Acoustic Wave Velocity Measurements Research Articles

Experimental Study on the Fracture Toughness of Granite Affected by Coupled Mechanical-Thermo

Abstract Hot dry rock geothermal energy is deep geological energy. Its ability to resist fracture is an important basis for effective reconstruction and scientific evaluation of the stability of geothermal reservoirs. Hot dry rock is typically buried deeply, and the reservoir is often in a high-temperature and high stress environment. There have been limited studies conducted on the effect of different three-dimensional stress and temperature on granite fracture toughness. Thereby, herein an experimental study is conducted on the heat treatment of granite under different external loads and temperatures. The variation in fracture toughness of granite with temperature and pressure is studied using a three-point bending fracture mechanics experiment, scanning electron microscope (SEM) observation, and acoustic wave velocity measurement. The results show that under the joint influence of 25 MPa deviator stress and 200 °C temperature, the Mode I, Mixed mode (I + II), and Mode II fracture toughness of granite show a nonlinear change trend of decreasing and increasing. Among the three modes, the change range of Mode I fracture toughness is not more than 10% which is not significant. Contrarily, the degradation effect of rock mechanical properties caused by the joint action of stress and temperature in Mode II and Mixed mode (I + II) is predominant. The maximum range of Mode II fracture toughness is reduced by 22%, whereas the maximum range of Mixed mode (I + II) fracture toughness is reduced by 18%. However, the compression action of three-dimensional stress causes a slight enhancement in granite mechanical properties, wherein the maximum range of Mixed mode (I + II) fracture toughness is increased by 12%. Furthermore, the change of granite’s ability to resist tensile, shear, and composite (tensile + shear) fracture is not coordinated under the joint action of different temperatures and external loads. This may be due to the small deviator stress effect, which is similar to the early loading stage of uniaxial compression. External loads and thermal stress damage occur in the rock along with the compaction of pore cracks. These mechanisms have different dominant positions under varied temperature and three-dimensional stress coupling conditions, resulting in either the enhancement or weakening of the mechanical properties of granite. The results of this experimental study are conducive to gaining an in-depth understanding of the change law of deep rock mechanical properties and the exploration of hot dry rock reservoir reconstruction.

Acoustic Emission Wave Velocity Measurement of Asphalt Mixture by Arbitrary Wave Method

The wave velocity of acoustic emission (AE) can reflect the properties of materials, the types of AE sources and the propagation characteristics of AE in materials. At the same time, the wave velocity of AE is also an important parameter in source location calculation by the time-difference method. In this paper, a new AE wave velocity measurement method, the arbitrary wave (AW) method, is proposed and designed to measure the AE wave velocity of an asphalt mixture. This method is compared with the pencil lead break (PLB) method and the automatic sensor test (AST) method. Through comparison and analysis, as a new wave velocity measurement method of AE, the AW method shows the following advantages: A continuous AE signal with small attenuation, no crosstalk and a fixed waveform can be obtained by the AW method, which is more advantageous to distinguish the first arrival time of the acoustic wave and calculate the wave velocity of AE more accurately; the AE signal measured by the AW method has the characteristics of a high frequency and large amplitude, which is easy to distinguish from the noise signal with the characteristics of a low frequency and small amplitude; and the dispersion of the AE wave velocity measured by the AW method is smaller, which is more suitable for the measurement of the AE wave velocity of an asphalt mixture.

Determination of all piezoelectric coefficients and elastic stiffness constants in LiTaO3 crystals based on measurements of acoustic wave velocities

Determination of all piezoelectric coefficients and elastic stiffness constants in LiTaO₃ crystals based on measurements of acoustic wave velocities

Determining the crystallographic orientation of hexagonal crystal structure materials with surface acoustic wave velocity measurements

