Biomedical Engineering Reference
In-Depth Information
vectors, they add vectorally. Thus, when two or more waves emanating from the same
source are split and travel along different paths, they can then reunite and interfere con-
structively or destructively. When the constructive and destructive interferences are seen
to alternate in a spatial display, the interference is said to produce a series or pattern of
fringes. If one of the paths in which the light travels is altered by any small perturbation,
such as that due to temperature, pressure, or index of refraction changes, then once recom-
bined with the unaltered reference beam, the perturbation causes a shift in the fringe pat-
tern that can be readily observed with optoelectronic techniques to about 10
-4
of the
fringe spacing. The useful information regarding the changing variable of interest can be
measured quite accurately as a path length change on the order of one-hundredth of a
wavelength or 5
10
-9
meters for visible light.
There are several variations for producing light interference, including one of the first
instruments known as the Rayleigh refractometer from which came the Mach-Zehnder
interferometer. For the sake of brevity, this section focuses on two more sophisticated
variations of the Rayleigh idea: the dual beam Michelson interferometer and the multiple
beam Fabry-Perot interferometer. As shown in Figure 17.9, the Michelson interferometer
begins with a light source that is split into two beams by means of a beam-splitting mir-
ror or fiber optics, which also serves to recombine the light after reflection from fully sil-
vered mirrors. A compensating plate is sometimes needed to provide equal optical paths
before introduction of any perturbation or sample to be measured. The perturbation can
take the form of a pressure or temperature change, causing a strain and thus a path
length change in the sample arm of the fiber optic or as a change due to the addition
of a tissue sample or replacement of the mirror with a tissue sample. For example, the
Michelson interferometer has been investigated for measuring tissue thickness, particu-
larly for corneal tissue as feedback for the radial keratectomy procedure (laser removal
or shaving of the cornea to correct vision), and this interferometer, when used with a
low coherent light source, has been researched for use in optical coherence tomographic
imaging of superficial tissues. The governing equation for the irradiance of the fringe
system of circles concentric with the optic axis in which the two interfering beams are
of equal amplitude is given as
cos
2
I
¼
4
I
o
ðd=
2
Þ
ð
17
:
56
Þ
Disturbance
Mirrors
Converting
Plate
Mirrors
Beam Splitter
Reference
Arm
FIGURE 17.9
Michelson interferometer: (a) bulk optics and (b) fiber optics.
