Theoretical analysis of moiré fringe multiplication under a scanning electron microscope

In this study, theoretical analysis and experimental verification of fringe multiplication under a scanning electron microscope (SEM) are presented. Fringe multiplication can be realized by enhancing the magnification or the number of scanning lines under the SEM. A universal expression of the pitch of moiré fringes is deduced. To apply this method to deformation measurement, the calculation formulas of strain and displacement are derived. Compared to natural moiré, the displacement sensitivity is increased by fringe multiplication while the strain sensitivity may be retained or enhanced depending on the number of scanning lines used. The moiré patterns are formed by the interference of a 2000 lines mm^-1 grating with the scanning lines of SEM, and the measured parameters of moiré fringes from experimental results agree well with theoretical analysis.