Introduction

The wavelength calibration files employed by the CalFUSE pipeline provide a mapping between corrected detector pixel position and wavelength. This mapping accounts for both distortions in the detector imaging along the X-coordinate axis (the dispersion direction) and the smoothly-varying dependence of wavelength on detector X position expected from the spectrograph optics. The average dispersion across each of the four FUSE detectors ranges from 0.006 to 0.008 Å per pixel.

The wavelength calibration is applied to the data simply by copying values from the appropriate extension in the calibration file to the first column (labeled ``WAVE'') of the binary table of a CalFUSE output file. An updated wavelength calibration may be applied to a data file simply by replacing the contents of this column in the binary table with those of a new calibration file.

The FUSE wavelength calibration is based on the observed positions of interstellar molecular-hydrogen features in astigmatism-corrected, point-source (stellar) spectra. The exact recipe by which the calibration is derived is described below, along with the two remaining limits to our wavelength calibration: residuals in the detector-distortion correction and zero-point offsets in the wavelength scales of individual spectra.

Corrections within CalFUSE

By ``corrected detector pixel position,'' we mean the detector X and Y positions after correction for the following effects:

Spacecraft motion: The CalFUSE pipeline corrects the data for Doppler shifts induced by the satellite's orbital motion and for the relative velocity of the geocentric and heliocentric reference frames. FUSE wavelengths are thus reported with respect to a heliocentric frame of reference.

Walk: The FUSE detector electronics systematically miscalculate the X location of photon events with low pulse heights, an effect called ``walk.'' For time-tagged data, CalFUSE can reposition low-pulse-height photons, correcting for this effect. Histogram data, for which pulse-height information is unavailable, are only partially corrected for walk.

Mirror and grating motion: On orbital timescales, sources appear to move on the detector due to motions of both the spectrograph gratings and the primary mirrors. CalFUSE presently corrects for the grating motion, but NOT for the mirror motion.

Detector distortion: In the raw detector image, the spectrum is not straight, but wiggles in the Y direction. These wiggles are artifacts imposed by the detector electronics. They are highly repeatable, and CalFUSE is able to shift the data in Y to correct for them. Distortions in the X direction are presently folded into the wavelength calibration.

Astigmatism: Absorption features in the raw detector image are banana shaped, especially near the ends of the detectors, due to astigmatism in the FUSE optics. CalFUSE shifts the data to correct for this curvature. At present, no astigmatism correction is defined for diffuse sources, and none is applied.

FPA shifts: Wavelength-calibration files are defined for a specific X position of the Focal Plane Assemblies (FPA's), which contain the spectrograph apertures. Spectra obtained at other FPA positions are shifted to their expected locations on the detector by the CalFUSE software.

Detector Distortions

The main challenge in determining the FUSE wavelength calibration lies in characterizing the detector distortions. These distortions have (at least) two sources: non-linearities in the X scale caused by pulse-propagation effects in the delay-line anode and its interaction with the external cabling and electronics, and localized defects in the microchannel plates (MCP's), such as the boundaries of fiber bundles.

The non-linear terms in the wavelength solution are plotted below for each aperture and detector segment. The data are from in-flight measurements of interstellar absorption lines. The solid curve in each plot is a spline fit to the distortion; this spline is then combined with a quadratic polynomial to create the wavelength solution for each channel and aperture. The non-linearities are substantial, and a large number of measurements are required to characterize them accurately.

The scatter of individual measurements about the spline fit is caused in some cases by blended absorption lines and in some cases by localized distortions induced by the fiber-bundle structure of the MCP's. This scatter is thus a fair estimate of the inaccuracies that the user may expect in the relative measurement of the wavelength of any given feature.

The wavelength inaccuracies caused by localized distortions are 3-4 pixels (0.025 Å or 8 km/s) at most wavelengths, but may be as large as 6-8 pixels. They occur in tiny windows about 1 to 3 Å wide, depending on the channel and segment. Some data sets show much larger residuals. These distortions are inherent in the FUSE data set and represent the ultimate limit to the accuracy of the FUSE wavelength calibration.

