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4.12 Instrumental Polarisation

The Stokes parameters measured on astronomical targets may be contaminated by unplanned polarisation within the instrument and polarisation of the sky background. The instrumental polarisation must be derived. However, this requires knowledge of calibration parameters such as the polariser throughputs and their polarisation efficiencies. Both of these parameters could not be derived from laboratory measurements at the required accuracy. We here introduce polarisation weight factors (${w_i}$) applied to the measured polariser intensities $S_i$. The polarisation weight factors serve as calibration parameters to correct for the instrumental polarisation. They are given by:
\begin{displaymath} w_i = 2 \cdot \frac{S_i}{I} \end{displaymath} (4.3)

and its standard deviation can be estimated according to:
\begin{displaymath} \Delta w_i = \sqrt{ (2 \cdot \frac {\Delta S_i}{I})^2 + (2 \cdot \frac {S_i \cdot \Delta I}{I^2})^2} \end{displaymath} (4.4)

where I is the total intensity as measured through ISOCAM's entrance hole, $\Delta I$ is its standard deviation and $\Delta S_i$ is the standard deviation of the three polariser intensities.
We define the corrected intensities as:
\begin{displaymath} s_i = \frac {S_i}{w_i} \end{displaymath} (4.5)

The best measure of the instrumental polarisation is given by CAM05 raster observations on the zodiacal background. Assuming that the zodiacal background is flat and unpolarised, it is natural that any measured degree of polarisation should reflect the instrumental polarisation of ISOCAM. For the zodiacal light, we therefore write the Stokes parameters as:
\begin{displaymath}S(zodi) = (I, 0, 0).\end{displaymath} (4.6)

The weight factors ($w_i$) for all observed configurations are given in Table 4.4. If one sets the polarisation weight factors to unity, one derives from the zodiacal light images a polarisation vector. Those vectors are given in Table 4.5. They do not suggest a dependency on wavelength nor on lens (pfov). Already for the 3 $^{\prime \prime }$ pfov the signal of the zodiacal light tends to be weak and yields poor precision. For the 6 $^{\prime \prime }$ lens the mean instrumental polarisation is around $p$ = 1.0$\pm$0.3%.
Table 4.4: Polarisation weight factors $w_1$, $w_2$ normalised to $w_3$ = 1.
Filter $\lambda_{ref}$ lens $w_1$ $\Delta w_1$ $w_2$ $\Delta w_2$
  [$\mu$m] [ $^{\prime \prime }$]   [%]   [%]
LW2 6.7 6 0.9862 $<$0.1 0.9937 $<$0.1
LW10 12.0 6 0.9763 $<$0.1 0.9926 $<$0.1
LW8 11.3 6 0.9829 $<$0.1 0.9886 $<$0.1
LW3 14.3 6 0.9845 $<$0.1 0.9937 $<$0.1
LW9 14.9 6 0.9873 $<$0.1 0.9957 $<$0.1
LW7 9.6 3 0.9824 2.1 0.9845 1.9
LW8 11.3 3 0.9638 3.0 0.9740 3.0
LW3 14.3 3 0.9614 0.4 0.9987 0.2
LW9 14.9 3 0.9749 2.0 0.9865 2.2
LW3 14.3 1.5 0.9737 4.4 1.0022 4.2


Table 4.5: Instrumental polarisation.
Filter $\lambda_{ref}$ lens $p$ $\Theta$
  [$\mu$m] [ $^{\prime \prime }$] [%] [$^{\circ}$]
LW2 6.7 6 0.80 $\pm$ 0.1 24 $\pm$ 4
LW10 12.0 6 1.41 $\pm$ 0.1 29 $\pm$ 3
LW8 11.3 6 1.02 $\pm$ 0.1 18 $\pm$ 3
LW3 14.3 6 0.91 $\pm$ 0.1 26 $\pm$ 3
LW9 14.9 6 0.75 $\pm$ 0.1 28 $\pm$ 4
LW7 9.6 3 1.12 $\pm$ 1.28 11 $\pm$ 37
LW8 11.3 3 2.20 $\pm$ 2.05 16 $\pm$ 27
LW3 14.3 3 2.56 $\pm$ 0.90 37 $\pm$ 18
LW9 14.9 3 1.47 $\pm$ 1.47 22 $\pm$ 27
LW3 14.3 1.5 1.85 $\pm$ 3.3 40 $\pm$ 38

The zodiacal light calibration observations give a good measure of the LW flat-fields (Biviano et al. 1998c, [7]). By combining the flat-fields through the polarisers to calculate, for each detector element, a Stokes vector, residual polarisation patterns can be noticed. There is no strong dependency of the polarisation pattern on the filter. It is quite similar for the 1.5 $^{\prime \prime }$ and 3 $^{\prime \prime }$ lens but shows a more aligned structure using the 6 $^{\prime \prime }$ lens. One corrects for this instrumental pattern in the data by using the polarisation flat-fields. If such flat-fields cannot be derived from one's own observation one may use those stored in the calibration flat-field library. For a detailed description of CAM's polarisation capabilities and how the instrumental polarisation was determined see Siebenmorgen 1999, [55].
next up previous contents index
Next: 4.13 Global Error Budget Up: 4. Calibration and Performance Previous: 4.11 Astrometric Uncertainties
ISO Handbook Volume II (CAM), Version 2.0, SAI/1999-057/Dc