Newport LBP2 Series User Manual

LBP2 User Guide Document No: 50306-001 Rev G 3/12/2020 Page 76
When measurements of the beam widths are performed on the cameras X and Y axes
results are denoted with the letters X and Y. When a rotated elliptical beam is being
measured the notions X/Y become M/m to denote the beam widths in the
orthogonal Major and minor axes respectively.
The absence of either the X/Y or M/m notation indicates when a Diameter result is
being designated.
According to ISO when the ratio of the Beam Widths exceed 0.85, then the beam can
be described as circular and the Diameter result is appropriate.
5.9.1 D4-Sigma Method
D4σX/M, D4σY/m, D4σ
Second moment method, ISO 11145, ISO 11146-1 and ISO 11146-3.
From laser beam propagation theory, the Second Moment or 4-Sigma beam width
definition is found to be of fundamental significance. It is defined as 4 times the
standard deviation of the energy distribution evaluated separately in the X and Y
transverse directions over the beam intensity profile.
D4σX:
d
x x 
  4
D4σY:
yy
d 

 4
Where: d
σ
= The 4-Sigma beam width
σ = The standard deviation of the beam intensity
The standard deviations are derived from the distribution variances and are equal
to the square root of the variance. The variances are:

x
yx
yx
x x Z x y
Z x y
2
2

 


( ) ( , )
( , )

y
yx
yx
y y Z x y
Z x y
2
2

 


( ) ( , )
( , )
Where: Z = the intensity of the pixel at x,y
y and x
are the coordinates of the centroid
For the second moment diameter of a circular beam:
D4σ:
)(22)( zzd 



Newport LBP2 Series Specifications

General

Brand	Newport
Model	LBP2 Series
Category	Measuring Instruments
Language	English