The user should thus assume a systematic uncertainty in the relative position of any single feature of 3-4 pixels across most of the spectrum and 6-8 pixels in certain regions, as shown in the plots below.

The small black dots in the above figures are the data points for all apertures and both channels for the given detector segment. They are included in the distortion fit, but weighted 100 times less than the data points for the channel/aperture being fitted. This helps control the fits in wavelength regions where the data are sparce or missing.

Zero-Point Offsets

The FUSE wavelength calibration assumes that the spectrum falls at a precise location on the detector. If it does not, the wavelength scale will be shifted relative to the spectrum, an effect we call a ``zero-point offset.'' The two effects most responsible for these offsets are miscentering of the source within the spectrograph aperture and thermally-induced rotations of the spectrograph gratings, which depend on the satellite attitude.

The source may be offset from the center of the spectrograph aperture because of coordinate errors in either the target or the guide stars or, for channels other than LiF1, because of misalignments of the primary mirrors. For the LWRS aperture, positional uncertainties may yield errors of up to ± 0.15 Å in the absolute wavelength. These offsets are less than ± 0.02 Å for the MDRS aperture and are negligible for the HIRS aperture.

We do not yet have a calibration of the mean grating rotation as a function of satellite attitude. We do correct the data for changes in the grating rotation on orbital timescales; this recovers most of the spectral resolution that would otherwise be lost, but not the zero point of the wavelength scale. This error is independent of spectrograph aperture.

While the combined error from these two sources can be as much as 0.25 Å in the LWRS aperture, a recent analysis by Bowen, et al. (2004, in preparation) indicates that it is generally much smaller. For 47 stars for which the velocity of the interstellar Cl I 1347 line can be determined from STIS echelle spectra, the mean velocity error of the interstellar H₂ features in the stars' FUSE spectra is +10 ± 6 km/s.

Because the spectral zero point can vary from one exposure to another, users may wish to shift the spectra from individual exposures of bright targets to a common zero point before combining them. See Section 3.2.1 of the FUSE Data Analysis Cookbook for details. For targets too faint to allow cross correlation, we recommend that spectra from individual exposures be combined without any shifting, as the dispersion in their wavelength shifts is likely to be less than the instrument resolution. ( = 6 km/s corresponds to a FWHM of 14 km/s.)

We do not recommend the use of airglow lines to fix the absolute wavelength scale of point-source spectra for two reasons: First, airglow emission fills the aperture, so the resulting airglow lines provide no information about the position of the target relative to the aperture center. Second, because the effects of instrumental astigmatism are different in point-source and diffuse spectra, airglow lines may be distorted by the astigmatism correction applied to point-source spectra.

A number of users have asked about the relative zero points of segments A and B on each of the FUSE detectors. From the measured wavelengths of interstellar H₂ and other species with lines on both segments, we find that any such offset is less than or approximately equal to the systematic uncertainty in our measured wavelengths due to the detector distortions discussed above.

Diffuse Emission

The FUSE wavelength scale is derived from astigmatism-corrected, point-source spectra. Extended-source (diffuse) spectra are not presently corrected for astigmatism. If point-source data are processed with the astigmatism correction turned off, the resulting wavelength errors are less than about 4 pixels, consistent with the uncertainties in the wavelength scale. Therefore, the present FUSE wavelength calibration should be adequate for extended-source spectra.

Acknowledgements

This document was written by Paule Sonnentrucker and Jeff Kruk and edited by Van Dixon. The data reduction, line identification, and line-profile fits were performed by Zan Cha, Don Lindler, Kathy Roth, David Sahnow, and Paule Sonnentrucker, and the distortion analysis was performed by Don Lindler. The analysis of the GCRV12336 sight line was performed by Stephan McCandliss.

Questions? Please address questions to fuse_support@pha.jhu.edu.

straight to the top

WebMasters: Bill Blair, Humberto Calvani
Last Update: July 14, 2004