Errors and uncertainties in the ultrasonic pulse-echo reflectometry method for measuring acoustic impedance

Ultrasonic pulse-echo reflectometry provides a convenient method to measure the acoustic impedance of a layer of unknown material bonded to a substrate of another material whose acoustic properties are known. The amplitudes of echoes from the interface are used to calculate the interface reflection coefficient and, from this and a knowledge of the properties of the substrate material, the unknown impedance is obtained. The technique has potential for assessment of adhesive cure and measurement of mechanical moduli. The calculation is poorly conditioned in that small errors in raw echo data can result in unacceptably large errors in the estimate of the required impedance. This paper gives an analysis which demonstrates how bias and variance errors in raw data lead to bias and variance errors in the calculated reflection coefficient and how these lead to errors in impedance estimation which can be very much greater and which depend on the value of the coefficient of reflection at the interface. Experimental results are given which verify the analytical predictions of the error generation process. The effects of interface conditions such as transducer coupling film and paint coatings are considered quantitatively by a simulation of the wave system. The effects of substrate surface roughness are considered briefly in a series of experiments.