Smooth Wavefront Research Articles

Unfocused Field Analysis of a Density-Tapered Spiral Array for High-Volume-Rate 3-D Ultrasound Imaging.

Spiral array transducers with a sparse 2-D aperture have demonstrated their potential in realizing 3-D ultrasound imaging with reduced data rates. Nevertheless, their feasibility in high-volume-rate imaging based on unfocused transmissions has yet to be established. From a metrology standpoint, it is essential to characterize the acoustic field of unfocused transmissions from spiral arrays not only to assess their safety but also to identify the root cause of imaging irregularities due to the array's sparse aperture. Here, we present a field profile analysis of unfocused transmissions from a density-tapered spiral array transducer (256 hexagonal elements, 220- [Formula: see text] element diameter, and 1-cm aperture diameter) through both simulations and hydrophone measurements. We investigated plane- and diverging-wave transmissions (five-cycle, 7.5-MHz pulses) from 0° to 10° steering for their beam intensity characteristics and wavefront arrival time profiles. Unfocused firings were also tested for B-mode imaging performance (ten compounded angles, -5° to 5° span). The array was found to produce unfocused transmissions with a peak negative pressure of 93.9 kPa at 2 cm depth. All transmissions steered up to 5° were free of secondary lobes within 12 dB of the main beam peak intensity. All wavefront arrival time profiles were found to closely match the expected profiles with maximum root-mean-squared errors of [Formula: see text] for plane wave (PW) and [Formula: see text] for diverging wave. The B-mode images showed good spatial resolution with a penetration depth of 22 mm in PW imaging. Overall, these results demonstrate that the density-tapered spiral array can facilitate unfocused transmissions below regulatory limits (mechanical index: 0.034; spatial-peak, pulse-average intensity: 0.298 W/cm2) and with suppressed secondary lobes while maintaining smooth wavefronts.

Enhanced fixed plane phase retrieval using wavelength-to-distance transformation and unordered propagations

Stagnation errors in iterative smooth object wavefront reconstruction occur because of insufficient intensity variation despite employing experimental methods that increase intensity variation such as the use of multiple illumination wavelengths. In this study, an algorithmic technique for optimized multiple wavelength phase retrieval that uses wavelength-to-distance transformation and unordered wave propagations sequence is demonstrated. Simulations show that the technique significantly accelerates the reconstruction compared to conventional methods based on sequential propagations. The number and tuning range (or spacing) of the illumination wavelengths are also optimized resulting in the enhanced reconstruction of the test object waves used. The main advantage of the technique is the reduced number of illumination wavelengths needed for enhanced object wave reconstruction.

Refracting and reflecting interfaces transforming a given wavefront into another one

The aim of this work is threefold. First, following Luneburg and using our own notation, we review the Cartesian ovals. Second, we obtain analytical expressions for the reflecting and refracting surfaces that transform a prescribed smooth two-dimensional wavefront into a spherical one. These results are applied to show that the reflecting surface that connects a plane wavefront to a spherical one is a parabolical surface, and we design a lens, with two freeform surfaces, that transforms a spherical wavefront into another spherical one. These examples show that our equations provide the well-known solution for these problems, which is given by the Cartesian ovals method. Third, we present a procedure to obtain exact expressions for the refracting and reflecting surfaces that connect two given arbitrary wavefronts; that is, by assuming that the optical path length between two points on the prescribed wavefronts is given by the designer the refracting and reflecting surfaces we are looking for are determined by a set of two algebraic equations, which in the general case have to be solved in a numerical way. These general results are applied to compute the analytical expressions for the reflecting and refracting surfaces that transform a parabolical initial wavefront into a plane one.

Freeform surface for light shaping by iterative design via Fourier domain.

We extend our previous work [Yang et al., Opt. Express29, 3621 (2021)10.1364/OE.415649] and propose an iterative algorithm to design a freeform surface for far-field light shaping. The algorithm alternately performs a wavefront phase design step and a freeform surface construction step. The smooth wavefront phase is designed by the mapping-type Fourier pair synthesis method, and the freeform surface is constructed by using the obtained wavefront phase. The algorithm provides a solid approach that ensures the introduction of the required wavefront phase manipulation for light shaping. Moreover, the related physical effects such as the Fresnel effect and polarization effect are included in the algorithm. We demonstrate the flexibility of the algorithm by examples.

Smooth multifocal wavefronts with a prescribed mean curvature for visual optics applications.

