Design of an optical linear-discriminant filter: optimization for enhancement of filter transmittance and discrimination accuracy.

To discriminate fine concave and convex defects on a dielectric substrate, an optical machine learning system is proposed. This system comprises an optical linear-discriminant filter (OLDF) that performs linear discriminant analysis (LDA) of the scattered-wave distribution from target samples. However, the filter output from the OLDF is considerably weak and cannot be measured experimentally. Therefore, an algorithm is also proposed to improve the discrimination accuracy and filter transmittance. The designed filter is validated using a rigorous optical simulator based on vector diffraction theory. We also analyze and discuss a mechanism that provides high transmittance with high discrimination accuracy.