Three-dimensional ultrafast ultrasound imaging of blood flow using row-column addressing array: A simulation study

Fu Ya-Peng; Sun Qian-Dong; Li Bo-Yi; Ta De-An; Xu Kai-Liang

doi:10.7498/aps.72.20222106

Abstract

Three-dimensional (3D) ultrafast imaging is important for ultrasound technology development. The traditional 3D imaging method based on fully sampled two-dimensional (2D) matrix often requires a large number of electronic channels with high density which limits the aperture size and imaging resolution in application. Recently developed row-column addressing (RCA) matrix effectively reduces the number of electronic channels from N × N to N + N by addressing the row and column elements. The beamforming strategy designed for 3D ultrasound imaging was based on the coherent compounding of orthogonal plane waves (OPW). Such a multi-angle OPW compounding strategy achieves virtual transmit focusing in both directions by transmitting a set of plane waves in one direction and receiving along the orthogonal direction, which finally leads to an isotropic point spread function (PSF). In this paper, multi-angle OPW method was investigated for 3D blood flow imaging using an RCA matrix with 128 rows and 128 columns, centered at 6 MHz. The delay and sum (DAS) beamforming was developed for coherent OPW compounding, and the singular value decomposition (SVD) filtering method was used for separating the dynamic blood flow signals from the static tissue signals and low-amplitude noise. The Doppler velocity was computed by the autocorrelation method, and finally the 3D power Doppler and color Doppler imaging of the blood flow were realized. To evaluate the imaging quality and investigate the effect of different OPW tilting angles, quantitative analysis was carried out using multiple parameters, including –6 dB resolution measurements of the PSF, SNR of the power Doppler images and velocity distribution of the color Doppler. The –6 dB resolution is improved from 0.986 mm to 0.493 mm with the number of angles increasing from 5 to 33. With 17 plane wave angles, the SNR of the power Doppler image reaches 30 dB, and the average deviation between the velocity distribution along the diameter of the blood flow phantom and the actual value is about 26.0%. In conclusion, results show that the ultrafast 3D imaging method based on RCA matrix can obtain 3D B-mode, power Doppler and color Doppler images. Increasing the number of tilting angles and enlarging the angle range can significantly improve the imaging quality. The proposed method can be helpful for developing 3D ultrafast ultrasound Doppler imaging and functional ultrasound imaging based on neuro-vascular coupling.

Keywords:

Authors and contacts

1.
Center for Biomedical Engineering, School of Information Science and Technology, Fudan University, Shanghai 200438, China
2.
State Key Laboratory of Integrated Chips and Systems, Fudan University, Shanghai 201203, China
3.
Academy for Engineering and Technology, Fudan University, Shanghai 200438, China

Corresponding author: Xu Kai-Liang, xukl@fudan.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11974081, 12274093), and the Shanghai Rising Star Program, China (Grant No. 20QC1400200).

