Use of modulated excitation signals in medical ultrasound. Part I: Basic concepts and expected benefits

This paper, the first from a series of three papers on the application of coded excitation signals in medical ultrasound, discusses the basic principles and ultrasound-related problems of pulse compression. The concepts of signal modulation and matched filtering are given, and a simple model of attenuation relates the matched filter response with the ambiguity function, known from radar. Based on this analysis and the properties of the ambiguity function, the selection of coded waveforms suitable for ultrasound imaging is discussed. It is shown that linear frequency modulation (FM) signals have the best and most robust features for ultrasound imaging. Other coded signals such as nonlinear FM and binary complementary Golay codes also have been considered and characterized in terms of signal-to-noise ratio (SNR) and sensitivity to frequency shifts. Using the simulation program Field II, it is found that in the case of linear FM signals, a SNR improvement of 12 to 18 dB can be expected for large imaging depths in attenuating media, without any depth-dependent filter compensation. In contrast, nonlinear FM modulation and binary codes are shown to give a SNR improvement of only 4 to 9 dB when processed with a matched filter. Other issues, such as depth-dependent matched filtering and use of filters other than the matched filter (inverse and Wiener filters) also are addressed.     

Use of modulated excitation signals in medical ultrasound. Part III: High frame rate imaging

This paper, the last from a series of three papers on the application of coded excitation signals in medical ultrasound, investigates the possibility of increasing the frame rate in ultrasound imaging by using modulated excitation signals. Linear array-coded imaging and sparse synthetic transmit aperture imaging are considered, and the trade-offs between frame rate, image quality, and SNR are discussed. It is shown that FM codes can be used to increase the frame rate by a factor of two without a degradation in image quality and by a factor of 5, if a slight decrease in image quality can be accepted. The use of synthetic transmit aperture imaging is also considered, and it is here shown that Hadamard spatial encoding in transmit with FM emission signals can be used to increase the frame rate by 12 to 25 times with either a slight or no reduction in signal-to-noise ratio and image quality. By using these techniques a complete ultrasound-phased array image can be created using only two emissions.     

Frequency division transmission imaging and synthetic aperture reconstruction

In synthetic transmit aperture imaging only a few transducer elements are used in every transmission, which limits the signal-to-noise ratio (SNR). The penetration depth can be increased by using all transmitters in every transmission. In this paper, a method for exciting all transmitters in every transmission and separating them at the receiver is proposed. The coding is done by designing narrow-band linearly frequency modulated signals, which are approximately disjointed in the frequency domain and assigning one waveform to each transmitter. By designing a filterbank consisting of the matched filters corresponding to the excitation waveforms, the different transmitters can be decoded at the receiver. The matched filter of a specific waveform will allow information only from this waveform to pass through, thereby separating it from the other waveforms. This means that all transmitters can be used in every transmission, and the information from the different transmitters can be separated instantaneously. Compared to traditional synthetic transmit aperture (STA) imaging, in which the different transmitters are excited sequentially, more energy is transmitted in every transmission, and a better signal-to-noise-ratio is attained. The method has been tested in simulation, in which the resolution and contrast was compared to a standard synthetic transmit aperture system with a single sinusoid excitation. The resolution and contrast was comparable for the two systems. The method also has been tested using the experimental ultrasound scanner RASMUS. The resolution was evaluated using a string phantom. The method was compared to a conventional STA using both sinusoidal excitation and linear frequency modulated (FM) signals as excitation. The system using the FM signals and the frequency division approach yielded the same performance concerning both axial (of approximately equal to 3 wavelengths) and lateral resolution (of approximately equal to 4.5 wavelengths). A SNR measurement showed an increase in SNR of 6.5 dB compared to the system using the conventional STA method and FM signal excitation.     

Harmonic chirp imaging method for ultrasound contrast agent

Coded excitation is currently used in medical ultrasound to increase signal-to-noise ratio (SNR) and penetration depth. We propose a chirp excitation method for contrast agents using the second harmonic component of the response. This method is based on a compression filter that selectively compresses and extracts the second harmonic component from the received echo signal. Simulations have shown a clear increase in response for chirp excitation over pulse excitation with the same peak amplitude. This was confirmed by two-dimensional (2-D) optical observations of bubble response with a fast framing camera. To evaluate the harmonic compression method, we applied it to simulated bubble echoes, to measured propagation harmonics, and to B-mode scans of a flow phantom and compared it to regular pulse excitation imaging. An increase of approximately 10 dB in SNR was found for chirp excitation. The compression method was found to perform well in terms of resolution. Axial resolution was in all cases within 10% of the axial resolution from pulse excitation. Range side-lobe levels were 30 dB below the main lobe for the simulated bubble echoes and measured propagation harmonics. However, side-lobes were visible in the B-mode contrast images.     

