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32.8 Wavelength Calibration

The principal sources of uncertainty in FOS wavelength calibration are:

Filter-grating wheel (FGW) non-repeatability (includes systematics).
Residual image displacement after GIM correction.
Target miscentering (target acquisition).
Accuracy and applicability of the dispersion solutions.
Internal and external wavelength system offsets.
Spacecraft motions.

All FOS wavelengths are vacuum wavelengths! This is different from IUE and, of course, ground-based observations.

The FOS dispersion relations are polynomial fits, typically cubics, that relate the measured x-position, in diodes, of the centroids of well-known internal Pt-Ne lamp emission lines, the template spectra, to their vacuum wavelengths. The arc spectra were secured by observations entirely internal to the FOS, called WAVECALS, which were not impacted by the spherical aberration of the primary mirror or the introduction of COSTAR. Although dozens of epochs of internal WAVECAL exposures were obtained over the lifetime of the instrument, the FOS default (pipeline) wavelength calibration is a set of dispersion relations based upon a single epoch of observation made in June, 1991.

Systematic differences of up to 1 diode (~250 km/sec at high dispersion; ~1250 km/sec at low dispersion) between the default wavelength calibration and the wavelength scale appropriate to a random observation were possible. The bulk of these differences were attributable to FGW non-repeatability. In order to remove the influence of FGW position differences and achieve the full capability of FOS wavelength accuracy, a WAVECAL exposure had to be taken consecutively with the science exposure without any motion of the FGW in between.

For any individual disperser, the applicability of the default dispersion relation to your observation, that is the uncertainty in the routine standard FOS wavelength calibration, depended on the factors discussed below:

Filter-grating wheel (FGW) non-repeatability: The FGW non-repeatability introduces a 1 uncertainty of ~0.12 diodes. This corresponds to ~30 km s^-1 for the high dispersion gratings. The largest (peak-to-peak) variations observed were of the order of 1 diode. The full range of variation was as likely to occur over a few days as over a few years. On average no large time-related changes have been observed for the wavelength calibration for any disperser and detector combination.

Recall that the standard wavelength solution is not a mean of many dispersion curves, rather it is based on a single epoch. As a result, we must consider the possibility that the reference epoch could have been obtained near an extremum of the FGW positional distribution. There is evidence to suggest this may be the case for several gratings. Therefore, a possible systematic shift of up to one full diode (250 km/sec at high dispersion) may exist between the standard wavelength calibration and the calibration appropriate to your data.

The only way to avoid the large uncertainties introduced by FGW non-repeatability was to have included a WAVECAL exposure before or after the science exposure without any intervening motion of the FGW. If you have an FOS/BL G130H or G160L observation, you can estimate the FGW offset by determining the observed wavelength of Lyman alpha.

Target mis-centering (target acquisition accuracy): The second largest (and most common) component of FOS wavelength uncertainty is that produced by the target not being at the center of the science aperture. For the most precise FOS acquisitions, the worst-case centering accuracy was 0.025" or 0.08 diodes (20 km/sec at high dispersion).

Even if the target was well centered in the aperture, the highest possible accuracy could be achieved only if wavelength calibration spectra were taken together with the science data without moving the FGW in between.

Target centering accuracy can be assessed with the FOS paper products.

GIM effects: Residual inaccuracies in the magnetic deflection after GIM correction can result in peak-to-peak spectral displacements of 0.06 diodes (~15 km/sec at high dispersion).

You can examine the individual readouts of a RAPID sequence or use task deaccum (see Chapter 33) for an ACCUM spectrum to see if the centroids of your features are displaced from one group to another.

Accuracy and applicability of the dispersion solution: The rms errors in the various pipeline dispersion relations range between 0.01 and 0.08 diodes ¹ with 0.035 diodes being a typical value for FOS dispersion fits in general. However, some spectral regions in the arc spectra have fewer lines than do others (see FOS ISR 067).

Line measurement: The typical 1 centroiding accuracy for FOS arc lines at high dispersion is 0.02 diodes. You should also consider the measurement uncertainty for lines in your spectrum and may have poorer accuracies.

Spacecraft motion: No correction is made for spacecraft orbital motion around the Earth or for Earth orbital motion around the Sun (see section 33.3 for determining heliocentric corrections for Earth orbital motion only). HST orbital motion can produce an uncertainty of up to 0.034 diodes. Uncorrected Earth orbital motion can produce an uncertainty of up to 0.12 diodes.

Internal-to-external wavelength system offsets: Since the beam from the internal lamps, unlike that for an external source, does not completely fill the collimator, there can be a slight difference in illumination of the dispersers by the two types of sources that leads to a small shift between the measured positions of the same wavelength in internal and external source spectra. A correction for this offset has to be taken into account in the absolute wavelength calibration. Consecutive observations of a radial velocity standard source and an internal WAVECAL were used to determine this internal-to-external offset of the wavelength scale. Internal-to-external offsets appear to be grating dependent and there is weak evidence of some wavelength dependence for at least one grating.

For example, the FOS/RD G570H appears to record velocities in the 4800-5000 Å region that are approximately 50 km/sec more positive than those in the 5800-6500 Å region. Whether this effect is due to a paucity of lines for an adequate definition of the dispersion relation shortward of 5000 Å. or is a wavelength-dependent internal-to-external offset inherent to the grating is currently under investigation. Regardless of the resolution of this matter, the effect is real and should be included in any comparison of velocities measured in these two wavelength regions.

The mean internal-to-external offsets of the FOS wavelength calibration are 0.102 +/- 0.1 diodes for FOS/BL and 0.176 +/- 0.105 diodes for FOS/RD.

Summary: Addition of all the random uncertainties listed above in quadrature allows us to characterize the wavelength uncertainty in the measurement of a well-defined line in the spectrum of an object that has been precisely centered in the science aperture with the most accurate FOS target acquisition strategy.

If, as was usually the case, no contemporaneous WAVECAL was taken, the overall 1 random uncertainty is 0.16 diodes for the accuracy with which the wavelength scale is known in an individual FOS spectrum. The absolute wavelength accuracy is compromised by the single epoch nature of the default dispersion fits, and the possibility of a residual FGW displacement between your observation and that of the observations that defined the dispersion relation. At this time, therefore, the worst-case disagreement between your observations and the standard wavelength scale must be assumed for any given grating setting unless you have independent confirmation of the wavelength scale. This is 1 diode.
If a contemporaneous WAVECAL allows the removal of FGW uncertainty, the overall 1 uncertainty is 0.11 diodes.

If the full measure of wavelength accuracy is important for your purposes, you should check the exposure logsheet or Phase II RPS2 (pre-COSTAR RPSS) specification file as described in section 30.4 in order to determine whether a WAVECAL exposure was made consecutively with the science exposures without motion of the FGW.

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¹ FOS ISRs 067, 149, and 156.

stevens@stsci.edu