FullText HTML : translate this paragraph

References

[1]	Fenster A, Downey D B 1996 IEEE Eng. Med. Biol. 15 41 Google Scholar
[2]	Huang Q, Zeng Z 2017 BioMed Res. Int. 2017 1 Google Scholar
[3]	许凯亮, 付亚鹏, 闫少渊, 隋怡晖, 他得安, 王威琪 2023 声学学报 48 173 Google Scholar Xu K L, Fu Y P, Yan S Y, Sui Y H, Ta D A, Wang W Q 2023 Acta Acustica 48 173 Google Scholar
[4]	Brinkley J F, Moritz W E, Baker D W 1978 Ultrasound Med. Biol. 4 317 Google Scholar
[5]	Baranger J, Demene C, Frerot A, Faure F, Delanoë C, Serroune H, Houdouin A, Mairesse J, Biran V, Baud O, Tanter M 2021 Nat. Commun. 12 1 Google Scholar
[6]	Logan A S, Wong L L P, Chen A I H, Yeow J T W 2011 IEEE T. Ultrason. Ferr. 58 1266 Google Scholar
[7]	Von Ramm O T, Smith S W 1990 J. Digit. Imaging 3 261 Google Scholar
[8]	Von Ramm O T, Smith S W, Pavy H G 1991 IEEE T. Ultrason. Ferr. 38 109 Google Scholar
[9]	Li P C, Huang J J 2002 IEEE T. Ultrason. Ferr. 49 1191 Google Scholar
[10]	Eames M, Zhou S, Hossack J 2005 2005 IEEE International Ultrasonics Symposium(IUS) Rotterdam, The Netherlands, September 18–21, 2005 p2243
[11]	Provost J, Papadacci C, Demene C, Gennisson J L, Tanter M, Pernot M 2015 IEEE T. Ultrason. Ferr. 62 1467 Google Scholar
[12]	Papadacci C, Bunting E A, Konofagou E E 2017 IEEE Trans. Med. Imaging 36 357 Google Scholar
[13]	Heiles B, Correia M, Hingot V, Pernot M, Provost J, Tanter M, Couture O 2019 IEEE Trans. Med. Imaging 38 2005 Google Scholar
[14]	Hara K, Sakano J, Mori M, Tamano S, Sinomura R, Yamazaki K Proceedings. ISPSD '05. The 17th International Symposium on Power Semiconductor Devices and ICs Santa Barbara CA, USA, May 23–26, 2005 p359
[15]	Matrone G, Savoia A S, Terenzi M, Caliano G, Quaglia F, Magenes G 2014 IEEE T. Ultrason. Ferr. 61 792 Google Scholar
[16]	Ramalli A, Boni E, Savoia A S, Tortoli P 2015 IEEE T. Ultrason. Ferr. 62 1580 Google Scholar
[17]	Diarra B, Robini M, Tortoli P, Cachard C, Liebgott H 2013 IEEE T. Biomed. Eng. 60 3093 Google Scholar
[18]	Morton C E, Lockwood G R 2003 IEEE International Symposium on Ultrasonics(IUS) Honolulu, Hawaii, October 5–8, 2003 p968
[19]	Seo C H, Yen J T 2009 IEEE T. Ultrason. Ferr. 56 837 Google Scholar
[20]	Denarie B, Tangen T A, Ekroll I K, Rolim N, Torp H, Bjåstad T, Lovstakken L 2013 IEEE Trans. Med. Imaging 32 1265 Google Scholar
[21]	Flesch M, Pernot M, Provost J, Ferin G, Nguyen-Dinh A, Tanter M, Deffieux T 2017 Phys. Med. Bio. 62 4571 Google Scholar
[22]	Sauvage J, Porée J, Rabut C, Férin G, Flesch M, Rosinski B, Nguyen-Dinh A, Tanter M, Pernot M, Deffieux T 2020 IEEE T. Med. Imaging 39 1884 Google Scholar
[23]	Deffieux T, Demené C, Tanter M 2021 Neuroscience 474 110 Google Scholar
[24]	Montaldo G, Tanter M, Bercoff J, Benech N, Fink M 2009 IEEE T. Ultrason. Ferr. 56 489 Google Scholar
[25]	Rasmussen M F, Christiansen T L, Thomsen E V, Jensen J A 2015 IEEE T. Ultrason. Ferr. 62 947 Google Scholar
[26]	Xu K, Minonzio J G, Ta D, Hu B, Wang W, Laugier P 2016 I IEEE T. Ultrason. Ferr. 63 1514 Google Scholar
[27]	Jensen J A 1996 Proceedings of the 10th Nordic-Baltic Conference on Biomedical Imaging Published in Medical & Biological Engineering & Computing Tempere, Finland, June 9–13, 1996 p351
[28]	Jensen J A, Svendsen N B 1992 IEEE T. Ultrason. Ferr. 39 262 Google Scholar
[29]	Taghavi I, Schou M, Panduro N S, Andersen B G, Tomov B G, Sørensen, C M, Stuart M B, Jensen J A 2022 2022 IEEE International Ultrasonics Symposium (IUS) Venice, Italy, October 10–13, 2022 p1
[30]	Alfred C H, Lovstakken L 2010 IEEE T. Ultrason. Ferr. 57 1096 Google Scholar
[31]	郁钧瑾, 郭星奕, 隋怡晖, 宋剑平, 他得安, 梅永丰, 许凯亮 2022 物理学报 71 174302 Google Scholar Yu J J, Guo X Y, Sui Y H, Song J P, Ta D A, Mei Y F, Xu K L 2022 Acta Phys. Sin. 71 174302 Google Scholar
[32]	臧佳琦, 许凯亮, 韩清见, 陆起涌, 梅永丰, 他得安 2021 物理学报 70 114304 Google Scholar Zang J Q, Xu K L, Han Q J, Lu Q Y, Mei Y F, Ta D A 2021 Acta Phys. Sin. 70 114304 Google Scholar
[33]	Sui Y, Yan S, Yu J, Song J, Ta D, Wang W, Xu K 2022 IEEE T. Ultrason. Ferr. 69 2425 Google Scholar
[34]	Xu K, Guo X, Sui Y, Hingot V, Couture O, Ta D, Wang W 2021 IEEE International Ultrasonics Symposium (IUS) Xi'an, China, September 11–16, 2021 p1

