CalFUSE Version 3: A Data Reduction Pipeline for the Far Ultraviolet Spectroscopic Explorer¹

The first subroutine of this module, cf_check_digitizer, merely compares a set of 16 IDF file header keywords that record various detector settings with reference values stored in the calibration file DIGI_CAL. Significant differences result in warning messages being written to both the file header and the exposure trailer file. Such warning messages should be taken seriously, as data obtained when the detectors are not properly configured are likely to be unusable. Besides issuing a warning, the program sets the EXP_STAT keyword in the IDF header to −2.

The term "dead time" refers specifically to the finite time interval required by the detector electronics to process a photon event. During this interval, the detector is "dead" to incoming photons. The term is more generally applied to any loss of data that is count‐rate dependent. There are three major contributions to the effective detector dead time on FUSE. The first is due to limitations in the detector electronics, which at high count rates may not be able to process photon events as fast as they arrive. The correction for this effect is computed separately for each segment from the count rate measured at the detector anode by the Fast Event Counter (FEC) and recorded to the engineering data stream, typically once every 16 s. The functional form of the correction was provided by the detector development group at the University of California, Berkeley, and its numerical constants were determined from in‐flight calibration data. It is applied by the subroutine cf_electronics_dead_time.

A second contribution to the dead time comes from the way that the Instrument Data System processes counts coming from the detector. The IDS can accept at most 8000 counts s⁻¹ in time‐tag mode and 32,000 counts s⁻¹ in histogram mode from the four detector segments (combined). At higher count rates, photon events are lost. To correct for such losses, the subroutine cf_ids_dead_time compares the Active Image Counter (AIC) count rate, measured at the back end of the detector electronics, with the maximum allowed rate. The IDS dead‐time correction is the ratio of these two numbers (or unity, whichever is greater).

A third contribution occurs when time‐tag data are bundled into 64 kbyte data blocks in the IDS bulk memory. This memory is organized as a software FIFO (first‐in, first‐out) memory buffer, and the maximum data transfer rate from it to the spacecraft recorder (the FIFO drain rate) is approximately 3500 events s⁻¹. At higher count rates, the FIFO will eventually fill, resulting in the loss of one or more data blocks. The effect appears as a series of data dropouts, each a few seconds in length, in the raw data files. The correction, computed by the subroutine cf_fifo_dead_time, is simply the ratio of the AIC count rate to the FIFO drain rate. When triggered, this correction incorporates (and replaces) the IDS correction discussed above.

The total dead‐time correction (always ≥1.0) is simply the product of the detector electronics and IDS corrections. It is computed (by the subroutine cf_apply_dead_time) once each second and applied to the data by scaling the WEIGHT associated with each photon event. The mean value of the detector electronics, IDS, and total dead‐time corrections are stored in the DET_DEAD, IDS_DEAD, and TOT_DEAD header keywords, respectively. Other possible sources of dead time, such as losses due to the finite response time of the MCPs, have a much smaller effect and are ignored.

Caveats: Our dead‐time correction algorithms are inappropriate for very bright targets. If the header keyword TOT_DEAD > 1.5, then the exposure should not be considered photometric. If DET_DEAD > 1.5 or if IDS_DEAD > 1.5 and its value is dubious (the housekeeping file for that exposure is missing and the file header keywords from which the count rates are estimated appear to be corrupted), then the dead‐time correction is assumed to be meaningless and is set to unity. Warning messages are written to the file header and the trailer file.

The X and Y coordinates of a photon event do not correspond to a physical pixel on the detector, but are calculated from timing and voltage measurements of the incoming charge cloud (Siegmund et al. 1997; Sahnow et al. 2000a). As a result, the detector coordinate system is subject to drifts in the detector electronics caused by temperature changes and other effects. To track these drifts, two signals are periodically injected into the detector electronics. These "stim pulses" appear near the upper left and upper right corners of each detector, outside of the active spectral region. The stim pulses are well placed for tracking changes in the scale and offset of the X coordinate, but they are not separated enough in Y to track scale changes along that axis. The subroutine cf_thermal_distort determines the X and Y centroids of the stim pulses, computes the linear transformation necessary to move them to their reference positions, and applies that transformation to the X and Y coordinates of each photon event in the regions of the stim pulses and in the active region of the detector. Events falling within 64 pixels (in X and Y) of the expected stim‐pulse positions are flagged by setting the stim‐pulse bit in the LOC_FLGS array (§ A3). In raw histogram files, the stim pulses are stored in a pair of image extensions. If either of these extensions is missing, the pipeline reads the expected positions of the stim pulses from the calibration file STIM_CAL and applies the corresponding correction. This works (to first order) because the stim pulses drift slowly with time, although short‐timescale variations cannot be corrected if the stim pulses are absent.

For reasons not yet understood, the detector Y scale varies with the count rate, in the sense that the detector image for a high–count‐rate exposure is expanded in Y. To measure this effect, we tabulated the positions of individual detector features (particularly bad‐pixel regions) as a function of the FEC count rate (§ 4.3.2) and determined the Y corrections necessary to shift each detector feature to its observed position in a low–count‐rate exposure. From this information, we derived the calibration file RATE_CAL for each detector segment. The correction is stored as a two‐dimensional image: the first dimension represents the count rate, and the second is the observed Y pixel value. The value of each image pixel is the Y shift (in pixels) necessary to move a photon to its corrected position. The subroutine cf_count_rate_y_distort applies this correction to each photon event in the active region of the detector. For time‐tag data, the FEC count rate is used to compute a time‐ and Y‐dependent correction; for histogram data, the weighted mean of the FEC count rate is used to derive a set of shifts that depends only on Y.

As the detector and its electronics age, their properties change, resulting in small drifts in the computed coordinates of photon events. These changes are most apparent in the Lyβ airglow features observed in each of the three apertures of the LiF and SiC channels (Fig. 3), which drift slowly apart in Y as the mission progresses, indicating a time‐dependent stretch in the detector Y scale. To correct for this stretch, the subroutine cf_time_xy_distort applies a time‐dependent correction (stored in the calibration file TMXY_CAL) to the Y coordinate of each photon event in the active region of the detector.

Caveats: Although there is likely to be a similar change to the X coordinate, no measurement of time‐dependent drifts in that dimension is available, so no correction is applied.

In an image of the detector generated from raw X and Y coordinates, the spectrum is not straight, but wiggles in the Y dimension (Fig. 4). To map these geometric distortions, we made use of two wire grids (the so‐called quantum efficiency and plasma grids) that lie in front of each detector segment. Both grids are regularly spaced and cover the entire active area of the detectors. Although designed to be invisible in the spectra, they cast sharp shadows on the detector when illuminated directly by onboard stimulation (or "stim") lamps. We determined the shifts necessary to straighten these shadows. Their spacing is approximately 1 mm, too great to measure fine‐scale structure in the X dimension, but sufficient for the Y distortion. Geometric distortions in the X dimension have the effect of compressing and expanding the spectrum in the dispersion direction, so the X distortion correction is derived in parallel with the wavelength calibration, as described in § 5.1. The geometric distortion corrections are stored in a set of calibration files (GEOM_CAL) as pairs of 16,384 × 1024 images, one each for the X and Y corrections. The value of each image pixel is the shift necessary to move a photon to its corrected position. This shift is applied by the subroutine cf_geometric_distort.

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Caveats: Although designed to be invisible, the wire grids can cast shadows that are visible in the spectra of astrophysical targets. These shadows are the worms discussed in § 6.3.

