Showing papers on "Bessel function published in 2013"
TL;DR: The results reveal that light-sheets generated by pulsed near-infrared Bessel beams and two photon excitation provide the best image resolution, contrast at both a minimum amount of artifacts and signal degradation along the propagation of the beam into the sample.
Abstract: In this study we show that it is possible to successfully combine the benefits of light-sheet microscopy, self-reconstructing Bessel beams and two-photon fluorescence excitation to improve imaging in large, scattering media such as cancer cell clusters. We achieved a nearly two-fold increase in axial image resolution and 5–10 fold increase in contrast relative to linear excitation with Bessel beams. The light-sheet penetration depth could be increased by a factor of 3–5 relative to linear excitation with Gaussian beams. These finding arise from both experiments and computer simulations. In addition, we provide a theoretical description of how these results are composed. We investigated the change of image quality along the propagation direction of the illumination beams both for clusters of spheres and tumor multicellular spheroids. The results reveal that light-sheets generated by pulsed near-infrared Bessel beams and two photon excitation provide the best image resolution, contrast at both a minimum amount of artifacts and signal degradation along the propagation of the beam into the sample.
171 citations
TL;DR: Since nondiffracting modes with circular polarizations possessing different orbital angular momenta are able to encode, it is suggested these modes will be of interest in optical trapping, microscopy, and optical communication.
Abstract: Nondiffracting vector Bessel beams are of considerable interest due to their nondiffracting nature and unique high-numerical-aperture focusing properties. Here we demonstrate their creation by a simple procedure requiring only a spatial light modulator and an azimuthally varying birefringent plate, known as a q-plate. We extend our control of both the geometric and dynamic phases to perform a polarization and modal decomposition on the vector field. We study both single-charged Bessel beams as well as superpositions and find good agreement with theory. Since we are able to encode nondiffracting modes with circular polarizations possessing different orbital angular momenta, we suggest these modes will be of interest in optical trapping, microscopy, and optical communication.
83 citations
TL;DR: In this article, the authors proposed the use of two-dimensional antenna arrays as realizable launchers for quasi-optical applications, and the optimal excitation function for such arrays greatly departs from the Bessel one.
Abstract: Bessel beams are proposed as a practical way to generate well collimated and confined beams at mm-waves or THz for quasi-optical applications. To achieve that, we propose the use of two-dimensional antenna arrays as realizable launchers. Truncated Bessel beams with a main lobe width of few wavelengths $(\lambda)$ can propagate over several hundreds of $\lambda$ if the antenna aperture is electrically large. Because such a large aperture would require a large number of antenna elements, sub-sampling distributions are proposed in this work. It is found that arrays with spacings of approximately $4\lambda$ generate high quality beams with very low amplitude oscillations over distances of about $300\lambda$ in vacuum. The optimal excitation function for such arrays greatly departs from the Bessel one. It is synthesized with an analytical method based on a least mean square error minimization. The synthesis method is scalar, but the pseudo-Bessel beams obtained are vectorial and linearly polarized. Theoretical predictions are confirmed by full-wave simulations using Ansoft Designer.
82 citations
TL;DR: This Fourier-Bessel-based PCA detects more meaningful eigenimages and has improved denoising capability compared to traditional PCA for a finite number of noisy images.
Abstract: We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two-dimensional images and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by expanding each image, originally given on a Cartesian grid, in the Fourier–Bessel basis for the disk. Because the images are essentially band limited in the Fourier domain, we use a sampling criterion to truncate the Fourier–Bessel expansion such that the maximum amount of information is preserved without the effect of aliasing. The constructed covariance matrix is invariant to rotation and reflection and has a special block diagonal structure. PCA is efficiently done for each block separately. This Fourier–Bessel-based PCA detects more meaningful eigenimages and has improved denoising capability compared to traditional PCA for a finite number of noisy images.
81 citations
TL;DR: In this article, a numerical technique is presented for the approximate solution of the Bagley-Torvik equation, which is a class of fractional differential equations, by using the collocation points, the matrix operations and a generalization of the Bessel functions of the first kind.