Cited By

图 1 正交平面波复合　(a)行发射列接收; (b)列发射行接收; (c)各向同性的PSF图像

Figure 1. OPW compounding: (a) Row transmission and column reception; (b) column transmission and row reception; (c) coherent summation to obtain an isotropic PSF.

DownLoad: Full-Size Img PowerPoint

图 2 RCA阵列延时计算, 以行发射列接收为例　(a)发射距离; (b)接收距离

Figure 2. RCA matrix delay computation using row transmission and column reception as an example: (a) Forward distances; (b) back distances.

DownLoad: Full-Size Img PowerPoint

图 3 PSF图像($ \Delta \alpha = $1°), 角度数分别为:　(a) 5; (b) 17; (c) 33 (1, 2为单次发射得到的PSF; 3为正交复合后的PSF)

Figure 3. PSF results ($ \Delta \alpha = $1°): (a) 5 angles; (b) 17 angles; (c) 33 angles (Images labeled 1 and 2 are the PSFs from single emission; images labeled 3 are the compounded PSFs).

DownLoad: Full-Size Img PowerPoint

图 4 $ \Delta \alpha = $0.5°时的PSF图像　(a) 9个角度; (b) 33个角度; (c) 65个角度

Figure 4. PSF results of $ \Delta \alpha = $0.5°: (a) 9 angles; (b)33 angles; (c) 65 angles.

DownLoad: Full-Size Img PowerPoint

图 5 角度数为5时, 不同角度范围的PSF图像　(a) [–4°, 4°]; (b) [–8°, 8°]; (c) [–12°, 12°]

Figure 5. PSF results of 5 angles: (a) [–4°, 4°]; (b) [–8°, 8°]; (c) [–12°, 12°].

DownLoad: Full-Size Img PowerPoint

图 6 PSF图像的–6 dB分辨率　(a) 图3; (b) 图4; (c) 图5

Figure 6. –6 dB resolution of the PSF: (a) Fig. 3; (b) Fig. 4; (c) Fig. 5.

DownLoad: Full-Size Img PowerPoint

图 7 仿体血流成像结果　(a) SVD滤波前的二维B超图像; (b) SVD滤波后的二维B超图像; (c) 滤波后的三维功率多普勒图像; (d) 滤波后的三维彩色多普勒图像

Figure 7. Imaging results of the phantom blood flow: (a) B mode image before the clutter filtering; (b)B mode image after the clutter filtering; (c)3 D power Doppler image; (d)3 D color Doppler image.

DownLoad: Full-Size Img PowerPoint

图 8 不同平面波复合角度下的功率多普勒图像及分析　(a) 9个角度; (b) 13个角度; (c) 17个角度; (d) SNR; (e) 沿虚线的功率多普勒能量分布

Figure 8. Power Doppler results with different numbers of steering angles: (a) 9 angles; (b) 13 angles; (c) 17 angles; (d) SNR; (e) power Doppler distribution along the dash line.

DownLoad: Full-Size Img PowerPoint

图 9 不同平面波复合角度下的彩色多普勒图像和速度分布情况　(a) 9个角度; (b) 13个角度; (c) 17个角度; (d) 沿虚线1的速度分布; (e) 沿虚线2的速度分布

Figure 9. Color Doppler image results with different numbers of steering angles: (a) 9 angles; (b) 13 angles; (c) 17 angles; (d) velocity distribution along the dash line 1; (e) velocity distribution along the dash line 2.

DownLoad: Full-Size Img PowerPoint

表 1 RCA阵列参数设置

Table 1. Parameters of the RCA matrix.

阵元数 128+128

中心频率 f₀/MHz 6

声速 c/(m·s^–1) 1540
波长 λ/μm 256.7
阵元中心间距/mm 0.2
阵元宽度/mm 0.175
阵列孔径/mm² 25.6$ \times $25.6

DownLoad: CSV

表 2 彩色多普勒图像速度分布的平均误差

Table 2. Average error of the velocity distribution of the color Doppler.