The FUSE detectors convert each ultraviolet photon into a shower of electrons, for which the detector electronics calculate the X and Y coordinates and the total charge, or pulse height. Prolonged exposure to photons causes the detectors to become less efficient at this photon‐to‐electron conversion (a phenomenon called "gain sag"), and the mean pulse height slowly decreases. Unfortunately, the X coordinate of low–pulse‐height photon events is systematically miscalculated by the detector electronics. As the pulse height decreases with time, spectral features appear to "walk" across the detector. The strength of the effect depends on the cumulative photon exposure experienced by each pixel and therefore varies with location on the detector.

To measure the error in X as a function of pulse height, we used data from long stim lamp exposures to construct a series of 32 detector images, each containing events with a single pulse height (allowed values range from 0 to 31). We stepped through each image in X, computing the shift (ΔX) necessary to align the shadow of each grid wire with the corresponding shadow in a standard image constructed from photon events with pulse heights between 16 and 20. The shifts were smoothed to eliminate discontinuities and stored in calibration files (PHAX_CAL) as a two‐dimensional image: the first dimension represents the observed X coordinate, and the second is the pulse height. The value of each image pixel is the walk correction (ΔX) to be added to the observed value of X. This correction, assumed to be independent of detector Y position, is applied by the subroutine cf_pha_x_distort.

Caveats: For time‐tag data, the walk correction is straightforward and reasonably accurate. For histogram data, pulse‐height information is unavailable, so the subroutine cf_modify_hist_pha assigns to each photon event the mean pulse height for that aperture, derived from contemporaneous time‐tag observations and stored in the calibration file PHAH_CAL. While this trick places time‐tag and histogram data on the same overall wavelength scale, small‐scale coordinate errors due to localized regions of gain sag (e.g., around bright airglow lines, particularly Lyβ) remain uncorrected in histogram spectra.

When the IDF is first created, photon events with coordinates outside the active region of the detector are flagged as bad (§ 4.2). Once their coordinates are converted to the FARF, the subroutine cf_active_region flags as bad any photons that have been repositioned beyond the active region of the detector. These limits are read from the electronics calibration file (stored under the header keyword ELEC_CAL). Allowed values are 800≤XFARF≤15,583 and 0≤YFARF≤1023. The active‐area bit is written to the LOC_FLGS array.

CalFUSE does not perform any sort of flat‐field correction. Prelaunch flat‐field observations differ sufficiently from in‐flight data to make them unsuitable for this purpose, and in‐flight flat‐field data are unavailable. (Even if such data were available, any flat‐field correction would be only approximate, because MCPs do not have physical pixels for which pixel‐to‐pixel variations can be clearly delineated; § 4.3.3). As a result, detector fixed‐pattern noise limits the signal‐to‐noise ratio achievable in observations of bright targets. To the extent that grating, mirror, and spacecraft motions shift the spectrum on the detector during an exposure, these fixed‐pattern features can be averaged out. For some targets, we deliberately move the FPAs between exposures to place the spectrum on different regions of the detector. Combining the extracted spectra from these exposures can significantly improve the resulting signal‐to‐noise ratio (§ 4.5.5). Other detector effects (including the moiré pattern discussed in § 6.4) are described in the FUSE Instrument and Data Handbook.

Numerous geocoronal emission features lie within the FUSE wave band (Feldman et al. 2001). While the pipeline processes airglow photons in the same manner as all other photon events in the target aperture, it is occasionally helpful to exclude from consideration regions of the detector likely to be contaminated by geocoronal or scattered solar emission. These regions are listed in the calibration file AIRG_CAL; the subroutine cf_screen_airglow flags as airglow (by setting the airglow bit of the LOC_FLGS array in the photon‐event list) all photon events falling within the tabulated regions—even for data obtained during orbital night, when many airglow features are absent.

Spectra obtained when a target lies near the Earth's limb are contaminated by scattered light from strong geocoronal Lyα and O i emission. To minimize this effect, the subroutine cf_screen_limb_angle reads the LIMB_ANGLE array of the time‐line table, identifies periods when the target violates the limb‐angle constraint, and sets the corresponding flag in the STATUS_FLAGS array of the time‐line table. Minimum limb angles for day and night observations are read from the BRITLIMB and DARKLIMB keywords of the screening parameter file and copied to the IDF file header. The default limits are 15° during orbital day and 10° during orbital night.

The South Atlantic Anomaly marks a depression in the Earth's magnetic field that allows particles trapped in the Van Allen belts to reach low altitudes. The high particle flux in this region raises the background count rate of the FUSE detectors to unacceptable levels. The subroutine cf_screen_saa compares the spacecraft's ground track, recorded in the LONGITUDE and LATITUDE arrays of the time‐line table, with the limits of the SAA (stored in the calibration file SAAC_CAL as a binary table of latitude‐longitude pairs) and flags as bad periods when data were taken within the SAA. Our SAA model was derived from orbital information and onboard counter data from the first 3 years of the FUSE mission.

Caveats: Because the SAA particle flux is great enough to damage the FUSE detectors, we end most exposures before entering the SAA and lower the detector high voltage during each SAA pass. As a result, very little data is actually flagged by this screening step.

The detector high voltage is set independently for each detector segment (1A, 1B, 2A, 2B). During normal operations, the voltage on each segment alternates between its nominal full voltage and a reduced SAA level. The SAA level is low enough that the detectors are not damaged by the high count rates that result from SAA passes, and it is often used between science exposures to minimize detector exposure to bright airglow emission. The full‐voltage level is the normal operating voltage used during science exposures. It is raised regularly to compensate for the effects of detector gain sag. Without this compensation, the mean pulse height of real photon events would gradually fall below our detection threshold. Unfortunately, there is a limit above which the full‐voltage level cannot be raised. Detector segment 2A reached this limit in 2003 and has not been raised since; it will gradually become less sensitive as the fraction of low–pulse‐height events increases. The subroutine cf_screen_high_voltage reads the instantaneous value of the detector high voltage from the HIGH_VOLTAGE array of the time‐line table, compares it with the nominal full‐voltage level (stored as a function of time in the calibration file VOLT_CAL), and flags periods of low voltage as bad.

For any number of reasons, an exposure can be obtained with the detector high voltage at less than the full‐voltage level. To preserve as much of this data as possible, we examined all of the low‐voltage exposures taken during the first 4 years of the mission and found that for detector segments 1A, 1B, and 2B, the data quality is good whenever the detector high voltage is greater than 85% of the nominal (time dependent) full‐voltage level. For segment 2A, data obtained with the high voltage greater than 90% of full are good, lower than 80% are bad, and between 80% and 90% are of variable quality. In this regime, the pipeline flags the affected data as good but writes warning messages to both the IDF header and the trailer file. When this warning is present in time‐tag data, the user should examine the distribution of pulse heights in the target aperture to ensure that the photon events are well separated from the background (§ 4.4.12). For histogram data, the spectral photometry and wavelength scale are most likely to be affected.

Caveats: If the header keywords indicate that the detector voltage was high, low, or changed during an exposure, the IDF initialization routines (§ 4.2) write a warning message to the trailer file. If a valid housekeeping file is available for the exposure, this warning may be safely ignored, because the pipeline uses housekeeping information to populate the HIGH_VOLTAGE array in the time‐line table and properly excludes time intervals when the voltage was low. If the housekeeping file is not present, each entry of the HIGH_VOLTAGE array is set to the "HV bias maximum setting" reported in the IDF header. In this case, the pipeline has no information about time‐dependent changes in the detector high voltage, and warnings about voltage level changes should be investigated by the user.

