Sensors for Ultrasonic Nondestructive Testing (NDT) in Harsh Environments.

In this special issue of Sensors, seven peer-reviewed manuscripts appear on the topic of ultrasonic transducer design and operation in harsh environments: elevated temperature, high gamma and neutron fields, or the presence of chemically aggressive species. Motivations for these research and development projects are strongly focused on nuclear power plant inspections (particularly liquid-sodium cooled reactors), and nondestructive testing of high-temperature piping installations. It is anticipated that we may eventually see extensive use of permanently mounted robust transducers for in-service monitoring of petrochemical plants and power generations stations; quality control in manufacturing plants; and primary and secondary process monitoring in the fabrication of engineering materials.

Elastic wave propagation in bars of arbitrary cross section: a generalized Fourier expansion collocation method.

The problem of elastic wave propagation in an infinite bar of arbitrary cross section is studied via a generalized version of the Fourier expansion collocation method. In the current formulation, the exact three dimensional solution to Navier's equation in cylindrical coordinates is used to obtain the boundary traction vector as a periodic, piecewise continuous/differentiable function of the angular coordinate. Traction free conditions are then met by setting the Fourier coefficients of the boundary traction vector to zero without approximating the bounding surface by multi-sided polygons as in the method presented by Nagaya. The method is derived for a general cross section with no axial planes of symmetry. Using the general formulation it is shown that the symmetric and asymmetric modes decouple for cross sections having one axial plane of symmetry. An efficient algorithm for computing dispersion curves based on the current method is presented and used to obtain the fundamental longitudinal and flexural wave speeds for a bar of elliptical cross section. The results are compared to those obtained by previous researchers using exact and approximate treatments.

An Ultrasonic Adaptive Beamforming Method and Its Application for Trans-Skull Imaging of Certain Types of Head Injuries; Part II: Reception Mode and Adaptive Imaging.

OBJECTIVE: Background theory and a new algorithm for single-point adaptive focusing in transmission mode through ultrasonic barriers via one-dimensional phased arrays were reported in part I. In this paper the algorithm is further extended and implemented into a full adaptive beamforming process, including complete transmission and reception modes. METHODS: Corrected time delay patterns, adapted to the local acoustical and geometrical properties of the barrier, are calculated and applied in both modes. Further, an adaptive imaging process is also developed that implements the proposed beamforming process for two-dimensional imaging through randomly shaped multilayered phase-aberrating structures. The method is optimized for the case of human skull as the ultrasound barrier and its application for transcranial imaging is discussed. RESULTS: Laboratory results of adaptive imaging through realistic skull-mimicking phantoms are presented. The algorithms are implemented on a 64-channel ultrasound open-source phased array platform controlling a standard 128-element biomedical phased array. Irregularly shaped reflectors with characteristic dimensions of the order of ∼0.5 mm to ∼4.5 mm were used as targets behind the skull phantoms in our experiments. Minimum and maximum distortional target displacements of 2.2 mm and 25.3 mm (in 12 cm depth) were observed in sonograms when uncompensated time delays were used. By contrast, the positioning errors ranged from 0.0 to 0.9 mm when our algorithm was employed. CONCLUSION AND SIGNIFICANCE: The adaptive imaging results demonstrate strong potential of the proposed technique for diagnostic imaging of acoustically reflective head injuries directly through intact human skull.

Spectral Shift Originating from Non-linear Ultrasonic Wave Propagation and Its Effect on Imaging Resolution.

An amplitude-dependent downshift in the fundamental wave spectrum of a propagating ultrasonic pulse caused by non-linear wave propagation is described. The effects of non-linearity and the associated downshift on spatial resolution are also studied. The amounts of downshift and spatial resolution are extracted from the numerically simulated beam profile based on the KZK equation. Results for a 25-MHz transducer reveal that non-linear effects can lead to 58% additional downshift in the centre frequency of a pulse compared with a linear case with downshift caused only by attenuation. This additional downshift causes about 50% degradation in axial resolution. However, as the beam becomes narrower from the non-linear effects, the overall effect of non-linearity still leads to improved lateral resolution (≤26%). Therefore, as non-linearity increases with wave pressure, it is concluded that the increase in source pressure improves lateral resolution and degrades axial resolution.

Determination of the Ultrasonic Non-linearity Parameter B/A versus Frequency for Water.

For tissue characterization, it is desirable to determine B/A using high-frequency transducers. Moreover, an accurate estimate of B/A at elevated frequencies (or at least the assumption of frequency independence of B/A) is required to evaluate the safety of high-frequency systems. However, common finite-amplitude approaches become increasingly inaccurate at high frequencies. In this article, a practical variation of the finite-amplitude method is proposed which combines experiments with numerical simulations of the Khokhlov-Zabolotskaya-Kuznetsov equation and can be used at elevated frequencies. The results at low frequencies show that the proposed approach is accurate with lower uncertainties compared with the finite-amplitude method because it avoids assumptions and approximations. The measured values of B/A versus frequency for water at 2.25-20 MHz show that there is no statistically significant variation in B/A values with frequency, and therefore the assumption of frequency independence of B/A is realistic.

Non-linear Wave Propagation and Safety Standards for Diagnostic Ultrasound Devices.

Safety standards for clinical diagnostic ultrasonic devices were developed for use in relatively low-frequency systems (1-10 MHz), under the assumption that non-linear effects would be negligible. This article reviews ways in which neglecting non-linear wave propagation affects the measurements and calculations required to comply with safety standards and U.S. Food and Drug Administration guidance that recognizes these standards. An attempt is made to evaluate whether ignoring non-linear effects could result in significant error in the exposure quantities defined in these standards at either low or high frequencies, based on published literature. This article maintains that although non-linear effects have been considered in some parts of safety standards related to hydrophone requirements, the coverage is inadequate, especially for modern equipment with high working frequencies. A new approach is required to assess the magnitude of thermal heating for recently developed high-frequency systems to incorporate non-linear effects. In contrast, the current approach for evaluating the risk of cavitation can be used after appropriate modifications.