Binary code design for high-frequency ultrasound

This paper proposes an approach to designing binary codes suitable for high-frequency applications of coded excitation in medical ultrasound. For a high-frequency ultrasound system, transmitting well-designed binary codes with a low sampling ratio (i.e., the bit rate divided by the transducer center frequency) is a practical way to improve the signal-to-noise ratio (SNR) because the challenge of implementing arbitrary-waveform generators for transmitting nonbinary codes increases with the frequency and the switching speed of square-wave pulsers are limited. One conventional approach designs codes using a base sequence that modulates wideband sequences up to the transducer passband. Because a major portion of codes is excluded as a candidate, codes designed using this approach typically need long compression filters for restoring the axial resolution, and they do not improve the SNR efficiently. In contrast, the approach proposed here searches all the codes that match the transducer passband; hence, the resultant codes exhibit better performance. The technique was tested using a bit rate of 50 MHz and a sampling ratio of 2. For a transducer with an ideal Gaussian frequency response with a center frequency of 25 MHz and a -6 dB bandwidth of 15 MHz, the SNR for the same side-lobe extent was 1 to 6 dB higher for the codes designed using the proposed approach compared with those designed using the conventional approach. When a real transducer response with a center frequency of 26.4 MHz and a one-way -6 dB bandwidth of 20.7 MHz was considered, the codes designed using the proposed approach were superior by 0.5 to 5 dB. Therefore, our approach is better than the conventional approach for designing binary codes for high-frequency ultrasound, with the results indicating that the moderate bit rate of 50 MHz will suffice when the ultrasonic center frequency is 25 MHz.     

Arbitrary waveform coded excitation using bipolar square wave pulsers in medical ultrasound

This paper presents a new coded excitation scheme that efficiently synthesizes codes for arbitrary waveforms using a bipolar square wave pulser. In a coded excitation system, pulse compression is performed to restore the axial resolution. In order to maintain low range sidelobes, the system needs to transmit signals that have smooth spectra. However, such a transmitter requires the generation of arbitrary waveforms and, therefore, is more expensive. In other words, a trade-off is necessary between the compression performance and the transmitter cost. Here we propose a method that preserves the low-cost advantage of a bipolar pulser while achieving approximately the same compression performance as an arbitrary waveform generator. The key idea of the proposed method is the conversion of a nonbinary code (i.e., requiring an arbitrary waveform generator) with good compression performance into a binary code (i.e., requiring only a bipolar pulser) by code translation and code tuning. The code translation is implemented by sending the nonbinary code into a virtual one-bit, sigma-delta modulator, and the code tuning involves minimizing the root-mean-square error between the resultant binary code and the original nonbinary code by sequential and iterative tuning while taking the transducer response into account. Tukey-windowed chirps are known to have good compression performance. Such chirps of different durations (16, 20, and 24 micros), all with a taper ratio of 0.15, a center frequency of 2.5 MHz, and an equivalent bandwidth of 1.5 MHz, were converted into binary Tukey-windowed chirps that were compared with pseudochirps (i.e., direct binary approximations of the original chirp) over the same spectral band. The bit rate was 40 MHz. Simulation results show that the use of binary Tukey-windowed chirps can reduce the code duration by 20.6% or the peak sidelobe level by 6 dB compared to the commonly used pseudochirps. Experimental results obtained under the same settings were in agreement with the simulations. Our results demonstrate that arbitrary waveform coded excitation can be realized using bipolar square wave pulsers for applications in medical ultrasound.     