Occasionally, the FUSE detectors register large count rates for short periods of time. These event bursts can occur on one or more detectors and often have a complex distribution across the detector, including scalloping and sharp edges (Fig. 5). CalFUSE includes a module that screens the data to identify and exclude bursts. The subroutine cf_screen_burst computes the time‐dependent count rate using data from background regions of the detector (excluding airglow features) and applies a median filter to reject time intervals whose count rates differ by more than 5 standard deviations (the value can be set by the user) from the mean. The algorithm rejects any time interval in which the background rate rises rapidly, as when an exposure extends into an SAA or the target nears the Earth limb. The background rate computed by the burst‐rejection algorithm is stored in the BKGD_CNT_RATE array of the time‐line table and included on the count‐rate plots generated for each exposure (§ 4.10). Burst rejection is possible only for data obtained in time‐tag mode.

Caveats: Careful examination of long background observations reveals that many are contaminated by emission from bursts too faint to trigger the burst‐detection algorithm. Observers studying, for example, diffuse emission from the interstellar medium should be alert to the possibility of such contamination.

Pointing of the FUSE spacecraft was originally controlled with four reaction wheels, which typically maintained a pointing accuracy of 0.2^''–0.3^''. In late 2001, two of the reaction wheels failed, and it became necessary to control the spacecraft orientation along one axis with magnetic torquer bars. The torquer bars can exert only about 10% of the force produced by the reaction wheels, and the available force depends on the strength and relative orientation of the Earth's magnetic field. Thus, spacecraft drift increased dramatically along this axis, termed the antisymmetric or A axis. Drifts about the A axis shift the spectra of point‐source targets in a direction 45° from the dispersion direction (i.e., ΔX = ΔY). These motions can substantially degrade the resolution of the spectra, so procedures have been implemented to correct the data for spacecraft motion during an exposure. For time‐tag observations of point sources, we reposition individual photon events. For histogram observations, we correct only for the exposure time lost to large excursions of the spacecraft. The ability to correct for spacecraft drift became even more important when a third reaction wheel failed in 2004 December.

The correction of photon‐event coordinates for spacecraft motion is discussed in § 4.5.7. During screening, the subroutine cf_screen_jitter merely flags times when the target is out of the aperture, defined as those for which either ΔX or ΔY, the pointing error in the dispersion or cross‐dispersion direction, respectively, is greater than 30^'', the width of the LWRS aperture. These limits, set by the keywords DX_MAX and DY_MAX in the CalFUSE parameter file (PARM_CAL), underestimate the time lost to pointing excursions, but smaller limits can lead to the rejection of good data for some channels. Also flagged as bad are times when the jitter‐tracking flag TRKFLG = −1, indicating that the spacecraft is not tracking properly. If TRKFLG = 0, no tracking information is available and no times are flagged as bad. Pointing information is read from the jitter file (JITR_CAL; § A2). If the jitter file is not present or the header keyword JIT_STAT = 1 (indicating that the jitter file is corrupted), cf_screen_jitter issues a warning and exits; again, no times are flagged as bad.

One bit of the status array is reserved for user‐defined GTIs. For example, to extract data corresponding to a particular phase of a binary star orbit, one would flag data from all other phases as bad. A number of tools exist to set this flag, including cf_edit (available from MAST). CalFUSE users can specify good‐time intervals by setting the appropriate keywords (NUSERGTI, GTIBEG01, GTIEND01, etc.) in the screening parameter file. (Times are in seconds from the exposure start time.) If these keywords are set, the subroutine cf_set_user_gtis flags times outside of these good‐time intervals as bad.

Once the status flags in the time‐line table are populated, the subroutine cf_set_photon_flags copies them to the corresponding entries in the photon‐event list. For time‐tag data, this process is straightforward: match the times and copy the flags. Header keywords in the IDF record the number of photon events falling in bad‐time intervals or outside of the detector active area; the number of seconds lost to bursts, SAAs, etc.; and the remaining night exposure time. If more than 90% of the exposure is lost to a single cause, an explanatory note is written to the trailer file.

The task is more difficult for histogram data, for which photon‐arrival information is unavailable. We distinguish between time flags that represent periods of lost exposure time (low detector voltage or target out of aperture) and those that represent periods of data contamination (limb‐angle violations or SAAs). For the former, we need only modify the exposure time; for the latter, we must flag the exposure as being contaminated. Our goal is to set the individual photon flags and header keywords so that the pipeline behaves in the following way: when processing a single exposure, it treats all photon events as good. When combining data from multiple exposures, it excludes contaminated exposures (defined below). To this end, we generate an 8 bit status word containing only day/night information: if the exposure is more than 10% day, the day bit is set. This status word is copied onto the time‐dependent status flag of each photon event. We generate a second 8 bit status word containing information about limb‐angle violations and SAAs: if a single second is lost to one of these events, the corresponding flag is set and a message is written to the trailer file. (To avoid rejecting an exposure that, for example, abuts an SAA, we ignore its initial and final 20 s in this analysis.) The status word is stored in the file header keyword EXP_STAT (unless that keyword has already been set; see §§ 4.2 and 4.3.1). The routines used by the pipeline to combine data from multiple exposures into a single spectrum (§ 4.11) reject data files in which this keyword is nonzero. The number of bad events, the exposure time lost to periods of low detector voltage or spacecraft jitter, and the exposure time during orbital night are written to the file header, just as for time‐tag data.

Only in this subroutine is the DAYNIGHT keyword read from the screening parameter file and written to the IDF file header. Allowed values are DAY, NIGHT, and BOTH. The default is BOTH. For most flags, if the bit is set to 1, the photon event is rejected. The day/night flag is different: it is always 1 for day and 0 for night. The pipeline must read and interpret the DAYNIGHT keyword before accepting or rejecting an event based on the value of its day/night flag.

Once the time‐dependent screening is complete, the subroutine cf_set_good_time_intervals calculates a new set of good‐time intervals from information in the time‐line table and writes them to the second extension of the IDF (§ 4.2). For time‐tag data, all of the TIMEFLGS bits are used and the DAYNIGHT filter is applied. For histogram data, the bits corresponding to limb‐angle violations and SAAs are ignored, since data arriving during these events cannot be excluded. The DAYNIGHT filter is applied (assuming that all are day photons if the exposure is more than 10% day). The exposure time, EXPTIME = Σ (STOP − START), summed over all entries in the GTI table, is then written to the IDF file header.

For histogram data, all of the photon events in an IDF are initially assigned an arrival time equal to the midpoint of the exposure. Should this instant fall in a bad‐time interval, the data may be rejected by a subsequent step of the pipeline or one of our postprocessing tools. To avoid this possibility, the subroutine cf_modify_hist_times resets all photon‐arrival times to the midpoint of the exposure's longest good‐time interval. This subroutine is not called for time‐tag data.

Images of the FUSE detectors reveal a number of dead spots that may be surrounded by a bright ring (see the FUSE Instrument and Data Handbook for examples). The subroutine cf_screen_bad_pixels reads a list of bad‐pixel regions from a calibration file (QUAL_CAL) and flags as bad all photon events whose XFARF and YFARF coordinates fall within the tabulated limits. A bad‐pixel map, constructed later in the pipeline (§ 4.8), is used by the optimal‐extraction algorithm to correct for flux lost to dead spots.

