Thickness Measurement of a Film on a Substrate by Low-Frequency Ultrasound

We describe a new simple technique for the low-frequency ultrasonic thickness measurement of an air-backed soft thin layer attached on a hard substrate of finite thickness through the frequency-shifts of the substrate resonances by the substrate-side insonification. A plane compressive wave impinging normally on the substrate surface from a liquid is studied. Low frequency here means an interrogating acoustical wave frequency of less than half of the ‘half-wavelength resonance frequency’of the thin layer depending on the acoustical impedance ratio of the coating to the substrate. Equations for the frequency-shifts are derived and solved by the Newton iterative method and the Taylor expansion method, respectively, indicating satisfactory agreement within the range of interest of thickness ratio of the thin layer to the substrate for a polymer-aluminium structure. An experimental setup is constructed to verify the validity of the technique.