Minimum Variance Beamforming Combined with Adaptive Coherence Weighting Applied to Medical Ultrasound Imaging

Currently, the nonadaptive delay-and-sum (DAS) beamformer is used in medical ultrasound imaging. However, due to its data-independent nature, DAS leads to images with limited resolution and contrast. In this paper, an adaptive minimum variance (MV)-based beamformer that combines the MV and coherence factor (CF) weighting is introduced and adapted to medical ultrasound imaging. MV-adaptive beamformers can improve the image quality in terms of resolution and sidelobes by suppressing off-axis signals, while keeping onaxis ones. In addition, CF weighting can improve contrast and sidelobes by emphasizing the in-phase signals and reducing the out-of-phase ones. Combining MV and CF weighting results in simultaneous improvement of imaging resolution and contrast, outperforming both DAS and MV beamformers. In addition, because of the power of CF in reducing the focusing errors, the proposed method presents satisfactory robustness against sound velocity inhomogeneities, outperforming the regularized MV beamformer. The excellent performance of the proposed beamforming approach is demonstrated by several simulated examples.     

Coded excitation for diagnostic ultrasound: a system developer's perspective

Resolution and penetration are primary criteria for clinical image quality. Conventionally, high bandwidth for resolution was achieved with a short pulse, which results in a tradeoff between resolution and penetration. Coded excitation extends the bounds of this tradeoff by increasing signal-to-noise ratio (SNR) through appropriate coding on transmit and decoding on receive. Although used for about 50 years in radar, coded excitation was successfully introduced into commercial ultrasound scanners only within the last 5 years. This delay is at least partly due to practical implementation issues particular to diagnostic ultrasound, which are the focus of this paper. After reviewing the basics of biphase and chirp coding, we present simulation results to quantify tradeoffs between penetration and resolution under frequency-dependent attenuation, dynamic focusing, and nonlinear propagation. Next we compare chirp and Golay code performance with respect to image quality and system requirements, then we show clinical images that illustrate the current applications of coded excitation in B-mode, harmonic, and flow imaging.     

Bandwidth and resolution enhancement through pulse compression

A novel pulse compression technique is developed that improves the axial resolution of an ultrasonic imaging system and provides a boost in the echo signal-to-noise ratio (eSNR). The new technique, called the resolution enhancement compression (REC) technique, was validated with simulations and experimental measurements. Image quality was examined in terms of three metrics: the eSNR, the bandwidth, and the axial resolution through the modulation transfer function (MTF). Simulations were conducted with a weakly-focused, single-element ultrasound source with a center frequency of 2.25 MHz. Experimental measurements were carried out with a single-element transducer (f/3) with a center frequency of 2.25 MHz from a planar reflector and wire targets. In simulations, axial resolution of the ultrasonic imaging system was almost doubled using the REC technique (0.29 mm) versus conventional pulsing techniques (0.60 mm). The -3 dB pulse/echo bandwidth was more than doubled from 48% to 97%, and maximum range sidelobes were -40 dB. Experimental measurements revealed an improvement in axial resolution using the REC technique (0.31 mm) versus conventional pulsing (0.44 mm). The -3 dB pulse/echo bandwidth was doubled from 56% to 113%, and maximum range sidelobes were observed at -45 dB. In addition, a significant gain in eSNR (9 to 16.2 dB) was achieved.     

Coded pulse excitation for ultrasonic strain imaging

Decorrelation strain noise can be significantly reduced in low echo-signal-to-noise (eSNR) conditions using coded excitation. Large time-bandwidth-product (>30) pulses are transmitted into tissue mimicking phantoms with 2.5-mm diameter inclusions that mimic the elastic properties of breast lesions. We observed a 5-10 dB improvement in eSNR that led to a doubling of the depth of focus for strain images with no reduction of spatial resolution. In high eSNR conditions, coded excitation permits the use of higher carrier frequencies and shorter correlation windows to improve the attainable spatial resolution for strain relative to that obtained with conventional short pulses. This paper summarizes comparative studies of strain imaging in noise-limited conditions obtained by short pulses and four common aperiodic codes (chirp, Barker, suboptimal, and Golay) as a function of attenuation, eSNR and applied strain. Imaging performance is quantified using SNR for displacement (SNRd), local modulation transfer function (LMTF), and contrast-to-noise ratio for strain (CNRepsilon). We found that chirp and Golay codes are the most robust for imaging soft tissue deformation using matched filter decoding. Their superior performance is obtained by balancing the need for low-range lobes, large eSNR improvement, and short-code duration.     

