C-1
C Basics of the Measurement Procedure
Appendix C: Basics of the Measurement Procedure
C.1 Theory of Interferometric Velocity and Displacement Measurement
Optical interference can be observed when two coherent light beams are
made to coincide. The resulting intensity e.g. on a photo detector varies with
the phase difference
∆ϕ
between the two beams according to the equation
Equation C.1
The phase difference
∆ϕ
is a function of the path difference
∆
L between the
two beams according to
Equation C.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.
On scattering from the object the object beam is subjected to a small
frequency shift which is called Doppler shift f
D
and is a function of the velocity
component in the direction of the object beam according to
Equation C.3
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 ratio
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. Thus the resulting frequency at the detector f
mod
is given by
Equation C.4
Interferometers of this type which are directionally sensitive are described as
heterodyne.
I
∆ϕ
(
)
I
max
2
---------
1
∆ϕ
cos
+
(
)
⋅
=
∆ϕ
2
π ∆
L
λ
-------
⋅
=
f
D
2
v
λ
-----
⋅
=
f
mod
f
B
2
v
λ
---
⋅
+
=
