All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2990fg1a.eps}\hspace*{2mm} \includegraphics[width=8.8cm,clip]{2990fg1b.eps}\end{figure}$ Figure 1: $P(\lambda ^2)$ for a simple, yet non-trivial Faraday dispersion function: a synchrotron emitting and Faraday rotating slab at $-2 \le \phi \le +2\ \mbox{rad}\ \mbox{m}^{-2}$ (the Galactic foreground) and a Faraday thin source at $\phi = +10\ \mbox{rad}\ \mbox{m}^{-2}$ (a distant radio lobe). The lefthand panel shows qualitatively how the individual (Q, U) vectors of the foreground and the lobe relate to the total polarization $\Vert P\Vert$ and the polarization angle $\chi$ . It reflects the situation around $\lambda ^2\approx 0.38$ m². $P_{\rm l}$ rotates counter clockwise around the moving pivot $P_{\rm fg}$ . The righthand panel shows the polarization angle as a function of $\lambda ^2$ , plotted along the lefthand vertical axis. The total polarization and Stokes Q of the foreground are plotted along the righthand vertical axis.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2990fg2.eps}\end{figure}$ Figure 2: Cartoon sketching the relation between emission, $n_{\rm e}\vec{B}_\parallel$ , Faraday depth $\phi$ , location x, and observed Faraday spectrum. The top panel depicts the physical situation. The arrows represent $n_{\rm e}\vec{B}_\parallel$ . Longer arrows mean larger $\Vert n_{\rm e}\vec{B}_\parallel\Vert$ . The direction of the arrow indicates the direction of the parallel component of the magnetic field. The x coordinate represents physical distance from the observer. The observer is located at the far left of the plots. The x axis is severely compressed in two places. Empty areas have neither emission nor rotation. White blocks represent areas with only Faraday rotation. Grey areas with an arrow have both emission and rotation (area A and B) and grey areas without an arrow have only emission (area C). There are two lines of sight, labelled 1 and 2. Line of sight 1 goes through areas A, B, and C. Line of sight 2 misses area B as well as the adjacent non emitting Faraday rotating white boxes. The middle panel plots Faraday depth $\phi$ as a function of physical distance x for both lines of sight. The bottom panel shows $\Vert F(\phi)\Vert$ , the observed polarized surface brightness $\left(\mbox{rad}\ \mbox{m}^{-2}\right)^{-1}$ , for both lines of sight. The peaks in the spectra are labelled with the associated areas.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{2990fg3.eps}\end{figure}$ Figure 3: RMTF of a 92 cm dataset taken with the Westerbork Synthesis Radio Telescope. There are 126 usable channels in the dataset. All (Q,U) vectors have been derotated to $\lambda ^2_0 = 0$ . Note the rapid rotation of the RMTF, making it difficult to measure accurate polarization angles in a sampled RM cube.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{2990fg4.eps}\end{figure}$ Figure 4: RMTF of the same dataset as described in Fig. 3. This time, however, all $\vec{P}$ vectors have been derotated to the average $\lambda ^2$ . It is seen that the imaginary part remains almost constant within the central peak of the RMTF.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{2990fg5.eps}\end{figure}$ Figure 5: Absolute value of the approximated Faraday dispersion function of several Faraday thin sources with different spectral indices. The $\lambda ^2$ grid is the same previously mentioned 126 channel dataset. The overall bandwidth $\Delta \nu /\nu = 17\%$ . Steeper spectra give deeper nulls. For comparison the normalized approximated Faraday dispersion function of a Faraday thick slab was included.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{2990fg6.eps}\end{figure}$ Figure 6: Comparison of merit function $\rho$ ( top) and $-\Vert R\Vert$ ( bottom). The dotted line through $\rho$ is at $y = \pi ^2/12$ .
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In the text

$\begin{figure} \par\mbox{ \includegraphics[width=8.7cm,clip]{2990fg7a.eps}\hspace*{2mm} \includegraphics[width=8.7cm,clip]{2990fg7b.eps} } \end{figure}$ Figure 7: Both plots show, from top to bottom, merit function $\rho$ and $-\Vert R(\phi)\Vert$ . The lefthand panel uses eight sample points, equally spaced in frequency. The frequency sampling of the righthand panel is identical to the sampling used in Fig. 6. The sampling in the lefthand panel has the same extent in $\lambda ^2$ -space as the sampling of the righthand panel.
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In the text

$\begin{figure} \mbox{ \includegraphics[width=8.7cm,clip]{2990fg8a.eps}\hspace*{2mm} \includegraphics[width=8.7cm,clip]{2990fg8b.eps} } \end{figure}$ Figure 8: This plot shows the effect of tweaking the exact frequencies of eight sampling points. The lefthand panel shows the same RMTF as the lefthand panel of Fig. 7. In the righthand plot, however, we stretched the frequency intervals such that low frequency intervals are wider than high frequency intervals. This eliminates the resonances from the lefthand plot.
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In the text