For time‐tag data, the pulse height of each photon event is recorded in the IDF. Values range from 0 to 31 in arbitrary units. A typical pulse‐height distribution has a peak at low values due to the intrinsic detector background, a Gaussian‐like peak near the middle of the range due to "real" photons, and a tail of high–pulse‐height events, which likely represent the superposition of two photons and therefore are not reliable. In addition, the detector electronics selectively discard high pulse‐height events near the top and bottom of the detectors (i.e., with large or small values of Y). We can thus improve the signal‐to‐noise ratio of faint targets by rejecting photon events with extreme pulse‐height values. Pulse‐height limits (roughly 2–24) are defined for each detector segment in the screening parameter file (SCRN_CAL). The subroutine cf_screen_pulse_height flags photon events with pulse heights outside of this range (by setting the appropriate bit in the LOC_FLGS array; § A3) and writes the pulse‐height limits used and the number of photon events rejected to the IDF file header. This procedure is not performed on histogram data.

Caveats: We do not recommend the use of narrow pulse‐height ranges to reduce the detector background in FUSE data. Careful analysis has shown that limits that are more stringent than the default values can result in significant flux losses across small regions of the detector, particularly in the LiF 1B channel, resulting in apparent absorption features that are not real.

The LiF and SiC channels each produce three spectra, one from each aperture, for a total of six spectra per detector segment (Fig. 3). Because motions of the optical components can shift these spectra on the detector, the first step is to determine the Y centroid of each. To do this, we use the following algorithm: First, we project the airglow photons onto the Y axis (summing all values of X for each value of Y) and search the resulting histogram for peaks within 70 pixels of the expected Y position of the LWRS spectrum. If the airglow feature is sufficiently bright (33 counts in 141 Y pixels), we adopt its centroid as the airglow centroid for the LWRS aperture and compute its offset from the expected value stored in the CHID_CAL calibration file. If the airglow feature is too faint, we adopt the expected centroid and assume an offset of zero. We apply the offset to the expected centroids of the MDRS and HIRS apertures to obtain their airglow centroids. Second, we project the nonairglow photons onto the Y axis and subtract a uniform background. Airglow features fill the aperture, but point‐source spectra are considerably narrower in Y and need not be centered in the aperture. For each aperture, we search for a 5 σ peak within 40 pixels of the airglow centroid. If we find it, we use its centroid; otherwise, we use the airglow centroid. This scheme, implemented in the subroutine cf_find_spectra, allows for the possibility that an astrophysical spectrum may appear in a nontarget aperture.

For each of the six spectra, two keywords are written to the IDF file header: YCENT contains the computed Y centroid, and YQUAL contains a quality flag. The flag is HIGH if the centroid was computed from a point‐source spectrum, MEDIUM if computed from an airglow spectrum, and LOW if the tabulated centroid was used. It is possible for the user to specify the target centroid by setting the SPEX_SIC and SPEC_LIF keywords in the CalFUSE parameter file (PARM_CAL). Two other keywords, EMAX_SIC and EMAX_LIF, limit the offset between the expected and calculated centroids: if the calculated centroid differs from the predicted value by more than this limit, the pipeline uses the default centroid.

Caveats: On detector 1, the SiC LWRS spectrum falls near the bottom edge of the detector (Fig. 3). Because the background level rises steeply near this edge, the calculated centroid can be pulled (incorrectly) to lower values of Y, especially for faint targets.

The subroutine cf_identify_channel assigns each photon to a channel, where "channel" now refers to one of the six spectra on each detector (Fig. 3). For each channel, extraction windows for both point‐source and extended targets are tabulated in the calibration file CHID_CAL, along with their corresponding spectral Y centroids. These extraction limits encompass at least 99.5% of the target flux. For the target channels, identified in the APERTURE header keyword, we use either the point‐source or extended extraction windows, as indicated by the SRC_TYPE keyword; for the other (presumably airglow) channels, we use the extended extraction windows. The offset between the calculated and tabulated spectral Y centroids (§ 4.5.1) is used to shift each extraction window to match the data.

To ensure that, in the event that two extraction windows overlap, photon events falling in the overlap region are assigned to the more likely channel, photon coordinates (XFARF and YFARF) are compared with the extraction limits of the six spectral channels in the following order: first the target channels (LiF and SiC), then the airglow channels (LiF and SiC) corresponding to the larger nontarget aperture, and finally the airglow channels (LiF and SiC) corresponding to the smaller nontarget aperture. For example, if the target were in the MDRS aperture, the search order would be MDRS LiF, MDRS SiC, LWRS LiF, LWRS SiC, HIRS LiF, and HIRS SiC. The process stops when a match is made. The channel assignment of each photon event is stored in the CHANNEL array (§ A3); photon events that do not fall in an extraction window are assigned a CHANNEL value of 0.

Channel assignment is performed twice, once before the motion corrections and once after. The first time, all extraction windows are padded by ±10 Y pixels to accommodate errors in the channel centroids. The second time, no padding is applied to time‐tag data. Histogram data, which are generally binned by 8 pixels in Y, present a special challenge: the geometric correction (§ 4.3.6) can move a row of data out of the extraction window, producing a significant loss of flux. To prevent this, histogram extraction windows are padded by an additional ±8 Y pixels (or an amount equal to the binning factor in Y, if other than 8).

For the LiF and SiC target apertures, the subroutine cf_calculate_ycent_motion computes the spectral Y centroid as a function of time throughout the exposure. The algorithm requires 500 photon events to compute an average, so the centroid is updated more often for bright targets than for faint ones. Photon events flagged as airglow are ignored. The results are stored in the YCENT_LIF and YCENT_SIC arrays of the time‐line table, but are not currently used by the pipeline. This calculation is not performed for data obtained in histogram mode.

The FUSE spectrograph gratings are subject to small, thermally induced motions on orbital, diurnal, and precessional (60 day) timescales; an additional long‐term, nonperiodic drift is also apparent. These motions can shift the target and airglow spectra by as much as 15 pixels (peak to peak) in both the X and Y dimensions. Measurements of the Lyβ airglow line in thousands of exposures obtained throughout the mission reveal that the gratings' orbital motion depends on three parameters: beta angle (the angle between the target and the anti‐Sun vector), pole angle (the angle between the target and the orbit pole), and spacecraft roll angle (east of north, stored in the file header keyword APER_PA). The subroutine cf_grating_motion compares the beta, pole, and roll angles of the spacecraft with a grid of values in the calibration file GRAT_CAL, reads the appropriate correction, and computes the X and Y photon shifts. The grating‐motion correction is applied to all photon events with CHANNEL > 0; photon events not assigned to a channel are not moved.

Caveats: Some combinations of beta and pole angle are too poorly sampled for us to derive a grating‐motion correction; for these regions, no correction is applied. At present, only corrections for the orbital and long‐term grating motions are available. Because all photon events in histogram data are assigned the same arrival time (the midpoint of the longest good‐time interval), they receive the same grating‐motion correction.

The four focal plane assemblies (shown in Fig. 1) can be moved independently in either the X or Z direction. FPA motions in the X direction are used to correct for mirror misalignments and to perform FP splits (described below). FPA motions in the Z direction are used to place the apertures in the focal plane of the spectrograph. (Strictly speaking, an FPA moves along the tangent to or the radius of the spectrograph Rowland circle, not the X and Z axes shown in Fig. 1.) Both motions change the spectrograph entrance angle, shifting the target spectrum on the detector. The FUSE wavelength calibration is derived from a single stellar observation obtained at a particular FPA position. The subroutine cf_fpa_position computes the shift in pixels (ΔX) necessary to move each spectrum from its observed X position on the detector to that of the wavelength‐calibration target. The X and Z positions of the LiF and SiC FPAs are stored in file header keywords, various spectrograph parameters are stored in a calibration file (SPEC_CAL), and the wavelength calibration and the FPA position of the wavelength‐calibration target are stored in the WAVE_CAL file. Shifts are computed for both the LiF and SiC channels. The appropriate shift is applied to all photon events with CHANNEL > 0; photon events not assigned to a channel are ignored.

