Schlick's approximation

In 3D computer graphics, Schlick’s approximation, named after Christophe Schlick, is a formula for approximating the contribution of the Fresnel factor in the specular reflection of light from a non-conducting interface (surface) between two media.¹

According to Schlick’s model, the specular reflection coefficient R can be approximated by: $${\displaystyle R(\theta )=R_{0}+(1-R_{0})(1-\cos \theta )^{5}}$$ where $${\displaystyle R_{0}=\left({\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}\right)^{2}}$$ where ${\displaystyle \theta }$ is half the angle between the incoming and outgoing light directions. And ${\displaystyle n_{1},\,n_{2}}$ are the indices of refraction of the two media at the interface and ${\displaystyle R_{0}}$ is the reflection coefficient for light incoming parallel to the normal (i.e., the value of the Fresnel term when ${\displaystyle \theta =0}$ or minimal reflection). In computer graphics, one medium is usually air, meaning that ${\displaystyle n_{1}}$ can be approximated very well as 1.

In microfacet models it is assumed that there is always a perfect reflection, but that the normal changes according to a certain distribution, resulting in a non-perfect overall reflection. When using Schlick’s approximation, the normal in the above computation is replaced by the halfway vector. Either the viewing or light direction can be used as the second vector.²