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Subsections



5.11 Grating Resolution and Characterisation of the Line
Profiles

5.11.1 Preparation of the data

The study of the grating profile was performed with data obtained over the ISO lifetime for wavelength calibration (see Table 5.12 and Figure 5.22). In order to have a homogeneous sampling, only those data obtained with AOT L01, an oversampling of 8, 6 scans of the full grating range and the same number of forward and backward scans were used.

The data processing was performed with the ISAP software. The standard processing of the selected observations is summarized by the following scheme:

The products were thus one spectrum per scan direction per spectral line per detector per observation per object.


5.11.2 Stability of the line profiles

In order to define as general a profile as possible, parameters susceptible of inducing profile variations were looked for in a step by step approach. When a parameter had proved not to induce any significant variation, the profiles were averaged over this parameter for the subsequent study.

In conclusion, we have created two mean grating profiles (one for SW and one for LW detectors) which are the average of all lines listed in Table 5.12 except the 57 $\mu $m line on SW2.


5.11.3 Characteristics of the profiles. Comparison to Gaussians.

When considering all the LWS optical elements and detector characteristics, the wavelength response function is not expected to be Gaussian. It is however always convenient when measuring a line intensity to be able to use a Gaussian aproximation.

Figure 5.24: Measured grating profiles (plus signs) and comparison with a Gaussian fit (solid line). The residuals, i.e. the difference between the measured profile and the Gaussian fit, are also shown (dashed line). Up: profile for short wavelength detectors (SW1 to SW5) ; down: profile for long wavelength detectors (LW1 to LW5).
\rotatebox {90}{\resizebox{8cm}{!}{\includegraphics{sw_fit_point.ps}}} \rotatebox {90}{\resizebox{8cm}{!}{\includegraphics{lw_fit_point.ps}}}

Figure 5.24 shows the comparison of the measured mean profiles with a Gaussian function fitted to them. It also shows the residuals, i.e. the differences between the two profiles.
Table 5.16 lists the line flux, full width at half maximum (FWHM) and peak heights both for the measured profiles and for the fitted Gaussian. This shows that the error made on the determination of the flux with a Gaussian fit is only of the order of $2\%$.


Table 5.16: Parameters of the measured grating profiles compared with the results of Gaussian fits.
  Observed mean profile   Gaussian fit to the mean profile
  FWHM line flux height   FWHM line flux height
  [$\mu $m] (normalised     [$\mu $m] (normalised  
    to peak=1)       to peak=1)  
SW detectors $0.308\pm0.005$ $0.314\pm0.008$ 1.00   $0.283\pm0.009$ $0.322\pm0.010$ $1.06\pm0.02$
               
LW detectors $0.611\pm0.014$ $0.637\pm0.014$ 1.00   $0.584\pm0.015$ $0.644\pm0.016$ $1.04\pm0.02$

The line full widths at half maximum that we measure on our profiles are slightly larger than those measured before launch: 0.31 instead of 0.29 for the short wavelength detectors, and 0.61 instead of 0.60 for the long wavelength detectors. This is likely due to the broadening effect of transients.


5.11.4 Effect of a lower spectral sampling

The above study of the line profile has been conducted with the highest oversampling permitted in the observations, an oversamping of 8, i.e. eight points per spectral element. However, in AOTs L01 and L02, four different oversamplings were permitted: 8, 4, 2 and 1. Following the Nyquist theorem, an oversampling of two or higher allows derivation of the line flux with a precision better than 5% (a sampling of 1 point per spectral resolution element would be clearly insufficient). However, we would like to warn the user that a Gaussian fit to observations obtained with an oversampling of 2 or even 4 might give results with a higher error than the one quoted above for an oversampling of 8. This is due to the fact that when a line is scanned quickly, the transient effects are more important and tend to broaden the line. This effect should be reduced once a transient correction (Section 6.9) is available.


next up previous contents index
Next: 5.12 Fabry-Pérot Wavelength Calibration Up: 5. Calibration and Performance Previous: 5.10 Grating Wavelength Calibration
ISO Handbook Volume III (LWS), Version 2.1, SAI/1999-057/Dc