assume there is a power loss of 0.8 dB at each port of the coupler. If a power
level of 10 mW enters the coupler from the SMFfiber attached to the light
source, show that the power level at the tissue surface is 4.7 dBm
(2.95 mW).
7 :4 Suppose an opticalfiber has a 365-μm core diameter and a 400-μm cladding
diameter. (a) Show that the outer diameter is 1.2 mm for a hexagonally
packed bundle that has one ring offibers. (b) Show that the outer diameter is
2.0 mm for a bundle that has two rings.
7 :5 Consider an opticalfiber that has a 200-μm core diameter and a 240-μm
cladding diameter. (a) Show that the size of the active area in a bundle with
one ring is 0.32 m^2. (b) Show that the ratio of the active area to the total cross
sectional area of the bundle is 78 %.
7 :6 Consider an opticalfiber that has a 200-μm core diameter and a 240-μm
cladding diameter. (a) Show that the size of the active area in a bundle with
two rings is 0.86 m^2. (b) Show that the ratio of the active area to the total
cross sectional area of the bundle is 76 %.
7 :7 Consider a conventional silica glassfiber that has a 100-μm core diameter
and for which the NA = 0.26. If thisfiber is used to illuminate a tissue
sample, show that the diameter of the light spot on the tissue at a distance of
1 mm from the end of thefiber is 0.64 mm.
7 :8 Two identical step-index fibers each have a 50-μm core radius and an
acceptance angle of 15°. Assume the twofibers are perfectly aligned axially
and angularly. Show that the variation in the insertion loss when the lon-
gitudinal separation changes from 0.020 to 0.025 mm is 0.11 dB.
7 :9 Suppose that a step-indexfiber with a 100-μm core radius and an acceptance
angle of 14° is used in the reflective sensor shown in Fig.7.16. Show that the
variation in the insertion loss when the longitudinal separation between the
fiber end and the reflector changes from 0.040 mm to 0.050 mm is 0.18 dB.
7 :10 Consider a microbending pressure sensor that has the following character-
istics: Ap=1cm^2 and kf^1 ¼ 33 10 ^8 cm/dyn. If the minimum measur-
able displacement isΔXmin=10−^8 cm, show that the minimum detectable
pressureΔPminis 3× 10 −^3 Pa (pascals).
7 :11 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= 1.36. Using a test wavelength of 760 nm, the fringe
pattern shifts by 45 fringes. Show that the thickness of the tissue slice is 47.5
μm.
228 7 Optical Probes and Biosensors