Abstract: In this article, a numerical technique is presented for the approximate solution of the Bagley–Torvik equation, which is a class of fractional differential equations. The basic idea of this method is to obtain the approximate solution in a generalized form of the Bessel functions of the first kind. For this purpose, by using the collocation points, the matrix operations and a generalization of the Bessel functions of the first kind, this technique transforms the Bagley–Torvik equation into a system of the linear algebraic equations. Hence, by solving this system, the unknown Bessel coefficients are computed. The reliability and efficiency of the proposed scheme are demonstrated by some numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.
78 citations
TL;DR: The efficient sorter of Bessel beams separating both the azimuthal and radial components is demonstrated, based upon the recently reported transformation of angular to transverse momentum states.
Abstract: We demonstrate the efficient sorter of Bessel beams separating both the azimuthal and radial components. This is based upon the recently reported transformation of angular to transverse momentum states. We separately identify over forty azimuthal and radial components, with a radial spacing of 1588 m−1, and outline how the device could be used to identify the two spatial dimensions simultaneously.
70 citations
70 citations
TL;DR: In this article, the first hitting times of the Bessel process are considered and explicit expressions for the distribution functions and for the densities by means of the zeros of Bessel functions are given.
Abstract: We consider the first hitting times of the Bessel processes. We give explicit expressions for the distribution functions and for the densities by means of the zeros of the Bessel functions. The results extend the classical ones and cover all the cases.
65 citations
TL;DR: These observations demonstrate that the DMD offers a simple and efficient method to generate Bessel beams with distinct nondiffracting and self-reconstruction behaviors, and will potentially expand the applications to the optical manipulation and high-resolution fluorescence imaging owing to the unique nondIFFracting property.
Abstract: We experimentally demonstrated Bessel-like beams utilizing digital micromirror device (DMD). DMD with images imitating the equivalent axicon can shape the collimated Gaussian beam into Bessel beam. We reconstructed the 3D spatial field of the generated beam through a stack of measured cross-sectional images. The output beams have the profile of Bessel function after intensity modulation, and the beams extend at least 50 mm while the lateral dimension of the spot remains nearly invariant. Furthermore, the self-healing property has also been investigated, and all the experimental results agree well with simulated results numerically calculated through beam propagation method. Our observations demonstrate that the DMD offers a simple and efficient method to generate Bessel beams with distinct nondiffracting and self-reconstruction behaviors. The generated Bessel beams will potentially expand the applications to the optical manipulation and high-resolution fluorescence imaging owing to the unique nondiffracting property.
65 citations
TL;DR: In this article, both axial and transverse components of the force exerted on a silicone-oil sphere are obtained for a zero-and first-order Bessel vortex beam.
Abstract: Acoustic Bessel beams are known to produce an axial radiation force on a sphere centered on the beam axis (on-axial configuration) that exhibits both repulsor and tractor behaviors. The repulsor and the tractor forces are oriented along the beam's direction of propagation and opposite to it, respectively. The behavior of the acoustic radiation force generated by Bessel beams when the sphere lies outside the beam's axis (off-axial configuration) is unknown. Using the 3-D radiation force formulas given in terms of the partial wave expansion coefficients for the incident and scattered waves, both axial and transverse components of the force exerted on a silicone- oil sphere are obtained for a zero- and a first-order Bessel vortex beam. As the sphere departs from the beam's axis, the tractor force becomes weaker. Moreover, the behavior of the transverse radiation force field may vary with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on ka values. These results are particularly important for the design of acoustical tractor beam devices operating with Bessel beams.
55 citations
TL;DR: In this paper, a class of non-paraxial accelerating optical waves is introduced, which are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space.
Abstract: A class of nonparaxial accelerating optical waves is introduced. These are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space. The concept expands on our previous proposal of paraxial accelerating Bessel-like beams to include beams with subwavelength lobes and/or large trajectory angles. Such waves are produced when the phase at the input plane is engineered so that the interfering ray cones are made to focus along the prespecified path. When the angle of these cones is fixed, the beams possess a diffraction-free Bessel profile on planes that stay normal to their trajectory, which can be considered as a generalized definition of diffractionless propagation in the nonparaxial regime. The analytical procedure leading to these results is based on a ray-optics interpretation of Rayleigh-Sommerfeld diffraction and is presented in detail. The evolution of the proposed waves is demonstrated through a series of numerical examples and a variety of trajectories.
