Simultaneous measurement of the acoustical properties of a thin-layered medium: The inverse problem

Abstract

This paper presents a frequency-domain ultrasonic technique for a simultaneous determination of the thickness (h) and wave speed (c) of the individual layers comprising a multilayered medium. The layers may be ‘‘thin’’; by thin we mean that the successive reflections of an ultrasonic pulse from the two faces of a layer are nonseparable in the time domain. Plane longitudinal waves which are normally incident upon the medium are considered. A systematic analysis of the sensitivity of the complex-valued transfer function to the acoustical parameters of each layer has been carried out. An inverse algorithm, which utilizes either the Newton–Raphson or the Simplex method in conjunction with the incremental search method, has been developed to reconstruct simultaneously the thickness and phase velocity of each layer by minimizing the difference between the theoretical and the experimental results in the mean-sum-square sense; the entire complex spectrum, i.e., the amplitude as well as the phase spectrum, was used. The technique is fully automated and computer controlled and can be readily used for in situ NDE applications. Results are presented for several three-layer specimens; aluminum/water/aluminum, aluminum/water/titanium, and titanium/water/titanium. Successful inversion was obtained for the following cases (1) simultaneous determination of h and c of any one of the three layers, given h and c of the remaining two layers; (2) simultaneous measurement of the three thicknesses, given the three wave speeds; (3) simultaneous measurement of the three wave speeds, given the three thicknesses; (4) simultaneous determination of all three thicknesses and one wave speed, given the remaining two wave speeds. The precision of our measurements was found to be excellent; typically, ±3 μm in h (for h of the order of 1 mm) and ± one part per thousand in c. The accuracy was found to be about one order of magnitude lower than the precision; typically, ±10 μm in h and ±2% in c.