Beamage Series User Manual
Revision 9.0
78
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 centroid 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 i
s the angle between the usual X’ axis and all computed centroids, is given by
the following equation:
where we have the following definitions:
In the beam axis coordinate system (X,Y,Z), the beam positional stability values in the azimuth direction
(X) and perpendicularly to the azimuth direction (Y), which are 4 times the standard deviations of all
computed centroid values, are given by the following equations:
The overall positional stability is given by:
