SIMULTANEOUS MEASUREMENT OF THE ACOUSTICAL PROPERTIES OF A THIN-LAYERED MEDIUM - THE INVERSE PROBLEM

This paper presents a frequency-domain ultrasonic technique for a simu ltaneous determination of the thickness (h) and wave sped (c) of the i ndividual layers comprising a multilayered medium. The layers may be ' 'thin''; by thin we mean that the successive reflections of an ultraso nic pulse from the two faces of a layer are nonseparable in the time d omain. Plane longitudinal waves which are normally incident upon the m edium 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 eithe r the Newton-Raphson or the Simplex method in conjunction with the inc remental search method, has been developed to reconstruct simultaneous ly the thickness and phase velocity of each layer by minimizing the di fference between the theoretical and the experimental results in the m ean-sum-square sense; the entire complex spectrum, i.e., the amplitude as well as the phase spectrum, was used. The technique is fully autom ated and computer controlled and can be readily used for in situ NDE a pplications. Results are presented for several three-layer specimens; aluminum/water/aluminum, aluminum/water/titanium, and titanium/water/t itanium. 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 measureme nt of the three thicknesses, given the three wave speeds; (3) simultan eous 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 meas urements was found to be excellent; typically, +/- 3 mu m 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 mu m in h and +/- 2% in c.