Biomedical Engineering Reference
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Fig. 5.2
(
a
) Free-space Michelson interferometer setup, (
b
) comparison between the photode-
tector outputs in cases when a high-coherence source (
top
) or a low-coherence source (
bottom
)
is used
sites in the sample. LCI measures the delay and intensity of backscattered light
by comparing it with the light that has traveled a known reference path length
and delay through use of a Michelson interferometer. Another variant form of
LCI called optical time-domain reflectometry (OTDR) is used to determine the
location of defects in optical fibers and characterization of optical waveguides in
the telecommunication industry [
14
,
15
]. Figure
5.2
a shows the schematic diagram
of a simple free-space implementation of a Michelson-type interferometer.
The incident optical beam is directed onto a beam splitter, which splits the beam
into two, from where one beam leads to a sample mirror, while the other acts as a
reference beam with variable path length. The sample beam
E
S
.t
L
S
=c/,which
reflects from the sample mirror, is interfered with the reference beam
E
R
.t
L
R
=c/
at the output of the interferometer, where L
S
and L
R
are the corresponding optical
paths of the sample arm and reference arm, respectively, and c is the speed of light.
According to the wave theory, interference is the superposition of two or more
waves, resulting in a new wave pattern. If we consider wave as electromagnetic
radiation, then the electric field can be described as [
16
]
D
E
0
e
i.
kr
!
t C
/
;
E
(5.1)
where
k
.
D
2=/ is the propagation vector,
r
is the unit vector,
!
.
D
2f/ is the
angular frequency, and
is the phase, the resulting field of the beams at the output
of the interferometer can be written as
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