Biomedical Engineering Reference
In-Depth Information
EXAMPLE PROBLEM 17.6
A 5 mW collimated laser beam passes through a 4 cm nonabsorbing, scattering medium. The
collimated transmission was measured through a small aperture to be 0.035 mW. Calculate the
scattering coefficient.
Solution
Based on Beer's law,
1.2 cm
-1
.
m
s
¼
ln(5/0.035)/4
¼
One of the earliest techniques developed for experimentally measuring absorption and
scatter is the integrating sphere measurement method. In this technique, a thin slice of tis-
sue is sandwiched between two integrating spheres (spheres with an entrance and exit port
whose inner surface is coated with a diffuse reflecting material). A collimated beam is inci-
dent upon the tissue sample. Both the diffuse reflectance and transmittance are measured
by integrating the diffusely reflected and transmitted light, respectively. These two mea-
surements are used to deduce the absorption coefficient (
m
a
) and the reduced scattering
0
s
coefficient (
) with a model. The model could be based on the adding-doubling method,
the delta-Eddington method, the Monte Carlo method, or other light transport theories.
Another technique is normal incidence video reflectometry. A collimated light beam is
normally incident upon a tissue. The spatial distribution of diffuse reflectance is collected
using either a CCD camera or an optical fiber bundle. Diffusion theory is used to fit the
measured spatial distribution of diffuse reflectance to determine the optical properties.
The measured spatial distribution of diffuse reflectance must be in absolute units unless
total diffuse reflectance is measured along with the diffuse reflectance profile. Calibration
to absolute units is a sensitive procedure, so this method is not ideal for a clinical setting.
It is possible to use time-resolved or frequency-domain techniques to measure optical
properties. But these techniques require instrumentation that may not be cost effective for
nonresearch applications. One promising approach for in vivo optical property measure-
ments is fiber optic-based oblique incidence reflectometry. It is a fairly accurate method
for measuring the absorption and reduced scattering coefficients,
m
0
s
, providing the
sample can be regarded as a semi-infinite turbid media, as is the case for most in vivo tis-
sues. Therefore, this approach will be covered in more detail in this section.
Obliquely incident light produces a spatial distribution of diffuse reflectance that is not
centered about the point of light incidence. The amount of shift in the center of diffuse
reflectance is directly related to the medium's diffusion length,
m
a
and
m
. A fiber optic probe
may be used to deliver light obliquely and sample the relative profile of diffuse reflectance.
Measurement in absolute units is not necessary. From the profile, it is possible to measure
D
D
, perform a curve fit for the effective attenuation coefficient,
m
eff
, and then calculate
m
a
and
0
s
m
. Here,
m
eff
is defined as
p
m
a
=
D
m
eff
¼
ð
17
:
43
Þ
The spatial distribution of diffuse reflectance of normally incident light has previously
been modeled using two isotropic point sources, one positive source located 1 transport
