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

Abstract

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.

High-Frequency Rheological Characterization of Homogeneous Polymer Films with the Quartz Crystal Microbalance

“…In eq 2 Z q is the acoustic impedance of the quartz (i.e., Z q = (μ q ρ q ) 1/2 ), where μ q is the shear modulus of quartz in the plane of the quartz disc used as the oscillator and ρ q is the density of quartz. Quartz has a density of 2.66 g/cm 3 . The shear modulus for the AT cut quartz used in our experiments is 2.95 × 10 10 Pa, giving Z q = 8.84 × 10 6 kg/m 2 s. The complex impedance is defined as the ratio of the interfacial shear stress, σ n *, to the velocity of the shear wave, uṅ *:…”

“…22 Equation 10 can be used to determine some general guidelines for the use of quartz crystal resonators as sensors immersed in bulk fluids. For an AT cut quartz crystal operating at a fundamental resonance frequency of 5 MHz exposed on one side to water (η = 10 −3 Pa s and ρ = 1 g/cm 3 ), ΔΓ = −Δf = 713 Hz. As a general rule, we have found that high-quality data can be obtained when Γ is less than ∼20 kHz, corresponding to solution viscosities of less than about 0.5 Pa s (for ρ = 1 g/ cm 3 ).…”

Large frequency bands viscoelastic properties of honey

“…However, it has been shown that the measurements done via the reflection method are less accurate than those done with a transmission configuration [12]. In order to improve the accuracy of the measurements done by reflectometry, one can work with multiple reflections instead of simple one, as it was done by Longin et al [13] on polydimethylsiloxane polymers.…”

Enhanced multiple ultrasonic shear reflection method for the determination of high frequency viscoelastic properties

“…The values and errors obtained for the reflection coefficient, phase shift and loss modulus as a function of the delay line material are reported in Table 2 [25]. One can notice that according to theory and to viscosity measurements, G 00 should be equal to 81.7 MPa because G 00 = xg.…”