All non-metallic materials are translucent to some degree. This means that light scatters inside the material before being either absorbed or leaving the material at a different location. This phenomenon is called subsurface scattering.

I started looking at techniques for simulating volumetric subsurface scattering at MIT in 1998. Previous methods had only considered 1d transport wrapped into a BRDF model and therefore ignored the transport of light through the material. At MIT, we developed techniques based on photon mapping and path tracing to simulate the darkening of many wet materials as well as the translucency of weathered stone. Photon mapping is quite good at simulating subsurface scattering, but it becomes costly for highly scattering materials such as milk and skin. In the fall of 2000, we were investigating alternatives to the Monte Carlo methods, which resulted in the development of a new technique based on a diffusion approximation. The diffusion approximation is much faster than tracing individual photons, and it is simple enough that a BSSRDF can be formulated. The BSSRDF is particularly suited for highly scattering translucent materials where the assumptions in the ubiquitous BRDF approximation break down. As an example, the BSSRDF was used to render the translucent marble bust that is shown here. Note how the BSSRDF captures the the soft and smooth appearance as well as the light diffusing through the marble - something that a BRDF cannot simulate. The BSSRDF research has been adapted rapidly by the movie industry and it won an academy award in 2004. Lately, we have worked on techniques for rapid evaluation of the BSSRDF model, and extensions to simulate diffusion in multilayered translucent materials such as human skin. Recently, we developed a generalized Lorenz-Mie theory for computing the optical properties of translucent materials and scattering media.

Photon Mapping (1998)	BRDF Model (2001)	BSSRDF Model (2001)

This sequence of images shows a translucent marble bust (Diana the Huntress) illuminated from behind. The images illustrate some of the different techniques for simulating subsurface scattering. The image on the left was rendered using photon mapping with 200,000 photons used to simulate multiple scattering inside the material. The image in the center was rendered using a BRDF based model for subsurface scattering. Notice how the BRDF fails to capture the light transport through the material, and even though the shape of the reflected light is correct the material does not look translucent. The right image shows the marble bust rendered using the BSSRDF from 2001. The BSSRDF uses a dipole diffusion approximation instead of photon mapping for simulating multiple scattering inside the material. As with photon mapping it also uses an explicit Monte Carlo integration of the single scattering term.

This face model was rendered using a layered skin model described in this paper. The skin is composed of three layers: epidermis, dermis, and the bloody dermis. The scattering parameters for the individual layers are from measured data available in the medical physics literature. Note that the multilayered model gives the skin a less waxy look compared to the standard BSSRDF (dipole diffusion) based skin rendering shown below.

This image shows how milk can be rendered realistically using the BSSRDF model. From left to right we see skim milk, whole milk, and diffuse milk. The diffuse milk has been rendered using a traditional BRDF model, which results in a hard appearance making the milk look more like white paint rather than milk. The difference is even more noticable once the light moves - this can be seen in the animation "Rendering Translucent Materials" on the animations webpage.

This translucent teapot was rendered in 7 seconds on a 800MHz dual-P3 PC using a new fast hierarchical rendering technique for translucent materials. This method was developed with Juan Buhler from PDI and it is described in this paper.

BRDF rendering	BSSRDF rendering

This face model has been rendered using the BRDF and BSSRDF described in this paper. The BRDF model is a simplified version of the BSSRDF that does not account for subsurface light transport (it assumes that the light scatters at a single point on the surface). Note that the BRDF model does include subsurface scattering - the subsurface scattering component is split into a single scattering term and a diffuse term. In contrast to the BRDF the BSSRDF simulates subsurface light transport (e.g. the light enters and leaves at different locations on the surface) and gives the skin a more natural translucent appearance. Note the translucency around the nose and the color bleeding in the shadows. These effects are achieved even though the setup is very simple - one light source, only one binary map is used to distinguish the lip from the skin region, and a bumpmap is used to add more detail to the skin. The face was modeled by Steven Stahlberg.

This is the same marble bust as shown above. The difference is that the entire bust is shown and that the light source is in front of the bust. This reduces the translucency effect significantly. This was one of the first images with subsurface scattering that I rendered.

Even though granite seems like a solid material it still scatters light below the surface. This is due to micro cracks and small air bubbles in the material. For granite the translucency is most noticeable in the quartz grains.

A granite and a marble version of the Stanford bunny.