Nonlinear Scatterers Research Articles

Nonlinear scattering at HF: Prospects for exploitation in OTH radar systems

HF skywave `over-the-horizon' radars experience exceptionally high levels of clutter from the earth's surface as a consequence of their `look-down' propagation geometry. While Doppler processing is effective in separating aircraft echoes from the clutter, thereby enabling detection, the same does not always hold for slow moving targets. In particular, ship echoes occupy the same region of Doppler space as the sea clutter, so the likelihood of target echo obscuration is high. By exploiting the known dependence of the characteristic spectral form of the clutter Doppler spectrum on radar frequency and other parameters, HF radars can maximise the prospects for detectability against particular ranges of target parameters. Nevertheless, even assuming that a radar makes use of all available a priori knowledge to optimise its parameters, small ships and boats often escape detection because their echoes are still masked by clutter in the same Doppler subspace. This is particularly likely to occur if the vessels concerned wish to remain undetected, and hence use the properties of sea clutter to their advantage. In this paper we examine the feasibility of a novel approach to the problem of detection against sea clutter -- detection via nonlinear scattering mechanisms. The nonlinear scatterers of concern here include electronic systems as well as metal-oxide-metal junctions formed by corrosion in the marine environment. This so-called `rusty bolt' effect has previously been considered in the context of electromagnetic compatibility of communication systems. Here we explore the possibility of exploiting it to achieve a form of `clutter-free' radar.

Pulse subtraction Doppler

Recent advances have demonstrated the feasibility of molecular imaging using targeted microbubbles and ultrasound. One technical challenge is to selectively detect attached bubbles from those freely flowing bubbles and surrounding tissue. Pulse Inversion Doppler is an imaging technique enabling the selective detection of both static and moving ultrasound contrast agents: linear scatterers generate a single band Doppler spectrum, while non-linear scatterers generate a double band spectrum, one being uniquely correlated with the presence of contrast agents and non-linear tissue signals. We demonstrate that similar spectrums, and thus the same discrimination, can be obtained through a Doppler implementation of Pulse Subtraction. This is achieved by reconstructing a virtual echo using the echo generated from a short pulse transmission. Moreover by subtracting from this virtual echo the one generated from a longer pulse transmission, it is possible to fully suppress the echo from linear scatterers, while for non-linear scatterers, a signal will remain, allowing classical agent detection. Simulations of a single moving microbubble and a moving linear scatterer subject to these pulses show that when the virtual echo and the long pulse echo are used to perform pulsed Doppler, the power Doppler spectrum allows separation of linear and non-linear moving scattering. Similar results are obtained on experimental data acquired on a flow containing either microbubble contrast agents or linear blood mimicking fluid. This new Doppler method constitutes an alternative to Pulse Inversion Doppler and preliminary results suggest that similar dual band spectrums could be obtained by the combination of any non-linear detection technique with Doppler demodulation.

Separation of multiple scatterers in NEWS experiments using Independent Component Analysis (ICA)

Nonlinear elastic wave spectroscopy combined with imaging techniques such as acoustic time reversal (NEWS-TR) or sparse array tomography is a promising new methodology for detecting microdamage at an early stage. When dealing with structures which could potentially contain many point-like nonlinear scatterers, there is a need to develop techniques for separately imaging the defects using a distributed sensor network which can be used either in time-reversal imaging processes or for tomographic imaging.. In this contribution, we discuss the application of Independent Component Analysis (ICA) methods to solve the problem of separating multiple nonlinear scatterers distributed throughout a sample, either by combining ICA with time reversal or by using ICA in conjunction with a tomographic experiment. We illustrate the procedure for ICA based tomographic imaging of multiple scatterers in an infinite medium.

Localization of material defects using nonlinear resonant ultrasound spectroscopy under asymmetric boundary conditions

The position of microscopic defects in a one-dimensional bar is analyzed by means of the nonlinear resonant ultrasound spectroscopy technique under asymmetric boundary conditions. Experimental results on cementitious material confirm the feasibility of the method to locate nonlinear scatterers. Good agreement between the real damage position and the inferred experimental prediction is obtained based on information about the nonlinear frequency shift and about the amplitude ratio of the third and fifth harmonic for the fundamental resonance mode.