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TL;DR: In this paper, a parabolic Schauder-type estimate with respect to conical metrics was proved for short-lived conical Kahler-Ricci flow, where the key is to establish the relevant heat kernel estimates, where they use the Weber's formula on Bessel function of the second kind and Carslaw's heat kernel representation in \cite{Car}.
Abstract: Following Donaldson's oppenness theorem on deforming a conical Kahler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical Kahler-Ricci Flow exists for short time. The key is to establish the relevant heat kernel estimates, where we use the Weber's formula on Bessel function of the second kind and Carslaw's heat kernel representation in \cite{Car}.
TL;DR: In this paper, the beam shape coefficients for high-order Bessel beams were calculated using analytical expressions obtained by the integral localized approximation (ILA) for different types of cells, including a real Chinese Hamster Ovary (CHO) cell and a lymphocyte which are respectively modeled by a coated and five-layered sphere.
Abstract: Debye series expansion (DSE) is employed to the analysis of radiation pressure force (RPF) exerted on biological cells induced by high-order Bessel beams (BB). The beam shape coefficients (BSCs) for high-order Bessel beams are calculated using analytical expressions obtained by the integral localized approximation (ILA). Different types of cells, including a real Chinese Hamster Ovary (CHO) cell and a lymphocyte which are respectively modeled by a coated and five-layered sphere, are considered. The RPF induced by high-order Bessel beams is compared with that by Gaussian beams and zeroth-order Bessel beams, and the effect of different scattering processes on RPF is studied. Numerical calculations show that high-order Bessel beams with zero central intensity can also transversely trap particle in the beam center, and some scattering processes can provide longitudinal pulling force.
TL;DR: In this paper, the authors presented a numerical scheme for approximate solutions of the fractional Volterra's model for population growth of a species in a closed system, which is extended by using the time-fractional derivative in the Caputo sense to give solutions for the mentioned model problem.
TL;DR: In this article, the authors find necessary and sufficient conditions for a difference between the exponential function αe β/t and the trigamma function ψ′(t) to be completely monotonic on (0, ∞).
Abstract: In the paper, the authors find necessary and sufficient conditions for a difference between the exponential function αe
β/t
, α, β > 0, and the trigamma function ψ′(t) to be completely monotonic on (0, ∞). While proving the complete monotonicity, the authors discover some properties related to the first order modified Bessel function of the first kind I
1, including inequalities, monotonicity, unimodality, and convexity.
TL;DR: In this article, a simple and very general approximation of the gravitational potential for a nonspherical body is presented, where the potential is expanded using spherical harmonics and spherical Bessel functions.
Abstract: In this paper a simple and very general approximation of the gravitational potential for a nonspherical body is presented. The gravitational potential is expanded using spherical harmonics and spherical Bessel functions, and it satisfies Laplace’s equation outside the circumscribing sphere and Poisson’s equation inside the circumscribing sphere. Therefore, trajectories can be integrated near the surface of the asteroid, as well as far away from it. This paper focuses on the construction of a simple expansion of the gravitational potential that preserves the critical nonlinear dynamical behavior of other gravitational models for a nonspherical asteroid that are more complex and computationally more demanding.
TL;DR: In this paper, the effect of using TiO2-water nanofluid (ϕ≤2%) on entropy generation between two corotating cylinders in the presence of magnetohydrodynamic flow is investigated.
Abstract: The flow between two cylinders where one or both of the cylinders rotate has many practical applications such as swirl nozzles, rotating electrical machines, rotating disks, standard commercial rhymesters, and chemical and mechanical mixing equipment. In this paper, the effect of using TiO2-water nanofluid (ϕ≤2%) on entropy generation between two corotating cylinders in the presence of magnetohydrodynamic flow is investigated. An analytical approach is applied to solve the simplified governing equations in the cylindrical coordinate system. To calculate the thermal conductivity and viscosity of the nanofluid, two correlations, which are based on the experimental data, are used. The velocity field is obtained as modified Bessel functions, and then, using the expansions of these Bessel functions with three terms, the temperature field and, subsequently, the entropy generation rate are estimated. The results are presented for various parameters, including the entropy generation number (NS), Bejan number (Be)...
TL;DR: In this paper, the authors introduced efficient methods for the approximation of solutions to weakly singular Volterra integral equations of the second kind with highly oscillatory Bessel kernels based on the asymptotic analysis of the solution, and derived corresponding convergence rates in terms of the frequency for the Filon method, and for piecewise constant and linear collocation methods.
