Parabolic Wavefront Research Articles

Oxygenation heterogeneity facilitates spatiotemporal flow pattern visualization inside human blood vessels using photoacoustic computed tomography

Hemodynamics can be explored through various biomedical imaging techniques. However, observing transient spatiotemporal variations in the saturation of oxygen (sO2) within human blood vessels proves challenging with conventional methods. In this study, we employed photoacoustic computed tomography (PACT) to reconstruct the evolving spatiotemporal patterns in a human vein. Through analysis of the multi-wavelength photoacoustic (PA) spectrum, we illustrated the dynamic distribution within blood vessels. Additionally, we computationally rendered the dynamic process of venous blood flowing into the major vein and entering a branching vessel. Notably, we successfully recovered, in real time, the parabolic wavefront profile of laminar flow inside a deep vein in vivo—a first-time achievement. While the study is preliminary, the demonstrated capability of dynamic sO2 imaging holds promise for new applications in biology and medicine.

Wavefront control of subcycle vortex pulses via carrier-envelope-phase tailoring

The carrier-envelope phase (CEP) of an ultrashort laser pulse is becoming more crucial to specify the temporal characteristic of the pulse’s electric field when the pulse duration becomes shorter and attains the subcycle regime; here, the pulse duration of the intensity envelope is shorter than one cycle period of the carrier field oscillation. When this subcycle pulse involves a structured wavefront as is contained in an optical vortex (OV) pulse, the CEP has an impact on not only the temporal but also the spatial characteristics owing to the spatiotemporal coupling in the structured optical pulse. However, the direct observation of the spatial effect of the CEP control has not yet been demonstrated. In this study, we report on the measurement and control of the spatial wavefront of a subcycle OV pulse by adjusting the CEP. To generate subcycle OV pulses, an optical parametric amplifier delivering subcycle Gaussian pulses and a Sagnac interferometer as a mode converter were integrated and provided an adequate spectral adaptability. The pulse duration of the generated OV pulse was 4.7 fs at a carrier wavelength of 1.54 µm. To confirm the wavefront control with the alteration of the CEP, we developed a novel f-2f interferometer that exhibited spiral fringes originating from the spatial interference between the subcycle OV pulse and the second harmonic of the subcycle Gaussian pulse producing a parabolic wavefront as a reference; this resulted in the successful observation of the rotation of spiral interference fringes during CEP manipulation.

Parabolic Wavefront Model for Line-of-Sight MIMO Channels

Motivated by the widespread adoption of the parabolic wavefront model for line-of-sight (LOS) multiple-input multiple-output (MIMO) communication, this paper presents a comprehensive analysis of this model’s validity and simple conditions that ensure its applicability. Then, with the model’s scope clearly delineated, the paper expounds a number of properties of the channel that results from applying it. Connections are drawn among these properties under the umbrella of a Fourier interpretation, and their significance to LOS MIMO communication is substantiated.

Electrically tunable gradient-index lenses via liquid crystals: beyond the power law.

In this study we present an investigation of electrically tunable progressive lenses utilizing liquid crystals (LC). We introduce a polarized progressive LC lens capable of dynamically adjusting its focal length, functioning as either a positive or negative lens. Our findings reveal that the spatial distribution of lens power within the progressive LC lens, ranging from +4D to -3D, far surpassing the range of -0.87D to +0.87D which one may expect within the parabolic wavefront approximation. For a lens with a 30 mm aperture a total tunable range is 7.6 D (from +5.6D to -2D) which is 4.75 times larger than the traditional parabolic prediction∼1.6D (from +0.8D to -0.8D). This study not only challenges conventional limitations set by optical phase differences in gradient-index LC lenses (the power law) but also ushers in a new possibility for ophthalmic applications. The profound insights and outcomes presented in this paper redefine the landscape of LC lenses, paving the way for transformative advancements in optics and beyond.

