near the disk of the galaxy. (The single bright star in the field, AGK 3+69 428 [[Bettoni & Galletta 1982]], 2.'5 southwest of the nucleus, saturated the detector.) Fractional pixel shifts were made by two-dimensional spline interpolation of the images. The spatial registration is accurate to better than one pixel ().
We note here that, although the HIFI system and the tilted etalon provide a field that is relatively free of ghost reflections, the location of the bright star AGK 3+69 428 in the southwest corner of the frame was such that a pair of concentric ghost images of the star appear opposite the optical axis, in the southeast corner of the frame. Following frame registration, a region encompassing the ghost images was masked from further analysis. This is unfortunate, in that the minor axis emission of M82 runs directly through this region, but it demonstrates the care that must be taken when observing with Fabry-Perot systems, which always have prevalent ghost patterns.
Ring fitting. Temperature and humidity variations produce drifts in the the expected spectral response of the Fabry-Perot etalon. In order to parametrize the spectral and spatial drifts in the Fabry-Perot system, we obtained a set of calibration lamp images, taken periodically throughout the night, all at the same etalon spacing. Elliptical fits to the rings revealed no noticeable variations in the radius or circularity of the rings, indicating that the spectral stability of the etalon was extremely good. Flexure of the telescope system was detectable as a two pixel (1.''5) shift of the ring centers (i.e., the optical axis) over the course of each night. The frame alignment procedure has removed this, with minimal effect along the wavelength axis.
Data cube resampling and smoothing. While our H+[NII] data was sampled regularly at 0.99Å (45 km s-1) intervals across the H line, observing time constraints required us to interpolate several frames across the [NII] portion of the spectra, where the sampling was a factor of two coarser. Although a spline interpolation was performed without difficulty, a slightly larger error should be assumed for the final [NII] fluxes and velocities. The [OIII] data set required extrapolation of a single (continuum) frame at either end of the spectra.
A light Hanning filter was then applied along the spectral axis of each cube, in order to allow efficient automated fitting of the large numbers of the spectra. Tests indicate this had a negligible effect on the final fit parameters.
Phase calibration. The instrumental profile of a Fabry-Perot interferometer is a complex function of spatial position, wavelength, and optical gap spacing, given by the well-known Airy function ([Bland & Tully 1989]). Due to the large free spectral range and low interference order of the etalons, the monochromatic ``phase surfaces,'' as observed in the emission lines of a calibration lamp, were well parametrized by the analytical expression for the three-dimensional Airy function. A fit to this function determined several system constants listed in Table 2. This fit was then used to shift each spectrum in the data cube by the appropriate value to generate monochromatic frames. The convergence of two night sky lines into a single frame each confirmed the accuracy of the phase correction for the H+[NII] data set. For the [OIII] data set, however, a poorly sampled calibration cube prevented us from performing an accurate phase correction. Therefore the [OIII] observations will be used for flux measurements and morphology, but not for kinematic studies.
Sky subtraction. A limited field of view prevented us from obtaining a sky spectrum devoid of galaxy emission. We therefore removed the two bright night sky lines in the H+[NII] data set by subtracting Gaussian components with the proper velocity and a mean flux level as observed across the field. The lines were identified as OH emission at 6553.61Å and 6577.28Å ([Osterbrock & Martel 1992]), providing the wavelength calibration for the spectral axis. The night sky continuum was not removed from the data. The [OIII] data were not sky-subtracted, due to the low level of sky flux and the difficulties associated with the non-phase-corrected data. Resulting errors in the final spectral fits are negligible.