Biophotonics_Concepts_to_Applications

7.5.2 Michelson Interferometer

A Michelson Interferometer (MI) is similar to an MZI and is widely used for optical
coherence tomography (see Chap. 10 ) and radial keratectomy procedures (removal or
shaving of the cornea with a laser to correct vision). Similar to the MZI, the basic MI
concept is the implementation of interference between light beams traveling in two
arms of the interferometer. However, the difference from the MZI is that in the MI
each beam is reflected by a mirror at the end of each arm, as is shown in Fig.7.22.
After the reference and sensor beams are reflected by mirrors Mrefand Msensor,
respectively, they are recombined with an optical coupler. As with the MZI, the
resulting observed constructive and destructive interference patterns then allow an
assessment of the external parameter being examined.
When the two interfering beams are of equal amplitude, the relationship
describing the interference pattern is given by

I¼4I 0 cos^2 ðd= 2 Þð 7 : 7 Þ

Here I 0 is the intensity of the input light and the phase differenceδbetween the
sensing and reference beams is defined by

d¼ 2 pD=k ð 7 : 8 Þ

withλbeing the wavelength of the input light andΔis the difference in the optical
path lengths between the two beams, which is defined by

D¼2d coshþk= 2 ¼ðmþ 0 : 5 Þk ð 7 : 9 Þ

Here 2d is the difference in the path lengths from the optical splitter, m is the
number of interference fringes, andθis the angle of incidence (θ= 0° for a normal
or on-axis beam). Consider the case when a thin slice of tissue that has a uniform
refractive index nsis inserted in one of the beam paths. Assume that there is
minimal absorption and scattering in this tissue slice. Then

Laser

input

signal

2 2 optical

coupler

Reference arm

Sensing arm

Light/analyte

interaction

To optical

signal analyzer

Msensor

Mref

Fig. 7.22 Operation of a basic Michelson interferometer

7.5 Interferometric Sensors 219