Thermal expansion and stress and measurement using high-order diffraction: Possibilities and theoretical limits

We investigate the theoretical limits of using diffraction of a single laser beam by a patterned surface as a way to measure surface deformation caused by stress or thermal expansion. Applying Gaussian beam optics to a lens-grating system, we identify the relevant parameters of the grating, the laser beam and the diffraction order and other conditions to the sensitivity limits. Theory suggests that sensitivity increases linearly with the diffraction order, regardless of the diffracted angle, and that relative deformation of the order of 10−6 should be detectable with common optical components and laser beams. This corresponds to thermal expansion coefficients as low as 10−8 °C−1 measured over 100 °C and stresses as low as 10−6. The proposed technique would be applicable to transparent or opaque samples and very small sample volumes.