7.11 Wavelength Scale and Resolution

  Over the extent of a single image, the true grating equation $m\lambda=d(\sin \alpha + \sin \beta)$ can be approximated by a straight linear relationship between $\lambda$ and x. The result is accurate to pixel (0.3 km s ^-1), provided the correct number is chosen for the Å per pixel. The actual dispersion (0.0015 mm)/[2(1800 mm) tan $\beta$] with $\alpha=\beta$ ranges from $2.088\times 10^{-6}\lambda$ for position 1 ($\alpha$ and $\beta$ = 63°.38) to
2.054×10^-6$\lambda$ in the vertical direction due to the fact that the dispersion planes of the two gratings are not precisely perpendicular.

For wavelength zero points, the telluric absorption features from atomic oxygen in either of the two excited fine-structure levels provide a good absolute reference. These features are fairly plentiful in the IMAPS spectral range (Morton 1991), and, unlike the absorptions from the ground fine-structure level, they rarely arise from the interstellar medium. There is always enough atomic oxygen above the 295 km altitude of Astro-SPAS to show strong features, regardless of zenith angle or position in the orbit (day/night).

If the oxygen features are not strongly saturated, they can be used to measure a lower limit for the wavelength resolving power. Provided that there are no differences in the bulk motions of the atmosphere along the line of sight, the line widths should be consistent with the thermal doppler broadening for T = 1000 K (Meier 1991). For observations of $\gamma^2$ Vel, Fitzpatrick & Jenkins (1995, in preparation) found the instrumental profile FWHM to be 7 pixels (4 km s^-1)after modeling the expected thermal profile widths of the oxygen features. This profile, somewhat worse than we hoped for, represents the combined effect of various types of smearing, such as any residual defocus or aberrations, the occasional small movements of the grating (§7.7), and the size of the limit cycle in the Astro-SPAS pointing control system.