This article describes the distortion correction phase of data processing. The FIMS and SPEAR teams both followed a similar procedure for this step.
The coordinates on the detector plane, expressed in units of mm, were converted to the wavelength (λ, Å) parallel to the dispersion direction, and to the angle (φ, degree) perpendicular to the dispersion direction. They were then recorded as WAVELENGTH and PHI in FITS files after the additional correction for distortion as described below.
Microchannel plate detectors typically show 1% to 2% local distortions in position caused by non-uniformities in the electric field. These distortions caused small shifts in wavelength (~1 Å) and sky position (~2 arcmin) of sources imaged on the SPEAR detectors (which are manifest as wiggles in the terrestrial aurora spectral features in the figure below). Spatial distortions are best removed by obtaining uniform grid pinhole mask data on the ground. Because of time constraints, these calibration data were not performed on FIMS-SPEAR detectors. Instead, the aurora data were used for local corrections in the dispersion direction, and stellar continua spectra were used to correct distortions in the imaging direction.
L band aurora (Figure 1a from Wavelength Calibration).
The aurora and sky survey images both showed many spectral features that were well defined, but had no reliable wavelength identifications. By utilizing the polynomial fit wavelength solutions, empirical wavelengths were assigned to these features. By combining the features with known wavelengths and the features with assigned effective wavelengths, the entire detector of each channel was covered with features of known wavelength. To ensure adequate statistics, the images were rebinned into 32 rows and centroids determined for each spectral feature in each row. A spline interpolation along each row yielded a wavelength map which assigned a wavelength for each pixel. In effect, each of the 32 rows had its own local wavelength solution. To assign a correct wavelength to a photon event, the wavelength map was simply subscripted (with sub-pixel interpolation) by its X,Y location. Detector distortions in the dispersion direction were directly eliminated. Integrated spectra of the S band show a spectral resolution (FWHM) of 1.37 Å. For the L band, no unblended features have been observed, but the line width is no more than 3.3 Å at FWHM.
The detector distortions in the imaging direction were removed in a similar manner, except that instead of emission lines, 477 stellar continuum spectra images were employed. Each image was rebinned into 32 columns, and the centroid of each star determined for each column. A Legendre polynomial was then fit to the 477 centroids in each of the 32 columns. At any given X,Y location on the detector, the Y distortion was defined as the difference between the polynomial fit Y value and the mean Y value of all 32 columns. These differences were saved as a Y distortion map. To remove the Y distortion of each photon event, the Y distortion map was subscripted by the X,Y location of the photon, and the value subtracted from the Y coordinate. Typical corrections were less than 2 arcmin for the L Band spectrometer. Because the stellar continua are very faint or partially absent shortward of 1000 Å, no distortion corrections in the imaging dimension were applied for the S band spectrometer. Hence, the positional uncertainties and PSF are somewhat larger (~2 arcmin) for sources in the S band.