All Figures

$\begin{figure} \par\includegraphics[width=4.1cm,clip]{3273f01a.ps}\hspace*{0.1mm} \includegraphics[width=4.1cm,clip]{3273f01b.ps}\end{figure}$ Figure 1: Intensity image of Uranus ( left) and Neptune ( right) in the i-Band. North is up and East to the left. The size of the images is $6.1''\times 6.1''$ .
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In the text

$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f02a.ps}\hspace*{-1mm} \includegraphics[width=4.2cm,clip]{3273f02b.ps}\end{figure}$ Figure 2: Stokes Q ( left) and U ( right) images for Uranus in the i-band. The grey scale in the Stokes Q and U images is normalized to the peak intensity $I_{\rm peak}$ and spans the range from $-0.5\%$ (black) to $+0.5\%$ (white).
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In the text

$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f03a.ps}\hspace*{-1mm}... ...3c.ps}\hspace*{-1mm} \includegraphics[width=4.2cm,clip]{3273f03d.ps}\end{figure}$ Figure 3: Stokes Q and U images for Neptune taken in the R-filter ( top) and z-filter ( bottom). The grey scale is normalized to the peak intensity $I_{\rm peak}$ and ranges from $-0.5\%$ (black) to $+0.5\%$ (white).
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In the text

$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f04a.ps}\hspace*{-0.5mm} \includegraphics[width=4.2cm,clip]{3273f04b.ps}\end{figure}$ Figure 4: Radial Stokes $Q_{\rm r}$ ( left) and $U_{\rm r}$ ( right) for Uranus in the i-band. The grey scale is normalized to the peak intensity $I_{\rm peak}$ and goes from $-0.5\%$ (black) to $+0.5\%$ (white).
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In the text

$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f05a.ps}\hspace*{-0.5mm} \includegraphics[width=4.2cm,clip]{3273f05b.ps}\end{figure}$ Figure 5: Radial Stokes $Q_{\rm r}$ ( left) and $U_{\rm r}$ ( right) for Neptune in the R-band. The grey scale is normalized to the peak intensity $I_{\rm peak}$ and goes from $-0.5\%$ (black) to $+0.5\%$ (white).
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In the text

$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f06a.ps}\hspace*{-0.5mm} \includegraphics[width=4.2cm,clip]{3273f06b.ps}\end{figure}$ Figure 6: Radial Stokes parameter $Q_{\rm r}$ for Uranus in the narrow $\lambda$ 673 nm filter ( left) and the z filter ( right); grey scale as in Fig. 5.
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In the text

$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f07a.ps}\hspace*{-0.5mm} \includegraphics[width=4.2cm,clip]{3273f07b.ps}\end{figure}$ Figure 7: Radial Stokes parameter $Q_{\rm r}$ for Neptune in the i ( left) and z filters ( right); grey scale as in Fig. 5.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.3cm,clip]{3273f08.ps}\end{figure}$ Figure 8: Uranus radial profile for intensity I and radial polarization $Q_{\rm r}$ ( upper panel) in the i and z filters. Both I and $Q_{\rm r}$ are normalized to the peak flux at r=0. The lower panel shows the corresponding normalized radial polarization $Q_{\rm r}/I$ . The squares indicate the same curve for the narrow-band filter $\lambda =673$ nm. The error bars for the latter points are about twice the size of the broad-band filters. The radial distance is given in arcsec; $R_{\rm planet} = 1.75''$ for Uranus.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.3cm,clip]{3273f09.ps}\end{figure}$ Figure 9: The radial profile of Neptune with intensity I and the radial polarization $Q_{\rm r}$ ( upper panel) and the corresponding normalized radial polarization $Q_{\rm r}/I$ ( lower panels) in the R, i, and z filters (as in Fig. 8). The radial distance is given in arcsec; $R_{\rm planet} = 1.12''$ for Neptune.
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In the text

