\begin{table}
\caption{\label{tab:raytau30}Reflectivity $I(\alpha)$, polarization fraction $q(\alpha)$ and polarized intensity $Q(\alpha)$ phase curves for a very deep 
   ($\tau=30$) conservative $(\omega=1)$ Rayleigh scattering atmosphere above a perfectly
  reflecting Lambert surface (surface albedo $A_{\rm S}=1$). }
\small%\centerline
 {
\begin{tabular}{rcrcc}
\hline\hline
$\alpha$ [$^\circ$] & $I(\alpha)$ & $q(\alpha)$ [\%]& $Q(\alpha)$ & $a(\alpha)$ \\
\hline
2.5     &       0.795   &       0.0     &       0.0000  &               \\
7.5     &       0.785   &       0.4     &       0.0031  &               \\
12.5    &       0.766   &       1.1     &       0.0084  &               \\
17.5    &       0.740   &       2.1     &       0.0155  &               \\
22.5    &       0.708   &       3.4     &       0.0241  &       1.85    \\
27.5    &       0.671   &       5.1     &       0.0342  &       1.86    \\
32.5    &       0.630   &       6.9     &       0.0435  &       1.87    \\
37.5    &       0.587   &       9.1     &       0.0534  &       1.89    \\
42.5    &       0.542   &       11.4    &       0.0618  &       1.91    \\
47.5    &       0.497   &       13.9    &       0.0691  &       1.94    \\
52.5    &       0.453   &       16.6    &       0.0752  &       1.98    \\
57.5    &       0.410   &       19.3    &       0.0791  &       2.03    \\
62.5    &       0.368   &       22.0    &       0.0810  &       2.08    \\
67.5    &       0.329   &       24.6    &       0.0809  &       2.14    \\
72.5    &       0.292   &       27.0    &       0.0788  &       2.21    \\
77.5    &       0.259   &       29.1    &       0.0754  &       2.29    \\
82.5    &       0.228   &       30.7    &       0.0700  &       2.39    \\
87.5    &       0.199   &       31.9    &       0.0635  &       2.49    \\
92.5    &       0.174   &       32.5    &       0.0566  &       2.62    \\
97.5    &       0.150   &       32.5    &       0.0488  &       2.77    \\
102.5   &       0.130   &       31.8    &       0.0413  &       2.95    \\
107.5   &       0.111   &       30.5    &       0.0339  &       3.16    \\
112.5   &       0.094   &       28.6    &       0.0269  &       3.42    \\
117.5   &       0.079   &       26.2    &       0.0207  &       3.76    \\
122.5   &       0.066   &       23.4    &       0.0154  &               \\
127.5   &       0.054   &       20.3    &       0.0110  &               \\
132.5   &       0.043   &       17.0    &       0.0073  &               \\
137.5   &       0.033   &       13.7    &       0.0045  &               \\
142.5   &       0.025   &       10.4    &       0.0026  &               \\
147.5   &       0.018   &       7.3     &       0.0013  &               \\
152.5   &       0.013   &       4.4     &       0.0006  &               \\
157.5   &       0.008   &       2.0     &       0.0002  &               \\
162.5   &       0.005   &       0.0     &       0.0000  &               \\
167.5   &       0.002   &       -1.4    &       0.0000  &               \\
172.5   &       0.001   &       -1.9    &       0.0000  &               \\
177.5   &       0.000   &               &               &               \\     
\hline                                                           
\end{tabular}}
\medskip
This model approximates well a conservative, semi-infinite Rayleigh scattering atmosphere. Additionally the fit parameter $a(\alpha)$ for the parametrization of the polarized intensity $Q(\alpha)$ (Eq.~(\ref{eq:Qfit})) is given for relevant phase angles.\protect\\
The statistical error of the Monte Carlo calculation for $I(\alpha)$ is smaller than 0.001 for all $\alpha$. The uncertainty of the polarization fraction is less than 0.1\% for phase angles between 5 and 165 degrees. Extrapolating the intensity $I$ towards $\alpha=0^\circ$ with a quadratic least-squares fit to the first four points ($\alpha = 2.5^\circ,\ldots, 17.5^\circ$) yields a value $I(0^\circ) = 0.7970$. This agrees with the exact solution $I(0^\circ)=0.7975$ from Prather (\cite{prather74}) to the third digit. 
\end{table}