The FUSE detectors suffer from fixed‐pattern noise. Astigmatism in the instrument spreads a typical resolution element over several hundred detector pixels (predominantly in the cross‐dispersion dimension), mitigating this effect, but to achieve a signal‐to‐noise ratio greater than ∼30, one must remove the remaining fixed‐pattern noise. A useful technique is the focal‐plane split. FP splits are performed by obtaining a series of MDRS or HIRS exposures at several FPA X positions. Moving the FPA in the X dimension (and moving the satellite to center the target in the aperture) between exposures shifts both target and airglow spectra in the dispersion direction on the detector. CalFUSE shifts each spectrum to the standard X position expected by our wavelength calibration routines. If the signal‐to‐noise ratio in the spectra obtained at each FPA position is high enough, it is possible for the user to disentangle the source spectrum from the detector fixed‐pattern noise; however, simply combining extracted spectra obtained at different FPA positions will average out most of the small‐scale detector features.

The spectrograph mirrors are subject to thermal motions that shift the target's image within the spectrograph aperture and thus its spectrum in both X and Y on the detector. A source in either of the SiC channels may move as much as 6^'' in a period of 2 ks. This motion has two effects on the data: first, flux will be lost if the source drifts (partially or completely) out of the aperture; second, spectral resolution will be degraded (for LWRS observations) as the spectrum shifts on the detector. Diffuse sources, such as airglow emission, fill the aperture, so their spectra are unaffected by mirror motion.

When the LiF 1 channel is used for guiding, motions of the LiF 1 mirror are corrected by the spacecraft itself. Only the LiF 2 and SiC spectra must be corrected by CalFUSE. In theory, the switch from LiF 1 to LiF 2 as the primary channel for guiding the spacecraft (§ 2) should require another set of calibration files. In practice, the LiF 2 mirror motion in the dispersion direction tracks that of the LiF 1 mirror. The mirror‐motion correction is stored as a function of time since orbital sunset (via the TIME_SUNSET array in the time‐line table) in the calibration file MIRR_CAL. The correction (ΔX) is applied by the subroutine cf_mirror_motion to all photon events within the target aperture; photon events in other apertures and those not assigned to a channel are ignored. This correction is not applied to extended sources. Because all photon events in histogram data are assigned the same arrival time (generally the midpoint of the exposure), they receive the same mirror‐motion correction.

Caveats: We correct only the relative mirror motion during an orbit, not the absolute mirror offset based on longer term trends. We do not correct for mirror motions in the Y dimension. Finally, because the shifts for the SiC 1 and SiC 2 mirrors are similar, we adopt a single correction for both channels.

Spacecraft motions during an exposure shift the target spectrum on the detector and thus degrade spectral resolution. The subroutine cf_satellite_jitter uses pointing information stored in the jitter file (JITR_CAL; § A2) to correct the observed coordinates of photon events for these motions. Pointing errors in arcseconds are converted to X and Y pixel shifts and applied to all photon events within the target aperture; events in other apertures and those not assigned to a channel are ignored. The correction is applied only if the jitter‐tracking flag TRKFLG > 0, indicating that valid tracking information is available. TRKFLG values rise from 1 to 5 as the reliability of the pointing information increases. The minimum acceptable value of the TRKFLG can be adjusted by modifying the TRKFLG keyword in the CalFUSE parameter file (PARM_CAL).

Once all spectral motions are removed from the data, the subroutine cf_calculate_y_centroid recomputes the spectral Y centroids. Separate source and airglow centroids are determined for each aperture in turn, from largest to smallest. (The former is meaningless if the aperture does not contain a source.) The offset between the measured airglow centroid in the LWRS aperture and the tabulated centroid (from the calibration file CHID_CAL) is used to compute the airglow centroids for the MDRS and HIRS apertures; the computed MDRS and HIRS airglow centroids are ignored. The YCENT value written to the IDF file header is determined by the quality flag previously set by cf_find_spectra (§ 4.5.1): if YQUAL = HIGH, the source centroid is used; if YQUAL = MEDIUM, the airglow centroid is used; and if YQUAL = LOW, the tabulated centroid is used. The SPEX_SIC, SPEC_LIF, EMAX_SIC, and EMAX_LIF keywords in the CalFUSE parameter file (PARM_CAL) have the effects discussed in § 4.5.1.

The final assignment of each photon event to a channel is performed by cf_identify_channel, just as in § 4.5.2, but with two modifications: First, we consider only photon events with CHANNEL > 0; unassigned events (which are not motion corrected) remain unassigned. Second, we do not pad the extraction windows by an additional ±10 pixels in Y, although the extraction windows for histogram data are padded by ±8 Y pixels (or an amount equal to the binning factor in Y, if other than 8), as before.

For time‐tag data, cf_target_count_rate computes the count rate in the target aperture for the LiF and SiC channels. To account for dead‐time effects, the contents of the WEIGHT array are used. Events in airglow regions are excluded, but no other filters are applied to the data. Results are written to the LIF_CNT_RATE and SIC_CNT_RATE arrays of the time‐line table. For histogram data, the initial values of these arrays, taken from the housekeeping file (§ A3), are scaled by the value of the header keyword DET_DEAD.

The astigmatic height of FUSE spectra perpendicular to the dispersion axis is significant and varies as a function of wavelength (Fig. 3). Moreover, spectral features show considerable curvature, especially near the ends of the detectors, where the astigmatism is greatest. The subroutine cf_astigmatism shifts each photon event in X to correct for the spectral‐line curvature introduced by the FUSE optics, providing a noticeable improvement in spectral resolution for point sources (Fig. 6).

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The astigmatism correction is derived from observations of GCRV 12336, the central star of the Dumbbell Nebula (M27), which exhibits H₂ absorption features across the FUSE wave band. We cross‐correlate and combine the absorption features from a small range in X, fit a parabola to each set of combined features, compute the shift required to straighten each parabola, and interpolate the shifts across the wave band. Because an astigmatism correction has been derived only for point sources, no correction is performed on the spectra of extended sources, airglow spectra, or observations with APERTURE = RFPT.

The correction is stored in the calibration file ASTG_CAL as a two‐dimensional image representing the region of the detector containing the target spectrum. A separate image is provided for each aperture. The value of each image pixel is the astigmatism correction (ΔX in pixels) to be applied to that pixel. The entire image is shifted in Y to match the centroid of the target spectrum, and the appropriate correction is applied to each photon event in the target aperture. The corrected X coordinates are not written to the IDF, but are passed immediately to the wavelength‐assignment subroutine. In effect, we apply a two‐dimensional wavelength calibration that depends on both the X and Y coordinates of each photon event.

The wavelength calibration is stored as a binary table extension in the calibration file WAVE_CAL (§ 5.1); a separate extension is provided for each aperture. Wavelengths are tabulated for integral values of X, assumed to be in motion‐corrected FARF coordinates. Given the astigmatism‐corrected X and CHANNEL arrays, the subroutine cf_dispersion considers each aperture in turn and reads the corresponding calibration table. It interpolates between tabulated values of X to derive the wavelength of each photon event. Photon events not assigned to an aperture (CHANNEL = 0) are not wavelength calibrated.