Non-Paraxial Effects in the Laser Beams Sharply Focused to Skin Revealed by Unidirectional Helmholtz Equation Approximation

Laser beams converging at significant focusing angles have diverse applications, including quartz-enhanced photoacoustic spectroscopy, high spatial resolution imaging, and profilometry. Due to the limited applicability of the paraxial approximation, which is valid solely for smooth focusing scenarios, numerical modeling becomes necessary to achieve optimal parameter optimization for imaging diagnostic systems that utilize converged laser beams. We introduce a novel methodology for the modeling of laser beams sharply focused on the turbid tissue-like scattering medium by employing the unidirectional Helmholtz equation approximation. The suggested modeling approach takes into account the intricate structure of biological tissues, showcasing its ability to effectively simulate a wide variety of random multi-layered media resembling tissue. By applying this methodology to the Gaussian-shaped laser beam with a parabolic wavefront, the prediction reveals the presence of two hotspots near the focus area. The close-to-maximal intensity hotspot area has a longitudinal size of about 3–5 μm and a transversal size of about 1–2 μm. These values are suitable for estimating spatial resolution in tissue imaging when employing sharply focused laser beams. The simulation also predicts a close-to-maximal intensity hotspot area with approximately 1 μm transversal and longitudinal sizes located just behind the focus distance for Bessel-shaped laser beams with a parabolic wavefront. The results of the simulation suggest that optical imaging methods utilizing laser beams with a wavefront produced by an axicon lens would exhibit a limited spatial resolution. The wavelength employed in the modeling studies to evaluate the sizes of the focus spot is selected within a range typical for optical coherence tomography, offering insights into the limitation of spatial resolution. The key advantage of the unidirectional Helmholtz equation approximation approach over the paraxial approximation lies in its capability to simulate the propagation of a laser beam with a non-parabolic wavefront.

Reconstruction of Talbot self-image using Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is used to merge a sequence of low-resolution Talbot images into a high-resolution image with a large field of view such that both integer and fractional Talbot lengths are clearly resolved. It is also revealed that the diffraction orders present in the dark field Fourier plane images reconstructed based on the Talbot effect i.e. the microscope’s back focal plane images are the ones responsible for rendering FPM amenable for the self-imaging phenomena. These diffraction spots have an arced-shaped diffraction patterns which are consistent with the Talbot image when illuminated with a parabolic wavefront. i.e. Gaussian sums only for the dark field images, and are crucial for FPM to successfully achieve a full complex image recovery. Herein, the Talbot image is treated as a phase-recovery problem, and further analyses are presented by comparing the performance of FPM when the periodic grating Talbot effect is imaged with other standard phase-recovery methods, namely the Fienup and Gercberg-Saxton algorithms.

Efficient calculation scheme for high pixel resolution non-hogel-based computer generated hologram from light field.

We propose a method that reduces the computation time and memory requirement in non-hogel-based hologram synthesis from light field data. The non-hogel-based technique synthesizes coherent complex field for a three-dimensional scene from its light field. Unlike conventional holographic stereogram, the non-hogel-based technique reconstructs continuous parabolic wavefront for individual three-dimensional object point by globally processing the light field. However, the global processing increases the computational load significantly, making it hard to synthesize holograms with high pixel resolution. The proposed technique reduces the computational burden by processing each two-dimensional angular frequency slice of the four-dimensional light field independently. Hologram tiling technique is also proposed to make the hologram synthesis process scalable. Using the hologram tiling and the angular-frequency-slice-based processing, 25K×25 K pixel resolution hologram was synthesized successfully.

Huygens principle: exact and approximate wavefronts propagated through conic lenses.

Exact and approximate formulae for refracted wavefronts through singlet lenses are obtained by considering an incident plane wavefront propagating along the optical axis. We provide two different approaches for the wavefronts approximated at the second order based on the Huygens principle and the Malus-Dupin theorem. We have in the first method found a way to use iterative wavelets instead of the usual evaluated integral to arrive at these formulae, showing a physical and mathematical correspondence between both methods. Finally, we introduce a parabolic wavefront into the irradiance transport equation in order to provide an analytical solution for the distribution of illumination.

