Resolving femtometer spacing changes and corresponding quasi-static nanostrain via grazing excidence optical diffraction experiments (GEODE)

• Ultra-High Strain Resolution: Achieved a strain resolution of ∼800 picostrain under quasi-static conditions using Grazing Excidence Optical Diffraction (GEOD), surpassing previously reported resolutions. • Non-Contact Measurement: Developed a non-contact optical strain measurement technique suitable for applications in extreme environments where contact methods are impractical. • Novel Methodology: Introduced Grazing Excidence Optical Diffraction (GEOD), a technique that leverages near-grazing diffracted beams to significantly enhance the sensitivity of strain measurements. • Integrated System: Created a self-validating grating system incorporating joule-heating for controlled strain generation and resistance-based temperature sensing for independent verification. • Reference Grating Amplification: Demonstrated a novel method to amplify the sensitivity of GEOD using a reference grating, enabling high-resolution measurements with a compact setup. Although strain measurement via optical diffraction is conceptually simple and well understood, it has thus far been limited with respect to strain resolution. The development of non-contact strain measurement capabilities is critical for a number of applications including high-temperature material characterization and stand-off sensing of dynamically loaded components, among others. This work, based on a simple one-dimensional diffraction grating, builds on prior optical diffraction techniques to significantly extend the resolution with which strain may be measured. A new approach termed grazing excidence optical diffraction (GEOD) is introduced, demonstrating an ultimate strain resolution of ∼800 picostrain, corresponding to a thermal expansion due to ∼300 μ K change in temperature in single crystal silicon, under true quasi-static loading conditions, i.e. without any signal averaging. We designate the condition, θ → π 2 , grazing excidence, to describe a diffracted beam that is nearly parallel to the surface of the grating. To our knowledge, this is the finest strain resolution reported to date for a true quasi-static measurement. To put this into some perspective, for the grating used ( d = 1.266 μ m ), 800 picostrain corresponds to a change in average grating spacing of approximately one femtometer, or 1/100,000 the atomic radius of a silicon atom.