where:f’ = resonant frequency ofplatform with mirror [Hz]f Using the resonant frequencyof the unloaded platform (see
individual technical data table)
and the moment of inertia of
the mirror substrate, the sys-
tem resonant frequency is cal-
culated according to the
following equation: Resonant frequency of a tilt
platform/mirror system
Piezo • Nano • Positioning Dynamic Behavior
The maximum operating fre-quency of a tilt platform is
heavily dependent on its
mechanical resonant frequen-
cy. The performance character-
istics of the amplifier,
servo controller and sensors are also
very important. To estimate the
effective resonant frequency of
the tilt mirror system (platform+ mirror), the moment of iner-tia of the mirror substrate must
first be calculated.Moment of inertia of a rota-tionally symmetric mirror: Moment of inertia of a rectan-gular mirror:
Piezo actuators Nanopositioning &
Scanning Systems Active Optics / Steering Mirrors Tutorial: Piezo-electrics in Positioning where:m = mirror mass [g]I
Capacitive Industrial position sensors Piezo Drivers & Nano-
positioning controllers Hexapods /
Micropositioning Photonics Alignment
Solutions = resonant frequency ofunloaded platform [Hz]I
Motion controllers Ceramic Linear motors & Stages = moment of inertia of theplatform (see technicaldata table for the individ-
ual model) [g · mm
2 Index ]I
M = moment of inertia of themirror [g · mm
2 ]
M = moment of inertia of themirror [g · mm For more information on staticand dynamic behavior of piezo
actuators, see pp. 4-25 ff. in the“Tutorial” section.
2 ]L = mirror length perpendicu-lar to the tilt axis [mm]H= mirror thickness [mm]
T= distance, pivot point toplatform surface (see tech-
nical data table for
individual model) [mm]R= mirror radius [mm]
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