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Get Information clear JSmol Viewer clear first_page Download PDF settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing: Column Width: Background: Open AccessArticle Methods for Grating Lobe Suppression in Ultrasound Plane Wave Imaging by Sua BaeSua Bae SciProfiles Scilit Preprints.org Google Scholar and Tai-Kyong SongTai-Kyong Song SciProfiles Scilit Preprints.org Google Scholar * Department of Electronic Engineering, Sogang University, Seoul 04107, Korea * Author to whom correspondence should be addressed. Appl. Sci. 2018, 8(10), 1881; https://doi.org/10.3390/app8101881 Submission received: 29 August 2018 / Revised: 4 October 2018 / Accepted: 9 October 2018 / Published: 11 October 2018 (This article belongs to the Special Issue Ultrasound B-mode Imaging: Beamforming and Image Formation Techniques) Download keyboard_arrow_down Download PDF Download PDF with Cover Download XML Download Epub Browse Figures Versions NotesAbstract: Plane wave imaging has been proven to provide transmit beams with a narrow and uniform beam width throughout the imaging depth. The transmit beam pattern, however, exhibits strong grating lobes that have to be suppressed by a tightly focused receive beam pattern. In this paper, we present the conditions of grating lobe occurrence by analyzing the synthetic transmit beam pattern. Based on the analysis, the threshold of the angle interval is presented to completely eliminate grating lobe problems when using uniformly distributed plane wave angles. However, this threshold requires a very small angle interval (or, equivalently, too many angles). We propose the use of non-uniform plane wave angles to disperse the grating lobes in the spatial domain. In this paper, we present an approach using two uniform angle sets with different intervals to generate a non-uniform angle set. The proposed methods were verified by continuous-wave transmit beam patterns and broad-band 2D point spread functions obtained by computer simulations. Keywords: ultrasonic imaging; beamforming; plane wave imaging; grating lobe suppression 1. IntroductionPlane wave imaging (PWI) has drawn a large amount of attention from researchers in the field of medical ultrasound imaging [1,2,3]. First, PWI can provide ultra-fast ultrasound imaging that is essential for a growing number of applications, such as the estimation of shear elasticity [1,4,5] and vector Doppler [6,7] as well as high-frame-rate B-mode imaging [8]. In PWI, plane waves (PWs) with different travelling angles are successively transmitted instead of traditionally focused ultrasound waves; after each firing, the returned ultrasound waves are received at all array elements. Synthetic transmit (Tx) focusing at each imaging point is achieved by compounding PWs with proper delays, while receive (Rx) focusing is performed in the conventional manner. As a result, ultrasound beams are focused at all imaging points for transmission and reception. Theoretically, the Tx beam pattern of PWI maintains the same main lobe width at all depths; the width is determined by the range of compounded PW angles.When using a finite number of PWs with uniformly distributed steering angles, the synthetically focused beam has not only the main lobe, but also side lobes and grating lobes (GLs), which create artifacts in ultrasound image and deteriorate the image quality [2]. A large number of compounded PWs allow for the mitigation of the side lobe and GLs in the synthetic beam pattern and provide better image contrast, as illustrated in Figure 1. However, the frame rate of PWI decreases as the number of PWs increases. To reduce the side lobe without compromising the frame rate, various adaptive beamforming methods have been proposed. Austeng et al. proposed a minimum variance beamforming method for PWI [9]. In this method, the optimized weighting factors are applied when compounding the low-resolution images of different steered PWs. The joint Tx and Rx adaptive beamformer has also been proposed to apply the data-dependent weighting factors to both the receiving array domain and PW angle domain (i.e., frame domain) [10]. In addition, as the side lobes from different angles are uncorrelated, some beamformers have been suggested to reject less coherent signals [11,12,13]. A global effective distance-based side lobe suppressing method has also been proposed to achieve high quality images of PWI with a small number of PWs [14].Only a few studies, however, have been reported that consider GLs in PWI. Though PW angles with a constant angle interval are employed in most studies, they introduce uniformly spaced grating lobes (GLs), the interval of which is governed by the angle