Apodized Conical Focusing for Ultrasound Imaging

Optics Letters, 2013

A method to evaluate the physical realizability of an arbitrary three-dimensional vectorial field distribution in the focal area is proposed. A parameter that measures the similarity between the designed (target) field and the physically achievable beam is provided. This analysis is carried out within the framework of the closest electromagnetic field to a given vectorial function, and the procedure is applied to two illustrative cases.

Microwave and Optical Technology Letters, 1997

a and 6 b plot the reconstructed permittivity profiles, from the eleventh twelfth iterations, respectively, with the use of the TDDBIM, Ž . Ž . and b display the corresponding conduc-Ž . Ž . Ž . tivity profiles. A comparison of Figures 2 k , 6 b , 3 k , and Ž . 7 b shows that the TDDBIM algorithm recovers the profile well. Next, we add a 10% background noise and repeat the Ž . Ž . reconstruction experiment. 8 b show the permittivity profiles after the first and second iterations, respectively, derived by with the use of the FCT, and Figures Ž . Ž . 9 a and 9 b plot the corresponding conductivity profiles. A Ž . Ž . Ž . Ž . comparison of Figures 4 b , 5 b , 8 b , and 9 b lead us to conclude that the FCT algorithm performs well in reconstructing the profiles.

The Journal of the Acoustical Society of America, 2007

This article gives an analytical, computational, and experimental treatment of the spatial resolution encoded in unfocused regions of focused ultrasound beams. This topic is important in diagnostic ultrasound since ultrasound array systems are limited to a single transmit focal point per acoustic transmission, hence there is a loss of spatial resolution away from the transmit focus, even with the use of dynamic receive focusing. It is demonstrated that the spatial bandwidth of a Gaussian-apodized beam is approximately constant with depth, which means that there is just as much encoded spatial resolution away from the transmit focus as there is in the focal region. The practical application of this principle is discussed, an algorithm for retrospectively focusing signals from unfocused regions of fixed-focus beams is presented, and a quantitative comparison between the authors' methods and dynamic-receive beamforming is provided.

Optics Express, 2010

A method to design isotropic inhomogeneous refractive index distribution is presented, in which the scalar wave field solutions propagate exactly on an eikonal function (i.e., remaining constant on the Geometrical Optics wavefronts). This method is applied to the design of "dipole lenses", which perfectly focus a scalar wave field emitted from a point source onto a point absorber, in both two and three dimensions. Also, the Maxwell fish-eye lens in two and three dimensions is analysed.

The influence of nonlinear and diffraction effects on distortion of the spatial structure of peak positive and negative pressures in focused acoustic beams was studied for a weakly dissipative propagation medium. The problem was solved numerically based on the Khokhlov−Zabolotskaya−Kuznetsov equation for beams with uniform and Gaussian distributions of the harmonic signal amplitude at the source.

Ultrasonics, 2009

In medical ultrasound imaging, the desired lateral field distribution at each focal distance can be obtained by optimal apodization. On the other hand, the lateral field is a function of focal distance. Hence, finding the optimal apodization is a very arduous process. To overcome this, we have introduced a suboptimal method by which optimal apodization can be calculated in any distance through a nonlinear transformation by the knowledge of the optimal one at a distance. This transformation is established on a fact that the lateral field distribution at focal distance can be expressed as the Fourier transform of a nonlinear function of the aperture weighting, instead of direct expression as the Fourier transform of the above. We have applied this method to map the apodization which obtains the desired beam pattern into the apodization which maintains the same properties on the lateral field distribution. For example, applying this method on a 50-elements lambda/2 spaced linear array with length D has resulted in apodization that is optimal at distances D or D/2 by precision better than 9%. This method is useful especially in optimization problems, having no explicit constraint on the main lobe width, such as minimizing the sidelobe levels or minimizing main lobe width constrained to a predetermined value of sidelobe level. However, as the results show, this technique provides acceptable results in other cases.

Physical Review A, 2009

Closed formulas are derived for the field in the focal region of a diffraction limited lens, such that the electric field component in a given direction at the focal point is larger than that of all other focused fields with the same power in the entrance pupil of the lens. Furthermore, closed formulas are derived for the corresponding optimum field distribution in the lens pupil. Focused fields with maximum longitudinal or maximum transverse are considered in detail. The latter field is similar, but not identical, to the focused linearly polarized plane wave.

