BRDF Scatter Measurement Services

The SphereOptics Reflectance Measurement Laboratory is equipped with a ScatterScope 4 scatterometer and provides measurement services for optical scatter, either BRDF (bidirectional reflectance distribution function) or BTDF (bidirectional transmittance distribution function).

The ScatterScope4 is a table-top scatterometer capable of performing both reflective BRDF and transmissive BTDF scatter measurements. It uses multiple silicon detectors that scan 180° to measure hemispherical and incident plane scatter in both reflection and transmission. It measures to within 5-10° of the specular direction and is specified with a visible NEBRDF (noise-equivalent BRDF) of 10 E-06 sr^-1. The SphereOptics ScatterScope 4 is equipped with interchangeable red (638nm) and NIR (830nm) laser sources for measurements of BRDF, BTDF and TIS (total integrated scatter).

Materials simplistically fall into one of two optical categories – those that are specular reflectors, and those that are diffuse reflectors. The practical reality is that most materials exhibit strongly specular reflectance with a small degree of diffuse reflectance (scatter), or are highly diffuse but exhibit a degree of specular reflectance (gloss).

A mirror is a specular reflector, from which a ray of light incident at a given angle to the surface normal is reflected at the exact opposite angle. As commonly expressed for a mirror (or a mirror-like surface), the angle of incidence equals the angle of reflectance. Implicit in this definition is that the intensity of light reflected is equal to that incident on to the specular surface, reduced only by the reflectance factor of the material at that wavelength.

Conversely, diffuse reflecting materials behave very differently to a perfect mirror. Instead of all of the light reflecting in the specular direction, the light reflects in all directions. For a theoretical perfect Lambertian (or diffuse) reflector, the intensity of light reflected obeys Lambert’s Cosine Law. The 18th century Swiss polymath Johann Heinrich Lambert (1728-1777), described the concept of a perfect diffuse reflector in his 1760 book “Photometria”. The adjective “Lambertian” has become synonymous with materials that are matte or diffuse. A perfect Lambertian reflector will reflect light with an intensity that drops with the cosine of the angle subtended to the surface normal, or with a radiance that remains constant over all directions of view.

A scatterometer is an instrument which characterises how diffuse or how specular an optical material is. The metrics that are commonly used are BRDF for reflectance and BTDF for transmittance. BRDF is the ratio of incident irradiance to reflected radiance for a given angle of illumination and for a defined angle of view. The respective planes of illumination and collection must also be specified. Similarly, BTDF is the ratio of incident irradiance to transmitted radiance, again for defined angles (and planes) or illumination and view. The summation of scatter over a hemisphere is called the total integrated scatter (TIS).

Scatter data is an important input to optical design and ray-tracing software. Rather than assuming that a material is a perfect mirror or an ideal diffuser, BRDF or BTDF data sets can be read into commercial optical design software so as to greatly improve their modelling accuracy.