Ultrasound Doppler System's Resolution Using Coherent Plane-Wave Compounding Technique

Three plane waves in two dimensions or four plane waves in three dimensions interfere to produce patterns of amplitude and phase. If there is a rational relation between the wavevectors, both patterns repeat on a lattice, but the unit cell for amplitude (modulus of the complex wavefunction) is smaller than that for phase. Although the symmetry of the amplitude pattern is describable by the usual space groups, this is not so for the phase pattern, which requires colours to characterize it. An example is given that needs five colours, but, in general, the number needed is unlimited.

We propose a color CCD crosstalk elimination method based on the interference of plane waves. This method only requires capturing one hologram to determine the crosstalk matrix, and improving the calculation accuracy.

Optical target recognition using correlators is an important technique for fast verification and identification of images. The hybrid opto-electronic correlator (HOC) recently proposed by us bypasses the need for nonlinear materials such as photorefractive polymer films by using detectors instead, and the phase information is yet conserved by the interference of plane waves with the images. In this paper, we demonstrate experimentally the basic working principle of the HOC architecture using currently available technologies. For matched reference and query images, the output signal shows a sharp peak, indicating a match is found. For an unmatched case, a much lower peak value is observed, indicating no match. We also demonstrate the dependence of the output signal on the phases of the interfering plane waves and describe a technique using an interferometer and a servo for optimizing the output signal. As such, the work reported here paves the way for further development of the HOC for practical applications.

As three-plane waves are the minimum number required for the formation of vortex-embedded lattice structures by plane wave interference, we present our experimental investigation on the formation of complex 3D photonic vortex lattice structures by a designed superposition of multiples of phase-engineered three-plane waves. The unfolding of the generated complex photonic lattice structures with higher order helical phase is realized by perturbing the superposition of a relatively phase-encoded, axially equidistant multiple of three noncoplanar plane waves. Through a programmable spatial light modulator assisted single step fabrication approach, the unfolded 3D vortex lattice structures are experimentally realized, well matched to our computer simulations. The formation of higher order intertwined helices embedded in these 3D spiraling vortex lattice structures by the superposition of the multiples of phase-engineered three-plane waves interference is also studied.

SUMMARY Properties of homogeneous and inhomogeneous plane waves propagating in an unbounded viscoelastic anisotropic medium in an arbitrarily specified direction N are studied analytically. The method used for their calculation is based on the so-called mixed specification of the slowness vector. It is quite universal and can be applied to homogeneous and inhomogeneous plane waves propagating in perfectly elastic or viscoelastic, isotropic or anisotropic media. The method leads to the solution of a complex-valued algebraic equation of the sixth degree. Standard methods can be used to solve the algebraic equation. Once the solution has been found, the phase velocities, exponential decays of amplitudes, attenuation angles, polarization vectors, etc., of P, S1 and S2 plane waves, propagating along and against N, can be easily determined. Although the method can be used for an unrestricted anisotropy, a special case of P, SV and SH plane waves, propagating in a plane of symmetry of a monoclinic (orthorhombic, hexagonal) viscoelastic medium is discussed in greater detail. In this plane the waves can be studied as functions of propagation direction N and of the real-valued inhomogeneity parameter D .F or inhomogeneous plane waves, D �= 0, and for homogeneous plane waves, D = 0. The use of the inhomogeneity parameter D offers many advantages in comparison with the conventionally used attenuation angle γ .I nthe N, D domain, any combination of N and D is physically acceptable. This is, however, not the case in the N, γ domain, where certain combinations of N and γ yield non-physical solutions. Another advantage of the use of inhomogeneity parameter D is the simplicity and universality of the algorithms in the N, D domain. Combined effects of attenuation and anisotropy, not known in viscoelastic isotropic media or purely elastic anisotropic media, are studied. It is shown that, in anisotropic viscoelastic media, the slowness vector and the related quantities are not symmetrical with respect to D = 0a s inisotropic viscoelastic media. The phase velocity of an inhomogeneous plane wave may be higher than the phase velocity of the relevant homogeneous plane wave, propagating in the same direction N. Similarly, the modulus of the attenuation vector of an inhomogeneous plane wave may be lower than that for the relevant homogeneous plane wave. The amplitudes of inhomogeneous plane waves in anisotropic viscoelastic media may increase exponentially in the direction of propagation N for certain D. The attenuation angle γ cannot exceed its boundary value, γ ∗ . The boundary attenuation angle γ ∗ is, in general, different from 90 ◦ , and depends both on the direction of propagation N and on the sign of the inhomogeneity parameter D. The polarization of P and SV plane waves is, in general, elliptical, both for homogeneous and inhomogeneous waves. Simple quantitative expressions or estimates for all these effects (and for many others) are presented. The results of the numerical treatment are presented in a companion paper (Paper II, this issue).

The pulsed field of a circular ultrasonic transducer can be described as the interaction of its two components: plane waves, radiated from the whole face of the transducer, and edge waves, radiated from its edge. The diffraction in the acoustic field can be modeled as the result of the interference of edge and plane waves and defines the near field (characterized by pressure maxima and minima) and far field regions of the acoustic field1,2. KeywordsField MappingDirectivity FunctionPoling FieldUltrasound TransducerEdge WaveThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Partial results are given on a conjecture in inverse scattering theory concerning the interference of two-dimensional plane waves. The conjecture states that an odd number of plane waves of the same frequency can only cancel each other at isolated points and not along a simple continuous curve. It is partially confirmed here for curves which are nearly flat at some point. An analysis is also made for various possible nodes for an even number of plane waves.