角度数N

9 13 17
平均误差1/% 48.73 40.48 25.03
平均误差2/% 43.55 49.70 26.86

DownLoad: CSV

[1]	Fenster A, Downey D B 1996 IEEE Eng. Med. Biol. 15 41 Google Scholar
[2]	Huang Q, Zeng Z 2017 BioMed Res. Int. 2017 1 Google Scholar
[3]	许凯亮, 付亚鹏, 闫少渊, 隋怡晖, 他得安, 王威琪 2023 声学学报 48 173 Google Scholar Xu K L, Fu Y P, Yan S Y, Sui Y H, Ta D A, Wang W Q 2023 Acta Acustica 48 173 Google Scholar
[4]	Brinkley J F, Moritz W E, Baker D W 1978 Ultrasound Med. Biol. 4 317 Google Scholar
[5]	Baranger J, Demene C, Frerot A, Faure F, Delanoë C, Serroune H, Houdouin A, Mairesse J, Biran V, Baud O, Tanter M 2021 Nat. Commun. 12 1 Google Scholar
[6]	Logan A S, Wong L L P, Chen A I H, Yeow J T W 2011 IEEE T. Ultrason. Ferr. 58 1266 Google Scholar
[7]	Von Ramm O T, Smith S W 1990 J. Digit. Imaging 3 261 Google Scholar
[8]	Von Ramm O T, Smith S W, Pavy H G 1991 IEEE T. Ultrason. Ferr. 38 109 Google Scholar
[9]	Li P C, Huang J J 2002 IEEE T. Ultrason. Ferr. 49 1191 Google Scholar
[10]	Eames M, Zhou S, Hossack J 2005 2005 IEEE International Ultrasonics Symposium(IUS) Rotterdam, The Netherlands, September 18–21, 2005 p2243
[11]	Provost J, Papadacci C, Demene C, Gennisson J L, Tanter M, Pernot M 2015 IEEE T. Ultrason. Ferr. 62 1467 Google Scholar
[12]	Papadacci C, Bunting E A, Konofagou E E 2017 IEEE Trans. Med. Imaging 36 357 Google Scholar
[13]	Heiles B, Correia M, Hingot V, Pernot M, Provost J, Tanter M, Couture O 2019 IEEE Trans. Med. Imaging 38 2005 Google Scholar
[14]	Hara K, Sakano J, Mori M, Tamano S, Sinomura R, Yamazaki K Proceedings. ISPSD '05. The 17th International Symposium on Power Semiconductor Devices and ICs Santa Barbara CA, USA, May 23–26, 2005 p359
[15]	Matrone G, Savoia A S, Terenzi M, Caliano G, Quaglia F, Magenes G 2014 IEEE T. Ultrason. Ferr. 61 792 Google Scholar
[16]	Ramalli A, Boni E, Savoia A S, Tortoli P 2015 IEEE T. Ultrason. Ferr. 62 1580 Google Scholar
[17]	Diarra B, Robini M, Tortoli P, Cachard C, Liebgott H 2013 IEEE T. Biomed. Eng. 60 3093 Google Scholar
[18]	Morton C E, Lockwood G R 2003 IEEE International Symposium on Ultrasonics(IUS) Honolulu, Hawaii, October 5–8, 2003 p968
[19]	Seo C H, Yen J T 2009 IEEE T. Ultrason. Ferr. 56 837 Google Scholar
[20]	Denarie B, Tangen T A, Ekroll I K, Rolim N, Torp H, Bjåstad T, Lovstakken L 2013 IEEE Trans. Med. Imaging 32 1265 Google Scholar
[21]	Flesch M, Pernot M, Provost J, Ferin G, Nguyen-Dinh A, Tanter M, Deffieux T 2017 Phys. Med. Bio. 62 4571 Google Scholar
[22]	Sauvage J, Porée J, Rabut C, Férin G, Flesch M, Rosinski B, Nguyen-Dinh A, Tanter M, Pernot M, Deffieux T 2020 IEEE T. Med. Imaging 39 1884 Google Scholar
[23]	Deffieux T, Demené C, Tanter M 2021 Neuroscience 474 110 Google Scholar
[24]	Montaldo G, Tanter M, Bercoff J, Benech N, Fink M 2009 IEEE T. Ultrason. Ferr. 56 489 Google Scholar
[25]	Rasmussen M F, Christiansen T L, Thomsen E V, Jensen J A 2015 IEEE T. Ultrason. Ferr. 62 947 Google Scholar
[26]	Xu K, Minonzio J G, Ta D, Hu B, Wang W, Laugier P 2016 I IEEE T. Ultrason. Ferr. 63 1514 Google Scholar
[27]	Jensen J A 1996 Proceedings of the 10th Nordic-Baltic Conference on Biomedical Imaging Published in Medical & Biological Engineering & Computing Tempere, Finland, June 9–13, 1996 p351
[28]	Jensen J A, Svendsen N B 1992 IEEE T. Ultrason. Ferr. 39 262 Google Scholar
[29]	Taghavi I, Schou M, Panduro N S, Andersen B G, Tomov B G, Sørensen, C M, Stuart M B, Jensen J A 2022 2022 IEEE International Ultrasonics Symposium (IUS) Venice, Italy, October 10–13, 2022 p1
[30]	Alfred C H, Lovstakken L 2010 IEEE T. Ultrason. Ferr. 57 1096 Google Scholar
[31]	郁钧瑾, 郭星奕, 隋怡晖, 宋剑平, 他得安, 梅永丰, 许凯亮 2022 物理学报 71 174302 Google Scholar Yu J J, Guo X Y, Sui Y H, Song J P, Ta D A, Mei Y F, Xu K L 2022 Acta Phys. Sin. 71 174302 Google Scholar
[32]	臧佳琦, 许凯亮, 韩清见, 陆起涌, 梅永丰, 他得安 2021 物理学报 70 114304 Google Scholar Zang J Q, Xu K L, Han Q J, Lu Q Y, Mei Y F, Ta D A 2021 Acta Phys. Sin. 70 114304 Google Scholar
[33]	Sui Y, Yan S, Yu J, Song J, Ta D, Wang W, Xu K 2022 IEEE T. Ultrason. Ferr. 69 2425 Google Scholar
[34]	Xu K, Guo X, Sui Y, Hingot V, Couture O, Ta D, Wang W 2021 IEEE International Ultrasonics Symposium (IUS) Xi'an, China, September 11–16, 2021 p1

