As shown in figure 
there are really three angular cuts which
have to be made on the data: 
, the sector half-angle; 
,
the minimum polar scattering angle; and 
, the maximum polar
scattering angle. It has been shown in a derivation of the FOM
[Mer93] that the FOM is maximized when 
is a
minimum, and this is true when 
or
. Further Monte Carlo studies of this estimate show
that it is valid and that the FOM is fairly insensitive to changes in the
sector half-angle [Mer93]. Therefore, 
is used for
all of the analysis in this thesis. A histogram showing the event
distribution in 
for an average run is shown in figure .
Figure: Raw azimuthal 
distribution of double-scattering events in
the polarimeter. 
is defined as a horizontal scatter to the left.
The spikes are the result of finite size of the detector cells.
The sinusoidal nature of the 
distribution that would be expected
from equation is not obvious in figure . In
order to show that there is an actual asymmetry in the 
distribution
it is necessary to take a difference between the 
distribution when
the beam is in a 
state and when it is a 
state. The
results of this subtraction can be seen in figure along with
a smooth spline fit to the data which makes obvious the sinusoidal
asymmetry.
Figure: Difference between the 
distributions in the 
state and
the 
state for a single sample run. The dotted line is the actual
difference in the data and the solid line is a smooth spline fit to that
difference.
The polar scattering angle 
window also needs to be adjusted in
order to optimize FOM. A raw 
distribution is shown in figure
.
Figure: Raw histogram of the polar scattering angle, 
,
distribution in the polarimeter. The spikes are the result of the limited
position resolution of the detector cells.
A lower bound, 
, on the polar scattering angle is used
because the events with a small 
have a large uncertainty in
. As 
becomes smaller the finite position resolution of
the detector cells makes it difficult to determine if a scattering took
place to the left sector or right sector. The upper bound 
on 
serves to cut off the point at which the analyzing power of the
reaction 
becomes negative. Obviously, including such
events will dilute the analyzing power of the detector and reduce the FOM.
This takes place at 
[Arn96] as shown
in figure .
Figure: Calculated values for the Analyzing Power of the
reaction [Arn96].
In the same manner that figure shows the difference between
the 
distributions of the (+) and (-) beam states figure
shows the full angular distribution of that same difference.
Figure: Full angular distribution of the difference between (+) and (-)
beam state. 
is shown in the angular direction and 
in the
radial direction. Relative height indicates the event count.
The asymmetry in the distribution of scatters from the analyzer plane is very obvious.