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In nonlinear ultrasound testing, the relative nonlinear parameter is conveniently measured as a sensitive means of detecting and imaging overall variation of microstructures and damages. Compared to the quadratic nonlinear parameter ( β ′ ), the cubic nonlinear parameter ( γ ′ ), calculated as the third harmonic amplitude divided by the cube of the fundamental amplitude, has generally a higher value, providing better sensitivity in nonlinear parameter mapping. Since the third harmonic amplitude is about two orders of magnitude lower than the fundamental amplitude, efficient excitation and highly sensitive reception of third harmonic is very important. In this paper, we explore an odd harmonic thickness resonant transducer that meets the requirements for pulse-echo third harmonic generation (THG) measurements. We also address the problem of source nonlinearity that may be present in the measured amplitude of the third harmonic and propose a method to properly correct it. First, we measure γ ′ for a series of aluminum specimens using the through-transmission method to observe the behavior of γ ′ as a function of specimen thickness and input voltage, and examine the effects of various corrections such as attenuation, diffraction and source nonlinearity. Next, we apply the odd harmonic resonant transducer to pulse-echo THG measurements of precipitation heat-treated specimens. It is shown that such transducer is very effective in generation and detection of fundamental and third harmonics under finite amplitude toneburst excitation. The highly sensitive detectability of γ ′ are presented as a function of aging time, and the sensitivity of γ ′ is compared with that of β ′ and β ′ 2 . [ABSTRACT FROM AUTHOR]

Harmonic generation measurement is recognized as a promising tool for inspecting material state or micro-damage and is an ongoing research topic. Second harmonic generation is most frequently employed and provides the quadratic nonlinearity parameter (β) that is calculated by the measurement of fundamental and second harmonic amplitudes. The cubic nonlinearity parameter ( β 2 ), which dominates the third harmonic amplitude and is obtained by third harmonic generation, is often used as a more sensitive parameter in many applications. This paper presents a detailed procedure for determining the correct β 2 of ductile polycrystalline metal samples such as aluminum alloys when there exists source nonlinearity. The procedure includes receiver calibration, diffraction, and attenuation correction and, more importantly, source nonlinearity correction for third harmonic amplitudes. The effect of these corrections on the measurement of   β 2 is presented for aluminum specimens of various thicknesses at various input power levels. By correcting the source nonlinearity of the third harmonic and further verifying the approximate relationship between the cubic nonlinearity parameter and the square of the quadratic nonlinearity parameter ( β ∗ β ), β 2 ≈ β ∗ β , the cubic nonlinearity parameters could be accurately determined even with thinner samples and lower input voltages. [ABSTRACT FROM AUTHOR]

With respect to harmonic generation measurements in isotropic materials, the amplitude of the third-harmonic wave generally depends on both $\beta ^{2}$ (the square of the second-order nonlinear parameter $\beta $) and $\gamma $ (the third-order nonlinear parameter). Therefore, some care should be taken when measuring these parameters using the third-harmonic amplitude. The purpose of this paper is to investigate detailed theoretical and measurement techniques for the accurate determination of $\beta ^{2}$ which dominates the third-harmonic amplitude in most biological fluids and crystalline solids. The theory deals with harmonic generation in materials with cubic nonlinearity and defines the formula for measuring $\beta ^{2}$ with corrections for diffraction and attenuation. These corrections are derived from the Westervelt equation and play an important role in the measurement of nonlinear parameters. The third-harmonic amplitude that varies with the distance in water is obtained for the measurement of $\beta ^{2}$. $\beta $ is also measured from the second-harmonic amplitude for comparison. We also confirm the required input voltage to stably generate the third harmonic and discuss the effects of diffraction and attenuation correction on the $\beta ^{2}$ determination. The measured $\beta ^{2}$ in the propagation range of 0.05–0.2 m agrees well with the square of the measured $\beta $ , revealing that the third-harmonic amplitude is closely related to $\beta ^{2}$ , not $\gamma $. This paper covers comprehensive theories, experimentation, and analysis related to the measurement of third-harmonic generation in isotropic media and can be immediately applied to crystalline solids. [ABSTRACT FROM AUTHOR]

In nonlinear acoustic measurements involving reflection from the stress-free boundary, the pulse-echo method could not be used because such a boundary is known to destructively change the second harmonic generation (SHG) process. The use of a focusing acoustic beam, however, can improve SHG after reflection from the specimen boundary, and nonlinear pulse-echo methods can be implemented as a practical means of measuring the acoustic nonlinear parameter (β) of solid specimens. This paper investigates the optimal sensor design for pulse-echo SHG and β measurements using Fresnel zone plate (FZP) focused beams. The conceptual design of a sensor configuration uses separate transmission and reception, where a broadband receiver is located at the center and a four-element FZP transmitter is positioned outside the receiver to create a focused beam at the specified position in a solid sample. Comprehensive simulations are performed for focused beam fields analysis and to determine the optimal sensor design using various combinations of focal length, receiver size and frequency. It is shown that the optimally designed sensors for 1 cm thick aluminum can produce the second harmonic amplitude and the uncorrected nonlinear parameter corresponding to the through-transmission method. The sensitivity of the optimal sensors to the changes in the designed sound velocity is analyzed and compared between the odd- and even-type FZPs. [ABSTRACT FROM AUTHOR]

The practical implementation of nonlinear ultrasonic technique has been limited to the through-transmission setup for measuring the second harmonic component induced by the nonlinearity or microstructural changes of test material. A more practical technique such as the pulse-echo testing has been ruled out because a traction-free reflecting boundary destructively alters the nonlinear generation process. A focusing acoustic beam or rigid boundary condition was often employed for biomedical imaging and fluid nonlinearity in the pulse-echo inspection. In this article, we further explore a more general and efficient method to improve the generation of the second harmonic component in the pulse-echo mode with traction-free surface. A dual element planar transdcer with optimal phase shift of the input signal in one element relative to another is proposed for this purpose. The validity of the phase shift concept is confirmed by comparing the enhanced generation of second harmonic amplitudes and the resulting nonlinear parameters with the rigid-boundary case equivalent to the conventional through-transmission setup. [ABSTRACT FROM AUTHOR]