Experimental verification of nondiffracting X waves

The propagation of acoustic waves in isotropic/homogeneous media and electromagnetic waves in free space is governed by the isotropic/homogeneous (or free space) scalar wave equation. A zeroth-order acoustic X wave (axially symmetric) was experimentally produced with an acoustic annular array transducer. The generalized expression includes a term for the frequency response of the system and parameters for varying depth of field versus beam width of the resulting family of beams. Excellent agreement between theoretical predictions and experiment was obtained. An X wave of finite aperture driven with realizable (causal, finite energy) pulses is found to travel with a large depth of field (nondiffracting length).     

Producing bowtie limited diffraction beams with synthetic arrayexperiment

Limited diffraction beams have a large depth of field and could have applications in medical ultrasound and other wave related areas such as electromagnetics and optics. However, these beams have higher sidelobes than conventional focused beams at their focuses. Recently, a new type of beam, called bowtie limited diffraction beams, was developed. These beams can achieve both low sidelobes and a large depth of field in medical imaging. In this paper, the production of bowtie beams in water with a synthetic array experiment is reported. A broad-band PZT ceramic/polymer composite transducer of about 1 mm diameter and 2.5 MHz central frequency was scanned in a raster format and placed at the centers of elements of an equivalent two-dimensional array of 50 mm diameter aperture. A polyvinylidene fluoride (PVDF) needle hydrophone of 0.5 mm diameter was used to receive the waves produced by the transducer. Proper weighting functions were applied to the received signals to produce various beams. Results show that the bowtie beams produced with the synthetic array experiment are in good agreement with those derived from theory and obtained by computer simulations. The depth of field of these beams is about 216 mm and sidelobes of a tenth derivative bowtie X wave in pulse-echo imaging are about 30 dB lower than those of rotary symmetric limited diffraction beams such as the zeroth-order X wave discovered previously     

Ultrasonic nondiffracting transducer for medical imaging

The nondiffracting J(0) Bessel beam is evaluated, and its application to medical imaging is suggested. Computer simulations and experimental results for a ten-ring annular Bessel shaded transducer are described. Both continuous-wave (CW) and pulse-wave (PW) excitations are shown and compared to conventional Gaussian beams. The nondiffracting beam has about 1.27-nm radius main lobe with a 20-cm depth of field compared to the Gaussian transducer of the same size with a 1.27-mm radius main lobe at a focus of 12 cm and 2x4-cm depth of field. The side lobes of the nondiffracting beam are the same as the J(0) Bessel function. The effects of heterogeneity due to tissue on the nondiffracting beam and on the focused Gaussian beam are also reported.     

Operational verification of a 40-MHz annular array transducer

An experimental system to take advantage of the imaging capabilities of a 5-ring polyvinylidene fluoride (PVDF)-based annular array is presented. The array has a 6-mm total aperture and a 12-mm geometric focus. The experimental system is designed to pulse a single element of the array and then digitize the received data of all array channels simultaneously. All transmit/receive pairs are digitized and then the data are post-processed with a synthetic-focusing technique to achieve an enhanced depth of field (DOF). The performance of the array is experimentally tested with a wire phantom consisting of 25-microm diameter wires diagonally spaced at 1-mm by 1-mm intervals. The phantom permitted the efficacy of the synthetic-focusing algorithm to be tested and was also used for two-way beam characterization. Experimental results are compared to a spatial impulse response method beam simulation. After synthetic focusing, the two-way echo amplitude was enhanced over the range of 8 to 19 mm and the 6-dB DOF spanned from 9 to 15 mm. For a wire at a fixed axial depth, the relative time delays between transmit/receive ring pairs agreed with theoretical predictions to within +/- 2 ns. To further test the system, B-mode images of an excised bovine eye were rendered.     

High frame rate imaging system for limited diffraction array beam imaging with square-wave aperture weightings.

