Biomedical Optics

Chapter 7 - Sensing of Optical Properties and Spectroscopy: Problems

PROBLEMS

7.1   (a) Prove Eq. (7.1). (b) Explain why it is important to measure a clear
medium first. (c) Assuming that the absorption coefficient of the clear
medium is significant, modify Eq. (7.1).

7.2   Prove Eq. (7.5).

7.3   Write a Monte Carlo program to validate Eq. (7.12).

7.4   If the transmittance is given by absorbance A, express the transmittance
in dB and then calculate the absorption coefficient in terms of A if the
thickness of the sample is known.

7.5   In the collimated transmission method, assuming that measurements I0, Is ,
and d have independent uncertainties that are quantified by standard deviations
σ0, σs, and σd , respectively, derive the expected standard deviation
in the predicted μt.

7.6   In a collimated transmission measurement, if the sample is optically thin
(d << 1/μt), the number of particles along the path can fluctuate significantly
as a result of, for example, Brownian motion. Estimate the standard
deviation of the number of received photons due to this fluctuation.

7.7   Write a Monte Carlo program to simulate the oblique-incidence diffuse
reflectance from a semiinfinite medium. Duplicate Figure 7.5.

7.8   Write a Monte Carlo program to simulate the total time-resolved diffuse
reflectance Rd(t) from a semiinfinite scattering medium in response
to a temporally ultrashort pencil beam. Compare it with the diffusion
theory predicted values in response to an equivalent isotropic source
located at (a) 1/(μa + μ's ), (b) 1/(0.35μa + μ's), (c) 1/μ's below the surface.
Assume nrel = 1.38, μa = 0.1 cm-1, μs = 100 cm-1, g = 0.9, and
αi = 45o.

7.9   Derive the time-resolved diffuse reflectance equations in Section 7.6
assuming a zero boundary condition. Then derive them again using the
extrapolated virtual boundary described in Chapter 5.

7.10   A fluorescent point object is placed at (x', y', z') below the surface of
a semiinfinite scattering sample, where the z axis starts at the sample
surface and points into the sample. A normally incident continuous-wave
pencil beam at (0, 0, 0) is used to excite the fluorophores. Use the diffusion
theory to model the fluorescent reflectance measured on the sample surface
at (x, y, 0). Assume that the optical properties of the medium and the
quantum yield of the fluorophores are known.

7.11   Explain why dB is sometimes defined by 10 log10 instead of 20 log10.

 

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