Updated March 2010

Scattering which results from surface microroughness can often be characterized by the K-correlation model¹. The bi-directional scatter distribution function (BSDF) associated with this model is provided by Dittman²:



where s is the effective RMS surface roughness, s is the log-log slope of the BSDF at large spatial frequencies, and b is defined as the sine of the scatter angle (q_s) minus the sine of the specular reflection/transmission angle, i.e. b in the above formula corresponds to the vector x used in ZEMAX:



We find that the K-correlation distribution is very similar to the Harvey-Shack (ABg) model. The main difference is that the K-correlation model provides a roll-off in scattering at small scatter angles:

Figure 1: A comparison between the K-correlation and Harvey-Shack scattering models. The K-correlation model exhibits a small-angle roll-off, which Dittman indicates is consistent with the observed behavior for many surface finishes. This figure was taken directly from reference [2] (corresponding to Figure 1 in that reference).


Dittman indicates that this roll-off is consistent with the observed scattering behavior for many surface finishes.

The BSDF for the K-correlation model cannot be analytically integrated. However, a Monte Carlo technique has been used to implement this scattering distribution in ZEMAX. An approximate form for the total integrated scatter (TIS), in which we ignore the cos(q_s) term in the BSDF equation and set q_i = 0, is also calculated:

TIS ≈ 4p²dn²s²/l²

As we can see, there are a number of inputs required by the K-correlation scatter model, and we will examine these in a bit more detail in the next section. All of these inputs must be provided by the user if they wish to model the K-correlation surface scattering distribution in ZEMAX. When the information available to the user for a particular scattering surface is measured BSDF data rather than parameters that would be obtained from fitting measured surface roughness data to the K-correlation model, we strongly recommend using the measured BSDF data directly in modeling the surface scattering distribution. The process of using measured BSDF data directly in ZEMAX is described in great detail in the article entitled "How To Use Tabular BSDF Data to Define the Surface Scattering Distribution".