Gentec-EO Beamage-3.0 - Manual (Page 69)

Beamage-3.0 User Manual Revision 6.0 68
√ ( )
The beam ellipticity is the “ratio between the minimum and maximum widths”
The beam orientation is the “angle between the x-axis […] and that or the principal axis of the power
density distribution which is closer to the x-axis .”. From this definition, the angle is comprised between
-45 o and 45 o .
( ) ( )
The beam’s divergences transformed by an aberration-free focusing element of focal length f are given
by the following equations:
In the laboratory or usual system of coordinates (X’,Y’,Z’), the coordinates of the latest calculated position
of the centroid for both X’ and Y’ axes are given by the following equations:
̅ ( )
∫ ∫ ( )
∫ ∫ ( )
̅ ( )
∫ ∫ ( )
∫ ∫ ( )
The coordinates of the mean position of all computed centroids for both X
’ and Y’ axes are thus defined
by the following equations, which are simple arithmetic means,
̅
∑ ̅
̅
∑ ̅
Where
̅
( ) and ̅ ( ) are the centroids coordinates for X’ and Y’ axes already saved in the buffer, and n
the number of computed centroid positions saved in the buffer.
The azimuth angle, which is the angle between the usual X’ axis and all computed centroids, is given by
the following equation:
(
̃
̃ ̃
)
Where we have the following definitions:
√
∑ ̅