New TracePro Feature: Bulk Scatter in Biological Tissue
October 21, 1999
Technical Background
Scattering of light in bulk material has been implemented in TracePro. When a ray enters an object that has bulk
scattering, the ray propagates a random distance, then the direction of the ray is deviated, similar to the way rays are
diffracted by an aperture in TracePro. Importance sampled rays may also be generated at the option of the user. The
ray deviation and importance sampled flux are governed by a probability distribution similar to a BSDF, but slightly
different. Whereas the BSDF is defined as the scattered radiance per unit incident irradiance, the scattering
distribution function or SDF is defined as the scattered intensity per unit incident flux,
SDF 
I (rˆ)
.

In addition, the SDF is independent of the direction of incidence. The particular SDF that has been implemented in
TracePro is after a paper by Jacques and Wang 1 that describes scattering in biological tissue and has the form
SDF  p( ) 
1 g 2
4 (1  g 2  2 g cos ) 3 / 2
where g is called the anisotropy factor, and g can take on values between –1 and 1. When g is positive, rays are
scattered more in the forward direction, and when g is negative, they are scattered more in the backward direction.
When g is zero, the scattering is isotropic, i.e. the same in all directions. Figure 1 shows an example scattering
distribution function for g = 0.5.
90
120
0.4
0.3
0.2
0.1
0
150
p( r( d ) )
180
0.477
60
30
0
210
0.018
330
240
300
270
r( d )
Figure 1 Polar plot of example scattering distribution with g = 0.5. Zero is the forward direction.
When a ray enters a scattering medium, it propagates a random distance x governed by the probability distribution
P( x)dx  e   s x dx
where s is called the scattering coefficient. The inverse of the scattering coefficient is the mean free path of the ray
in the material. When a ray enters a piece of material that is thin compared to the mean free path, it is likely to pass
through the material without being scattered. Conversely, if the material is thick compared to the mean free path, the
ray is almost certain to scatter within the material. When a strong scattering coefficient is combined with a strong
absorption coefficient, rays will be only weakly transmitted through the material.
Using Bulk Scattering in TracePro
In order to simulate bulk scattering in TracePro, select an object in which you wish scattering to occur and apply a
material property using the Apply Properties dialog box. Then apply a bulk scattering model to the object. Finally,
you may optionally apply importance sampling to the object in a way analogous to surface importance sampling.
To define new bulk scattering models, open the bulk scattering model editor. Create a new scattering property and
add a new wavelength entry at the desired wavelength. Enter values for g (the anisotropy factor) and s, the
scattering coefficient. The units for s are 1/mm, i.e. inverse millimeters. Most bulk scattering materials also have
some bulk absorption, so you should define a material property with the proper bulk absorption coefficient and
apply it to your scattering object.
You can find examples of scattering coefficients and anisotropy factors in a paper by Schmitt and Kumar. 2 However,
this reference does not give values of index of refraction or bulk absorption coefficient.
1
S.L. Jacques and L. Wang (still looking for this reference.)
J.M. Schmitt and G. Kumar, “Optical scattering properties of soft tissue: a discrete particle model,” Appl Opt. 37,
2788 (1998).
2