User guide

Page 106 Document No: 11294 LBA-USB User Guide
4.19 Top Hat Factor
The Top Hat Factor provides a numerical measure of quality for a Top Hat beam
profile. It is a normalized value that compares your beam profile against a perfect Top
Hat--a perfect Top Hat being a beam with vertical sides and an absolutely uniform
intensity on the top. A Factor value of 1.0 describes a perfect Top Hat.
Examining a plot of a beam’s energy fraction versus its normalized fluence derives the
Top Hat Factor. The energy fraction is defined as the fraction of total energy above a
particular fluence value. See figure below. If we calculate the area under the energy
fraction curve, we will have a single normalized 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 2 – Top Hat Factor