The component of the spacecraft's orbital velocity in the direction of the target is stored in the ORBITAL_VEL array of the time‐line table. The component of the Earth's orbital velocity in the direction of the target is stored in the IDF file header keyword V_HELIO. Their sum is used to compute a time‐dependent Doppler correction, which is applied to each photon event by the subroutine cf_doppler_and_heliocentric. The resulting wavelength scale is heliocentric. Because histogram data are assigned identical arrival times, their Doppler correction is not time dependent. Histogram exposures are kept short (approximately 500 s) to minimize the resulting loss of spectral resolution. The final wavelength assigned to each photon event is stored in the LAMBDA array of the IDF.

Microchannel plates contribute to the detector background via beta decay of ⁴⁰K in the MCP glass. On orbit, cosmic rays add to this intrinsic background to yield a total rate of ∼0.5 counts cm⁻² s⁻¹. Scattered light, primarily geocoronal Lyα, contributes a well‐defined illumination pattern (Fig. 7) that varies in intensity during the orbit, with detector‐averaged count rates as small as 20% of the intrinsic background during the night, and 1–3 times the intrinsic rate during the day. We assume that the observed background consists of three independent components: a spatially uniform dark count and spatially varying day‐ and nighttime scattered‐light components. Properly scaling them to the data is thus a problem with three unknown parameters. We attempt to fit as many of these parameters as possible directly from the data. When such a fit is not possible, we estimate one or more components and fit the remainder.

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Background events due to the detector generally have pulse‐height values lower than those of real photons (§ 4.4.12). The observed dark count thus depends on the pulse‐height limits imposed on the data. An initial estimate of the dark count as a function of the lower pulse‐height threshold is read from the background characterization file (BCHR_CAL). The day and night components of the scattered‐light model are read from separate extensions of the appropriate time‐dependent background calibration file (BKGD_CAL). The background models are scaled to match the counts observed on unilluminated regions of the detector. The Y limits of these regions (selected according to the target aperture) are read from header keywords in the IDF. Airglow photons in these regions are excluded from the analysis. The day and night counts in the background regions of the detector are summed and recorded.

In its default mode, the subroutine cf_scale_bkgd estimates the uniform background as follows: the background regions of the day and night scattered‐light models are scaled by their relative exposure times, summed, and projected onto the X axis (to produce a histogram in X). A similar histogram (called the "empirical background spectrum") is constructed from the data. An iterative process is used to determine the uniform component and scattered‐light scale factor that best reproduce the observed X distribution of background counts. The uniform component is then subtracted from the day and night totals computed above, and the day and night components of the scattered‐light model are scaled to match the remaining observed counts.

If the empirical background spectrum is too faint, we do not attempt to fit it, but assume that the uniform component of the background is equal to the tabulated dark‐count rate scaled by the exposure time. The day and night components of the scattered‐light model are calculated as above. Users who require a more accurate background model may wish to combine data from multiple exposures before extracting a spectrum (see § 6.6). If the empirical background spectrum is very bright—as, for example, when nebular emission or a background star contaminates one of the other apertures (and thus the background‐sample region)—no fit is performed. Instead, the day and night components of the scattered‐light model are scaled by the day and night exposure times, the tabulated dark‐count rate is scaled by the total exposure time, and the three components are summed to produce a background image. This scheme is also used for histogram data. Because histogram files contain data only from the region about the desired extraction window, the background cannot be estimated from other regions of the detector. Fortunately, histogram observations typically consist of short exposures of bright targets, so the background is comparatively faint.

Our day and night scattered‐light models were derived from the sum of many deep background observations spanning hundreds of kiloseconds. Individual exposures that differ markedly from the mean were excluded from the sum. The data were processed only through the FARF‐conversion and data‐screening steps of the pipeline. Airglow features were replaced with a mean background interpolated along the dispersion (X) axis of the detector. An estimate of the uniform background component was subtracted from the final image, and the data were binned by 16 detector pixels in X. This process was performed on both day‐ and night‐only data sets. We produce a new set of background images every 6 to 12 months, as the effects of gain sag and adjustments of the detector high voltage slowly alter the relative sensitivity of the illuminated and background regions of the detectors.

Caveats: While early versions of the pipeline (through ver. 2.4) assume a 10% uncertainty in the background flux, propagating it through to the final extracted spectrum, CalFUSE version 3 treats uncertainties in the background as systematic errors and does not include them in the (purely statistical) error bars of the extracted spectra.

The algorithm assumes that the intensity of the uniform background is constant throughout an exposure. This would be the case if it were due only to the detector dark count, but in fact the uniform background includes a substantial contribution from the scattered light and is thus brighter during daytime portions of an exposure. The assumption of a constant uniform background can lead the algorithm to overestimate the scale factors for both the uniform and spatially varying components of the background model. A better scheme would be to fit the day and night components of the uniform background separately. Similarly, when the empirical background spectrum is very faint, adopting the tabulated value of the uniform background is not the best solution. It is likely that the scattered‐light component of the uniform background would be better estimated from the observed day and night backgrounds. The difference between the tabulated and observed levels of the uniform background will become greater as the mission extends into solar minimum and the intensities of both individual airglow features and the scattered‐light component of the uniform background continue to weaken.

Grating scattering of point‐source photons along the dispersion direction is potentially significant and is not corrected by the CalFUSE pipeline. Typical values are 1%–1.5% of the continuum flux in the SiC channels, and 10 times less in the LiF channels.

The optimal‐extraction algorithm (§ 4.9.4) requires as input a two‐dimensional probability array representing the distribution of flux on the detector. Separate probability arrays derived from high signal‐to‐noise ratio stellar observations have been computed for each channel and stored as image extensions in the weights calibration file (WGTS_CAL).

By construction, the Y dimension of the probability array represents the maximum extent of the extraction window for a particular aperture. For simplicity, all arrays employed by the optimal‐extraction algorithm are trimmed to match the probability array in Y. The centroids of the probability distribution and the target spectrum (recorded in the corresponding file headers) are used to determine the offset between detector and probability coordinates. In the X dimension, all arrays are binned to the output wavelength scale requested by the user. Default wavelength parameters for each aperture are specified in the header of the wavelength calibration file (WAVE_CAL); the default binning for all channels is 0.013 Å per output spectral bin, which corresponds to approximately 2 detector pixels. The background array, originally binned by 16 pixels in X, is rescaled to the width of each output wavelength bin by the subroutine cf_rebin_background. The probability array is rescaled by the subroutine cf_rebin_probability_array to have a sum of unity in the Y dimension for each wavelength bin.

A bad‐pixel mask with the same wavelength scale and Y dimensions as the probability array is constructed from the BPM file (§ 4.8) by the subroutine cf_make_mask. The array is initialized to zero. For each entry in the BPM file, the value of the WEIGHT array is added to the corresponding pixel of the bad‐pixel mask. The mask is then normalized and inverted so that the center of the deepest dead spot has a value of 0 and the regions outside are set to 1. The conversion from pixel to wavelength coordinates can open gaps in the mask, which appear as values of unity surrounded by pixels with lower values. We search for array elements that are larger than their neighbors and replace them with the mean value of the adjoining pixels. If the BPM file is absent or a particular aperture is free of bad pixels, all elements of the bad‐pixel mask are set to 1.

The extraction subroutine, cf_optimal_extraction, is called separately for each of the two target spectra (LiF and SiC). Inputs include the photon‐event list and the indices of events that pass through the various screenings, as well as the two‐dimensional (2D) background, probability, and bad‐pixel arrays described above. For numerical simplicity, extraction is performed using the WEIGHT of each photon event, rather than its ERGCM2 value. A pair of 2D data and variance arrays with the same dimensions as the probability array are constructed from the good photons whose CHANNEL values correspond to the target aperture. For time‐tag data, this process is straightforward: the LAMBDA and Y values of each photon event correspond to a particular cell in the data and variance arrays. That cell in the data array is incremented by the photon weight, while the corresponding cell in the variance array is incremented by the square of the weight. A 1D raw‐counts spectrum (useful for the statistical analysis of low–count‐rate data) is constructed simultaneously: for each photon event added to the data array, the appropriate bin of the counts spectrum is incremented by 1.