[1]	Yan Shao-Yuan, Ding Yi-Ming, Ma Guo-Ao, Fu Ya-Peng, Xu Kai-Liang, Ta De-An. Ultrafast ultrasound coded vector Doppler imaging of blood flow velocity and resistivity. Acta Physica Sinica, 2025, 74(1): . doi: 10.7498/aps.74.20241454
[2]	Lin Ji-Yan, Sun Jiao-Xia, Lin Shu-Yu. Intelligent optimization design of large-scale three-dimensional ultrasonic vibration system. Acta Physica Sinica, 2024, 73(8): 084304. doi: 10.7498/aps.73.20240006
[3]	Zhang Hui, Zhu Wen-Fa, Fan Guo-Peng, Zhang Hai-Yan. Thinned array ultrasonic imaging of debonding defects in discontinuous impedance bonded structures. Acta Physica Sinica, 2023, 72(2): 024302. doi: 10.7498/aps.72.20221771
[4]	Zhang Yun-Yun, Li Yi-Fang, Shi Qin-Zhen, Xu Le-Xiu, Dai Fei, Xing Wen-Yu, Ta De-An. Phase shift migration based plane-wave imaging of cortical bone. Acta Physica Sinica, 2023, 72(15): 154303. doi: 10.7498/aps.72.20230581
[5]	Sui Yi-Hui, Guo Xing-Yi, Yu Jun-Jin, Alexander A. Solovev, Ta De-An, Xu Kai-Liang. Accelerating super-resolution ultrasound localization microscopy using generative adversarial net. Acta Physica Sinica, 2022, 71(22): 224301. doi: 10.7498/aps.71.20220954
[6]	Hu Jin-Hu, Lin Dan-Ying, Zhang Wei, Zhang Chen-Shuang, Qu Jun-Le, Yu Bin. Dual-sided illumination light-sheet fluorescence microscopy with virtual single-pixel imaging deconvolution. Acta Physica Sinica, 2022, 71(2): 028701. doi: 10.7498/aps.71.20211358
[7]	Yu Jun-Jin, Guo Xing-Yi, Sui Yi-Hui, Song Jian-Ping, Ta De-An, Mei Yong-Feng, Xu Kai-Liang. Ultrafast ultrasound localization microscopy method for spinal cord mircovasculature imaging. Acta Physica Sinica, 2022, 71(17): 174302. doi: 10.7498/aps.71.20220629
[8]	Wang Kang-Yu, Zhou Yu-Lin, He Li-Yuan, Lu Chun-Yao, Yu Run, Wu Da-Wei. Blood flow image by multi-angle composite ultrasonic Doppler vector. Acta Physica Sinica, 2022, 71(10): 104303. doi: 10.7498/aps.71.20211825
[9]	Zhang Hai-Yan, Song Jia-Xin, Ren Yan, Zhu Qi, Ma Xue-Fen. Ultrasonic imaging of wrinkles in carbon-fiber-reinforce-polymer composites. Acta Physica Sinica, 2021, 70(11): 114301. doi: 10.7498/aps.70.20210032
[10]	Zang Jia-Qi, Xu Kai-Liang, Han Qing-Jian, Lu Qi-Yong, Mei Yong-Feng, Ta De-An. Non-contrast-enhanced ultrafast ultrasound Doppler imaging of spinal cord micro-vessels. Acta Physica Sinica, 2021, 70(11): 114304. doi: 10.7498/aps.70.20201878
