%% $Date: 2012-07-06 17:42:54#$
%% $Revision: 152 $
\index{scattering\_angles}
\algdesc{Scattering Angles}
{ %%%%%% Algorithm name %%%%%%
scattering\_angles
}
{ %%%%%% Algorithm summary %%%%%%
Calculates the scattering angle for each pixel of an image given the camera viewing angle and solar vector.
}
{ %%%%%% Category %%%%%%
Radiation
}
{ %%%%%% Inputs %%%%%%
$n_x$ & Coeff & Number of pixels in x dimension \\
$n_y$ & Coeff & Number of pixels in y dimension \\
$\theta_c$ & Array[$n_x$, $n_y$] & Camera viewing zenith angle [degrees] \\
$\Phi_c$ & Array[$n_x$, $n_y$] & Camera viewing azimuth angle [degrees] (0\deg = flight direction) \\
$\theta_\odot$ & Coeff & Solar zenith angle [degrees] \\
$\Phi_\odot$ & Coeff & Solar azimuth angle [degrees] (0\deg = North)
}
{ %%%%%% Outputs %%%%%%
$\theta_{scat}$ & Array[$n_x$, $n_y$] & Scattering angles of each pixel [degrees] \\
}
{ %%%%%% Formula %%%%%%
\begin{align*}
 \theta_{scat} & = \cos^{-1} (-\sin{\theta_\odot} \cos{\Phi_\odot} \sin{\theta_c} \cos{\Phi_c} 
 - \sin{\theta_\odot} \sin{\Phi_\odot} \sin{\theta_c} \sin{\Phi_c} 
 + \cos{\theta_\odot} \cos{\theta_c})
\end{align*}
}
{ %%%%%% Author %%%%%%
Andre Ehrlich, Leipzig Institute for Meteorology (a.ehrlich@uni-leipzig.de)
}
{ %%%%%% References %%%%%% 

}