One of the most challenging intraoperative dilemmas continues to be determination of viability of ischemic bowel. Many techniques and devices are available to help the surgeon, probably the most useful of which is the ultrasound Doppler. A more recently developed system, the laser Doppler, has a flexible optical fiber and fine tip probe that can be approximated onto or endoscopically passed into the gastrointestinal tract. This study was undertaken to experimentally compare the He Ne laser and ultrasound Doppler systems in predicting viability of ischemic canine intestine. Twenty ischemic bowel zones were created in dogs by division of the mesenteric blood supply. Determination of the last site of antimesenteric serosal nor fusion was then marked with each Doppler. Additionally, the fine tip probe was endoscopically passed across the ischemic zone and mucosal perfusion determined. Thus, each zone was marked three times, each indicating the anticipated site of necrosis by each method. The animals were killed 24 hours later and the tissues studied histologically. The results demonstrated that both the serosally applied and endoscopically placed laser Doppler were closer to predicting the point of total transmural necrosis. The possible clinical advantage of this device in prevention of short gun syndromes is readily apparent. The additional asset of a flexible optical fiber than can be endoscopically or laparoscopically passed make it an even more attractive modality. The findings of this study attested to the superior sensitivity, ease of use, and objectivity of the laser Doppler when compared with the ultrasound system.

Improving Performance of Pulse Compression in a Doppler Ultrasound System Using Amplitude Modulated Chirps and Wiener Filtering

A high-frequency pulsed-wave Doppler ultrasound system for the detection and imaging of blood flow in the microcirculation

Previous work with a 40 MHz continuous-wave Doppler ultrasound system has demonstrated the potential of high frequency Doppler ultrasound (HFD) operating in the frequency range 20 to 100 MHz to detect blood flow in the microcirculation. This paper describes a directional, pulsed-wave Doppler ultrasound (PW HFD) system designed and constructed to further investigate this potential. The PW HFD system electronics have a dynamic range of 80 dB, a noise floor of 250 nV, a directional isolation of 45 dB and operate over the frequency range 1 to 200 MHz. Tests of the system with a focused 50 MHz PVDF transducer, string phantom and in vivo tissue have demonstrated that the PW HFD system is capable of detecting and measuring velocities on the order of 0.5 mm/s with suitable velocity and temporal resolutions and can detect and measure in vivo blood velocities of less than 5 mm/s in arterioles with diameters as small as 20 /spl mu/m and venules as small as 35 /spl mu/m. Preliminary experiments with high frequency colour Doppler (HFCD) and high frequency power Doppler (HFPD) flow imaging are also presented.

Laser beam shaping is an active discipline in optics owing to its importance to both illumination and detection processes. The formation of single or multiple optical vortices in a laser beam has taken on recent interest in areas ranging from electron and atom optics to astronomy. Here we describe our efforts to create localized vortex cores using only the interference of several laser beams with Gaussian profile, a method that may be particularly suited to the application of vortex modes to intense femtosecond laser pulses. For many years the study of optical vortex formation has been of interest as a problem in itself and one typical of many linear and nonlinear optical phenomena (Nye et al., 1988) such as the formation of speckles, the appearance of solitons, operation of laser and photorefractive oscillators in transverse modes, the self-action of the laser oscillation in nonlinear media (Swartzlander, Jr. & Law, 1992; Kreminskaya et al., 1995); creation of optical vortices in femtosecond pulses (I. Mariyenko et al., 2005); investigation of atomic vortex beams in focal regions (Helseth, 2004), etc. The investigation and explanation of the pattern formation by different optical systems was activated for recent years (Karman et al., 1997; Brambilla et al.,1991); efficient generation of optical vortices by a kinoform-type spiral phase plate (Moh et al., 2006; Kim et al., 1997). These two apparently different problems of pattern formation and vortex formation are the manifestation of the same phenomenon, which we explain by interference of many plane waves (Angelski et al., 1997; Kreminskaya et al., 1999; Masajada & Dubik, 2001). An optical vortex (or screw dislocation, phase defect or singularity) is defined as the locus of zero intensity accompanied by a jump of phase on ±2πm radians, occurring during a roundtrip (Nye & Berry, 1974; Basistiy et al., 1995; Abramochkin & Volostnikov; 1993). The integer m is the topological charge, the sign corresponds to the direction of the phase growth: “+” to counterclockwise and “-“to clockwise. In the transversal cross-section, the optical vortex reveals itself as a point, in the 3-D space it exists along the line. A doughnut mode of laser beam is the example of optical vortex. Other member of optical dislocations family is the edge dislocation. The phase changes here by π radians. The shape of the edge dislocation is a line in the transversal cross-section and a plane in 3-D space. Interference pattern of the Young’s experiment is the example of the edge dislocation. For the complex amplitude of the light, the condition of the zero intensity means simultaneous zero of the real and imaginary parts of the complex amplitude.

We present computational results for generation of first order screw dislocation by the interference of non-uniformly distributed plane waves. Non-uniform distribution of waves is in the form of spiral with increasing angle between them.

The new method of topological charge determination of optical vortices in the interference field of the optical vortex interferometer

We present a method for manipulating individual sites in a 2-D optical lattice that enables the creation of defects within otherwise periodic light patterns. The modified optical lattice is created by interference of plane waves and spiral phase waves. Spiral phase modulation creates an optical vortex that is well suited for addressing single rows of the optical lattice owing to the localized wrap of the phase front. Local fringes can be split, annihilated, or have their size tuned by controlling the charge and location of the vortex cores. These properties provide a connection between dislocations in crystals, waves, and optical lattices.