Theory and experiment of Fourier-Bessel field calculation and tuning of a pulsed wave annular array.

A one-dimensional (1D) Fourier-Bessel series method for computing and tuning (beamforming) the linear lossless field of flat pulsed wave annular arrays is developed and supported with both numerical simulation and experimental verification. The technique represents a new method for modeling and tuning the propagated field by linking the quantized surface pressure profile to a known set of limited diffraction Bessel beams propagating into the medium. This enables derivation of an analytic expression for the field at any point in space and time in terms of the transducer surface pressure profile. Tuning of the field then also follows by formulating a least-squares design for the transducer surface pressure with respect to a given desired field in space and time. Simulated and experimental results for both field computation and tuning are presented in the context of a 10-ring annular array operating at a central frequency of 2.5 MHz in water.

[1]  J. Arendt.  Paper presented at the 10th Nordic-Baltic Conference on Biomedical Imaging: Field: A Program for Simulating Ultrasound Systems , 1996 .

[2]  J Turunen,et al.  Realization of general nondiffracting beams with computer-generated holograms. , 1989, Journal of the Optical Society of America. A, Optics and image science.

[3]  A. Friberg,et al.  ANGULAR-SPECTRUM REPRESENTATION OF NONDIFFRACTING X WAVES , 1996 .

[4]  Modeling of CW annular arrays using limited diffraction Bessel beams , 2002, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[5]  F. R. Stepanishen.  Acoustic transients from planar axisymmetric vibrators using the impulse response approach , 1977 .

[6]  Cook,et al.  Evidence of localized wave transmission. , 1989, Physical review letters.

[7]  P. Stepanishen,et al.  Acoustic bullets: Transient Bessel beams generated by planar apertures , 1997 .

[8]  Jian-yu Lu,et al.  Fourier-bessel field calculation and tuning of a CW annular array , 2002, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[9]  P. Stepanishen.  Acoustic bullets/transient Bessel beams: Near to far field transition via an impulse response approach , 1998 .

[10]  Miceli,et al.  Diffraction-free beams. , 1987, Physical review letters.

[11]  J. Greenleaf,et al.  Application of Bessel beam for Doppler velocity estimation , 1995, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[12]  J. Durnin.  Exact solutions for nondiffracting beams. I. The scalar theory , 1987 .

[13]  J. Greenleaf,et al.  Ultrasonic nondiffracting transducer for medical imaging , 1990, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[14]  P. Stepanishen.  The Time‐Dependent Force and Radiation Impedance on a Piston in a Rigid Infinite Planar Baffle , 1971 .

[15]  J. Mcleod.  The Axicon: A New Type of Optical Element , 1954 .

[16]  S. Holm,et al.  Bessel and conical beams and approximation with annular arrays , 1998, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[17]  J. Greenleaf,et al.  Experimental verification of nondiffracting X waves , 1992, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[18]  M Arditi,et al.  Transient fields of concave annular arrays. , 1981, Ultrasonic imaging.

[19]  Jian-yu Lu.  2D and 3D high frame rate imaging with limited diffraction beams , 1997 .

[20]  J. Greenleaf,et al.  Evaluation of a nondiffracting transducer for tissue characterization , 1990, IEEE Symposium on Ultrasonics.

[21]  J. Brittingham,et al.  Focus waves modes in homogeneous Maxwell’s equations: Transverse electric mode , 1983 .

[22]  G. Tolstov.  Fourier Series , 1962 .

[23]  J. Ojeda-Castañeda,et al.  Nondiffracting wavefields in grin and free‐space , 1990 .

[24]  Jian-yu Lu,et al.  An X wave transform , 2000, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[25]  P. Stepanishen.  A generalized modal impulse response and Fourier transform approach to investigate acoustic transient Bessel beams and Bessel bullets , 1999 .

[26]  Holm,et al.  Decomposition of acoustic fields in quantised Bessel beams , 2000, Ultrasonics.

[27]  Heinz Hoffmann,et al.  Ultrasound Axicon: a device for focusing over a large depth , 1973 .

[28]  J F Greenleaf,et al.  Biomedical ultrasound beam forming. , 1994, Ultrasound in medicine & biology.

[29]  Richard W. Ziolkowski,et al.  Exact solutions of the wave equation with complex source locations , 1985 .

[30]  J. Greenleaf,et al.  Nondiffracting X waves-exact solutions to free-space scalar wave equation and their finite aperture realizations , 1992, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[31]  J F Greenleaf,et al.  Pulse-echo imaging using a nondiffracting beam transducer. , 1991, Ultrasound in medicine & biology.

[32]  Jørgen Arendt Jensen,et al.  A new calculation procedure for spatial impulse responses in ultrasound , 1999 .

[33]  J F Greenleaf,et al.  Producing deep depth of field and depth-independent resolution in NDE with limited diffraction beams. , 1993, Ultrasonic imaging.

[34]  Shiping He,et al.  Optical X wave communications , 1999 .

[35]  G. Tupholme.  Generation of acoustic pulses by baffled plane pistons , 1969 .

[36]  F. B..  Introduction to Bessel Functions , 1939, Nature.

[37]  H. Kikuchi,et al.  Generation of nearly diffraction-free laser beams , 1989 .