Remote detection of the pitch and orientation of a reflective diffraction grating: an optical strain gauge

Abstract

Measurement of surface strain in hostile environments remains a significant metrology challenge. An elegantly simple non–contact method is to measure the change in pitch of a reflective diffraction grating bonded to the surface of interest. The grating is probed with a laser beam and the change in angular position of diffracted orders is detected as the pitch changes due to surface strain. Robust application of this technique has not been possible due to assumptions such as near–normal incidence, which were necessary in predicting the angular position of diffracted orders from the existing two–dimensional theory. This paper introduces a new three–dimensional theory of diffraction, which obviates the need for these assumptions. Importantly, the theory shows that the angular position of orders can be determined for arbitrary orientation of the grating relative to the incident probe beam. This latter development is critical for success in a practical application. It is now possible to micro–machine reflective gratings directly into a surface or surface coating and thus avoid problems with creep in the bonding material. Together with the new theory, this idea now has the potential to revolutionize how strain will be measured in the future.