Multifocal lenses comprising progressive power surfaces are commonly used in contact and intraocular lens designs. Given a visual performance metric, a wavefront engineering approach to design such lenses is based on searching for the optimal wavefront at the exit pupil of the eye. Multifocal wavefronts distribute the energy along the different foci thanks to having a varying mean curvature. Therefore, a fundamental step in the wavefront engineering approach is to generate the wavefront from a prescribed mean curvature function. Conventionally, such a thing is done by superimposing spherical wavefront patches and maybe adding a certain component of spherical aberration to each spherical patch in order to increase the depth-of-field associated with each focus. However, such a procedure does not lead to smooth wavefront solutions and also restricts the type of available multifocal wavefronts. We derive a new, to the best of our knowledge, mathematical method to uniquely construct multifocal wavefronts from mean curvature functions (depending on radial and angular coordinates) under certain numerically justified approximations and restrictions. Additionally, our procedure leads to a particular family of wavefronts (line-umbilical multifocal wavefronts) described by 2 conditions: (1) to be smooth multiplicative separable functions in the radial and angular coordinates; (2) to be umbilical along a specific segment connecting the circle center with its edge. We provide several examples of multifocal wavefronts belonging to this family, including a smooth variant of the so-called light sword element.

Traveling wavefronts for density‐dependent diffusion reaction convection equation with time delay

We are concerned with the existence of traveling waves for density‐dependent diffusion reaction nonlinear convection equations with small time delay. We first study the existence and uniqueness of smooth and sharp‐type traveling wavefront solution of the wave speed c ≥ c∗ for equation without time delay, where c∗ is the minimal wave speed. Meanwhile, we construct a variational principle for c∗ from which the upper bound of c∗ is determined, while the lower bound of c∗ is attained by using the phase plane analysis. Then, we obtain the existence of smooth traveling wavefront solution for equation with small time delay for c > c∗ by applying the perturbation method and implicit function theorem.

On Christoffel roots for nondetached slowness surfaces

ABSTRACTThe only restriction on the values of the elasticity parameters is the stability condition. Within this condition, we examine the Christoffel equation for nondetached qP slowness surfaces in transversely isotropic media. If the qP slowness surface is detached, each root of the solubility condition corresponds to a distinct smooth wavefront. If the qP slowness surface is nondetached, the roots are elliptical but do not correspond to distinct wavefronts; also, the qP and qSV slowness surfaces are not smooth.

Stabilizing effects of oxidation on propagating formation reactions occurring in nanometer-scale metal multilayers

Reactive rare-earth/transition metal multilayers exhibit a variety of complex reaction behaviors depending on surrounding gaseous environment and material design. Small period (< 100 nm bilayer), 5 μm-thick Sc/Ag multilayers undergo self-sustained formation reactions when ignited in air or in vacuum. High-speed videography reveals unstable reaction waves in these samples, characterized by the repeated, transverse passage of narrow, spin bands. Intermediate Sc/Ag designs – with multilayer period between 100 and 200 nm – only react in air. These multilayers exhibit propagating reactions with alternating unstable and stable characteristics. Narrow, spin bands advance the reaction front stepwise. Soon after the passage of a transverse band, a trailing oxidation wave encroaches on the intermetallic reaction front temporarily pushing the stalled wave forward in a uniform manner. Viewed in full, these events repeat giving rise to a new oscillatory behavior. Sc/Ag multilayers having a large period (> 200 nm bilayer) also react exclusively in air but exhibit a different propagating mode. The oxidation of Sc combined with the exothermic reaction of metal species results in continually-stable waves characterized by a smooth wavefront morphology and uniform velocity. The flame temperatures associated with propagating waves are estimated using measured heats of reaction and enthalpy-temperature relationships in order to provide insight into the possible phase transformations that occur during these different exothermic reactions.

Decomposition of a field with smooth wavefront into a set of Gaussian beams with non-zero curvatures.

Decomposition of a general arbitrary field into a set of Gaussian beams has been one of the challenges in the Gaussian beam decomposition method for field propagation through optical systems. The most commonly used method in this regard is the Gabor expansion, which decomposes initial fields into shifted and rotated Gaussian beams in a plane. Since the Gaussian beams used have zero initial curvatures, the Gabor expansion method does not utilize the ability of the Gaussian beams to represent the quadratic behavior of the local wavefront. In this paper, we describe an alternative method of decomposing an arbitrary field with smooth wavefront into a set of Gaussian beams with non-zero initial curvatures. The individual Gaussian beams are used to represent up to the quadratic term in the Taylor expansion of the local wavefront. This significantly reduces the number of Gaussian beams required for the decomposition of the field with smooth wavefront and gives more accurate decomposition results. The proposed method directly gives the five ray sets representing the parabasal Gaussian beams, which can then be directly used for propagation of the Gaussian beams through optical systems. To demonstrate the application of the method, we have presented results for the decomposition of fields with strongly curved spherical wavefronts, a cone shaped wavefront, and a wavefront with large spherical aberration. The numerical comparison of the input field with the field reconstructed after the decomposition shows very good agreement in both amplitude and phase profiles. We also show results for the far field intensity distributions of the decomposed wavefronts by propagating in free space using the Gaussian beam propagation method.

