Linear Models of Reflectance

Obviously it is much harder to do the same for the reflectance of all possible surfaces in the world. Some strong limitations have to be applied in order to reduced the number of possible surfaces so that the model of linear combination can still generate meaningful results. For example, we could consider only the surfaces of interest in a certain application.

By using the same PCT method, we can find a set of basis functions $F_k(\lambda),\;\;(k=1,\cdots,n)$ so that the reflectance can be approximated by the first m<n terms

$$R(\lambda)\approx \sum_{k=1}^m f_k F_k(\lambda)$$

with minimum error.