Low-frequency vibration modulation of guided waves to image nonlinear scatterers forstructural health monitoring

Guided wave structural health monitoring offers the prospect of continuous interrogation oflarge plate-like structures with a sparse network of permanently attached sensors.Currently, the most common approach is to monitor changes in the received signalsby subtraction from a reference signal obtained when the structure was knownto be defect-free. In this paper a comparison is made between this defect-freesubtraction approach and a technique in which low-frequency vibration modulationof guided wave signals is used to detect nonlinear scatterers. The modulationtechnique potentially overcomes the need for the defect-free reference measurement asthe subtraction is now made between different parts of an externally appliedlow-frequency vibration. Linear defects were simulated by masses bonded onto a plate andnonlinear scatterers were simulated by loading a similar mass against the plate. Theexperimental results show that the defect-free subtraction technique performs well indetecting the bonded mass whereas the modulation technique is able to discriminatebetween the bonded and loaded masses. Furthermore, because the modulationtechnique does not require a defect-free reference, it is shown to be relativelyindependent of temperature effects, a significant problem for reference based subtractiontechniques.

Three component time reversal imaging using nonlinear elasticity.

The time reversed elastic nonlinearity diagnostic (TREND) has been shown to have the ability to image near surface nonlinear scatterers (e.g., cracks and disbonds) using the normal (out of plane) component of motion. This technique has been advanced with the addition of three‐component vector wave field detection using laser vibrometry. This advancement provides the ability of TREND to detect and image features of various orientations, increasing its capability and decreasing the likelihood of overlooking features due to the inability to excite them. Furthermore, the ability to selectively focus each component of motion provides the means to investigate the mechanism of the nonlinear wave generation at the nonlinear scattering sites. Experimental data are presented from samples containing known defects (location and orientation) confirming the sensitivity of three‐component time reversal imaging in both linear and nonlinear ultrasonics to feature orientation.

Nonlinear acoustic time reversal imaging using the scaling subtraction method

Lab experiments have shown that the imaging of nonlinear scatterers using time reversal acoustics can be a very promising tool for early stage damage detection. The potential applications are however limited by the need for an extremely accurate acquisition system. In order to let nonlinear features emerge from the background noise it is necessary to enhance the signal-to-noise ratio as much as possible. A comprehensive analysis to determine the nonlinear components in a recorded time signal, an alternative to those usually adopted (e.g. fast Fourier), is proposed here. The method is based on the nonlinear physical properties of the solution of the wave equation and takes advantage of the deficient system response scalability with the excitation amplitude. In this contribution, we outline the adopted procedure and apply it to a nonlinear time reversal imaging simulation to highlight the advantages with respect to traditional imaging based on a fast Fourier analysis of the recorded signals.

Computational time reversal acoustics imaging of embedded defects in solid media

Time reversal acoustics (TRA) techniques can exploit the nonlinear processes emerging from the interaction between the incident waves and nonlinear scatterers in solid media in order to localize and characterize the scatterers themselves. When nonlinear scatterers are embedded, their localization can be obtained through a mixed experimental/numerical TRA procedure: the forward propagation is performed experimentally, while the time reversal (TR) backward propagation is simulated using computational codes and a reference model of the solid. The synergetic use of dedicated processing of the forward propagation signals collected at the time reversal mirror (TRM), for example with nonlinear elastic wave spectroscopy (NEWS) techniques, and the calculation of the backpropagated wave fields at each point within the specimen leads to imaging of the nonlinear scatterers. We show examples of nonlinear scatterer (macroscopic cracks, distributed microcracks) imaging by such a procedure, exploiting high performance (parallel) computational codes. We address issues in the imaging method related to the discrepancy between the reference model of the specimen and the real specimen itself. Finally, we address the implementation of the technique for non-destructive Evaluation (NDE) real-world applications using multi-threaded computational codes to be run on common multicore desktop computers.

Separation of multiple scatterers in NEWS-TR experiments

Nonlinear elastic wave spectroscopy combined with acoustic time reversal (NEWS-TR) is a promising new methodology for detecting microdamage at an early stage. When dealing with structures which could potentially contain many pointlike nonlinear scatterers, there is a need to develop techniques for separately imaging the defects using a distributed sensor network which acts as a time-reversal mirror. In this contribution, we present numerical simulations of a newly developed version of the DORT method for nonlinear imaging and also discuss the possibility of applying PARAFAC (parallel factor analysis) and ICA (independent component analysis) methods to solve the problem of separating multiple nonlinear scatterers in the time-frequency domain.