Novel 3-D Non-Stationary Wideband Models for Massive MIMO Channels

In this paper, a novel 3-D non-stationary wideband geometry-based stochastic theoretical channel model for massive multiple-input multiple-output communication systems is proposed. First, a second-order approximation to the spherical wavefront in space and time domains, i.e., parabolic wavefront , is proposed to efficiently model near-field effects . Second, environment evolution effects are modeled by spatial-temporal cluster (re)appearance and shadowing processes. We propose (re)appearance processes to model the visibility of clusters with enhanced spatial-temporal consistency. Shadowing processes are used to capture smooth spatial-temporal variations of the clusters’ average power. In addition, a corresponding simulation model is derived along with a 3-D extension of the Riemann sum method for parameters computation. Key statistical properties of the proposed model, e.g., the spatial-temporal cross-correlation function, are derived and analyzed. Finally, we present numerical and simulation results showing an excellent agreement between the theoretical and simulation models and validating the proposed parameter computation method. The accuracy and flexibility of the proposed simulation model are demonstrated by comparing simulation results and measurements of the delay spread, slope of cluster power variations, and visibility regions’ size.

Propagation algorithms for Wigner functions

We propose an algorithm to remove a parabolic wavefront from a convergent or divergent beam in the Wigner function. Using this approach we numerically collimate the beam. This avoids a dense sampling in phase space to describe a convergent wavefront. Thereby we reduce the required computer memory, but maintain computational accuracy and physical effects. Furthermore, we compare two algorithms, shearing and Radon transform, to propagate the Wigner function in free space. We use the fast Fourier transform to accurately perform shearing. However, zero-padding is necessary to circumvent aliasing. We prove that the Radon transform is a more efficient approach for a long propagated distance.

Physical compensation of phase curvature in digital holographic microscopy by use of programmable liquid lens.

Quantitative phase measurements obtained with digital holographic microscopes are strongly dependent on the optical arrangement of the imaging system. The nontelecentric operation provides phase measurements affected by a parabolic phase factor and requires numerical postprocessing, which does not always remove all the perturbation. Accurate phase measurements are achieved by using the imaging system in telecentric mode. Unfortunately, this condition is not accomplished when a commercial microscope is used as the imaging system. In this paper, we present an approach for obtaining accurate phase measurements in nontelecentric imaging systems without the need for numerical postprocessing. The method uses an electrically tunable liquid lens to illuminate the sample so that the perturbing parabolic wavefront is cancelled out. Experimental holograms of a Fresnel lens and a section of the thorax of a Drosophila melanogaster fly are captured to verify the proposed method.

直视式合成孔径激光成像雷达电控抛物波面扫描器

直视式合成孔径激光成像雷达电控抛物波面扫描器

Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking

We have recently solved the inverse spectral problem for integrable partial differential equations (PDEs) in arbitrary dimensions arising as commutation of multidimensional vector fields depending on a spectral parameter λ. The associated inverse problem, in particular, can be formulated as a nonlinear Riemann–Hilbert (NRH) problem on a given contour of the complex λ plane. The most distinguished examples of integrable PDEs of this type, like the dispersionless Kadomtsev–Petviashivili (dKP), the heavenly and the two-dimensional dispersionless Toda equations, are real PDEs associated with Hamiltonian vector fields. The corresponding NRH data satisfy suitable reality and symplectic constraints. In this paper, generalizing the examples of solvable NRH problems illustrated in Manakov and Santini (2009 J. Phys. A: Math. Theor. 42 095203; 2008 J. Phys. A: Math. Theor. 41 055204; 2009 J. Phys. A: Math. Theor. 42 404013), we present a general procedure to construct solvable NRH problems for integrable real PDEs associated with Hamiltonian vector fields, allowing one to construct exact implicit solutions of such PDEs parametrized by an arbitrary number of real functions of a single variable. Then, we illustrate this theory on few distinguished examples for the dKP and heavenly equations. For the dKP case, we characterize a class of similarity solutions, of solutions constant on their parabolic wave front and breaking simultaneously on it, of localized solutions whose breaking point travels with constant speed along the wave front, and of localized solutions breaking in a point of the (x, y) plane. For the heavenly equation, we characterize two classes of symmetry reductions.