Throughout our engineered environment, many materials exhibit a crystalline lattice structure. The orientation of such lattices is crucial in determining functional properties of these structures, including elasticity and magnetism. Hence, tools for determining orientation are highly sought after. Surface acoustic wave velocities in multiple directions can not only highlight the microstructure contrast, but also determine the crystallographic orientation by comparison to a pre-calculated velocity model. This approach has been widely used for the recovery of orientation in cubic materials, with accurate results. However, there is a demand to probe the microstructure in anisotropic crystals - such as hexagonal close packed titanium. Uniquely, hexagonal structure materials exhibit transverse isotropic linear elasticity. In this work, both experimental and simulation results are used to study the discrete effects of both experimental parameters and varying lattice anisotropy across the orientation space, on orientation determination accuracy. Results summarise the theoretical and practical limits of hexagonal orientation determination by linear SAW measurements. Experimental results from a polycrystalline titanium specimen, obtained by electron back scatter diffraction and spatially resolved acoustic spectroscopy show good agreement (errors of ϕ1=5.14° and Φ=6.99°). Experimental errors are in accordance with those suggested by simulation, according to the experimental parameters. Further experimental results demonstrate dramatically improved orientation results (Φ error <1°). Demonstrating the possibility of achieving results near the theoretical limit by strict control of the experimental parameters.

Measuring mechanical wave speed, dispersion, and viscoelastic modulus of the cornea using optical coherence elastography

Acoustic wave velocity measurement based on optical coherence tomography (OCT) is a promising approach to assess the mechanical properties of biological tissues and soft materials. While studies to date have demonstrated proof of concept of different ways to excite and detect mechanical waves, the quantitative performance of this modality as mechanical measurement has been underdeveloped. Here, we investigate the frequency dependent measurement of the wave propagation in viscoelastic tissues, using a piezoelectric point-contact probe driven with various waveforms. We found that a frequency range of 2-10 kHz is a good window for corneal elastography, in which the lowest-order flexural waves can be identified in post processing. We tested our system on tissue-simulating phantoms and ex vivo porcine eyes, and demonstrate reproducibility and inter-sample variability. Using the Kelvin-Voigt model of viscoelasticity, we extracted the shear-elastic modulus and viscosity of the cornea and their correlation with the corneal thickness, curvature, and eyeball mass. Our results show that our method can be a quantitative, useful tool for the mechanical analysis of the cornea.

Flexural and visual characteristics of fibre-managed plantation Eucalyptus globulus timber

ABSTRACTThe main goal of this study was to investigate the visual characteristics, recovery rate, and flexural properties of sawn boards from a fibre-managed plantation Eucalyptus globulus resource as a potential raw material for structural building applications. The impacts of the visual characteristics, strength-reducing features, and variation in basic density and moisture content on the bending modulus of elasticity (MOE) and modulus of rupture (MOR) of the boards were investigated. The reliabilities of different non-destructive methods in predicting MOE and MOR of the boards were evaluated, including log acoustic wave velocity measurement and numerical modellings. The MOE and MOR of the boards were significantly affected by the slope of grain, percentage of clear wood, and total number of knots in the loading zone of the boards. The normal variation in basic density significantly influenced the MOE of the boards while its effect on the MOR was insignificant. The numerical models developed using the artificial neural network (ANN) showed better accuracies in predicting the MOE and MOR of the boards than traditional multi-regression modelling and log acoustic wave velocity measurement. The ANN models developed in this study showed more than 78.5% and 79.9% success in predicting the adjusted MOE and MOR of the boards, respectively.

Facile measurement of single-crystal elastic constants from polycrystalline samples

Elastic constants are among the most fundamental properties of materials. Simulations of microstructural evolution and constitutive/micro-mechanistic modeling of materials properties require elastic constants that are predominately measured from single crystals that are labor intensive to grow. A facile technique is developed to measure elastic constants from polycrystalline samples. The technique is based upon measurements of the surface acoustic wave velocities with the help of a polydimethylsiloxane film grating that is placed on a polished surface of a polycrystalline sample to confine surface acoustic waves that are induced by a femtosecond laser and measured using pump-probe time-domain thermoreflectance. Electron backscatter diffraction is employed to measure the crystallographic orientation along which the surface acoustic wave propagates in each grain (perpendicular to the polydimethylsiloxane grating). Such measurements are performed on several grains. A robust mathematical solution was developed to compute the surface acoustic wave velocity along any crystallographic orientation of any crystal structure with given elastic constants and density. By inputting various starting values of elastic constants to compute the surface acoustic wave velocities to match experimental measurements in several distinct crystallographic orientations using an optimization algorithm, accurate elastic constant values have been obtained from seven polycrystalline metal samples to be within 6.8% of single-crystal measurements. This new technique can help change the current scenario that experimentally measured elastic constants are available for only about 1% of the estimated 160,000 distinct solid compounds, not to mention the significant need for elastic constants of various solid solution compositions that are the base of structural materials.

