TY - JOUR

T1 - Theory and acoustic experiments of nondiffracting X waves

AU - Lu, J. Y.

AU - Greenleaf, J. F.

N1 - Funding Information:
Speed of X Waves The theoretical X waves (see Eq. (6)) are superluminal, i.e., the speed of the X wave peak is greater than the speed of sound in the acoustical case and the speed of light in the optical case. But the approximated X waves result from the interference of causal waveforms in a finite aperture and each of the wavelets causing the interference travels at the speed of sound or light. More discussions on the speed of X waves are contamed in Reference [7]. Parameters The parameter ao determines the fall-off speed of the high frequency components of the X waves (see Eq. (6)). Bigger @ results in a faster fall-off of the high frequency components and is associated with larger lateral and axial beamwidth of the X waves [71. ( is the angle of the propagation direction of the plane waves that compose the X waves relative to the z axis. The zeroth-order broadband X wave is a superposition of plane waves, all having the same amplitude and traveling at a fixed angle, (, with their anmuthal angle, 8, ranging from 0 to 27r over a large frequency range. Bigger ( will produce X waves of larger lateral resolution but bigger axial beamwidth and reduced depth of field (see Eq. (9)) L71. IV. CONCLUSION One subset of the families of nondiffractmg solutions to the iso@opic-homogeneouss calar wave equation which we termed "X waves" can be approximated closely with finite aperhxe and causal drive signals. The physically produced X waves have large depth of field and are non-diffracting over a finite distance. The large depth of field of the X waves make them potentially useful in medical imaging, tissue characterization, and nondestructive evaluation of materials. The effects of high sidelobes (X branches) of X waves in imaging could be reduced by using the X waves to transmit and conventional dynamically focused beams to receive. V. ACKNOWLEDGMENTS The authors appreciate the help of Thomas M. Kinter in developing softwate for data acquisitions. The authors also appreciate the help of Randall R. Kinnick in making transformers to drive the transducer. The authors appreciate the secretarial assistance of Elaine C. Quarve and the graphic assistance of Christine A. Welch. This work was supported in part by grants CA 43920 and CA54212-01 from the National Institutes of Health. VI. REFERENCES
Publisher Copyright:
© 1991 IEEE.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 1991

Y1 - 1991

N2 - Families of nondiffracting solutions of the isotropichomogeneous wave equation have been discovered recently by the authors. These families of solutions contain some of the nondiffracting beams known previously, such as the plane wave, Durnin's nondiffracting beams, etc. One subset of the new families of nondiffracting solutions represents waves of X-like shape in a plane through the axis of the waves, which we termed "X waves." We report here the theoretical implications of one family of the nondiffracting solutions and simulate the nondiffracting X waves with finite apertures using the Rayteigh-Sommerfeld formulation of diffraction. An acoustic superposition experiment of the nondiffracting X waves in water was performed to test the theory, and the experiment agrees closely with the theory.

AB - Families of nondiffracting solutions of the isotropichomogeneous wave equation have been discovered recently by the authors. These families of solutions contain some of the nondiffracting beams known previously, such as the plane wave, Durnin's nondiffracting beams, etc. One subset of the new families of nondiffracting solutions represents waves of X-like shape in a plane through the axis of the waves, which we termed "X waves." We report here the theoretical implications of one family of the nondiffracting solutions and simulate the nondiffracting X waves with finite apertures using the Rayteigh-Sommerfeld formulation of diffraction. An acoustic superposition experiment of the nondiffracting X waves in water was performed to test the theory, and the experiment agrees closely with the theory.

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U2 - 10.1109/ULTSYM.1991.234298

DO - 10.1109/ULTSYM.1991.234298

M3 - Conference article

AN - SCOPUS:84965791787

SP - 1155

EP - 1159

JO - Proceedings of the IEEE Ultrasonics Symposium

JF - Proceedings of the IEEE Ultrasonics Symposium

SN - 1051-0117

M1 - 234298

T2 - 1991 IEEE Ultrasonics Symposium. ULTSYM 1991

Y2 - 8 December 1991 through 11 December 1991

ER -