IEEE Transactions on Nuclear Science, 1985

Optics Express, 2004

We present an algorithm for calculating the field distribution in the focal region of stratified media which is fast and easy to implement. Using this algorithm we study the effect on the electric field distribution of an air gap separating a solid immersion lens and a sample, where we analyse the maximum distance for out-of-contact operation. Also, we study how the presence of a metallic substrate affects the field distribution in the focal region; the interference effects of the reflected field could be used as an alternative for 4Pi-microscopy.

2001 Conference Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2001

The non-linear propagation of ultrasound in medical imaging has recently been exploited to improve image resolution and remove near field artifacts generated by overlying tissue structures. The images are formed using the second harmonic energy generated by nonlinear propagation. Second harmonic beams have narrower beam width and lower side lobes than the fundamental. The second harmonic draws energy from the fundamental continuously along the propagation path. These characteristics contribute to improve the quality of medical ultrasound images.

MATEC Web of Conferences, 2018

Here is proposed the method for synthesizing the sources of an acoustic field on the basis of an approximation of the phase screen. The technology of manufacturing ultrasonic phased arrays providing the formation of a field of a given distribution is proposed. An experimental setup has been developed for the formation of a vortex field at a distance of 10 cm.

A modified multi-element synthetic transmit aperture (MSTA) method for ultrasound imaging with RF echoes correction taking into account the influence of the element directivity is presented. The property is significant as the element width becomes commensurable with the wavelength of the emitted signal. The angular dependence of the radiation efficiency of the transmit/receive aperture is obtained from exact solution of the corresponding mixed boundary-value problem for periodic baffle system, modeling the transducer array. It is evaluated at the nominal frequency of the excitation signal and is implemented in the developed MSTA algorithm as apodization weights calculated for each imaging point and all combinations of the transmit/receive apertures. The performance of developed method is tested using FIELDII simulated synthetic aperture data of the point reflectors to estimate the visualization depth and lateral resolution. Besides, a FIELDII simulated and measurement data of cyst phantom are used for qualitative assessment of the imaging contrast. Comparison of the results obtained by the modified and conventional MSTA algorithms is given which reveals considerable improvement of the image quality in the area neighboring to the transducer's aperture, and increase of the visualization depth at the cost of slight degradation of lateral resolution near the transducer face.

2002 IEEE Ultrasonics Symposium, …, 2002

An approach for simulating non-linear ultrasound imaging using Field II has been implemented using the operator splitting approach, where diffraction, attenuation, and non-linear propagation can be handled individually. The method uses the Earnshaw/Poisson solution to Burgers' equation for the non-linear propagation. The speed of sound is calculated from the instantaneous pressure of the pulse and the nonlinearity B/A parameter of the medium. The harmonic field is found by introducing a number of virtual planes in front of the aperture and then propagating the pulse using Burgers' solution between the planes. Simulations on the acoustical axis of an array transducer were performed and compared to measurements made in a water tank. A 3 MHz convex array transducer with a pitch of 0.53 mm and a height of 13 mm was used. The electronic focus was at 45 mm and 16 elements were used for emission. The emitted pressure was 1.4 MPa measured 6 mm from the aperture by a Force Institute MH25-5 needle hydrophone in a water bath. The build-up of higher harmonics can here be predicted accurately up to the 5th harmonic. The second harmonic is simulated with an accuracy of ± 2.6 dB and the third harmonic with ± 2 dB compared to the water bath measurements. Point spread functions (PSFs) were also calculated and measured. They all showed that the second and third harmonic PSFs are narrower than for the first harmonic, with a good resemblance between the measured and simulated PSFs. The approach can also be extended to simulate non-linear ultrasound imaging in 3D using filters or pulse inversion for any kind of transducer, focusing, apodization, pulse emission and scattering phantom. This is done by first simulating the non-linear emitted field and assuming that the scattered field is weak and linear. The received signal is then the spatial impulse response in receive convolved with the emitted field at the given point.

Optics Express, 2011

We study focused fields which, for a given total power and a given numerical aperture, have maximum electric field amplitude in some direction in the focal point and are linearly polarized along this direction. It is shown that the optimum field is identical to the image of an electric dipole with unit magnification. In particular, the field which is the image of an electric dipole whose dipole vector is parallel to the optical axis, is identical to the field whose longitudinal component is maximum at the image point.

Optics Express, 2014

This paper presents and compares two basis systems, spherical harmonics and plane waves, for studying diverging and converging beams in an optical system. We show a similarity between a converging field and the time reversed field of a radiation field. We present and analyze the differences between the Debye-Wolf diffraction integral and the multipole theory for focusing of polarized light. The Debye-Wolf diffraction integral gives a well-known anomalous behavior on the optical axis and at the edge of the focused beam that can be avoided by using the multipole theory.