Increase in elastic anisotropy of single crystal tungsten upon He-ion implantation measured with laser-generated surface acoustic waves

We report the experimental observation of an increase in the elastic anisotropy of tungsten upon He-ion implantation, probed optically using transient grating spectroscopy. Surface acoustic wave (SAW) velocity measurements were performed on a (110) oriented tungsten single crystal as a function of in-plane propagation direction for unimplanted and implanted samples. Our measurements allow us to finely resolve the remarkably small elastic anisotropy of the samples investigated. SAW velocity calculations are used to interpret the experimental data and to extract the Zener anisotropy parameter η and the elastic constant C44. Upon ion implantation, we observe an increase in the quantity (η−1) by a factor of 2.6. The surprising increase in elastic anisotropy agrees with previous theoretical predictions based on ab initio calculations of the effect of self-interstitial atoms and He-filled vacancy defects on the elastic properties of tungsten.

Ultrahigh-pressure acoustic wave velocities of SiO2-Al2O3 glasses up to 200 GPa

Extensive experimental studies on the structure and density of silicate glasses as laboratory analogs of natural silicate melts have attempted to address the nature of dense silicate melts that may be present at the base of the mantle. Previous ultrahigh-pressure experiments, however, have been performed on simple systems such as SiO2 or MgSiO3, and experiments in more complex system have been conducted under relatively low-pressure conditions below 60 GPa. The effect of other metal cations on structural changes that occur in dense silicate glasses under ultrahigh pressures has been poorly understood. Here, we used a Brillouin scattering spectroscopic method up to pressures of 196.9 GPa to conduct in situ high-pressure acoustic wave velocity measurements of SiO2-Al2O3 glasses in order to understand the effect of Al2O3 on pressure-induced structural changes in the glasses as analogs of aluminosilicate melts. From 10 to 40 GPa, the transverse acoustic wave velocity (V S ) of Al2O3-rich glass (SiO2 + 20.5 mol% Al2O3) was greater than that of Al2O3-poor glass (SiO2 + 3.9 mol% Al2O3). This result suggests that SiO2-Al2O3 glasses with higher proportions of Al ions with large oxygen coordination numbers (5 and 6) become elastically stiffer up to 40 GPa, depending on the Al2O3 content, but then soften above 40 GPa. At pressures from 40 to ~100 GPa, the increase in V S with increasing pressure became less steep than below 40 GPa. Above ~100 GPa, there were abrupt increases in the P-V S gradients (dV S /dP) at 130 GPa in Al2O3-poor glass and at 116 GPa in Al2O3-rich glass. These changes resemble previous experimental results on SiO2 glass and MgSiO3 glass. Given that changes of dV S /dP have commonly been related to changes in the Si-O coordination states in the glasses, our results, therefore, may indicate a drastic structural transformation in SiO2-Al2O3 glasses above 116 GPa, possibly associated with an average Si-O coordination number change to higher than 6. Compared to previous acoustic wave velocity data on SiO2 and MgSiO3 glasses, Al2O3 appears to promote a lowering of the pressure at which the abrupt increase of dV S /dP is observed. This suggests that the Al2O3 in silicate melts may help to stabilize those melts gravitationally in the lower mantle.

Chemical composition characterization of Ca3Ta(Ga0.5Al0.5)3Si2O14 single crystal by the line-focus-beam ultrasonic material characterization system

A new method for evaluation of homogeneity of Ca3Ta(Ga0.5Al0.5)3Si2O14 (CTGAS) single crystals was established based on leaky surface acoustic wave (LSAW) velocity measurements performed by the line-focus-beam ultrasonic material characterization (LFB-UMC) system. Three plate specimens cut perpendicular to X-, Y-, and Z-axes were prepared from the CTGAS crystal ingot and LSAW velocity distributions were examined for these specimens. LSAW velocity changes due to Al-substitution effect were successfully extracted by using a relationship between two LSAW velocities propagating along different directions for Ca3TaGa3Si2O14 (CTGS) and Al-substituted CTGS. Comparison of measured LSAW velocities and the results of chemical composition analysis performed by electron probe microanalysis (EPMA) demonstrated that LSAW velocity is mainly affected by Al-content change in CTGAS. Maximum velocity variation was observed in radial direction of the crystal ingot through the Z-axis propagating LSAW velocity measurements for Y-cut CTGAS specimen corresponding to Al-content change of 0.226mol%. Accuracy of evaluation of Al content by velocity measurement for Y-cut Z-propagating LSAW is estimated to be ±0.0047mol% and is superior to that by EPMA.

