Thermal expansion measurement using optical grating diffraction shifts

We demonstrate a novel optical method for accurately measuring thermal expansion in materials. When an optical grating expands or contracts, the Bragg diffraction condition is altered, and the diffracted beams undergo angular shifts. Using a diffracted laser beam, we demonstrate that this effect can be used to measure expansion coefficients as small as 10$^{-6}$ C$^{-1}$. By patterning samples of PMMA and chitosan with grating lines, we measure their thermal expansion coefficients by heating the sample by only a few degrees Celsius. The method can be generalized to opaque materials by texturing the surface and measuring diffraction in reflection. A theory is presented to determine the ideal experimental conditions and the limits of accuracy.