[11]	Qian Jia, Dang Shi-Pei, Zhou Xing, Dan Dan, Wang Zhao-Jun, Zhao Tian-Yu, Liang Yan-Sheng, Yao Bao-Li, Lei Ming. Fast structured illumination three-dimensional color microscopic imaging method based on Hilbert-transform. Acta Physica Sinica, 2020, 69(12): 128701. doi: 10.7498/aps.69.20200352
[12]	Feng Shuai, Chang Jun, Hu Yao-Yao, Wu Hao, Liu Xin. Design and analysis of polarization imaging lidar and short wave infrared composite optical receiving system. Acta Physica Sinica, 2020, 69(24): 244202. doi: 10.7498/aps.69.20200920
[13]	Wang Jia-Lin, Yan Wei, Zhang Jia, Wang Lu-Wei, Yang Zhi-Gang, Qu Jun-Le. New advances in the research of stimulated emission depletion super-resolution microscopy. Acta Physica Sinica, 2020, 69(10): 108702. doi: 10.7498/aps.69.20200168
[14]	Dai Bing, Wang Peng, Zhou Yu, You Cheng-Wu, Hu Jiang-Sheng, Yang Zhen-Gang, Wang Ke-Jia, Liu Jin-Song. Wavelet transform in the application of three-dimensional terahertz imaging for internal defect detection. Acta Physica Sinica, 2017, 66(8): 088701. doi: 10.7498/aps.66.088701
[15]	Chen He, Yu Bin, Chen Dan-Ni, Li Heng, Niu Han-Ben. Super-diffraction imaging in three-dimensional localization precision of the double-helix point spread function. Acta Physica Sinica, 2013, 62(14): 144201. doi: 10.7498/aps.62.144201
[16]	Peng Jing-Si, Peng Hu. Chaotic frequency-modulating continuous wave for an ultrasonic doppler blood flow velocity measurement system. Acta Physica Sinica, 2012, 61(24): 248701. doi: 10.7498/aps.61.248701
[17]	Zhao Gui-Min, Lu Ming-Zhu, Wan Ming-Xi, Fang Li. Study of vibro-acoustography with high spatial resolution based on sector array transducers. Acta Physica Sinica, 2009, 58(9): 6596-6603. doi: 10.7498/aps.58.6596
[18]	Dong Hui-Yuan, Liu Mei, Wu Zong-Han, Wang Jing, Wang Zhen-Lin. Band structures of three-dimensional photonic crystals consisting of dielectric spheres: a plane-wave approach. Acta Physica Sinica, 2005, 54(7): 3194-3199. doi: 10.7498/aps.54.3194
[19]	Wang Shao-Hong, B.Ferguson, Zhang Cun-Lin, Zhang Xi-Cheng. Terahertz computer tomography. Acta Physica Sinica, 2003, 52(1): 120-124. doi: 10.7498/aps.52.120
[20]	WANG YANG-PU, JIN QI-SHU. THE THEORY OF ULTRASONIC ATTENUATION IN SUPERIONIC GLASSES. Acta Physica Sinica, 1988, 37(7): 1083-1088. doi: 10.7498/aps.37.1083

Catalog

Vol. 72, Issue 7 - 2023-04-05

Metrics

Abstract views: 5208
PDF Downloads: 157
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板