Reliability of Phase Velocity Measurements of Flexural Acoustic Waves in the Human Tibia In-Vivo.

PurposeAxial-transmission acoustics have shown to be a promising technique to measure individual bone properties and detect bone pathologies. With the ultimate goal being the in-vivo application of such systems, quantification of the key aspects governing the reliability is crucial to bring this method towards clinical use.Materials and MethodsThis work presents a systematic reliability study quantifying the sources of variability and their magnitudes of in-vivo measurements using axial-transmission acoustics. 42 healthy subjects were measured by an experienced operator twice per week, over a four-month period, resulting in over 150000 wave measurements. In a complementary study to assess the influence of different operators performing the measurements, 10 novice operators were trained, and each measured 5 subjects on a single occasion, using the same measurement protocol as in the first part of the study.ResultsThe estimated standard error for the measurement protocol used to collect the study data was ∼ 17 m/s (∼ 4% of the grand mean) and the index of dependability, as a measure of reliability, was Φ = 0.81. It was shown that the method is suitable for multi-operator use and that the reliability can be improved efficiently by additional measurements with device repositioning, while additional measurements without repositioning cannot improve the reliability substantially. Phase velocity values were found to be significantly higher in males than in females (p < 10−5) and an intra-class correlation coefficient of r = 0.70 was found between the legs of each subject.ConclusionsThe high reliability of this non-invasive approach and its intrinsic sensitivity to mechanical properties opens perspectives for the rapid and inexpensive clinical assessment of bone pathologies, as well as for monitoring programmes without any radiation exposure for the patient.

Sound velocities of δ‐AlOOH up to core‐mantle boundary pressures with implications for the seismic anomalies in the deep mantle

AbstractRecent studies show that δ‐AlOOH is stable up to the base of the mantle. This phase is, therefore, a possible carrier and host of water in the deep mantle. To uncover the physical properties of δ‐AlOOH under deep mantle pressure conditions, we have conducted high‐pressure acoustic wave velocity measurements of δ‐AlOOH by using Brillouin spectroscopy combined with high‐pressure Raman spectroscopic measurements in a diamond anvil cell up to pressures of 134 GPa. There is a precipitous increase by ~14% in the acoustic velocities of δ‐AlOOH from 6 to 15 GPa, which suggests that pressure‐induced O‐H bond symmetrization occurs in this pressure range. The best fit values for the high‐pressure form of δ‐AlOOH of K0 = 190 (2) (GPa), G0 = 160.0 (9) (GPa), (∂K/∂P)0 = K0′ = 3.7 (1), and (∂G/∂P)0 = G0′ = 1.32 (1) indicate that δ‐AlOOH has a 20–30% higher VS value compared to those of the major constituent minerals in the mantle transition zone, such as wadsleyite, ringwoodite, and majorite. On the other hand, the VS of δ‐AlOOH is ~7% lower than that of Mg‐bridgmanite under lowermost mantle pressure conditions because of the significantly lower value of the pressure derivative of the shear modulus. By comparing our results with seismic observations, we can infer that δ‐AlOOH could be one of the potential causes of a positive VS anomaly observed at ~600 km depth beneath the Korean peninsula and a negative VS jump near 2800 km depth near the northern margin of the large low‐shear‐velocity province beneath the Pacific.

Evaluation of near-surface stress distributions in dissimilar welded joint by scanning acoustic microscopy

This paper presents the results from a set of experiments designed to ultrasonically measure the near surface stresses distributed within a dissimilar metal welded plate. A scanning acoustic microscope (SAM), with a tone-burst ultrasonic wave frequency of 200MHz, was used for the measurement of near surface stresses in the dissimilar welded plate between 304 stainless steel and low carbon steel. For quantitative data acquisition such as leaky surface acoustic wave (leaky SAW) velocity measurement, a point focus acoustic lens of frequency 200MHz was used and the leaky SAW velocities within the specimen were precisely measured. The distributions of the surface acoustic wave velocities change according to the near-surface stresses within the joint. A three dimensional (3D) finite element simulation was carried out to predict numerically the stress distributions and compare with the experimental results. The experiment and FE simulation results for the dissimilar welded plate showed good agreement. This research demonstrates that a combination of FE simulation and ultrasonic stress measurements using SAW velocity distributions appear promising for determining welding residual stresses in dissimilar material joints.

