Biophotonics_Concepts_to_Applications

where x = 2πnba/λ. The scattering efficiency gives the ratio of the energy scattered
by a particle to the total energy in the incident beam that is intercepted by the
geometric cross section of the particle.

6.3.3 Anisotropy Factor

Observations of scattering in biological tissues have shown that photons tend to be
scattered in the forward direction. In practice it is useful to define a probability
function p(θ) to predict the scattering direction of a photon at an angleθ, as shown
in Fig.6.15.Ifp(θ) does not depend onθ, then the scattering is isotropic (equal
intensity in all directions). If p(θ) does depend onθ, then the scattering is aniso-
tropic (having different values in different directions).
Anisotropyis a measure of the number of scattered photons continuing in the
forward direction after a single scattering event. A commonly used approximation for
p(θ) thatfits well with experimental data is the Henyey-Greenstein function [ 3 , 16 ]

pðÞ¼h

1 g^2

ðÞ 1 þg^2 2g cosh^3 =^2

ð 6 : 18 Þ

Thescattering anisotropy factorg is the mean cosine of the scattering angleθ. The
value of g varies from−1 to +1; g =−1 denotes purely backward scattering, g = 0
indicates isotropic scattering, and g = +1 denotes total forward scattering, which
describes Mie scattering for large particles.

Example 6.8From Eq. (6.18) plot the value of p(θ) for values of g = 0.8 and

0.9 for scattering angles ranging from 0 to 40°.

Solution: The curves from Eq. (6.18) are given in Fig.6.16. In most bio-

logical tissues scattering occurs predominantly in the forward direction, that

is, for g approaching the value 1.

Incident

photons

Scattering

event

Deflection

angle θ

P 0 cos θ

θ

Fig. 6.15 Illustration of
angular scattering

6.3 Scattering 167