FP Wavelength Calibration

The wavelengths transmitted by each FP were determined by the gap between the FP meshes (equation 1.12). The position of the FP meshes was recorded digitally by the electronics with FP encoder values between 0 and 4095. Calibration tests on the ground showed that the separation of the meshes, $d$, was a cubic function of encoder value and so equation 1.12 can be written as,

$$\frac{m \lambda}{2}=A + Bx + Cx^{2} + Dx^{3}$$ (A.14)

where $x$ is the FP encoder value and $A$, $B$, $C$ and $D$ are the cubic coefficients that form the calibration. In order to derive these coefficients, narrow lines of known wavelength were observed using several different FP orders. These observations were carried out using the instrument in a dedicated calibration mode using a `calibration observation implementation file' (COIF). Temporal trends were checked by weekly observations of a few selected sources and the results were found to be stable with time. The final accuracy achieved in the wavelength calibration depended on the FP encoder range used, with errors increasing towards higher encoder values. The overall accuracy for FPS was between 4 and 6 km s$^{-1}$. The root mean squared (RMS) errors for FPL were calculated from a study of 21 observations of NGC7027 and found to be between 2.7 and 4.4 km s$^{-1}$ (Gry et al., 2002). A further systematic check of the FPL calibration was carried out using 16 CO lines observed with the L03 mode towards Orion BN/KL (Hutchinson et al., 2002). This was carried out after reports of problems for a few specific line observations using FPL. The results showed that for L03 FPL data the residual velocity differences had an RMS of 6 km s$^{-1}$ and were never worse than 11 km s$^{-1}$. The recommended uncertainties given in the LWS Handbook are $\pm6$ km s$^{-1}$ for FPS and $\pm13$ km s$^{-1}$ for FPL, although the relative uncertainty within a given observation was generally much smaller than this.

Wavelength calibration for non-prime data that were recorded within each FPs nominal range should be exactly the same as for prime data. This is because there was no difference in instrumental configuration between prime and non-prime data. When FPL was used outside of its nominal range at wavelengths shorter than 70 $\mu$m a systematic shift is present in the wavelength calibration when compared with the prime data (using FPS). This may be due to the fact that the cubic fit was not carried out using lines below 70$\mu$m for FPL. A further possibility is that it is due to an effect from the extra phase shift in Equation 1.4 which becomes more important at shorter wavelengths. Wavelength shifts for the specific lines investigated in later chapters were 8 km s$^{-1}$ at 63 $\mu$m and 22 km s$^{-1}$ at 53 $\mu$m.