Excavation-induced relaxation effects and hydraulic conductivity variations in the surrounding rocks of a large-scale underground powerhouse cavern system

Located in the middle reach of Yalong River in China, the Jinping-I Hydropower Station consists of a large-scale cavern system for water conveyance and power generation. Compared to other typical large-scale underground powerhouse cavern systems in Southwestern China, the construction site is characteristic of higher in situ geostresses, lower uniaxial compressive strength (UCS) and poorer quality of the surrounding rocks, resulting in greater depth of the disturbed zone. In this study, the excavation-induced relaxation effects and their impacts on the hydraulic conductivity variations and seepage behaviors in the surrounding rocks of the Jinping-I underground powerhouse caverns were assessed with site characterization data and numerical simulations. The excavation-induced disturbance zones around the caverns were modeled using the plastic yield zone predicted with an equivalent elasto-plastic model and a constant deviatoric stress criterion based on the Hoek–Brown parameters of the surrounding rocks, respectively. The predicted results agree rather well with the disturbed zones detected by the in situ acoustic wave velocity measurements and borehole TV images. The excavation-induced permeability changes in the surrounding rocks were characterized with a strain-dependent hydraulic conductivity model that accounts for the development patterns and deformation behaviors of the critically-oriented fractures. The seepage behaviors with consideration of the permeability changes in the surrounding rocks were modeled with a variational inequality method at a steady state, and the numerical results imply the significance of proper characterizations of the excavation-induced disturbance effects and permeability changes in better understanding the groundwater flow and its controlled effect in the surrounding rocks.

Gigahertz acoustic wave velocity measurement in GaN single crystals considering acousto-electric effect.

The resistivity-frequency characteristics of longitudinal wave velocities propagating parallel to the c-axis in a GaN single crystal were theoretically estimated by considering the piezoelectric acousto-electric effect. The temperature and frequency dependences of longitudinal and shear wave velocities in conductive and semiconductive GaN single-crystal samples were experimentally investigated by Brillouin scattering. The temperature dependence of longitudinal and shear wave velocities had a linear tendency in the conductive sample, whereas in the semiconductive sample, those had a similar tendency to the predicted velocity changes resulting from the piezoelectric stiffening effect. However, the temperature dependence of shear wave velocity, which does not possess piezoelectric coupling, had a tendency similar to that of the longitudinal wave in the semiconductive sample, unexpectedly. The frequency dependence of longitudinal wave velocities in the semiconductive sample had a tendency similar to the predicted velocity changes resulting from the piezoelectric stiffening effect.

Role of Acoustic Shear Wave Velocity Measurement in Characterization of Breast Lesions

To analyze the value of acoustic radiation force impulse imaging quantification in characterization of breast lesions and to analyze the stiffness of glandular and subcutaneous fatty tissue in benign and malignant lesions. A total of 175 breast lesions (67 malignant and 108 benign) in 173 women were studied. With acoustic radiation force impulse imaging, shear wave velocity (SWV), which can reflect the stiffness of tissue, was measured within the lesion (internal SWV [SWVi]), in the boundary zone (boundary SWV [SWVb]), in normal-appearing glandular tissue (glandular SWV [SWVg]), and in subcutaneous fatty tissue (fatty SWV [SWVf]). All lesions underwent core needle biopsy or surgical excision. Differences among the SWV types in malignant and benign lesions were evaluated. We also assessed how different lesion types affected the SWV types. Receiver operating characteristic analysis was performed to assess the sensitivity and specificity of the SWV types in differentiating malignant from benign lesions. Internal SWV was significantly higher than SWVb, SWVg, and SWVf; SWVb was significantly higher than SWVg and SWVf; and SWVg was significantly higher than SWVf in both malignant and benign groups (P < .05). All 4 SWV types were significantly higher in the malignant group than the benign group (P < .05). In the malignant group, grade 3 invasive ductal carcinoma had the highest SWVi. The sensitivity and specificity for differentiating malignant lesions were 55.2% and 95.8% for SWVi, 85.1% and 53.3% for SWVb, 68.2% and 69.6% for SWVg, and 67.2% and 66.0% for SWVf. Acoustic radiation force impulse imaging has potential to characterize breast lesions, both internally and within the boundary zone, and to reflect changes in stiffness within surrounding glandular and subcutaneous fatty tissues caused by malignant tumors.