Abstract: In this paper, we introduce efficient methods for the approximation of solutions to weakly singular Volterra integral equations of the second kind with highly oscillatory Bessel kernels. Based on the asymptotic analysis of the solution, we derive corresponding convergence rates in terms of the frequency for the Filon method, and for piecewise constant and linear collocation methods. We also present asymptotic schemes for large values of the frequency. These schemes possess the property that the numerical solutions become more accurate as the frequency increases.
TL;DR: In this paper, the authors considered geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam and provided a general theoretical expression for the orbital angular momentum (OAM) spectrum and Schmidt number.
Abstract: In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum and Schmidt number in this basis and show how this may be varied by control over the radial degree of freedom, a continuous parameter in Bessel-Gaussian modes. As a test we first implement a back-projection technique to classically predict, by experiment, the quantum correlations for Bessel-Gaussian modes produced by three holographic masks: a blazed axicon, a binary axicon, and a binary Bessel function. We then proceed to test the theory on the down-converted photons using the binary Bessel mask. We experimentally quantify the number of usable OAM modes and confirm the theoretical prediction of a flattening in the OAM spectrum and a concomitant increase in the OAM bandwidth. The results have implications for the control of dimensionality in quantum states.
TL;DR: On a set of known test problems it is shown that the developed numerical method based on the SPPS representation is highly competitive in comparison to the best available solvers such as SLEIGN2, MATSLISE and some other codes and give an example of an exactly solvable test problem admitting complex eigenvalues to which the mentioned solvers are not applicable.
TL;DR: A numerical scheme based on the Bessel collocation method, which reduces the one-dimensional parabolic convection-diffusion model problems to a linear algebraic equation system and the unknown Bessel coefficients can be computed.
TL;DR: In this article, the Iwasawa decomposition of random real 2×2 matrices is used to identify a continuum regime where the mean values and the covariances of the three Iwasava parameters are simultaneously small, and the Lyapunov exponent of the product is assumed a scaling form.
Abstract: We study products of arbitrary random real 2×2 matrices that are close to the identity matrix. Using the Iwasawa decomposition of SL(2,ℝ), we identify a continuum regime where the mean values and the covariances of the three Iwasawa parameters are simultaneously small. In this regime, the Lyapunov exponent of the product is shown to assume a scaling form. In the general case, the corresponding scaling function is expressed in terms of Gauss’ hypergeometric function. A number of particular cases are also considered, where the scaling function of the Lyapunov exponent involves other special functions (Airy, Bessel, Whittaker, elliptic). The general solution thus obtained allows us, among other things, to recover in a unified framework many results known previously from exactly solvable models of one-dimensional disordered systems.
TL;DR: The modified Bessel collocation method is presented to obtain the approximate solutions of the linear Lane-Emden differential equations using the improvement of the Bessel polynomial solutions with the aid of the residual error function.
TL;DR: In this paper, an all-orders formula for the six-point amplitude of planar maximally supersymmetric planar kinematics is presented, which is based on the Yang-Mills theory in the leading-logarithmic approximation of multi-Regge kinematic variables.
Abstract: We present an all-orders formula for the six-point amplitude of planar maximally supersymmetric $ \mathcal{N}=4 $
Yang-Mills theory in the leading-logarithmic approximation of multi-Regge kinematics. In the MHV helicity configuration, our results agree with an integral formula of Lipatov and Prygarin through at least 14 loops. A differential equation linking the MHV and NMHV helicity configurations has a natural action in the space of functions relevant to this problem — the single-valued harmonic polylogarithms introduced by Brown. These functions depend on a single complex variable and its conjugate, w and w
*
, which are quadratically related to the original kinematic variables. We investigate the all-orders formula in the near-collinear limit, which is approached as |w| → 0. Up to power-suppressed terms, the resulting expansion may be organized by powers of log |w|. The leading term of this expansion agrees with the all-orders double-leading-logarithmic approximation of Bartels, Lipatov, and Prygarin. The explicit form for the sub-leading powers of log |w| is given in terms of modified Bessel functions.
TL;DR: In this paper, different waves representing a "flyby" close to a phase singularity are analysed, with the super-oscillations being fastest near phase singularities, despite being differently normalized, or not normalizable at all.