A New High-Temperature Ultrasonic Transducer for Continuous Inspection.

A novel design of piezoelectric ultrasonic transducer is introduced, suitable for operation at temperatures of up to 700 °C-800 °C. Lithium niobate single crystal is chosen as the piezoelectric element primarily due to the high Curie temperature of 1200 °C. A backing element based on a porous ceramic is designed for which the pore volume fraction and average pore diameter in the ceramic matrix can be controlled in the manufacturing process; this enables the acoustic impedance and attenuation to be selected to match their optimal values as predicted by a one-dimensional transducer model of the entire transducer. Porous zirconia is selected as the ceramic matrix material of the backing element to obtain an ultrasonic signal with center frequency of 2.7-3 MHz, and 3-dB bandwidth of 90%-95% at the targeted operating temperature. Acoustic coupling of the piezocrystal to the backing element and matching layer is investigated using commercially available high-temperature adhesives and brazing alloys. The performance of the transducer as a function of temperature is studied. Stable bonding and clear signals were obtained using an aluminum brazing alloy as the bonding agent.

An Ultrasonic-Adaptive Beamforming Method and Its Application for Trans-skull Imaging of Certain Types of Head Injuries; Part I: Transmission Mode.

A new adaptive beamforming algorithm for imaging via small-aperture 1-D ultrasonic-phased arrays through composite layered structures is reported. Such structures cause acoustic phase aberration and wave refraction at undulating interfaces and can lead to significant distortion of an ultrasonic field pattern produced by conventional beamforming techniques. This distortion takes the form of defocusing the ultrasonic field transmitted through the barrier and causes loss of resolution and overall degradation of image quality. To compensate for the phase aberration and the refractional effects, we developed and examined an adaptive beamforming algorithm for small-aperture linear-phased arrays. After accurately assessing the barrier's local geometry and sound speed, the method calculates a new timing scheme to refocus the distorted beam at its original location. As a tentative application, implementation of this method for trans-skull imaging of certain types of head injuries through human skull is discussed. Simulation and laboratory results of applying the method on skull-mimicking phantoms are presented. Correction of up to 2.5 cm focal point displacement at up to 10 cm depth under our skull phantom is demonstrated. Quantitative assessment of the method in a variety of temporal focusing scenarios is also reported. Overall temporal deviation on the order of a few nanoseconds was observed between the simulated and experimental results. The single-point adaptive focusing results demonstrate strong potential of our approach for diagnostic imaging through intact human skull. The algorithms were implemented on an ultrasound advanced open-platform controlling 64 active elements on a 128-element phased array.

Ultrasonic monitoring of erosion/corrosion thinning rates in industrial piping systems.

Monitoring pipe wall erosion/corrosion thinning rates is an important issue in petrochemical and power generation industries. In this paper, two signal processing techniques are utilized for estimating the thinning rate based on ultrasonic pipe wall thickness data collected over a short period of time. The first is a combination of cross-correlation and polynomial curve fitting and the second is a model-based estimation (MBE) scheme. These techniques are applied to data collected from an accelerated thinning rate apparatus and both show that they are capable of estimating the thinning rates quickly in short time periods with good accuracy. In laboratory applications, thinning rates as low as 10 µm/year were measured within 15 days with an uncertainty of ±1.5 µm/year by both techniques. Although the MBE technique can yield marginally better accuracy, the greater stability and computational speed of the cross-correlation technique make it the preferred choice for industrial use.

Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder.

Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675-682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka⩽0.1. The incidence angle α(c) at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka⩽0.1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.

An alternative method for plotting dispersion curves.

Solving the frequency equation and plotting the dispersion curves in problems of wave propagation in cylinders and plates, particularly when the material is anisotropic, are complicated tasks. The traditional numerical methods are usually based on determination of the zeros of the frequency equation by using an iterative find-root algorithm. In this paper, an alternative method is proposed which extracts the solution of the frequency equation in the form of dispersion curves from the three-dimensional illustration of the frequency equation. For this purpose, a three-dimensional representation of the real roots of the frequency equation is first plotted. The dispersion curves, which are the numerical solutions of the frequency equation, are then obtained by a suitable cut in the velocity-frequency plane. The advantages of this method include simplicity, high speed, low possibility of numerical error, and presentation of the results in a graphical form that promotes ease of interpretation. This method is not directly applicable to problems which incorporate high damping or leaky waves. However, if the damping is not very high, it could be a good estimate of the true dispersion curves.

Circumferential resonance modes of solid elastic cylinders excited by obliquely incident acoustic waves.

When an immersed solid elastic cylinder is insonified by an obliquely incident plane acoustic wave, some of the resonance modes of the cylinder are excited. These modes are directly related to the incidence angle of the insonifying wave. In this paper, the circumferential resonance modes of such immersed elastic cylinders are studied over a large range of incidence angles and frequencies and physical explanations are presented for singular features of the frequency-incidence angle plots. These features include the pairing of one axially guided mode with each transverse whispering gallery mode, the appearance of an anomalous pseudo-Rayleigh in the cylinder at incidence angles greater than the Rayleigh angle, and distortional effects of the longitudinal whispering gallery modes on the entire resonance spectrum of the cylinder. The physical explanations are derived from Resonance Scattering Theory (RST), which is employed to determine the interior displacement field of the cylinder and its dependence on insonification angle.