Coded excitation system for improving the penetration of real-time phased-array imaging systems

Based on an analysis of the inherent signal-to-noise ratio (SNR) in medical ultrasound imaging, SNR improvements of 15-20 dB are theoretically possible for real-time phased-array imagers using coded excitation. A very simple coded excitation for phased arrays based on the principles of ;pseudochirp' excitation and equalization filtering is described. This system is capable of SNR improvements of about 15 dB with range sidelobe levels acceptable for many medical imaging applications. Such improvements permit increased operating frequencies, and hence enhanced spatial resolution, for real-time array imagers. Both simulations and measurements are used to demonstrate the efficacy of the method.     

Design and performance of Huffman sequences in medical ultrasound coded excitation

This paper deals with coded-excitation techniques for ultrasound medical echography. Specifically, linear Huffman coding is proposed as an alternative approach to other widely established techniques, such as complementary Golay coding and linear frequency modulation. The code design is guided by an optimization procedure that boosts the signal-to-noise ratio gain (GSNR) and, interestingly, also makes the code robust in pulsed-Doppler applications. The paper capitalizes on a thorough analytical model that can be used to design any linear coded-excitation system. This model highlights that the performance in frequency-dependent attenuating media mostly depends on the pulse-shaping waveform when the codes are characterized by almost ideal (i.e., Kronecker delta) autocorrelation. In this framework, different pulse shapers and different code lengths are considered to identify coded signals that optimize the contrast resolution at the output of the receiver pulse compression. Computer simulations confirm that the proposed Huffman codes are particularly effective, and that there are scenarios in which they may be preferable to the other established approaches, both in attenuating and non-attenuating media. Specifically, for a single scatterer at 150 mm in a 0.7-dB/(MHz·cm) attenuating medium, the proposed Huffman design achieves a main-to-side lobe ratio (MSR) equal to 65 dB, whereas tapered linear frequency modulation and classical complementary Golay codes achieve 35 and 45 dB, respectively.     

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.     

Contrast imaging with chirped excitation

Coded excitation has been successfully used in imaging to increase the signal-to-noise ratio (SNR) and penetration depth. With a contrast agent, wideband signals have been hypothesized to increase the contrast-to-tissue ratio (CTR). However, nonlinear properties of contrast agents make decoding difficult when applying coded excitation to contrast imaging. We propose two chirped excitation methods to image contrast agents, with a mechanical index (MI) ranging from 0.05 to 0.34. In the single chirp method, one chirp is transmitted, followed by a clutter filter to reject tissue echoes, then a matched filter is used to recover range resolution. In the chirp sequence method, an increasing and decreasing chirp sequence is transmitted followed by subtraction of the compressed echoes to reject tissue echoes (assuming tissue is a linear scatterer at low MI). Ten independent acoustic experiments were performed to evaluate the CTR for chirp and tone burst insonation, with the same spatial peak temporal averaged intensity (I(SPTA)). A significant increase in CTR, ranging from 4 dB to 8 dB, is observed for chirped excitation as compared with tone burst insonation, at an I(SPTA) of 0.1 and 0.3 mW/cm2 (P < or = 5e-3). To achieve the same CTR of 15 dB, the spatial peak pulse averaged intensity (I(SPPA)) can be decreased by 6 dB for chirp insonation as compared with tone burst insonation (P < 1e-5). Additionally, an increase of more than 10 dB in tissue rejection ratio (TRR) is observed for a chirp sequence insonation compared to tone burst phase inversion for this set of parameters (P < or = 1e-9). Deconvolution of the linear microbubble response from the received echoes is proposed as a method to recover spatial resolution. The difference in the axial resolution resulting from chirp and three-cycle tone burst insonation is approximately 220 microm. The difference in the mainlobe width between experimental and predicted compressed echoes is less than 20%. The side-lobe amplitude is 9 dB to 16 dB below the mainlobe with a transmitted I(SPTA) from 0.1 to 6.6 mW/cm2.     

