4.8 The Spectral Response Function of the CVF

The Spectral Response Function (SRF) has been measured for all CVF segments using photometric calibration stars. The photometry of stars observed in CVF mode was done as described for the filter photometry (Section 4.1.1). For the SW detector, only one star (HIC 96441) was used, for which four individual CVF scan observations were available. For the LW detector, several observations of four stars: Sirius, HIC 96441, $\delta$ Draconis and $\gamma$ Draconis, were used for computing the SRF. The star fluxes were derived using aperture photometry in all cases. Special care was taken to avoid the ghost reflection (see Section 4.9). The integrated ghost flux can be up to a 30% of the star flux and can have a serious impact on the observed spectrum. Thus, for CVF aperture photometry on point sources, it is recommended to use the same apertures used for the calibration standards: radii of 6, 4, 3 pixels for 1.5, 3 and 6 $^{\prime \prime }$ pfov respectively and a background determination in an annulus 2 pixels wide.

**Table 4.3:** *Standard stars used for the derivation of the CVF Spectral Response Function.*
Name	HIC	HR	HD	SAO	R.A.	Dec.	Spec. Type
$\gamma$ Draconis	87833	6705	164058	30653	17:56:36.37	+51:29:20.0	K5III
$\delta$ Draconis	94376	7310	180711	18222	19:12:33.30	+67:39:41.5	G9III
-	96441	7469	185395	31815	19:36:26.54	+50:13:16.0	F4V
Sirius	32349	2491	48915	151881	06:45:08.92	16:42:58.0	A0m

The total signals measured in detector units were divided by the stellar flux densities (in Jy) predicted by stellar models (see also Section 4.1). For this we need to consider that the stars observed for the CVF calibration have quite different stellar types. The spectra of the earlier type stars are dominated by atomic lines whereas molecular bands dominate the spectra of the cool stars. Thus, for the star HIC 96441 (F4V) we used the Kurucz model provided by the Ground Based Preparatory Programme (Hammersley et al. 1998, [36]; Hammersley & Jourdain de Muizon 2001, [37]), while for the other three stars, with later spectral types, we used models provided by Decin et al. 2003b, [27] up to 12 $\mu$ m and by Cohen et al. 1995, [19] for the longer wavelengths. For more details on the characteristics and limitations of the different models used see Decin 2001, [25]. Their usage for the CVF calibration is discussed in Blommaert et al. 2001a, [12]; 2001b, [13]. A weighted average of all the resulting SRF estimates was computed, after carefully excluding measurements strongly affected by transient effects. The final SRFs were smoothed using a 3-pole digital low-pass filter, with a cut-off at 25%, in order to reduce the noise features (that could be misinterpreted as spectral lines when the SRF is used to derive the spectrum of a given object). The derived SW CVF SRF is shown in Figure 4.20 together with the associated error bars, which do not include systematic errors, i.e. due to `ghosts' (see Section 4.9). The average random error of the SW CVF SRF is $\sim$ 3%, but for some SW CVF positions the error can be as large as 23%.

**Figure 4.20:** *The SW CVF SRF within its $\pm 1 \sigma$ confidence band, where $\sigma$ is the rms derived from the set of measurements used to obtain the SRF.*
$\resizebox {13cm}{10cm}{\includegraphics{swcvflast.ps}}$

Before determining the average LW SRF, all measurements were corrected for the change of responsivity in orbit (a decrease of 6% from start to end, as was shown in Section 4.1.2). This correction reduced the overall rms from 4% to 3%. The observations divided by their input spectra are shown in Figure 4.21. The repeatability of the CVF photometry on the same star is excellent, $\pm$ 3% rms.

**Figure 4.21:** *The different LW SRF determinations based on the observations of 4 different calibration stars. It includes different pfov measurements. The rms is 3-4%.*
$\resizebox {13cm}{10cm}{\includegraphics{all_srfs.ps}}$

The rms of the LW CVF1 SRF is 3% of the measured value, on average, and always less than 5%, except for the CVF step positions of the shortest (4.96 $\mu m$ , rms = 11%) and the longest wavelength (9.58 $\mu m$ , rms = 48%). Fortunately, the longest wavelength of LW CVF1 is also covered by the LW CVF2, with a much higher accuracy. The mean rms of the CVF2 SRF is 4% of the measured value. Originally, a wavelength range was offered to the observer from 9.003 to 16.52 $\mu$ m. The SRF at CVF positions outside the recommended range is also available in the calibration files, but these are affected by larger errors (still below 10% rms up to 17.16 $\mu$ m but up to more than 100% for the extreme position at 17.34 $\mu$ m). When analysing a CVF spectrum of an astronomical target, the largest uncertainties come from the reflected light (Section 4.9) and the long time needed to stabilise the measured signal (Section 4.4) which will affect mostly the beginning of a CVF measurement or when there is a change between CVF segments. The resulting CVF SRFs and their error bars are given in the calibration files CSWCVF, CLWCVF1 and CLWCVF1 (Sections 6.1.15 and 6.1.16). The determination of the SRF of the LW CVF is described in detail in Blommaert et al. 2001a, [12] and for the SW SRF in Biviano et al. 1998b, [6].

4.8.1 Spectral purity

From observations of planetary nebulae taken during the PV Phase, the central wavelengths of two lines, [Ne II] $\lambda$ 12.81 $\mu$ m and [S IV] $\lambda$ 10.51 $\mu$ m, were derived (by simple Gaussian fitting over the continuum). They were found to fall at the expected CVF scan positions, within a few hundredths of a CVF step. Transient effects may slightly change the observed position of the line, by less than a tenth of a CVF step. However, the wavelength purity is reduced when the source is not centred at the middle of the array. An analysis of the [Ne III] $\lambda$ 15.55 $\mu$ m line central position in an ISOCAM CVF image of M17 showed that the central observed wavelength position of the [Ne III] line was red-shifted 0.09 $\mu$ m at the left edge of the ISOCAM array compared to the observed wavelength at the centre. At the position of CVF2 corresponding to the wavelength of the [Ne III] line such a shift corresponds to roughly one CVF step. At the right edge of the ISOCAM array, however, there is no significant wavelength shift. On the other hand, there is no wavelength-dependence in the top-down direction of the array, as expected from the orientation of the CVF with respect to the array. In addition, there is an indication that the wavelength shift is wavelength dependent, being larger at longer wavelengths.

Next: 4.9 Ghosts and Straylight Up: 4. Calibration and Performance Previous: 4.7 Spacecraft Pointing Jitter

ISO Handbook Volume II (CAM), Version 2.0, SAI/1999-057/Dc