Mutual transformations of fractional-order and integer-order optical vortices

We consider the problem of singular beams in optics as a part of the general questions of interactions, shaping and transformations of vortex states with fractional topological charges in physics, in particular, in hydrodynamic and quantum mechanic. Starting from the representation of the fractional-order vortex states as a superposition of infinite number of integer-order vortices with distinctive energy distributions (the vortex spectra) we showed that the smooth wave front of the fractional vortex beam can either decay into an asymmetric array of integer-order vortices or, vice versa, the array of optical vortices can be gathered together forming a smooth wave front with a helicoid-shaped phase distribution under propagation in free space. We revealed that a simple superposition of a finite number of the fractional-order vortex beams enables us to shape symmetric singular beams with the integer-order vortices of the desired topological charges.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

On Traveling Wave Fronts in a Degenerate Nonlinear Parabolic System Modeling Bacterial Pattern Formation

In this paper we consider a degenerate nonlinear parabolic system which models spatio-temporal patterns generated by bacterial colonies. A three-dimensional phase space analysis of wave fronts in this model system is performed. The existence of a sharp wave front for a minimum speed in addition to smooth wave fronts for large speeds is shown. Further, an accurate numerical computation of such wave front solutions is presented.

Enhanced intensity variation for multiple-plane phase retrieval using a spatial light modulator as a convenient tunable diffuser.

In the multiple-plane phase retrieval method, a tedious-to-fabricate phase diffuser plate is used to increase the axial intensity variation for a nonstagnating iterative reconstruction of a smooth object wavefront. Here we show that a spatial light modulator (SLM) can be used as an easily controllable diffuser for phase retrieval. The polarization modulation at the SLM facilitates independent formation of orthogonally polarized scattered and specularly reflected beams. Through an analyzer, the polarization states are filtered enabling beam interference, thereby efficiently encoding the phase information in the axially diverse speckle intensity measurements. The technique is described using wave propagation and Jones calculus, and demonstrated experimentally on technical and biological samples.

Computational hydrodynamics and optical performance of inductively-coupled plasma adaptive lenses

This study addresses the optical performance of a plasma adaptive lens for aero-optical applications by using both axisymmetric and three-dimensional numerical simulations. Plasma adaptive lenses are based on the effects of free electrons on the phase velocity of incident light, which, in theory, can be used as a phase-conjugation mechanism. A closed cylindrical chamber filled with Argon plasma is used as a model lens into which a beam of light is launched. The plasma is sustained by applying a radio-frequency electric current through a coil that envelops the chamber. Four different operating conditions, ranging from low to high powers and induction frequencies, are employed in the simulations. The numerical simulations reveal complex hydrodynamic phenomena related to buoyant and electromagnetic laminar transport, which generate, respectively, large recirculating cells and wall-normal compression stresses in the form of local stagnation-point flows. In the axisymmetric simulations, the plasma motion is coupled with near-wall axial striations in the electron-density field, some of which propagate in the form of low-frequency traveling disturbances adjacent to vortical quadrupoles that are reminiscent of Taylor-Gortler flow structures in centrifugally unstable flows. Although the refractive-index fields obtained from axisymmetric simulations lead to smooth beam wavefronts, they are found to be unstable to azimuthal disturbances in three of the four three-dimensional cases considered. The azimuthal striations are optically detrimental, since they produce high-order angular aberrations that account for most of the beam wavefront error. A fourth case is computed at high input power and high induction frequency, which displays the best optical properties among all the three-dimensional simulations considered. In particular, the increase in induction frequency prevents local thermalization and leads to an axisymmetric distribution of electrons even after introduction of spatial disturbances. The results highlight the importance of accounting for spatial effects in the numerical computations when optical analyses of plasma lenses are pursued in this range of operating conditions.

