Biophotonics_Concepts_to_Applications

d¼ðÞnsnairL ð 7 : 10 Þ

where L is the thickness of the tissue and nairis the refractive index of air.

Example 7.10 Consider a thin slice of tissue that is inserted normally to the

light beam in one path of a Michelson interferometer. Assume that the tissue

has a uniform refractive index ns= 1.33. Using a test wavelength of 620 nm,

the fringe pattern shifts by 50 fringes. What is the thickness of the tissue

slice?

Solution:Withθ= 0° for a normal beam, then Eq. (7.9) becomes d = mλ/2.

Thus the optical path length is d = 50(0.620μm)/2 = 15.50μm. Then from

Eq. (7.10), the thickness of the sample is

L¼d=ðÞ¼ðnsnair 15 : 50 lmÞ=ðÞ¼ 1 : 33  1 : 00 46 : 97 lm

7.5.3 Sagnac Interferometer

A Sagnac interferometer traditionally is used as a sensor for measuring rotation,
stress, and temperature [ 43 , 44 ]. The interferometry technique also has found
biomedical applications in spectral imaging for disease detection, optical
polarimetry procedures in pharmaceutical drug testing, quality control for food
products, and for noninvasive glucose sensing in diabetic patients.
The basic configuration of a Sagnac interferometer consists of a singlefiber loop
and a 3-dB opticalfiber coupler, as shown in Fig.7.23. The 3-dB coupler divides
the input light into two counter-propagating directions and also recombines the two
counter-rotating beams. The recombined beams then are sent to an optical signal
analyzer. The operational concept is based on measuring the difference in the
polarization-dependent modal propagating speeds between the two beams. This can
be achieved by using either a highly birefringentfiber or a polarization-maintaining
fiber in the sensing section. The polarization in the interferometer can be adjusted
by means of a polarization controller situated at the entrance to thefiber loop.
The measured signal at the output of the 3-dB coupler is determined by the
interference between the beams that are polarized along the slow axis and the fast
axis. The phaseδSIof the interference in the Sagnac interferometer is given by

dSI¼

2 p

k

BfL¼

2 p

k

jjnfnsL ð 7 : 11 Þ

where Bfis the birefringence coefficient of the sensingfiber of length L. The
parameters nfand nsare the effective refractive indices of the fast and slow modes,
respectively.

220 7 Optical Probes and Biosensors