$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f10a.ps}\hspace*{0.01m... ....ps}\hspace*{0.01mm} \includegraphics[width=4.2cm,clip]{3273f10d.ps}\end{figure}$ Figure 10: Modeling of the degradation of the polarization Q due to the cancellation of opposite polarization components +Q and -Qcaused by the seeing limited resolution; a) no seeing, b) seeing $0.3~R_{\rm planet}$ , c) seeing $0.5~R_{\rm planet}$ , and d) seeing $0.8~R_{\rm planet}$ . The grey scale spans for all panels the range from $-1\%$ (black) to $+1\%$ (white) of the peak intensity of the initial (no seeing) intensity image.
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In the text

$\begin{figure} \par {\includegraphics[width=8.2cm,clip]{3273f11.ps} } \end{figure}$ Figure 11: Measurable radial polarization $\langle Q_{\rm r}\rangle_{\rm seeing}$ relative to the initial radial polarization $\langle Q_{\rm r}\rangle_0$ as a function of the seeing for a planet with a (semi-infinite, conservative) Rayleigh-scattering atmosphere. The seeing (FWHM) is expressed in units of the radius of the planetary disk.
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In the text

$\begin{figure} \par {\includegraphics[width=8cm,clip]{3273f12.ps} } \end{figure}$ Figure 12: Normalized reflected intensity I, radial polarization flux $Q_{\rm r}$ and normalized polarization $Q_{\rm r}/I$ as functions of disk radius r for a planet at exact opposition (phase angle $\alpha =0^\circ$ ) with a semi-infinite, Rayleigh-scattering atmosphere and single scattering albedos $\omega =1$ (thick solid), 0.99 (dash dotted), 0.95 (dashed), 0.90 (dotted), 0.80, 0.60, 0.40 and 0.20 (thin solid). Where space permits the curves are labeled with the corresponding $\omega$ .
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In the text

$\begin{figure} \par {\includegraphics[width=8cm,clip]{3273f13.ps} } \end{figure}$ Figure 13: Intensity I ( top), radial polarization $Q_{\rm r}$ ( middle), and normalized polarization $Q_{\rm r}/I$ ( bottom) as functions of disk radius r for a planet at exact opposition (phase angle $\alpha =0^\circ$ ) with a finite Rayleigh scattering atmosphere. Models with an optical thickness of the Rayleigh-scattering layer of $b_\tau =1.0$ (thick lines) and $b_\tau =0.15$ (thin lines) are shown, each for three ground albedos $A_{\rm ground}=0.8,~0.25,$ or 0.0. The curves were constructed with a spline interpolation from the tabulated values from Coulson et al. (1960) indicated by $\diamond$ ( $A_{\rm ground}=0.8$ ), $\times$ ( $A_{\rm ground}=0.25$ ), and $\bigtriangleup$ ( $A_{\rm ground}=0.0$ ).
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In the text

$\begin{figure} \par {\includegraphics[width=8.8cm,clip]{3273f14.ps} } \end{figure}$ Figure 14: Geometric albedo $A_{\rm g}$ versus averaged radial polarization for the observations of Uranus (squares) and Neptune ( $\times$ ) and the Rayleigh scattering models. Broad band filters are indicated with R, i, and z, and narrow band filters for Uranus with CH₄( $\lambda =729$ nm) and "c'' for continuum ( $\lambda =673$ nm). The semi-infinite Rayleigh scattering models are plotted as triangles connected by a solid line, while the finite models define a grid (diamonds). Grid points with the same ground albedo $A_{\rm ground}=0.8,0.25,0.0$ are connected with a dashed line, and points with the same optical thickness for the Rayleigh scattering layer $b_\tau$ with a dotted curve. From top to bottom the $b_\tau$ -curves for 0.50, 0.25 (indicated), 0.15, 0.10, 0.05, and 0.02 are plotted. The limiting case $b_\tau =0$ , i.e. a bare Lambert surface, is indicated with filled circles ( $\bullet$ ).
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In the text

