Modeling micromechanical measurements of depth-varying properties with scanning acoustic microscopy

Scanning acoustic microscopy (SAM) has been applied to measure the near-surface elastic properties of materials. For many substrates, the near-surface property is not constant but varies with depth. In this paper, we aim to interpret the SAM data from such substrates by modeling the interaction of the focused ultrasonic field with a substrate having a near-surface graded layer. The focused ultrasonic field solutions were represented as spherical harmonic expansions while the substrate solutions were represented as plane wave expansions. The bridging of the two solutions was achieved through the decomposition of the ultrasonic pressure fields in their angular spectra. Parametric studies were performed, which showed that near-surface graded layers exhibit distinctive frequency dependence of their reflectance functions. This behavior is characteristic to the material property gradation profile as well as the extent of the property gradation. The developed model was used to explain the frequency-dependent reflection coefficients measured from an acid-etched dentin substrate. Based on the model calculations, the elastic property variations of the acid-etched dentin near-surface indicate that the topmost part of the etched layer is very soft (3–6 GPa) and transitions to the native dentin through a depth of 27 and 36 microns.