The spectral luminosity normalized to one for photon-photon collisions
$\lgg$ is given by the formula\footnote{The tilde denotes quantities
related to the second beam}\cite{ginzburg:2}
\input{lumifml}
with the conversion factor $k=\frac{N_{{\gamma}'}}{N_e}$ where $N_e$ is
the number of incoming electrons and $N_{{\gamma}'}$ is the number of scattered
photons. The fraction of $\eplus\eminus$ cms energy transformed to
$\gamma\gamma$ cms energy is given by $z$ with the definition $z^2=y\tilde{y}$.
Inserting equation \ref{cross_section} into \ref{lumi_formel} one
finds:
\input{l}
\input{la}
\input{lb}
\input{lc}
From the point of view of the requirements of the luminosity it is
ideal to choose the polarisation to get a spectral distribution as
hard as possible. This means $\pee\pge=\pez\pgz=-1$.
The difference between unpolarized and ideal polarized initial states is
shown in figure \ref{lumibild_1}.
\begin{figure}
\begin{center}
\mbox{\epsfig{file=bild3.eps,width=12cm}}
\end{center}
\caption{Spectral luminosity for $\pee=\pge=\pez=\pgz=0$ (dashed) and
\mbox{$\pee\pge=\pez\pgz=-1$ (solid), ${\omega}_0=1.26\, eV, E=250\, GeV$.}}
\label{lumibild_1}
\end{figure}
For the evaluation of top particle production rate it is interresting to
distinguish between
the four distributions for different final state photon polarisations. This is
done in figure \ref{lumibild_2} for ideal polarisation, where $h_{\gamma\gamma}
=\pgse-\pgsz$ denotes the total helicity of the photon-photon system.
The case $h_{\gamma\gamma}=0$ is appropriate for the production of $\esn$
toponium resonances so that $\pee=\pez$ and $\pge=\pgz$ is a suitable choise
for the Stokes parameters.
The contributions from $\pgse=-1,\pgsz=1$ and $\pgse=1,\pgsz=-1$ are identical
and therefor added to one curve.
\begin{figure}
\begin{center}
\mbox{\epsfig{file=bild4.eps,width=12cm}}
\end{center}
\caption{Spectral luminosity dependence on final state photon polarisation,
\mbox{${\omega}_0=1.26\, eV, E=250\, GeV$.}}
\label{lumibild_2}
\end{figure}