B-1
B Basics of the Measurement Procedure
Appendix B: Basics of the Measurement Procedure
B.1 Theory of Interferometric Velocity and Displacement Acquisition
Optical interference can be observed when two coherent light beams are
made to coincide. The resulting intensity fluctuation, e.g. on a photodetector,
varies with the phase difference φ between the two beams according to the
equation
Equation B.1
The phase difference φ is a function of the optical path difference L between
the two beams according to
Equation B.2
where λ is the laser wavelength.
If one of the two beams is scattered back from a moving object (the object
beam), the path difference becomes a function of time L = L(t). The
interference fringe pattern moves on the detector and the displacement of the
object can be determined using directionally sensitive counting of the passing
fringe pattern.
The velocity component in the direction of the object beam is a function of the
path difference L according to
Equation B.3
For a constant movement v
Equation B.4
applies with
Equation B.5
Thus a constant movement of the object causes a frequency shift at the object
beam which is called Doppler shift f
D
. Superimposing object beam and
internal reference beam, i.e. two electromagnetic waves with slightly different
frequencies, generates a beat frequency at the detector which is equal to the
Doppler shift. The equation f
D
(B.5) to determine the velocity is, however,
independent of its sign. The direction of the velocity can be determined by
introducing an additional fixed frequency shift f
B
in the interferometer to which
the Doppler shift is added with the correct sign.
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