All Figures

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{h4342f1a.ps}}\vspace*{5mm} \resizebox{8.8cm}{!}{\includegraphics{h4342f1b.ps}} \end{figure}$ Figure 1: Distribution of magnetic field strengths inferred from the analysis of a simulated internetwork region (10 000 pixels) where the actual distribution is $p(B) = C \exp{ (-B/250)}$ and each resolution element contains one single magnetic field ( $\beta =0$ ). Solid and dashed lines give the PDFs resulting from the infrared and the visible lines, respectively. The dotted line represents the original PDF. The binsize is 25 G. Top: Noise added to Stokes V at the level of 10^-4 of the continuum intensity $I_{\rm c}$ . Bottom: Noise at the level of $10^{-3}~I_{\rm c}$ .
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{h4342f2a.ps}}\vspace*{5mm} \resizebox{8.3cm}{!}{\includegraphics[clip]{h4342f2b.ps}} \end{figure}$ Figure 2: Distribution of magnetic field strengths inferred from the analysis of a simulated internetwork region (10 000 pixels) where the actual distribution is $p(B) = C \exp{ (-B/250)}$ and two magnetic fibrils coexist in each resolution element with $\beta = 0.5$ . Solid and dashed lines represent the PDFs resulting from the infrared and the visible lines, respectively. The dotted line gives the original field strength distribution. Top: Noise added at the level of $10^{-4}~I_{\rm c}$ . Bottom: Noise at the level of $10^{-3}~I_{\rm c}$ .
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In the text

$\begin{figure} \par\resizebox{8.6cm}{!}{\includegraphics[clip]{h4342f3.ps}} \end{figure}$ Figure 3: Distribution of magnetic field strengths determined from an inversion of the Stokes V profiles of the visible lines emerging from a simulated internetwork region where only fields of 200 G are present. Noise of $10^{-3}~I_{\rm c}$ has been added to the Stokes V profiles. If the resulting PDF is taken at face value, 27% of the pixels would be associated with strong fields (>800 G).
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{h4342f4.ps}} \end{figure}$ Figure 4: Stokes V signal simulated with a magnetic field strength of 200 G, $\alpha = 0.05$ , and noise at the level of $10^{-3}~I_{\rm c}$ (thin solid line). For this particular realization of the noise, the best-fit profile (thick solid line) indicates a field strength of 1250 G. The smooth thin solid line is the original spectrum without noise.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{h4342f5.ps}} \end{figure}$ Figure 5: Position of the peak of the PDF inferred from the visible lines as a function of the signal-to-noise ratio in Stokes V. Only fields of 200 G are present in the original distribution.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{h4342f6a.ps}}\vspace*{4mm} \resizebox{8.3cm}{!}{\includegraphics{h4342f6b.ps}} \end{figure}$ Figure 6: Top: simulated (solid line) and best-fit (dashed line) profiles of the visible lines for $\alpha =1$ and $\beta = 0.5$ . The fit is so good that the dashed line is indistinguishable. Bottom: same for the infrared lines.
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In the text

$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{h4342f7.ps}} \end{figure}$ Figure 7: Field strengths inferred from the fit of simulated profiles assuming that they are produced by one magnetic atmosphere, as a function of $\beta$ (the fraction of magnetized area covered by weak fields). The Stokes V spectra have been constructed by mixing the signals of two atmospheres having magnetic fields of 200 G and 1200 G.
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In the text

$\begin{figure} \par\resizebox{8.6cm}{!}{\includegraphics[clip]{h4342f3.ps}} \end{figure}$	Figure 3: Distribution of magnetic field strengths determined from an inversion of the Stokes V profiles of the visible lines emerging from a simulated internetwork region where only fields of 200 G are present. Noise of $10^{-3}~I_{\rm c}$ has been added to the Stokes V profiles. If the resulting PDF is taken at face value, 27% of the pixels would be associated with strong fields (>800 G).
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$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{h4342f4.ps}} \end{figure}$	Figure 4: Stokes V signal simulated with a magnetic field strength of 200 G, $\alpha = 0.05$ , and noise at the level of $10^{-3}~I_{\rm c}$ (thin solid line). For this particular realization of the noise, the best-fit profile (thick solid line) indicates a field strength of 1250 G. The smooth thin solid line is the original spectrum without noise.
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$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{h4342f5.ps}} \end{figure}$	Figure 5: Position of the peak of the PDF inferred from the visible lines as a function of the signal-to-noise ratio in Stokes V. Only fields of 200 G are present in the original distribution.
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$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{h4342f6a.ps}}\vspace*{4mm} \resizebox{8.3cm}{!}{\includegraphics{h4342f6b.ps}} \end{figure}$	Figure 6: Top: simulated (solid line) and best-fit (dashed line) profiles of the visible lines for $\alpha =1$ and $\beta = 0.5$ . The fit is so good that the dashed line is indistinguishable. Bottom: same for the infrared lines.
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$\begin{figure} \par\resizebox{8.3cm}{!}{\includegraphics[clip]{h4342f7.ps}} \end{figure}$	Figure 7: Field strengths inferred from the fit of simulated profiles assuming that they are produced by one magnetic atmosphere, as a function of $\beta$ (the fraction of magnetized area covered by weak fields). The Stokes V spectra have been constructed by mixing the signals of two atmospheres having magnetic fields of 200 G and 1200 G.
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