Wavefront watermarking of technical and biological samples using digital random phase modulation and phase retrieval

A technique for digital watermarking of smooth object wavefronts using digital random phase modulation and multiple-plane iterative phase retrieval is demonstrated experimentally. A complex-valued watermark is first encrypted using two random phase masks of known distributions before being superposed onto a set of host wavefront intensity patterns. Encryption scaling factor and depth of randomization of the masks are optimized such that the amplitude and phase watermarks are decrypted successfully and are not distorting the host wavefront. Given that the watermarked intensity patterns and the numerous decryption keys are available (i.e. distances between recording planes, light source wavelength, pixel size, random phase masks and their distances to the planes are all known), increasing the number of watermarked patterns used results in enhanced quality of decrypted watermarks. The main advantage of wavefront watermarking via the phase retrieval approach compared to the holographic approach is the avoidance of reference wave-induced aberration. Watermarking of wavefronts from lenses and unstained human cheek cells demonstrate the effectiveness of the technique.

Enhanced deterministic phase retrieval using a partially developed speckle field

A technique for enhanced deterministic phase retrieval using a partially developed speckle field (PDSF) and a spatial light modulator (SLM) is demonstrated experimentally. A smooth test wavefront impinges on a phase diffuser, forming a PDSF that is directed to a 4f setup. Two defocused speckle intensity measurements are recorded at the output plane corresponding to axially-propagated representations of the PDSF in the input plane. The speckle intensity measurements are then used in a conventional transport of intensity equation (TIE) to reconstruct directly the test wavefront. The PDSF in our technique increases the dynamic range of the axial intensity derivative for smooth phase objects, resulting in a more robust solution to the TIE. The SLM setup enables a fast and accurate recording of speckle intensity. Experimental results are in good agreement with those obtained using the iterative phase retrieval and digital holographic methods of wavefront reconstruction.

Investigation of smooth wave fronts using SLM-based phase retrieval and a phase diffuser

A phase retrieval technique using a spatial light modulator (SLM) and a phase diffuser for a fast reconstruction of smooth wave fronts is demonstrated experimentally. Diffuse illumination of a smooth test object with the aid of a phase diffuser (maximum phase shift, Δø = 0.85π) results in a significant diversity in the intensity measurements which, in turn, is beneficial for a non-stagnating iterative phase reconstruction. The use of the SLM enables accurate and fast speckle intensity recording and active correction of misalignments in the setup. The effectiveness of the technique is demonstrated in the optical testing of lenses.

Dynamics of a “collective” bubble in a magma melt flow behind the decompression wave front

Specific features of the dynamics of the wave field structure and growth of a “collective” bubble behind the decompression wave front in the “Lagrangian” section of the formed cavitation zone are numerically analyzed. Two cases are considered: with no diffusion of the dissolved gas from the melt to cavitation nuclei and with the diffusion flux providing an increase in the gas mass in the bubbles. In the first case, it is shown that an almost smooth decompression wave front approximately 100 m wide is formed, with minor perturbations that appear when the front of saturation of the cavitation zone with nuclei is passed. In the case of the diffusion process, the melt state behind the saturation front is principally different: jumps in mass velocity and viscosity are observed in the vicinity of the free surface, and the pressure in the “collective” cavitation bubble remains unchanged for a sufficiently long time interval, despite the bubble growth and intense diffusion of the gas from the melt. It is assumed that the diffusion process (and, therefore, viscosity) actually become factors determining the dynamics of growth of cavitation bubbles beginning from this time interval. A pressure jump is demonstrated to form near the free surface.

On Traveling Wave Fronts in a Bacterial Growth Model with Density-Dependent Diffusion and Chemotaxis

Bacterial colonies often generate patterns that are characterized by fingerlike projections growing out of the propagating front. In this paper, we analyze the traveling wave fronts in bacterial growth model that accounts for chemotactic movement as well as random motion in density-dependent diffusion. Specifically, the existence of traveling wave solutions to model equations is examined by means of methods of local linear and nonlinear analysis, and numerical simulations. The occurrence is shown of both sharp and smooth traveling wave fronts.

219403 矩形断面を有するベンド内におけるデトネーション波の伝播挙動(OS13 安全に寄与する熱工学2,オーガナイズド・セッション)

The detonation propagation phenomenon in a bend has not yet been sufficiently understood due to its complexity. In order to examine the detonation propagation in a bend, the detonation waves of a stoichiometric ethylene/oxygen mixture gas propagating through rectangular cross-section bends with different inner radii are visualized. The cell structure and wave front shape of the detonation are observed simultaneously using a new visualization technique developed in the present study. The ratio of inner radius of bend (r_i) to detonation cell width (λ) is an important factor determining the detonation propagation characteristics in the bends. The detonation propagation mode transitions from unstable to stable in the range 20 &le; r_i/λ &le; 33. The cell structure and smooth wave front of the detonation can be sustained in the stable propagation, however large-scale collapse of the cell structure and fluctuation of the detonation wave front shape are observed in the unstable propagation.