On the theoretical limitations in estimating thickness of a plate-like structure from a full-field single-tone response Lamb wave measurement

•Full-field measurements in two dimensions simulated for calculations.•Cramer-Rao bound is applied to thickness estimates from Lamb wave measurements.•Simulation model used to drive theoretical sensitivity computations.•Reflections accounted for in Cramer-Rao bound calculations.•Relation of sensitivity to frequency, source distance, number of sources explored. A persistent question in wavenumber analysis in the estimation of thickness from a steady-state wave field is identifying the theoretical sensitivity of the system. A well-known trade-off between spatial frequency/wavenumber resolution and thickness resolution exists. The current work presents a calculation of the Cramer-Rao Lower bound (CRLB), specifically as applied to thickness estimates, for a 2-dimensional multi-mode waveform in Gaussian noise. Cases of near-field and far-field excitation are considered, and transducer position with respect to the scan area is also varied. Additionally, we consider the CRLB in a plate with multiple sources, simulated as sources placed on the boundary of the plate. We conclude by presenting the CRLB values in terms of frequency for various thicknesses, and by presenting optimal excitation frequencies for a nominal thickness, based on the CRLB.