Sigma LBA-400 Manuel D’Utilisation

 
Notice:  In general it is not advisable to use the Auto Aperture feature when making Top Hat measurements. 

  

The computation of the Mean and Standard Deviation are described in the equations below: 
for the Mean, 
 

=

∑

 

 

Where: 

 =  Mean 

intensity 

n

 

= 

Number of summed pixels 

Σ

 Z 

= 

Sum of the pixel intensities above the clip level, 

 

 

or in the area, or on the line being evaluated. 

 

for the Deviation, 

 

(

)

σ

=

−

−

∑

n 1

2

 

 

Where: 

    σ

    = 

std. deviation.   

    n

    = 

Number of pixels summed. 

Σ

(

Z

 -  Z )²   = 

Sum of the square of the differences between  the mean 
intensity and the pixel intensity values  

 

 

above the clip level, or in the area, or on the  

 

 

line being evaluated. 

 

The values appearing here represent the highest and lowest energy intensities that are found within 
the Top Hat area, as defined by the Data, Area or Line Aperture selection. 

Note:  In Data mode, the Minimum will often be the clip level value determined by the Beam Width Method. 

 

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 

Operator’s Manual 

 

LBA-PC 

 

Doc. No. 10654-001, Rev 4.10 

139