For histogram data, the process is more complex, because the original detector image is generally binned by 8 pixels in Y, and because each entry in the photon‐event list represents the sum of many individual photons. In the Y dimension, an event's WEIGHT is divided among 8 pixels (or the actual Y binning for that exposure, if different), according to the distribution predicted by the probability array. In the X dimension, each event is assumed to have a width in wavelength space equal to the mean dispersion per pixel for the channel (read from the DISPAPIX keyword of the WAVE_CAL file), and the WEIGHT of an event that spans the boundary between two output wavelength bins is divided between them. This smoothing in X helps to mitigate the "beating" that would otherwise occur between detector pixels and output wavelength bins.

One‐dimensional background, weights, and variance spectra are then extracted from the two‐dimensional background, data, and variance arrays. To ensure that the three spectra sample the same region of the detector, only cells in the 2D arrays for which the corresponding cell in the probability array has a value greater than 10⁻⁴ are included in the sum. These limits differ slightly from those defined in the aperture (CHID_CAL) calibration files. As a result, the ratio of the final weights and counts spectra may not be a constant. (Ideally, their ratio would equal the mean dead‐time correction for the exposure.) An initial flux spectrum equal to the difference of the weights and background spectra is used as input to the optimal‐extraction algorithm.

CalFUSE employs the optimal‐extraction algorithm described by Horne (1986), which requires as input the 2D data, background, probability, and bad‐pixel arrays and the 1D initial flux spectrum. Originally designed for CCD spectroscopy, the algorithm has been modified for the FUSE detectors. Specifically, instead of constructing a 2D spatial profile from each data set, we use a tabulated probability array; the 2D cosmic‐ray mask, an integer array in the original algorithm, is replaced with the bad‐pixel mask, which is a floating‐point array; and the 2D variance estimate is scaled by the bad‐pixel mask. Extraction is iterative: in the original version, iteration is performed until the cosmic‐ray mask stops changing. In our version, iteration continues until the output flux spectrum changes by less than 0.01 counts in all pixels. If the loop repeats 50 times, the algorithm fails. The number of iterations performed is written to the OPT_EXTR keyword of the output‐file header.

If optimal extraction is successful, the variance of the optimal spectrum is computed using the recipe of Horne (1986). We have adapted this recipe to produce weights and background spectra such that FLUX = WEIGHTS − BKGD. The resulting background spectrum is not smooth. Optimal extraction is not performed on the spectra of extended sources or on those for which the quality of the computed spectral centroid is not HIGH. (Both the centroid and its quality flag are stored in file header keywords.) In these cases, or if the optimal‐extraction algorithm fails, the initial flux, variance, weights, and background spectra are adopted.

However they are constructed, the final FLUX, ERROR (equal to the square root of the variance), WEIGHTS, and BKGD arrays (all in units of counts) are returned to the calling routine. For time‐tag data, the COUNTS array as described above is returned. For histogram data, the COUNTS array is computed by dividing the final WEIGHTS array by the mean dead‐time correction, which is stored in a file header keyword TOT_DEAD. Also returned is the QUALITY array. It is the product of the probability array and the bad‐pixel map, projected onto the wavelength axis and expressed as an integer between 0 and 100. Its value is 0 if all the flux in a wavelength bin is lost to a detector dead spot, 100 if no flux is lost.

Caveats: The optimal‐extraction algorithm is designed to improve the signal‐to‐noise ratio of the spectra of faint point sources. Unfortunately, it is in precisely these cases that the spectral centroid is most likely to be uncertain. Because proper positioning of the probability array is essential to the weighting scheme, observers of faint targets may wish to combine the IDFs from multiple exposures and recompute their spectral centroids before attempting optimal extraction.

Because the optimal‐extraction routine returns the final FLUX and ERROR arrays in units of counts, the spectral extraction module applies a flux calibration to both arrays using the subroutine cf_convert_to_ergs described in § 4.7. Dividing each array element by (EXPTIME × WPC), where EXPTIME is the length in seconds of the (screened) exposure and WPC is the width in angstroms of each output wavelength bin, completes the conversion to units of ergs cm⁻² s⁻¹ Å⁻¹. The format of the extracted spectral files is described in § A5.

Our principal wavelength calibration target is GCRV 12336, central star of the planetary nebula M27, whose spectrum exhibits a myriad of molecular‐hydrogen absorption features (McCandliss et al. 2007). For the SiC 1B channel, these data are supplemented at the shortest wavelengths by spectra of the hot white dwarf G 191‐B2B (Lemoine et al. 2002). For each channel, an M27 spectrum was fully reduced, corrected for astigmatism, and used to derive an empirical mapping of pixel to wavelength. A theoretical dispersion solution, derived from standard optical expressions, was fitted to the empirical data with only its constant term (the zero point of the wavelength scale) as a free parameter. This shifted theoretical dispersion solution was then used to generate the wavelength calibration file.

Early versions of the pipeline relied on the wavelength calibration to correct for nonlinearities in the detector X scale (the geometric distortion discussed in § 4.3.6). Correcting for this effect separately has greatly improved the accuracy of the FUSE wavelength scale. To determine the geometric distortion in the X dimension, a spline was fitted to the residuals from each aperture (expected minus observed X coordinate of each absorption feature; Fig. 8). In practice, residuals from all six apertures (both LiF and SiC channels) were included in the fit, but data from the other five apertures were weighted 100 times less than those for the aperture being fitted. The additional data points help to constrain the fit in wavelength regions where the data are sparse or missing. The spline fits from all six apertures were then used to construct the 2D map of detector distortions in the X dimension that is used by the geometric‐distortion routine described in § 4.3.6. The process is iterative, with the residuals (ideally) becoming smaller with each iteration.

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The scatter of individual measurements about the spline fit is in some cases caused by blended absorption lines, and in others by localized distortions induced by the fiber‐bundle structure of the MCPs. 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 detector pixels (0.025 Å, or 7 km s⁻¹) 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 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 FUSE wavelength calibration assumes that the motion‐corrected spectrum falls at a precise location on the detector. If it is shifted in X, then the wavelength scale of the extracted spectrum will suffer a zero‐point offset. For the guide channel (either LiF 1 or LiF 2), the dominant source of wavelength errors is thermally induced rotations of the spectrograph gratings, which depend on the satellite attitude. For the other channels, additional wavelength errors come from mirror misalignments that shift the target away from the center of the aperture. Such misalignments may produce zero‐point offsets of up to ±0.15 Å for point sources in the LWRS aperture. Offsets are less than ±0.02 Å for the MDRS aperture and are negligible for the HIRS aperture.

We define the zero point of our wavelength scale by requiring that the Lyβ airglow feature, observed through the HIRS aperture and processed as if it were a point source, be at rest in spacecraft coordinates when all Doppler corrections are turned off. The use of an airglow feature eliminates errors due to mirror motions in the nonguide channels, but not errors in the grating‐motion correction, so we measure the Lyβ line in some 200 background exposures and shift their mean velocity to 0 km s⁻¹. For each channel, all three apertures (HIRS, MDRS, and LWRS) use this HIRS‐derived wavelength scale (WAVE_CAL ver. 022 and greater).