Improving signal analysis for nonlinear time reversed acoustics: simulation results

Nonlinear time reversed acoustics have attracted attention as a tool to localize and identify nonlinear defects in solids [1-4]. The procedure is based on extracting the features due to the nonlinear scatterers from the signals received at the transducer array and back-propagate only the resulting portion of the signals. The usual approach is to filter the received signals to keep only contributions due to higher order harmonics or sidebands. As a result, the signals are very small in amplitude and can be not detectable if transducers are located far from the scatterers. It is evident the need for novel signal processing tools to increase the signal-to-noise ratio of the nonlinear contributions. We have recently proposed a scaling subtraction method [5], which is applied here to nonlinear time reversal virtual experiments, showing the improvements in the signal-to-noise ratio, with resulting better imaging of the nonlinear scatterer. Results will be presented for two approaches to nonlinear time reversal. [1] A. S. Gliozzi et al., J. Acoust. Soc. Am. 120, 2506-2517 (2006). [2] T. J. Ulrich et al., J. Acoust. Soc. Am. 119, 1514-18 (2006). [3] T. J. Ulrich et al., Phys. Rev. Lett. 98, 10430 (2007). [4] T. Goursolle et al., J. Acoust. Soc. Am. 122, 3220 (2007). [5] M. Scalerandi et al., submitted to Appl. Phys. Lett. (2008).

Time reversal and non-linear elastic wave spectroscopy (TR NEWS) techniques

Non-linear elastic wave spectroscopy (NEWS) has been shown to exhibit a high degree of sensitivity to both distributed and isolated non-linear scatterers in solids. In the case of an isolated non-linear scatterer such as a crack, by combining the elastic energy localization of time reversal (TR) with NEWS, it is shown that one can isolate non-linear scatterers in solids. The experiments reviewed here present two distinct methods of combining TR and NEWS for this purpose. The techniques each have there own advantages and disadvantages, with respect to each other and other non-linear methods, which are discussed.

Quantitative Measurement of Ultrasound Disruption of Polymer-Shelled Microbubbles

The goal of this study was to assess the threshold of disruption and subsequent time-course of acoustic response of four experimental nitrogen-filled polymer-shelled microbubbles. Using an in vitro measurement system, a sequence of low-amplitude detection pulses measured the change in echo caused by a high-amplitude disruption pulse on a dilute suspension of bubbles. Detection pulses were transmitted 0.5 ms before disruption and between 1 and 200 ms after disruption. Separate transducers, aligned confocally and orthogonally, were used to transmit and receive bubble echoes. After disruption, all agents demonstrated a transient increase in scattered power. Above the disruption threshold, highly echogenic, nonlinear scatterers were observed. Their echoes slowly disappeared after disruption with median decay times from 7.4 to 13.6 ms, calculated by fitting to a mono-exponential decay. This is consistent with a process wherein the shell is disrupted, releasing the gas and generating free gas bubbles, which cause high-amplitude nonlinear scattering followed by relatively slow diffusion of the gas into solution. This picture has been observed optically with single bubbles and differs from the concept of “stimulated acoustic emission” from disrupted bubbles. (E-mail: burns@sri.utoronto.ca)

Nonlinear dynamics and time reversed acoustic imaging in damaged solids

Our ultimate goal is locating and imaging nonlinear scatterers in solids (e.g., cracks) without a priori knowledge of their existence. Toward that goal, two methods have been devised that combine the spatial and temporal focusing abilities of TRA with nonlinear elastic wave spectroscopy’s (NEWS) sensitivity to mechanical damage. The first method uses TRA to create large amplitude signals and induce a nonlinear response in a highly localized region on a sample surface. Repeating the process in a step‐scan approach provides the means to image the sample surface/near‐surface with high resolution, distinguishing nonlinear features (cracks) from the linear background (undamaged material). The second method takes advantage of TRA to focus acoustic energy from two input frequencies onto an unknown, but nonlinear, scattering source, creating nonlinear wave modulation. The time reversal mirror (TRM) array records the primary and scattering source waveforms. Filtering the recorded signals for a modulation sideband,...

Interaction Dynamics of Elastic Waves with a Complex Nonlinear Scatterer through the Use of a Time Reversal Mirror

This Letter reports on work performed to locate and interrogate a nonlinear scatterer in a linearly elastic medium through the use of a time reversal mirror in combination with nonlinear dynamics. Time reversal provides the means to spatially and temporally localize elastic energy on a scattering feature while the nonlinear dynamics spectrum allows one to determine whether the scatterer is nonlinear (e.g., mechanical damage). Here elastic waves are measured in a solid and processed to extract the nonlinear elastic response. The processed elastic signals are then time reversed, rebroadcast, and found to focus on the nonlinear scatterer, thus defining a time-reversed nonlinear elastic wave spectroscopy process. Additionally, the focusing process illuminates the complexity of the nonlinear scatterer in both space and time, providing a means to image and investigate the origins and physical mechanisms of the nonlinear elastic response.

