E f i npix total – SIGMA LBA-708 User Manual
Page 140
parameter to describe quality of a Top Hat’s energy distribution. A perfect Top Hat has a single fluence
value that makes up 100 percent of energy and plots curve A. The area under this curve yields the
Top Hat Factor value of 1.0. A Gaussian beam plots the curve labeled C. The area, and thus the
Factor, for beam C is 0.5.
Real-world Top Hat beams will plot curves somewhere between A and C, such as curve B. Thus, as the
area under the curve approaches unity, the quality of the Top Hat is seen to improve.
Figure 56
The equation below describes how the curve of a particular beam profile would be derived from the
pixel intensity data. The plot of such a curve is formed by the sum of the product of the number of
pixels and the corresponding fluence for each fluence value, in a range starting from the maximum
fluence value to the current value.
( )
E f
i NPix
Total
i Pk
f
=
×
=
∑
Where:
E
=
The fraction of
energy
contained between the fluence value and
the peak value.
f
=
The fluence value.
Pk
=
The peak fluence value.
Total
= The
total
energy
in the beam.
Npix
=
The number of pixels that have the value of I.
To find the Top Hat Factor, sum the area under the curve formed from the above equation, as shown
below:
F
E
E
Pk
f
f
f
Pk
=
+
∑
+
=
−
1
1
1
2
Operator’s Manual
LBA-PC
140