$\begin{figure} \par\includegraphics[width=4.1cm,clip]{3273f01a.ps}\hspace*{0.1mm} \includegraphics[width=4.1cm,clip]{3273f01b.ps}\end{figure}$	Figure 1: Intensity image of Uranus ( left) and Neptune ( right) in the i-Band. North is up and East to the left. The size of the images is $6.1''\times 6.1''$ .
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$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f02a.ps}\hspace*{-1mm} \includegraphics[width=4.2cm,clip]{3273f02b.ps}\end{figure}$	Figure 2: Stokes Q ( left) and U ( right) images for Uranus in the i-band. The grey scale in the Stokes Q and U images is normalized to the peak intensity $I_{\rm peak}$ and spans the range from $-0.5\%$ (black) to $+0.5\%$ (white).
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$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f03a.ps}\hspace{-1mm}... ...3c.ps}\hspace{-1mm} \includegraphics[width=4.2cm,clip]{3273f03d.ps}\end{figure}$	Figure 3: Stokes Q and U images for Neptune taken in the R-filter ( top) and z-filter ( bottom). The grey scale is normalized to the peak intensity $I_{\rm peak}$ and ranges from $-0.5\%$ (black) to $+0.5\%$ (white).
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$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f04a.ps}\hspace*{-0.5mm} \includegraphics[width=4.2cm,clip]{3273f04b.ps}\end{figure}$	Figure 4: Radial Stokes $Q_{\rm r}$ ( left) and $U_{\rm r}$ ( right) for Uranus in the i-band. The grey scale is normalized to the peak intensity $I_{\rm peak}$ and goes from $-0.5\%$ (black) to $+0.5\%$ (white).
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$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f05a.ps}\hspace*{-0.5mm} \includegraphics[width=4.2cm,clip]{3273f05b.ps}\end{figure}$	Figure 5: Radial Stokes $Q_{\rm r}$ ( left) and $U_{\rm r}$ ( right) for Neptune in the R-band. The grey scale is normalized to the peak intensity $I_{\rm peak}$ and goes from $-0.5\%$ (black) to $+0.5\%$ (white).
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$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f06a.ps}\hspace*{-0.5mm} \includegraphics[width=4.2cm,clip]{3273f06b.ps}\end{figure}$	Figure 6: Radial Stokes parameter $Q_{\rm r}$ for Uranus in the narrow $\lambda$ 673 nm filter ( left) and the z filter ( right); grey scale as in Fig. 5.
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$\begin{figure} \par\includegraphics[width=4.2cm,clip]{3273f07a.ps}\hspace*{-0.5mm} \includegraphics[width=4.2cm,clip]{3273f07b.ps}\end{figure}$	Figure 7: Radial Stokes parameter $Q_{\rm r}$ for Neptune in the i ( left) and z filters ( right); grey scale as in Fig. 5.
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$\begin{figure} \par\includegraphics[angle=-90,width=8.3cm,clip]{3273f09.ps}\end{figure}$	Figure 9: The radial profile of Neptune with intensity I and the radial polarization $Q_{\rm r}$ ( upper panel) and the corresponding normalized radial polarization $Q_{\rm r}/I$ ( lower panels) in the R, i, and z filters (as in Fig. 8). The radial distance is given in arcsec; $R_{\rm planet} = 1.12''$ for Neptune.
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$\begin{figure} \par {\includegraphics[width=8.2cm,clip]{3273f11.ps} } \end{figure}$	Figure 11: Measurable radial polarization $\langle Q_{\rm r}\rangle_{\rm seeing}$ relative to the initial radial polarization $\langle Q_{\rm r}\rangle_0$ as a function of the seeing for a planet with a (semi-infinite, conservative) Rayleigh-scattering atmosphere. The seeing (FWHM) is expressed in units of the radius of the planetary disk.
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