Focused ion beam preparation and characterization of single-crystal samples for high-pressure experiments in the diamond-anvil cell

We show that the focused ion beam (FIB) technique is well suited to prepare single-crystal samples with defined dimensions and shape and excellent surface qualities for use in high-pressure experiments carried out in the diamond-anvil cell. The method allows for cutting and polishing delicate samples, including tiny, brittle, or metastable phases and thereby extends the range of materials that can be routinely probed at extreme pressures and temperatures. In addition, the technique is capable of producing electron-transparent foils from the same sample material that can be characterized on the nanometer scale by transmission electron microscopy (TEM). The application of the method to the preparation of various geomaterials is discussed with a focus on the preparation of double-side polished, transparent sample platelets for the use in Brillouin scattering experiments at extreme conditions. Using one of our FIB-prepared samples, we were able to perform direct experimental measurements of acoustic wave velocities of antigorite along crystallographic directions, which were previously inaccessible to direct Brillouin scattering measurements. At 0.6 GPa, we measure a 39% anisotropy of compressional wave velocities.

Laboratory measurements of acoustic emissions and wave velocities associated with the formation of fractures in sandstones

AbstractAcoustic emission (AE), ultrasonic velocity and petrophysical property measurements are increasingly being used as tools to investigate mechanical, thermal and hydraulic changes in rock masses around underground excavations and in the exploration of oil and gas. In order to develop these measurements into an effective tool it is necessary to understand how they relate to changes in the fracture and fluid content under controlled laboratory conditions. A polyaxial (true triaxial) test system has been developed to perform high-resolution measurements of AE, ultrasonic velocities and fluid permeability characteristics in a cubic specimen under true-triaxial stress. The polyaxial system also allows the measurement of AEs using an array of small-diameter, high-frequency transducers. The measurements allow the AE source locations and mechanisms to be calculated, thus providing an analysis of the distribution, orientation and type of fracture growth in the specimens. Example results are given from an experiment, showing that AE mechanisms during crack initiation describe a dominant failure mode with a significant tensile component.

Local and noncontact measurements of bulk acoustic wave velocities in thin isotropic plates and shells using zero group velocity Lamb modes

An original method for material characterization with acoustic waves is presented. The measurement of the longitudinal and shear wave velocities in thin isotropic plates or shells is performed locally on the same face without any mechanical contact. We exploit the resonance that occurs at the minimum frequency thickness product of the first order symmetric (S1) and of the second order antisymmetric (A2) Lamb modes. At these frequencies the group velocity vanishes, whereas the phase velocity remains finite. Then, the energy, which cannot propagate in the structure, is localized in a zone of diameter half the wavelength. The vibrations are excited in the thermoelastic regime by a laser pulse and detected at the same point by an optical interferometer. For these two Lamb modes we have computed the variations of the frequency thickness product versus Poisson’s ratio. The resonance frequency ratio, which is independent of the plate or shell thickness, provides an absolute and local measurement of Poisson’s ratio. Provided that the plate thickness is known, each resonance frequency allows us to determine in a single shot the bulk acoustic wave velocities VL and VT. Since it is based on frequency measurements, the method, tested on a large number of materials, is very accurate.

A pulse ultrasonic gauge for measuring velocities of surface acoustic waves

A pulse broadband gauge designed for measurements of the velocities of surface acoustic waves is described. The gauge’s output signal is formed during mechanical translation of focused ultrasonic transducers relative to a specimen under study placed in an immersion liquid. A design of the device with line-focused lensless ultrasonic transducers for the frequency range 2–25 MHz is considered. The results of measurements of test samples are presented, and the algorithms for processing the output spatial-temporal signals for determining the frequency dependences of phase velocities of acoustic waves are described. Using a carbon steel sample as an example, it is shown that the random error component in acoustic-wave velocity measurements can be estimated as ±(2–8) and ±(1–3) m/s for longitudinal and lateral scanning modes, respectively.