A general-purpose high frame rate (HFR) medical imaging system has been developed. This system has 128 independent linear transmitters, each of which is capable of producing an arbitrary broadband (about 0.05-10 MHz) waveform of up to +/- 144 V peak voltage on a 75-ohm resistive load using a 12-bit/40-MHz digital-to-analog converter. The system also has 128 independent, broadband (about 0.25-10 MHz), and time-variable-gain receiver channels, each of which has a 12-bit/40-MHz analog-to-digital converter and up to 512 MB of memory. The system is controlled by a personal computer (PC), and radio frequency echo data of each channel are transferred to the same PC via a standard USB 2.0 port for image reconstructions. Using the HFR imaging system, we have developed a new limited-diffraction array beam imaging method with square-wave aperture voltage weightings. With this method, in principle, only one or two transmitters are required to excite a fully populated two-dimensional (2-D) array transducer to achieve an equivalent dynamic focusing in both transmission and reception to reconstruct a high-quality three-dimensional image without the need of the time delays of traditional beam focusing and steering, potentially simplifying the transmitter subsystem of an imager. To validate the method, for simplicity, 2-D imaging experiments were performed using the system. In the in vitro experiment, a custom-made, 128-element, 0.32-mm pitch, 3.5-MHz center frequency linear array transducer with about 50% fractional bandwidth was used to reconstruct images of an ATS 539 tissue-mimicking phantom at an axial distance of 130 mm with a field of view of more than 90 degrees. In the in vivo experiment of a human heart, images with a field of view of more than 90 degrees at 120-mm axial distance were obtained with a 128-element, 2.5-MHz center frequency, 0.15-mm pitch Acuson V2 phased array. To ensure that the system was operated under the limits set by the U.S. Food and Drug Administration, the mechanical index, thermal index, and acoustic output were measured. Results show that higher-quality images can be reconstructed with the square-wave aperture weighting method due to an increased penetration depth as compared to the exact weighting method developed previously, and a frame rate of 486 per second was achieved at a pulse repetition frequency of about 5348 Hz for the human heart.     

Orthogonal quadratic chirp signals for simultaneous multi-zone focusing in medical ultrasound imaging

In medical ultrasound imaging, multi-zone focusing on transmission is used to enhance the lateral resolution at the expense of frame rate. As an alternative, this paper proposes a simultaneous multi-zone focusing method using orthogonal quadratic chirp signals to improve lateral resolution without sacrificing frame rate. In the proposed method, two weighted quadratic chirp signals with different spectra are simultaneously transmitted with different transmit time delays for multi-zone focusing. Because the two weighted quadratic chirps can be designed to have a desired level of cross-correlation after compression, the degradation of axial resolution resulting from the division of a spectrum is minimized. Through simulation, the performances of the proposed method were evaluated and compared with those of two-cycle pulsed excitation as a gold standard and two sub-band weighted linear chirps. In the simulation, the proposed method improved -6-dB and -20-dB lateral beam widths by factors of 1.67 and 1.84, respectively, compared with the pulsed excitation. The degradation of axial resolution in the proposed method was maximally 43% less than that in the linear chirp case. The results demonstrate that the proposed method is useful in the improvement of overall ultrasound image quality because the axial resolution of conventional ultrasound images is generally a few times higher than the lateral resolution.     

Generation of sinc wave by a one-dimensional array for applicationsin ultrasonic imaging

A new solution to the 2-D scalar wave equation is presented which describes an ultrasonic beam maintaining the lateral field response expressed by the sinc function over a finite depth of field. This new beam is realizable with a linear array transducer, and less subject to diffraction spreading than conventional focused beams, physically, it is a superposition of plane waves having the same wavelength, but traveling at different angles. It is shown by numerical simulation that the beam can provide more uniform lateral beamwidth and smoother on-axis field magnitude over a greater depth of field than the rectangular transducers and Gaussian apodized transmitters which have been used to increase the limited depth of field of conventional focused beams. Compared with currently developed limited diffraction beams which must be generated by 2-D array transducers, the beam has a wider lateral beamwidth but with lower sidelobe levels. In ultrasonic medical imaging, the beam enables one to obtain a line focus using a 1-D array transducer and to eliminate the diffraction correction required in some applications such as tissue characterization     

Quasi-diffraction-free beams.

A diffraction-free beam is obtained by the superposing of plane waves whose wave vectors make an angle with the propagation axis. These plane waves are realized with point sources that are distributed uniformly around a circle and an infinitely large aperture lens. After the field passes through the lens it has nondiffracting properties and is described by the zero-order Bessel function. Relaxing these conditions makes the beam diffraction free within only a limited region. The beam generated from such a geometry is referred to as a quasi-diffraction-free beam. The effects of the width of the annular source on the beam spread are discussed and compared with those for a Gaussian beam. Approximate expressions for quasi-diffraction-free beams are also obtained.     

Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source

We consider the nonspherically decaying radiation field that is generated by a polarization current with a superluminally rotating distribution pattern in vacuum, a field that decays with the distance R(P) from its source as R(P)(-1/2), instead of R(P)(-1). It is shown (i) that the nonspherical decay of this emission remains in force at all distances from its source independently of the frequency of the radiation, (ii) that the part of the source that makes the main contribution toward the value of the nonspherically decaying field has a filamentary structure whose radial and azimuthal widths become narrower (as R(P)(-2) and R(P)(-3), respectively) the farther the observer is from the source, (iii) that the loci on which the waves emanating from this filament interfere constructively delineate a radiation subbeam that is nondiffracting in the polar direction, (iv) that the cross-sectional area of each nondiffracting subbeam increases as R(P), instead of R(P)(2), so that the requirements of conservation of energy are met by the nonspherically decaying radiation automatically, and (v) that the overall radiation beam within which the field decays nonspherically consists, in general, of the incoherent superposition of such coherent nondiffracting subbeams. These findings are related to the recent construction and use of superluminal sources in the laboratory and numerical models of the emission from them. We also briefly discuss the relevance of these results to the giant pulses received from pulsars.     

Chirp-coded excitation imaging with a high-frequency ultrasound annular array

High-frequency ultrasound (HFU, > 15 MHz) is an effective means of obtaining fine-resolution images of biological tissues for applications such as opthalmologic, dermatologic, and small animal imaging. HFU has two inherent drawbacks. First, HFU images have a limited depth of field (DOF) because of the short wavelength and the low fixed F-number of conventional HFU transducers. Second, HFU can be used to image only a few millimeters deep into a tissue because attenuation increases with frequency. In this study, a five-element annular array was used in conjunction with a synthetic-focusing algorithm to extend the DOF. The annular array had an aperture of 10 mm, a focal length of 31 mm, and a center frequency of 17 MHz. To increase penetration depth, 8-micros, chirp-coded signals were designed, input into an arbitrary waveform generator, and used to excite each array element. After data acquisition, the received signals were linearly filtered to restore axial resolution and increase the SNR. To compare the chirpcoded imaging method with conventional impulse imaging in terms of resolution, a 25-microm diameter wire was scanned and the -6-dB axial and lateral resolutions were computed at depths ranging from 20.5 to 40.5 mm. The results demonstrated that chirp-coded excitation did not degrade axial or lateral resolution. A tissue-mimicking phantom containing 10-microm glass beads was scanned, and backscattered signals were analyzed to evaluate SNR and penetration depth. Finally, ex vivo ophthalmic images were formed and chirpcoded images showed features that were not visible in conventional impulse images.     

An X wave transform

Limited diffraction beams such as X waves can propagate to an infinite distance without spreading if they are produced with an infinite aperture and energy. In practice, when the aperture and energy are finite, these beams have a large depth of field with only limited diffraction. Because of this property, limited diffraction beams could have applications in medical imaging, tissue characterization, blood flow velocity vector imaging, nondestructive evaluation of materials, communications, and other areas such as optics and electromagnetics. In this paper, a new transform, called X wave transform, is developed. In the transform, any well behaved solutions to the isotropic-homogeneous wave equation or limited diffraction beams can he expanded using X waves as basis functions. The coefficients of the expansions can be calculated with the properties that X waves are orthogonal. Examples are given to demonstrate the efficacy of the X wave transform. The X wave transform reveals an intrinsic relationship between any well behaved solutions to the wave equation and X waves, including limited diffraction beams. This provides a theoretical foundation to develop new limited diffraction beams or solutions to the wave equation that may have practical usefulness.     

New X-wave solutions of free-space scalar wave equation and their finite size realization

Based on the method proposed by Donnelly and Ziolkowski [1], [2], a new general solution has been obtained for the isotropic/homogeneous scalar wave equation in cylindrical coordinates. It is shown that well-known limited diffraction beams such as Durnin's Bessel beams [4], Lu and Greenleaf's X-wave [15], localized waves of Donnelly and Ziolkowski [1], [2], and limited-diffraction, band-limited waves of Li and Bharath [19], [20] can be obtained from this generic solution as particular cases. In addition, we have obtained new X-wave solutions and have calculated the field characteristics for one of them using a finite aperture realization. It is shown that with a proper choice of the free parameter values, well-behaved X-waves with narrow beamwidths and large depths of field can be achieved. For similar source spectra, the results are compared with Lu and Greenleaf's zeroth-order X-wave, and it is shown that the depth of field and beamwidth are very comparable.     