Detailed structure of fs pulses passing through straight and tapered optical waveguides

The detailed structure of the field distribution in an arbitrary femtosecond pulse passing through straight and tapered optical waveguides is found using the scalar diffraction theory and the method of images. It is shown that the wave propagates down the guide as the superposition of many pulses that diffract in the off-axis direction and interfere with each other. For the straight multimode guide the usual result is recovered; the spatial profile of the wave is undistorted along its path of propagation provided the input pulse is mode matched. In the case of the tapered guide excited by the 10-fs pulse, which propagates in the off-axis direction and has the parabolic field distribution and spherical wavefront, the new phenomenon is manifested by the appearance of the sub-fs pulse inside the guide.

The eikonal approximation to excitable reaction-diffusion systems: travelling non-planar wave fronts on the plane

Exact, non-planar travelling solutions of the eikonal equation on an infinite plane are presented for the first time. These solutions are matched to produce corrugated wave fronts and patterns such as ‘spot’ solutions as well as extended parabolic type wave fronts. The stability of these solutions is also analysed. The variational equation which belongs to a generalised Wangerin class of differential equations is solved, first with the aid of the Liouville-Green approximation for the estimated eigenvalues characterising stability and then by a more elaborate shooting-matching method. All of the three types of travelling solutions are found to be geometrically stable. It is suggested that some of these predictions are experimentally testable.

A theory of distortion of the reaction zone

A cylindrical detonating explosive behaves like a non-Newtonian viscous fluid emerging from a cylindrical pipe. The expression for non-Newtonian viscous flow has been applied to detonating explosives. The resultant fit to emerging flame fronts from detonation is excellent for a wide variety of detonating explosives both for transients (at various times) and for steady state. The quantities k'(lambda/lambda(1))(2/B) and 1/B and the rate constant k' increase abruptly at a time supporting a change in mechanism from deflagration to detonation in the transient during initiation. All of these parameters are temperature sensitive, indicating an abrupt temperature increase as a condition or indicator in the deflagration-to-detonation transition. Furthermore, a straight line results when log particle velocity u is plotted against log radial distance r, indicating that, for the explosives studied, the hyperbolic cosine wave front can be replaced by a parabolic wave front within the accuracy of the available experimental data.

Interferometric Testing of Large Optical Components with Circular Computer Holograms

In testing a large aspheric mirror such as a paraboloid, one uses as interferometric reference a small spherical mirror together with a test glass. The combination of mirror and test glass produces a parabolic wavefront for comparison. Recently holograms have been used as synthetic test glasses. The average fringe distance of the grating-like holograms has to be fine enough if separation of the diffraction orders is required. We propose to use holograms with circular fringes. Now the different diffraction orders come to focus at different locations on the optical axis, where all but one order can be eliminated. This is easily possible, since the waves coming from a mirror with a central hole are hollow cones. Several ways for making these computer-generated circular holograms are suggested.

Convolution Formulation of Fresnel Diffraction*

A convolution formulation of Fresnel diffraction is presented. The diffracted amplitude is expressed as a convolution in either direct or reciprocal space. Approximations involve the use of parabolic wavefronts and the omission of the obliquity factor. The formulation is readily applied to many optical phenomena.A theory of Fresnel transforms is given. The Fresnel transforms are expressed as a convolution in either direct or reciprocal space. Two examples of their use are given.