$\begin{figure} \par\includegraphics[width=8.6cm]{2990fg9.eps}\end{figure}$ Figure 9: Comparison between the standard error in RM obtained by traditional line fitting (line) to simulated RM-synthesis experiments where a parabola was fit to the main peak of the Faraday dispersion function (dots). The 126 $\lambda ^2$ points used for this figure are the same as the ones used in Fig. 3.
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In the text

$\begin{figure} \par\includegraphics[width=16cm,clip]{2990fg10.eps}\end{figure}$ Figure 10: Comparison of Q-only RM-synthesis ( left) and Q+URM-synthesis ( right) for Faraday depths $\phi = 8\ \mbox{rad}\ \mbox{m}^{-2}$ ( top) and $\phi = 74\ \mbox{rad}\ \mbox{m}^{-2}$ ( bottom). The panels show total linear polarization in grey scale. The scale runs from 0.15 mJy beam^-1 rmtf^-1 to 1.5 mJy beam^-1 rmtf^-1.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2990fg11}\end{figure}$ Figure 11: The three instrumental parameters that determine the output of a Faraday rotation experiment.
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In the text

$\begin{figure} \par\includegraphics[width=17.2cm,clip]{2990fgB1.eps}\end{figure}$ Figure B.1: Wavelength range: 3.6- $50\ \mbox{cm}$ .

In the text

$\begin{figure} \par\includegraphics[width=17.2cm,clip]{2990fgB2.eps}\end{figure}$ Figure B.2: Wavelength range: 60- $78\ \mbox{cm}$ .

In the text

$\begin{figure} \par\includegraphics[width=17.2cm,clip]{2990fgB3.eps}\end{figure}$ Figure B.3: Wavelength range: 81- $95\ \mbox{cm}$ .

In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{2990fg3.eps}\end{figure}$	Figure 3: RMTF of a 92 cm dataset taken with the Westerbork Synthesis Radio Telescope. There are 126 usable channels in the dataset. All (Q,U) vectors have been derotated to $\lambda ^2_0 = 0$ . Note the rapid rotation of the RMTF, making it difficult to measure accurate polarization angles in a sampled RM cube.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{2990fg4.eps}\end{figure}$	Figure 4: RMTF of the same dataset as described in Fig. 3. This time, however, all $\vec{P}$ vectors have been derotated to the average $\lambda ^2$ . It is seen that the imaginary part remains almost constant within the central peak of the RMTF.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{2990fg6.eps}\end{figure}$	Figure 6: Comparison of merit function $\rho$ ( top) and $-\Vert R\Vert$ ( bottom). The dotted line through $\rho$ is at $y = \pi ^2/12$ .
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$\begin{figure} \par\mbox{ \includegraphics[width=8.7cm,clip]{2990fg7a.eps}\hspace*{2mm} \includegraphics[width=8.7cm,clip]{2990fg7b.eps} } \end{figure}$	Figure 7: Both plots show, from top to bottom, merit function $\rho$ and $-\Vert R(\phi)\Vert$ . The lefthand panel uses eight sample points, equally spaced in frequency. The frequency sampling of the righthand panel is identical to the sampling used in Fig. 6. The sampling in the lefthand panel has the same extent in $\lambda ^2$ -space as the sampling of the righthand panel.
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$\begin{figure} \mbox{ \includegraphics[width=8.7cm,clip]{2990fg8a.eps}\hspace*{2mm} \includegraphics[width=8.7cm,clip]{2990fg8b.eps} } \end{figure}$	Figure 8: This plot shows the effect of tweaking the exact frequencies of eight sampling points. The lefthand panel shows the same RMTF as the lefthand panel of Fig. 7. In the righthand plot, however, we stretched the frequency intervals such that low frequency intervals are wider than high frequency intervals. This eliminates the resonances from the lefthand plot.
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$\begin{figure} \par\includegraphics[width=8.6cm]{2990fg9.eps}\end{figure}$	Figure 9: Comparison between the standard error in RM obtained by traditional line fitting (line) to simulated RM-synthesis experiments where a parabola was fit to the main peak of the Faraday dispersion function (dots). The 126 $\lambda ^2$ points used for this figure are the same as the ones used in Fig. 3.
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$\begin{figure} \par\includegraphics[width=16cm,clip]{2990fg10.eps}\end{figure}$	Figure 10: Comparison of Q-only RM-synthesis ( left) and Q+URM-synthesis ( right) for Faraday depths $\phi = 8\ \mbox{rad}\ \mbox{m}^{-2}$ ( top) and $\phi = 74\ \mbox{rad}\ \mbox{m}^{-2}$ ( bottom). The panels show total linear polarization in grey scale. The scale runs from 0.15 mJy beam^-1 rmtf^-1 to 1.5 mJy beam^-1 rmtf^-1.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2990fg11}\end{figure}$	Figure 11: The three instrumental parameters that determine the output of a Faraday rotation experiment.
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