Biophotonics_Concepts_to_Applications

9 :5 Consider thefluorescence decay for the two particular unquenched and
quenched fluorophores shown in Fig.9.7. Show that the approximate
fluorescence lifetimes areτ 0 ≈1.4 ns andτQ≈1.0 ns.
9 :6 The diffusion coefficients for O 2 is 2.10× 10 −^5 cm^2 /s for diffusion in water
at 25 °C. Show that the diffusion times in which an oxygen molecule travels
distances of 50 nm, 100μm, and 1 cm are 595 ns, 2.38 s, and 6.61 h,
respectively. This shows that diffusion alone is not an adequate mechanism
for distributing oxygen in the human body.
9 :7 Suppose that for the spheroid shown in Fig.9.9the radii of the equatorial
and polar axes are 0.3μm and 2.2μm, respectively. Show that the volume of
the spheroid is 0.91μm^3 = 0.91 fL.
9 :8 When interpreting optical signals, various autocorrelation functions are used
to analyze the characteristics of optical pulses in the femtosecond region. An
autocorrelation is an electronic tool used for examining the similarity of
observations of a signal at different points in time. Using Web or vendor
resources describe in a few paragraphs how an autocorrelator works.
9 :9 Consider the photon collection volume in Fig.9.12to be a simple semicircular
curved cylinder of tissue with a 250-μm diameter. If the separation between the
fiber cores is 350μm, show that is the volume of the cylinder is 0.027 mm^3.
9 :10 Consider the banana-shaped scattering region in Fig.9.12to consist of two
cylindrical cones and a semicircular curved cylinder as shown in Fig.9.23.
For the conical sections, let Dtop= 200μm, Dbottom= 300μm, and h = 100
μm. Thus, similar to the setup in Example9.8, the curved cylinder has a
length of 550μm and its diameter isa = 0.5 Dbottom= 150μm. For the
cylindrical conical section shown in Fig.9.23, the volume is given by
V¼p 12 h D^2 bottomþDbottomDtopþD^2 top



. Show that the total volume of the
banana-shaped region is 2(0.005) + 0.039 mm^3.
9 :11 Verify that the ratio of the anti-Stokes intensity Ianti-Stokes to the Stokes
intensity IStokesis 0.11 for the 459-cm−^1 Raman mode shown for CCl 4 in
Fig.9.17at a temperature of 20 °C.
9 :12 Consider a PCS test for examining a glucose molecule that is diffusing in
water. If D = 6.7× 10 −^6 cm^2 /s for hemoglobin in water and ifη=1× 10 −^3
N s/m^2 for water, show that the hydrodynamic diameter of the glucose
molecule is 0.64 nm.

Dtop

Dbottom

h

Cylindrical

cones

Fig. 9.23 Volume estimate
of a banana-shaped scattering
region

9.14 Problems 287