Biomedical Engineering Reference
In-Depth Information
It is well known that tissues scatter as well as absorb light, particularly in the visible and
near-infrared wavelength regions. Scattering, unlike absorption and luminescence, need not
involve a transition in energy between quantized energy levels in atoms or molecules but
rather is typically a result of random spatial variations in the dielectric constant. Therefore,
the actual light distributions can be substantially different from distributions estimated
using Beer's law. In fact, light scattered from a collimated beam undergoes multiple scatter-
ing events as it propagates through tissue. The transport equation that describes the transfer
of energy through a turbid medium (a medium that absorbs and scatters light) is an
approach that has been proven to be effective. The transport theory has been used to
describe scattering, absorption, and fluorescence, but until recently, polarization has not
been included, in part because it takes relatively few scattering events to completely ran-
domize the polarization of the light beam. The transport theory approach is discussed later
in this chapter and is a heuristic theory based on a statistical approximation of photon par-
ticle transport in a multiple scattering medium.
17.2 FUNDAMENTALS OF LIGHT PROPAGATION
IN BIOLOGICAL TISSUE
In this section the propagation of light through biological media such as tissue is dis-
cussed, beginning with a simple ray optics approach for light traveling through a nonpar-
ticipating media, where the effect of the absorption and scatter within the media is
ignored. The effects of absorption and scatter on light propagation are then discussed, along
with the consideration of boundary conditions and various means of measuring the optical
absorption and scattering properties.
17.2.1 Light Interactions with Nonparticipating Media
Previously we defined
as a set of electromagnetic waves traveling in the O
z
direc-
tion. In this section light is treated as a set of “rays” traveling in straight lines that, when
combined, make up the plane waves described using the preceding complex exponentials.
This approach is important in order to study the effect on the light at the boundaries
between two different optical media. In the treatment of geometrical or ray optics of the
light, it is first assumed that the incident, reflected, and refracted rays all lie in the same
plane of incidence. The propagation at the boundary between these two interfaces, as
shown in Figure 17.4, is based on two basic laws—namely, the angle of reflection equals
the angle of incidence, and the sine of the angle of refraction bears a constant ratio to the
sine of the angle of incidence (Snell's law). It should be noted that ray propagation can be
very useful for a good majority of the applications considered with the propagation of
the light through bulk optics such as in the design of lenses and prisms. It has severe lim-
itations, however, in that it cannot be used to predict the intensities of the refracted and
reflected rays, nor does it incorporate the effects of scatter and absorption. In addition,
when apertures are used that are smaller than the bulk combined rays, a wave process
known as diffraction occurs that causes the geometrical theory to break down and the
beams to diverge.
light