Abstract: Waves involving Bessel functions can oscillate faster than their band-limited Fourier transforms suggest, with the superoscillations being fastest near phase singularities. Different waves representing a ‘flyby’ close to a phase singularity are analysed. These can superoscillate similarly, despite being differently normalized, or not normalizable at all.
TL;DR: An analytical solution given by Bessel series to the transient and one-dimensional bioheat transfer equation in a multi-layer region with spatially dependent heat sources is derived and the potential of this model to study the effect of different environmental conditions in aMulti-layered human head model is explored.
TL;DR: In this paper, the singularly perturbed Laguerre unitary ensemble was studied and the eigenvalue correlation kernel has a new limit instead of the usual Bessel kernel at the hard edge 0.
Abstract: In this paper, we study the singularly perturbed Laguerre unitary ensemble $$ \frac{1}{Z_n} (\det M)^\alpha e^{- \textrm{tr}\, V_t(M)}dM, \qquad \alpha >0, $$ with $V_t(x) = x + t/x$, $x\in (0,+\infty)$ and $t>0$. Due to the effect of $t/x$ for varying $t$, the eigenvalue correlation kernel has a new limit instead of the usual Bessel kernel at the hard edge 0. This limiting kernel involves $\psi$-functions associated with a special solution to a new third-order nonlinear differential equation, which is then shown equivalent to a particular Painleve III equation. The transition of this limiting kernel to the Bessel and Airy kernels is also studied when the parameter $t$ changes in a finite interval $(0, d]$. Our approach is based on Deift-Zhou nonlinear steepest descent method for Riemann-Hilbert problems.
TL;DR: Preliminary results demonstrate reliable decomposition of superpositions of Laguerre-Gaussians, yielding the intensities and relative phases of each constituent mode.
Abstract: The modal characterization of various families of beams is a topic of current interest. We recently reported a new method for the simultaneous determination of both the azimuthal and radial mode indices for light fields possessing orbital angular momentum. The method is based upon probing the far-field diffraction pattern from a random aperture and using the recorded data as a ‘training set’. We then transform the observed data into uncorrelated variables using the principal component analysis (PCA) algorithm. Here, we show the generic nature of this approach for the simultaneous determination of the modal parameters of Hermite-Gaussian and Bessel beams. This reinforces the widespread applicability of this method for applications including information processing, spectroscopy and manipulation. Additionally, preliminary results demonstrate reliable decomposition of superpositions of Laguerre-Gaussians, yielding the intensities and relative phases of each constituent mode. Thus, this approach represents a powerful method for characterizing the optical multi-dimensional Hilbert space.
TL;DR: In this article, the authors investigate strategies to improve the accuracy and efficiency of the ultra weak variational formulation (UWVF) of the Helmholtz equation using three choices of basis function: propagating plane waves (original choice), Bessel basis functions, and evanescent wave basis functions.
Abstract: SUMMARY
In this paper, we investigate strategies to improve the accuracy and efficiency of the ultra weak variational formulation (UWVF) of the Helmholtz equation. The UWVF is a Trefftz type, nonpolynomial method using basis functions derived from solutions of the adjoint Helmholtz equation. We shall consider three choices of basis function: propagating plane waves (original choice), Bessel basis functions, and evanescent wave basis functions. Traditionally, two-dimensional triangular elements are used to discretize the computational domain. However, the element shapes affect the conditioning of the UWVF. Hence, we investigate the use of different element shapes aiming to lower the condition number and number of degrees of freedom. Our results include the first tests of a plane wave method on meshes of mixed element types. In many modeling problems, evanescent waves occur naturally and are challenging to model. Therefore, we introduce evanescent wave basis functions for the first time in the UWVF to tackle rapidly decaying wave modes. The advantages of an evanescent wave basis are verified by numerical simulations on domains including curved interfaces.Copyright © 2013 John Wiley & Sons, Ltd.
TL;DR: In this paper, an analytic solution to the general wavelength integro-differential equation describing the damping of tensor modes of gravitational waves due to free streaming neutrinos in the early universe is provided.
Abstract: We provide an analytic solution to the general wavelength integro-differential equation describing the damping of tensor modes of gravitational waves due to free streaming neutrinos in the early universe. Our result is expressed as a series of spherical Bessel functions whose coefficients are functions of the reduced wave number $Q$.