Acoustic wave dispersion in a one-dimensional lattice of nonlinear resonant scatterers

Nonlinear effects of acoustic wave propagation and dispersion are observed in a one-dimensional lattice made of Helmholtz resonators connected to a tube. These regularly spaced scatterers exhibit individually a wave frequency dependence, which induces a strong velocity dispersion. In addition, they exhibit a wave amplitude dependence (acoustic nonlinearity), which induces nonlinear effects on the dispersion relation of waves in the lattice. The usually observed forbidden frequency band gaps for the transmission coefficient through the lattice are shown to be amplitude dependent. Experimental results are compared to a developed model taking into account the nonlinear behavior of the Helmholtz resonator.

Observation of coherent backscattering ‘factor of three’ in a numerical experiment

We study coherent backscattering of light by nonlinear scatterers in the weakly nonlinear regime. We compare full numerical calculations with a diagrammatic approach; the validity of the latter is demonstrated by the excellent agreement between these two approaches. Especially it emphasizes the fact that, in the weakly nonlinear regime, the coherent backscattering phenomenon originates, in general, from the interference between three different scattering amplitudes. This effect reveals itself in the first nonlinear correction of the backscattered intensity, which is enhanced by almost a factor three as compared to the diffuse background.

Efficiency of time-reversed acoustics for nonlinear damage detection in solids

Time-reversed acoustics (TRA) has been developed in the last few years as a powerful tool for several applications, based on the theoretical properties emerging from the time reversal invariance of the wave equation. TRA is expected to be a good basis for the development of imaging techniques in the field of nondestructive evaluation. For this purpose, however, data processing is necessary to discriminate between images due to defects (in general nonlinear scatterers) and images due to linear inclusions, boundaries, etc. We propose here an approach based on the filtering of the time signals. The image of the scatterer is obtained through numerical simulations of the back propagation in a fictitious reference specimen. We validate the approach using the inversion of synthetic data. We also estimate the robustness of the procedure in the presence of constraints that can occur in any experimental procedure.

Imaging nonlinear scatterers applying the time reversal mirror

Nonlinear elastic wave spectroscopy (NEWS) has been shown to exhibit a high degree of sensitivity to both distributed and isolated nonlinear scatterers in solids. In the case of an isolated nonlinear scatterer such as a crack, by combining the elastic energy localization of the time reversal mirror with NEWS, it is shown here that one can isolate surfacial nonlinear scatterers in solids. The experiments presented here are conducted in a doped glass block applying two different fixed frequency time-reversed signals at each focal point and scanning over a localized nonlinear scatterer (a complex crack). The results show a distinct increase in nonlinear response, via intermodulation distortion, over the damaged area. The techniques described herein provide the means to discriminate between linear and nonlinear scatterers, and thus to ultimately image and characterize damaged regions.

Coherent backscattering of light with nonlinear atomic scatterers

We study coherent backscattering of a monochromatic laser by a dilute gas of cold two-level atoms in the weakly nonlinear regime. The nonlinear response of the atoms results in a modification of both the average field propagation (nonlinear refractive index) and the scattering events. Using a perturbative approach, the nonlinear effects arise from inelastic two-photon scattering processes. We present a detailed diagrammatic derivation of the elastic and inelastic components of the backscattering signal for both scalar and vectorial photons. In particular, we show that the coherent backscattering phenomenon originates in some cases from the interference between three different scattering amplitudes. This is in marked contrast with the linear regime where it is due to the interference between two different scattering amplitudes. In particular we show that, if elastically scattered photons are filtered out from the photodetection signal, the nonlinear backscattering enhancement factor exceeds the linear barrier of 2, consistently with a three-amplitude interference effect.

Coherent backscattering of light by nonlinear scatterers

We theoretically study the propagation of light in a disordered medium with nonlinear scatterers. We especially focus on interference effects between reversed multiple scattering paths, which lead to weak localization and coherent backscattering. We show that, in the presence of weakly nonlinear scattering, constructive interferences exist in general between three different scattering amplitudes. This effect influences the nonlinear backscattering enhancement factor, which may thus exceed the linear barrier two.