Ultrasonic characteristic of phase shift of layered structure and the determination of layer thickness

For the ultrasonic normally-incident reflected method, the phase shift of the mid-layer in a multi-layered structure has been theoretically derived and expressed as a sum form of the measured phase shift and the crossing phase shift. Using the sum form, the characteristics of phase shifts of a linear-viscoelastic layer on the two different elastic substrates of half-space of the infinite extent are first analyzed. By the replacement of phase shift of the upper elastic substrate with the corresponding measured phase shift, the substitution function of the input acoustical impedance of a next inaccessible layer has been developed. It is concluded that the corresponding relation of the layer phase shift with the minima/maxima of the absolute value of the input acoustical impedance of the inaccessible layer is repeated by those of the substitution function. Without giving the substrate thickness and considering the introduced misalignment and distortion problems, based on the corresponding relation, the thickness of the inaccessible layer can be determined by searching the frequencies of the minima/ maxima of the absolute value of the substitution function.