Non-Linear Effects in Optical Surface Metrology

This paper examines non-linear effects which appear in the measurement of surface topography by phase-shifting interference microscopy due to the non-linear relationship between the measured profile, Zm(x), and the true profile, Zt(x). To lowest order this is where P(x) is the point-spread function of the measurement. In an ideal system P(x) = δ(x), the non-linear functions Arg and Exp cancel, and Zm(x) = Zt(x). In real systems, however, P(x) has a finite width which upsets this proportionality. In earlier studies we developed comprehensive models for P(x) by comparing optical and mechanical measurements of smooth surfaces [1,2]. Here we use these models to explore the nature and magnitudes of the non-linear effects which arise in the measurement of rough deterministic and random surfaces for which the linearization of Eq. 1 is not possible. This is done both analytically and via Monte-Carlo simulations.