Design aspects of focal beams from high-intensity arrays

As the applications of ultrasonic thermal therapies expand, the design of the high-intensity array must address both the energy delivery of the main beam and the character and relevance of off-target beam energy. We simulate the acoustic field performance of a selected set of circular arrays organized by array format, including flat versus curved arrays, periodic versus random arrays, and center void diameter variations. Performance metrics are based on the -3-dB focal main lobe (FML) positioning range, axial grating lobe (AGL) temperatures, and side lobe levels. Using finite-element analysis, we evaluate the relative heating of the FML and the AGLs. All arrays have a maximum diameter of 100λ, with element count ranging from 64 to 1024 and continuous wave frequency of 1.5 MHz. First, we show that a 50% spherical annulus produces focus beam side lobes which decay as a function of lateral distance at nearly 87% of the exponential rate of a full aperture. Second, for the arrays studied, the efficiency of power delivery over the -3-dB focus positioning range for spherical arrays is at least 2-fold greater than for flat arrays; the 256-element case shows a 5-fold advantage for the spherical array. Third, AGL heating can be significant as the focal target is moved to its distal half-intensity depth from the natural focus. Increasing the element count of a randomized array to 256 elements decreases the AGL-to-FML heating ratio to 0.12 at the distal half-intensity depth. Further increases in element count yield modest improvements. A 49% improvement in the AGL-to-peak heating ratio is predicted by using the Sumanaweera spiral element pattern with randomization.     

A high-frequency linear ultrasonic array utilizing an interdigitally bonded 2-2 piezo-composite

This paper describes the development of a high-frequency 256-element linear ultrasonic array utilizing an interdigitally bonded (IB) piezo-composite. Several IB composites were fabricated with different commercial and experimental piezoelectric ceramics and evaluated to determine a suitable formulation for use in high-frequency linear arrays. It was found that the fabricated fine-scale 2-2 IB composites outperformed 1-3 IB composites with identical pillar- and kerf-widths. This result was not expected and lead to the conclusion that dicing damage was likely the cause of the discrepancy. Ultimately, a 2-2 composite fabricated using a fine-grain piezoelectric ceramic was chosen for the array. The composite was manufactured using one IB operation in the azimuth direction to produce approximately 19-μm-wide pillars separated by 6-μm-wide kerfs. The array had a 50 μm (one wavelength in water) azimuth pitch, two matching layers, and 2 mm elevation length focused to 7.3 mm using a polymethylpentene (TPX) lens. The measured pulse-echo center frequency for a representative array element was 28 MHz and -6-dB bandwidth was 61%. The measured single-element transmit -6-dB directivity was estimated to be 50°. The measured insertion loss was 19 dB after compensating for the effects of attenuation and diffraction in the water bath. A fine-wire phantom was used to assess the lateral and axial resolution of the array when paired with a prototype system utilizing a 64-channel analog beamformer. The -6-dB lateral and axial resolutions were estimated to be 125 and 68 μm, respectively. An anechoic cyst phantom was also imaged to determine the minimum detectable spherical inclusion, and thus the 3-D resolution of the array and beamformer. The minimum anechoic cyst detected was approximately 300 μm in diameter.     

Bowtie limited diffraction beams for low-sidelobe and large depthof field imaging

Limited diffraction beams such as Bessel beams and X waves have a large depth of field and thus could have many applications. However, these beams have higher sidelobes as compared to conventional focused beams in their focal planes. In this paper, a new class of limited diffraction beams is developed. These beams are termed bowtie limited diffraction beams because they have bowtie shapes in a plane perpendicular to the beam axis. To obtain pulse-echo images of low sidelobes and a large depth of field, a bowtie limited diffraction beam is used in transmission and its 90° rotated response (around the beam axis) is used in reception. Unlike the summation-subtraction method developed previously, this method does not reduce image frame rate or dynamic range of signals and is not motion sensitive. The theory of the bowtie limited diffraction beams is developed. Computer simulation of the theoretical beams under practical conditions, such as finite aperture, finite bandwidth, and causal excitation, is performed with the Rayleigh-Sommerfeld diffraction formula. The simulated beams are very close to those predicted analytically over a large depth of field     

Characterization of the Critically Refracted Longitudinal (LCR) Waves and Their Use in Defect Detection

The critically refracted longitudinal (L_CR) waves are used in various domains of nondestructive evaluation, especially for residual stress measurements. However, few works have characterized the associated ultrasonic beam. In this article, the characterization of the L_CR ultrasonic beam, both numerically and experimentally, is first clarified in order to provide some answers to questions that arise about its behavior in elastic solids. The aim of the second part of this work is to investigate the use of the L_CR waves for the detection of surface defects of different sizes in aluminum. For that, the effect of defects at fixed depth (5 mm) with various diameters (2, 4, 6, and 8 mm) and fixed diameter (8 mm) with various depths (5, 7, and 10 mm) in an aluminum sample have been investigated at frequencies around 1 MHz. It has been experimentally found that the amplitude of the (L_CR) wave decreases and its frequency spectrum changes with a given defect. The rate of the decrease of the amplitude and the change in the spectrum is related to the increase of the defect depth. The study shows that the effect on the propagating of the L_CR waves is larger as the defect depth increases.     