The grating‐motion correction (§ 4.5.4) is designed to place the centroid of each Lyβ airglow feature at a fixed location in FARF coordinates. On average, it achieves that goal: for our sample of 200 background exposures, the measured velocity of the Lyβ line has a standard deviation of between 2 and 3 km s⁻¹, depending on the channel. Unfortunately, some combinations of pole and beta angle are not well corrected, leading to velocity offsets of 10 km s⁻¹ or more, and additional motions—of either the gratings or some other optical component—can shift the extracted spectra by several km s⁻¹ from one exposure to the next.

Figure 9 presents the measured wavelength of the interstellar O i λ1039 absorption feature in 47 exposures of the hot white dwarf KPD 0005+5106 obtained through the HIRS aperture. The 2001 and 2002 data show little scatter and yield a mean velocity of −10.7 ± 1.9 km s⁻¹. The 2003 data (all from a single observation) span nearly 10 km s⁻¹. The 2004 data (again from a single observation) are tightly correlated but offset by ∼7 km s⁻¹. These data were obtained at a spacecraft orientation (beta and pole angles) that is generally well corrected by our grating‐motion algorithm; apparently, some other effect is at work. The 2006 data come from the LiF 2 channel, which became the default guide channel in 2005 (§ 6.1).

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We do not recommend the general use of airglow lines to fix the absolute wavelength scale of point‐source spectra, for several 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, the jitter correction (for all channels) and the mirror‐motion correction (for the SiC channels) are inappropriate for airglow emission. Third, the Doppler correction for the spacecraft's orbital motion can degrade their resolution.

The FUSE wavelength scale is derived from astigmatism‐corrected point‐source spectra. Extended‐source (diffuse) spectra are not corrected for astigmatism. If point‐source data are processed with the astigmatism correction turned off, the resulting wavelength errors are less than about 4 detector pixels, consistent with the uncertainties in the wavelength scale. Therefore, the present FUSE wavelength calibration should be adequate for extended‐source spectra. Airglow lines are useful for determining the wavelength zero point for extended sources that fill the aperture.

The FUSE flux calibration is based on in‐flight observations of the well‐studied DA (pure hydrogen) white dwarfs listed in Table 1, which have been observed at regular intervals throughout the mission. For each channel, data from multiple stars are combined to track changes in the instrument sensitivity, using a technique similar to that developed by Massa & Fitzpatrick (2000) for the International Ultraviolet Explorer (IUE) satellite. The algorithm yields a series of time‐ and wavelength‐dependent sensitivity curves, as well as the spectrum of each star, in units of raw counts, as it would have appeared on a date early in the mission, which we choose to be T₀ = 1999 December 31. (We refer to the latter as " T₀ spectra.")

For each star, we generated a synthetic spectrum using the programs TLUSTY (ver. 200) and SYNSPSEC (ver. 48) of Hubeny & Lanz (1995). The non‐LTE pure‐hydrogen model atmospheres were computed according to a prescription by I. Hubeny (2003, private communication), using 200 atmospheric layers to ensure an optimal absolute flux accuracy. The atmospheric parameters listed in Table 1, consistent with HST, IUE, and optical observations, were used to compute the models (J. Holberg 2003, private communication). For G 191‐B2B, we used the model employed by Kruk et al. (1999) for the final Astro‐2 calibration of the Hopkins Ultraviolet Telescope (HUT). Observations of these stars with the Faint Object Spectrograph aboard HST have shown that the models, including parameter uncertainties, are consistent to within 2% at wavelengths longer than Lyα (Bohlin et al. 1995; Bohlin 1996). Uncertainties in the far‐ultraviolet wave band are slightly higher, as discussed by Kruk et al. (1999).

For each channel, the effective area in units of cm² is computed by dividing one or more T₀ spectra in units of counts s⁻¹ Å⁻¹ by a synthetic white dwarf spectrum in units of photons cm⁻² s⁻¹ Å⁻¹. Sensitivity curves for the LiF 1A and SiC 1A channels are presented in Figure 10. (Effective‐area curves for all FUSE channels are available from MAST.) The sensitivity of the LiF 1A channel decreased by ∼15% over the first 3 years of the mission, but appears to have stabilized; that of the SiC 1 channel has declined by ∼45% since launch and is falling still (although slowly). Effective‐area curves (AEFF_CAL) for each channel and detector segment were generated at 3 month intervals until the loss of the third reaction wheel in 2004 December; we plan to generate them at 6 month intervals for the duration of the mission.

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Caveats: We do not attempt to correct spectra obtained through the MDRS and HIRS apertures for changes in instrument sensitivity, but employ a single effective‐area curve for each. The low throughput of these apertures, combined with the likelihood that their spectra are nonphotometric, makes tracking changes in their sensitivity both more difficult and less useful than for the LWRS aperture.

The greatest uncertainties in a line or continuum flux derived from a FUSE spectrum are due to systematic effects. An estimate of the uncertainty in our flux calibration can be obtained by comparing the effective‐area curves derived from different white dwarf stars. Differences among the curves reflect errors in both the model atmospheres and the stellar parameters on which they are based. In most channels, the scatter in the derived effective areas is between 2% and 4%.

The photometric accuracy of FUSE spectra is subject to numerous effects that cannot be fully corrected by the CalFUSE pipeline. A target centered in an aperture of the guide channel (LiF 1 or LiF 2) may not be centered in the corresponding apertures of the other three channels. Since the loss of the first two reaction wheels in 2001, spacecraft drifts may move the target out of even the guide‐channel aperture. While the pipeline does attempt to flag times when the target is out of the aperture, the algorithm used is conservative in that it underestimates the time lost to pointing errors (§ 4.4.6). The user is advised to consult the count‐rate plots generated by the pipeline (suffix "rat.gif"; § 4.10) and the LIF_CNT_RATE and SIC_CNT_RATE arrays of the IDF time‐line table to determine the photometric quality of an exposure. Using tools available from MAST or the user‐defined good‐time intervals discussed in § 4.4.7, users can reject time periods when the count rate is low, or rescale the flux of low–count‐rate exposures.

When a point‐source target falls near the top or bottom edge of an aperture, vignetting in the spectrograph may attenuate the target flux in a wavelength‐dependent way. Astigmatism gives FUSE spectra the shape of a bow tie (Fig. 3). If vignetting is important, then the spectrum will lie below the center of the aperture on one side of the bow tie, and above it on the other. Significant flux loss is possible in wavelength regions far from the center of the bow tie.

Other systematic uncertainties are imposed by various detector flat‐field effects; their relative importance depends on one's scientific goals. For narrow emission lines, flux uncertainties are dominated by the moiré pattern (high‐frequency ripples due to beating among the arrays of microchannel pores in the MCP stack; § 6.4), unless the observation was obtained using an FP split or the equivalent was achieved via grating and mirror motions. For broad features, the moiré is not important, but larger scale flat‐field features are. These effects are discussed in the FUSE Instrument and Data Handbook. Finally, when fitting a spectral energy distribution, the greatest uncertainty is caused by worms (§ 6.3), which may depress the observed flux over tens of angstroms by 50% or more.

The FUSE flux calibration is derived from point‐source targets. Because the distribution of flux in the cross‐dispersion direction differs for point and extended sources, it is possible that the instrumental sensitivity may also differ; this question has not been explored in detail. Extended spectra are less affected by worms (§ 6.3) than are point‐source spectra. Moreover, because the spectrum of a diffuse emitter is spread over a larger region of the detector, it will suffer less from local flat‐field effects.