interval, as shown in Figure 1 [2]. If the angle interval is sufficiently small to locate GLs far from the main lobe, the GLs might have little effect on the image quality. However, to preserve the ultra-fast frame rate without compromising the resolution (i.e., to use a small number of PWs for the given PW angle range), the angle interval should be large, which introduces GLs close to the main lobe and deteriorates the image quality.Here, we investigate the conditions of GL occurrence by analyzing the continuous wave (CW) synthetic transmit beam pattern. Based on the conditions of GL occurrence, the threshold of the angle interval for the elimination of GLs is presented with the use of uniformly distributed PW angles. In addition, we propose a method for GL level reduction using non-uniformly distributed PW angles, which consist of subsets of uniformly distributed angles, each of which has different angle intervals. To verify and evaluate the methods, simulation experiments are conducted using synthetic Tx beam patterns and round-trip point spread functions (PSFs). 2. Materials and Methods 2.1. GL Conditions in PWILet us consider N PWs with different steering angles, θ n ( n = 1 , 2 , … , N ), in a range of [ θ min , θ max ], which are selected in terms of α n ( = sin ( θ n ) ) for the convenience of analysis such that α n = α min + ( n − 1 ) d α , n = 1 , 2 , … , N , where α min = − ( N − 1 ) d α / 2 and d α is a constant α-interval between successive α n . Assuming that the monochromatic (i.e., CW) plane waves are emitted from an infinite-length transducer, PWI provides a synthetic Tx beam pattern given by: ψ ( x ′ ) = ∑ n = 1 N exp { − j k x ′ ( α min + ( n − 1 ) d α ) } = c 0 sin ( π x ′ d α N / λ ) sin ( π x ′ d α / λ ) , where c 0 = exp { − j k x ′ ( α min + ( N − 1 ) d α / 2 ) } , x ′ = x − x f , x f is the lateral position of a focus, λ is the wavelength, and k is the wave number (k = 2 π / λ ) [3]. Note that almost the same beam pattern can be obtained from Equation (1) when using PW angles spaced by a constant θ-interval, as in [1,2], if the angles are sufficiently small such that sin θ n ≈ θ n and d α ≈ d θ . In the beam pattern, the main lobe is at the focus, x ′ = 0 ( x = x f ), and its amplitude is N. GLs must be observed for which both the numerator and denominator of Equation (1) have zeros except x ′ = 0 , that occur at: x ′ = ± m λ / d α , m = 1 , 2 , 3 , … . By substituting Equation (2) into Equation (1), the amplitude of the m-th GL can be expressed as: ψ ( x ′ = ± m λ / d α ) = { ( − 1 ) m N for even N N for odd N . It should be noted that the GLs predicted by Equations (2) and (3) arise when (1) all of the N PWs pass through the GL positions, preserving their linear wave-front (LWF) (LWF condition), and (2) PWs with a constant α-interval are employed (uniform d α condition). 2.2. GL Suppression Method with Uniformly Distributed PW AnglesIn practice, PWs are transmitted by a finite aperture (i.e., a finite-length transducer array), resulting in a finite collimated beam area. Figure 2 shows three PWs with different steering angles (black solid lines) and their collimated beam areas (gray shaded areas) with preserved LWFs. In Figure 2, the focus and the main lobe of the focused beam pattern are in the region where all the PWs preserve their LWFs (i.e., the darkest area in Figure 2). If a GL locates at this same region and the constant PW angle interval is employed (i.e., if both LWF and uniform d α conditions are met), the amplitude of the GL would be as high as that of the main lobe because the number of compounded PWs should be the same at both the main lobe and GL locations. Note that by reducing d α , one can move the GL away from the main lobe towards a region where the LWF condition is satisfied by fewer PWs. In such a case, the GL level would be lower than that of the main lobe because the number of PWs coherently compounded becomes smaller at the GL location; the PWs that do not maintain LWFs at the grating lobe locations are compounded with phase errors, leading to a decrease in the corresponding GL levels. This indicates that GL levels would decrease as GLs are moved farther from the main lobe.One can expect that the GLs can be eliminated by locating all of the GLs in a region where none of the PWs preserve LWF (i.e., by completely violating the LWF condition). In Figure 2, for example, when the first GL position, x = x GL , 1 ( = x f + λ / d α ), falls onto point A that is out of all the collimated beam areas of PWs, no GLs can be formed, even when a uniform d α is employed. In this case, x GL , 1 > D / 2 + z f tan θ max . Consequently, the GL elimination requirement when using uniformly distributed PW angles can be defined as: d α