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4D User Manual
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10.3.9 "OCLM" (Motors Output Crosslink Matrix) Section
As discussed in the general description of 4D beam pointing stabilization the de-coupling of
the four degrees of freedom is done by the so-called "output crosslink matrix" (OCL matrix). It
defines the combination movements of the four output actuators, which has to be done, if one
of the fundamental movements (for example a position movement in X direction, or an angle
movement in Y direction) shall be performed.
Example of a position movement 100 µm to the right: In the ideal case, the X actuator of mirror
#1 has to do an angle movement, which causes a beam translation of 100 µm at the second
mirror (depending on the distance between the two moved mirrors M1 and M2). The second
mirror, however, has to do an angle movement into the opposite direction to compensate for
the beam angle, this way the wanted pure parallel position shift is performed.
Note: To achieve a simple position shift a combination movement of at least two actuators is
necessary.
In real systems even more complicated combinations are necessary:
If one additional (fixed) mirror is located between the two moved mirrors, it changes left and
right. So the necessary relative movement of the two actuator mirrors will be reversed.
(Same with 3, 5, ... reflexions, e.g. in case of a delay line.)
Often in a real setup, the beam path is reflected upwards and then aside again. This will
change X and Y of the relative movement.
Assume a Y shift of the beam is wanted to correct or perform a Y position drift of the laser
beam. Nearly all mirror mounts (and the Aligna mirror mounts as well) do not turn the mirror
exactly around the point of incidence at the mirror surface (gimbal). If a Y screw is moved,
this leads to the wanted Y beam angle variation, BUT it also leads to an additional X-shift of
the beam. This again has to be compensated for by both X screws.
If the beam leaves the horizontal plane, this leads to X/Y-coupling.
In real systems there may be even more effects of coupling between X and Y (lenses in the
beam path, non-ideal collimated beams, non-planar beam path, etc...), which will not be
discussed here.
As a result: All of the four basic beam movements (beam angle shift in X and Y "Ax", "Ay",
beam position shift in X and Y, "Bx", "By") need linear combination movements of the four
actuators "1x", "1y", "2x", "2y" at the two moved mirrors "M1" and "M2".
These linear combinations are described by the 4x4 "Output Cross-Link" matrix with 16 ele-
ments. It contains the information of the distance between the mirrors and to the detector unit,
as well as the relative mirror arrangement, properties of the motorized mirror mounts, etc.
Note: In Aligna systems with both, motors AND piezo actuators, there are two independent
OCL matrixes, OCL (piezo) and OCLM (motors).
As an example element “Ax1xM” defines the amount of movement from channel Ax (Angle x
direction) to actuator 1xM (actuator in x direction of motorized mirror mount #1).
“Ax1x” (without “M”) represents the same matrix coefficient, but of the piezo OCL (not of the
motor-related “OCLM”).
10.3.9.5 Scaling factors for each motorized actuator
For each motorized actuator (1x, 1y, 2x, 2y) there exists a scaling factor (“Scal1x”,
“Scal1y”, ...), which transforms the output of the OCL matrix to motor units.
In principle there is no need for these additional scaling factors; they could be part of the OCL
matrix coefficients. However, it helps for better clearness: For example, if Aligna 60 or Aligna
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