Development of a real-time, high-frequency ultrasound digital beamformer for high-frequency linear array transducers

A real-time digital beamformer for high-frequency (>20 MHz) linear ultrasonic arrays has been developed. The system can handle up to 64-element linear array transducers and excite 16 channels and receive simultaneously at 100 MHz sampling frequency with 8-bit precision. Radio frequency (RF) signals are digitized, delayed, and summed through a real-time digital beamformer, which is implemented using a field programmable gate array (FPGA). Using fractional delay filters, fine delays as small as 2 ns can be implemented. A frame rate of 30 frames per second is achieved. Wire phantom (20 microm tungsten) images were obtained and -6 dB axial and lateral widths were measured. The results showed that, using a 30 MHz, 48-element array with a pitch of 100 microm produced a -6 dB width of 68 microm in the axial and 370 microm in the lateral direction at 6.4 mm range. Images from an excised rabbit eye sample also were acquired, and fine anatomical structures, such as the cornea and lens, were resolved.     

Shallow Buried Defect Testing Method Based on Ultrasonic TOFD

Ultrasonic time of flight diffraction (TOFD) suffers from the shortcoming of lack of near surface resolution, primarily owning to the superposition of the lateral wave and the shallow buried defect (SBD) wave, and the insensitive region beneath the inspection surface because of the restricted beam width of the probes. This paper presents a method for the detection of SBD based on conventional TOFD. The method is named as TOFDW because it employs a three-fold reflected longitudinal wave whose propagation path in the testing piece looks like the letter “W”. Based on Pythagoras’s theory, mathematical models are developed to locate SBD. In TOFDW mode, the time difference between the lateral wave and the SBD wave can be enlarged greatly so that they would never be superposed. In addition, through reflecting the incident longitudinal wave by bottom surface, the near surface region of the testing piece is covered with an intense acoustic field, making TOFDW free of the restriction of the probes’ beam width. These contribute to the improvement of the near surface resolution. The experiments show that with the proposed TOFDW and mathematical models, the artificial defect tip with the buried depth of 1 mm can be detected, and the tips can be measured within an error of 0.3 mm; the weld defect with the buried depth of 2 mm can be identified effectively, and the location can be measured within an error of 0.5 mm.     

Intensity and phase measurements of nondiffracting beams generated with a magneto-optic spatial light modulator

Nondiffracting beams are of interest for optical metrology applications because the size of the beam does not change as the beam propagates. However, accuracy can be increased if the diameter of the beam is smaller. One technique for accomplishing this is to use the dark axial intensity profile associated with a higher-order nondiffracting Bessel function beam. We generate these higher-order Bessel function beams with a programmable spatial light modulator. We study the intensity patterns and the phase dependence of these nondiffracting beams. In addition, we examine interference effects caused by recording these patterns onto a binary spatial light modulator.     

Capacitive micromachined ultrasonic transducers: next-generation arrays for acoustic imaging?

Piezoelectric materials have dominated the ultrasonic transducer technology. Recently, capacitive micromachined ultrasonic transducers (CMUTs) have emerged as an alternative technology offering advantages such as wide bandwidth, ease of fabricating large arrays, and potential for integration with electronics. The aim of this paper is to demonstrate the viability of CMUTs for ultrasound imaging. We present the first pulse-echo phased array B-scan sector images using a 128-element, one-dimensional (1-D) linear CMUT array. We fabricated 64- and 128-element 1-D CMUT arrays with 100% yield and uniform element response across the arrays. These arrays have been operated in immersion with no failure or degradation in performance over the time. For imaging experiments, we built a resolution test phantom roughly mimicking the attenuation properties of soft tissue. We used a PC-based experimental system, including custom-designed electronic circuits to acquire the complete set of 128 x 128 RF A-scans from all transmit-receive element combinations. We obtained the pulse-echo frequency response by analyzing the echo signals from wire targets. These echo signals presented an 80% fractional bandwidth around 3 MHz, including the effect of attenuation in the propagating medium. We reconstructed the B-scan images with a sector angle of 90 degrees and an image depth of 210 mm through offline processing by using RF beamforming and synthetic phased array approaches. The measured 6-dB lateral and axial resolutions at 135 mm depth were 0.0144 radians and 0.3 mm, respectively. The electronic noise floor of the image was more than 50 dB below the maximum mainlobe magnitude. We also performed preliminary investigations on the effects of crosstalk among array elements on the image quality. In the near field, some artifacts were observable extending out from the array to a depth of 2 cm. A tail also was observed in the point spread function (PSF) in the axial direction, indicating the existence of crosstalk. The relative amplitude of this tail with respect to the mainlobe was less than -20 dB.