Coded ultrasound for blood flow estimation using subband processing

This paper investigates the use of coded excitation for blood flow estimation in medical ultrasound. Traditional autocorrelation estimators use narrow-band excitation signals to provide sufficient signal-to-noise-ratio (SNR) and velocity estimation performance. In this paper, broadband coded signals are used to increase SNR, followed by subband processing. The received broadband signal is filtered using a set of narrow-band filters. Estimating the velocity in each of the bands and averaging the results yields better performance compared with what would be possible when transmitting a narrow-band pulse directly. Also, the spatial resolution of the narrow-band pulse would be too poor for brightness-mode (B-mode) imaging, and additional transmissions would be required to update the B-mode image. For the described approach in the paper, there is no need for additional transmissions, because the excitation signal is broadband and has good spatial resolution after pulse compression. This means that time can be saved by using the same data for B-mode imaging and blood flow estimation. Two different coding schemes are used in this paper, Barker codes and Golay codes. The performance of the codes for velocity estimation is compared with a conventional approach transmitting a narrow-band pulse. The study was carried out using an experimental ultrasound scanner and a commercial linear array 7 MHz transducer. A circulating flow rig was scanned with a beam-to-flow angle of 60 degrees. The flow in the rig was laminar and had a parabolic flow-profile with a peak velocity of 0.09 m/s. The mean relative standard deviation of the velocity estimate using the reference method with an 8-cycle excitation pulse at 7 MHz was 0.544% compared with the peak velocity in the rig. Two Barker codes were tested with a length of 5 and 13 bits, respectively. The corresponding mean relative standard deviations were 0.367% and 0.310%, respectively. For the Golay coded experiment, two 8-bit codes were used, and the mean relative standard deviation was 0.335%.     

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.     

医学超声内镜中同步编码激励技术的设计与实现

为了提高医学超声内镜系统中的探测深度、分辨率及成像质量,在超声内镜成像系统中采用编码激励技术,首次将普遍用于开关电源电路设计中的"半桥"电路引入超声内镜编码激励电路.在只有正电压电源供电的情况下产生正负高压激励脉冲,利用电机转动的编码信号,设计了基于CPLD的同步编码激励电路,在保证与超声内镜主机FPGA同步的基础上,简化了超声内镜系统内信号的传递.实验中,同步编码激励电路发射的编码激励信号与理论码型一致,通过人体体模实验,获得的回波波形幅度达1.0Vpp,噪声20×10-3VPP~30×10-3Vpp,信噪比高达34 dB,波形与仿真结果一致.     

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.     

Echography using correlation techniques: choice of coding signal

Theoretical studies made in the early 1980's suggest that ultrasonic imaging using correlation technique can overcome some of the drawbacks of classical pulse echography. Indeed by transmitting a continuous coded signal and then compressing it into a short, high resolution pulse at the receiver the total signal to noise ratio (SNR) is improved. The target location is determined by cross correlation of the emitted and the received signal. The band compression allows, by increasing SNR, the retrieval of echo signals buried in the receiver noise. Thus in medical-type echography, where the signal attenuation at fixed depth is proportional to the frequency, the SNR improvement allows the use of higher frequency signals and leads to improved resolution. We report here the results of comparative experimental studies of simple echo B type images as obtained by the classical pulse echo and correlation techniques. Because the optimisation of the coded signal plays a crucial role in the performance of the correlation technique we will also present a comparative study of the performances of the most common codes (m-sequences and complementary series). In particular we shall emphasise the following points: the relative importance of the central lobe as compared to the side lobes of the correlation function, which is directly related to the dynamic of the imaging system, the width of the correlation peak which is directly related to the axial resolution of the system, the facility of the realisation. The merit of B-mode images obtained with the coded signals will be discussed showing that as far as signal modulation is used the best results are obtained with periodic m-sequences     

Intervening attenuation affects first-order statistical properties of ultrasound echo signals

Previous studies show that first-order statistical properties of ultrasound echo signals are related to the effective number of scatterers in the "resolution cell" of a pulse-echo ultrasound system. When the effective number of scatterers is large (~10 or more) this results in echo signals whose amplitude follows a Rayleigh distribution, with the RF echo signal obeying Gaussian statistics; deviation from Rayleigh or Gaussian statistics yields information on scatterer number densities. In this paper, the influence of the medium's attenuation on non-Gaussian properties of the echo signal is considered. Preferential attenuation of higher frequency components of a pulsed ultrasound beam effectively broadens the beam and increases the resolution cell size. Thus, the resultant non-Gaussian parameter for broad bandwidth excitation of the transducer depends not only on the scatterer number density but also on the attenuation in the medium. These effects can be reduced or eliminated by using narrow-band experiments.