Gaussian Aperture Research Articles

A theoretical study of a radiofrequency wave propagation through a realistic turbulent marine atmospheric boundary layer based on large eddy simulation

This study aims at modeling and investigating the impact of realistic turbulence inhomogeneity on radiowave propagation by utilizing large eddy simulations (LES). An up-to-date version of the X-LES method for generating realistic turbulent phase screens is first introduced. It combines atmospheric simulations with the classical Tatarski statistical modeling. This method naturally incorporates vertical turbulence inhomogeneity into phase screens at scales resolved by LES. It is then extended to sub-grid scales by weighting statistically generated phase variations with the vertical profile of the turbulent structure constant extracted from atmospheric data. This method is applied to replicate turbulence of a classical tropical marine atmospheric boundary layer. The impact of the generated medium on the propagation of a 10 GHz spherical wave emanating from a Gaussian aperture is analyzed through a statistical study of log-amplitude profiles performed for three different source altitudes. Results first show that contrary to a classical homogeneous turbulence modeling, log-amplitude profiles resulting from the propagation into inhomogeneous turbulence exhibit a statistical heterogeneity strongly dependent of source altitude. Furthermore, classical stochastic phase screen generation from a homogeneous Von-Kàrmàn Kolmogorov spectrum seems to give a statistically significant underestimation of the actual impact of turbulence compared to the X-LES method.

Phase locking of lasers with Gaussian coupling.

A unique approach for steady in-phase locking of lasers in an array, regardless of the array geometry, position, orientation, period or size, is presented. The approach relies on the insertion of an intra-cavity Gaussian aperture in the far-field plane of the laser array. Steady in-phase locking of 90 lasers, whose far-field patterns are comprised of sharp spots with extremely high power density, was obtained for various array geometries, even in the presence of near-degenerate solutions, geometric frustration or superimposed independent longitudinal modes. The internal phase structures of the lasers can also be suppressed so as to obtain pure Gaussian mode laser outputs with uniform phase and overall high beam quality. With such phase locking, the laser array can be focused to a sharp spot of high power density, useful for many applications and the research field.

Beam distortion regulation in Gaussian lasercircular aperture diffraction

从光波衍射的基本理论出发，利用高斯型分布的激光束，研究开普勒望远镜系统在衍射过程中光束畸变调控方法。利用中阶Zernike多项式构建像差函数法来模拟望远镜系统中的四叶畸变现象，并将该Zernike因子引入光学系统中弥补畸变效果。研究发现，波长和孔径会对奇异光强的分布产生明显的影响，波长增大的时候会改变光斑的形状，孔径会影响光斑强度和尺寸，11阶的Zernike四叶形变因子可以抵消望远镜系统的畸变现象。

Natural Rock Fractures: From Aperture to Fluid Flow

Fractures provide preferential flow paths and establish the internal “plumbing” of the rock mass. Fracture surface roughness and the matedness between surfaces combine to delineate the fracture geometric aperture. New and published measurements show the inherent relation between roughness wavelength and amplitude. In fact, data cluster along a power trend consistent with fractal topography. Synthetic fractal surfaces created using this power law, kinematic constraints and contact mechanics are used to explore the evolution of aperture size distribution during normal loading and shear displacement. Results show that increments in normal stress shift the Gaussian aperture size distribution toward smaller apertures. On the other hand, shear displacements do not affect the aperture size distribution of unmated fractures; however, the aperture mean and standard deviation increase with shear displacement in initially mated fractures. We demonstrate that the cubic law is locally valid when fracture roughness follows the observed power law and allows for efficient numerical analyses of transmissivity. Simulations show that flow trajectories redistribute and flow channeling becomes more pronounced with increasing normal stress. Shear displacement induces early aperture anisotropy in initially mated fractures as contact points detach transversely to the shear direction; however, anisotropy decreases as fractures become unmated after large shear displacements. Radial transmissivity measurements obtained using a torsional ring shear device and data gathered from the literature support the development of robust phenomenological models that satisfy asymptotic trends. A power function accurately captures the evolution of transmissivity with normal stress, while a logistic function represents changes with shear displacement. A complementary hydro-chemo-mechanical study shows that positive feedback during reactive fluid flow heightens channeling.

Average capacity of an absorptive turbulent ocean channel with diffraction-and attenuation-resistant beam carriers

The absorption and turbulent diffraction of seawater are important factors that restrict the channel capacity of an underwater optical communication system. Therefore, we derive the model for the capacity of the turbulent seawater communication channel with a diffraction-and attenuation-resistant random (DARR) vortex beam as a signal carrier, and study the influence of absorbing turbulent seawater on the capacity of optical communication channel. DARR beam is a large-scale Gaussian aperture truncated diffracting and absorption resistance waves. We find that with the increase of the number of channels, the total loss of channel capacity caused by absorptive turbulent ocean channel is basically unchanged, the optical communication channel with longer wavelength and smaller receiving diameter has higher channel capacity. Compared with the Laguerre–Gaussian beam and the Bessel–Gaussian beam, DARR beams are more resistant to seawater turbulence and seawater absorption.

Application of the cepstrum method for processing iridology television signals

The questions of the cepstrum method application for the processing of iridology television signals are considered. A cepstrum method for processing a delayed video signal of an aerospace television system is proposed. The application of the method greatly facilitates the determination of the delay and expands the dynamic range of the corrected signal. An expression for determining the power cepstrum at different apertures of the reading beam is received and a suboptimal model of an ideal corrector is designed. Keywords aperture correction; digital correction; linear and nonlinear correctors; cepstrum method; aperture; Gaussian aperture; exponential aperture; signal power cepstrum

Received Probability of Orbital-Angular-Momentum Modes Carried by Diffraction- and Attenuation- Resistant Beams in Weak Turbulent Oceans

High performance underwater wireless optical communication systems are the key to the construction of high quality underwater optical communication networks. However, seawater absorption and seawater turbulent diffraction should be the main factors limiting the performance of underwater optical communication systems. For this reason, we established the probability model of the orbital angular momentum (OAM) mode received by the communication system to study the influence of the absorbable turbulent seawater channel on the underwater optical communication system with an anti-diffraction and anti-attenuation random (DARR) beam as the signal carrier. In the study, the DARR beam with a large truncated Gaussian aperture was adopted as the signal carrier, seawater absorption was characterized by the complex refractive index of seawater, and seawater turbulence was described by the power spectrum of the refractive index of seawater. By analyzing the relationship between the received probability of the OAM mode of DARR beams and the dissipation rate of kinetic energy per unit of mass of fluid, the ratio of temperature and salinity, dissipation rate of the mean-squared temperature, and other parameters, we show that one can select longer wavelength, smaller OAM quantum number and smaller received diameter to increase the received probability of OAM signal modes. The disturbance of turbulent seawater to the OAM modes with different quantum numbers carried by the DARR beam is less than the corresponding OAM modes carried by the Laguerre–Gaussian beam. Our paper shows that the DARR beam can mitigate the absorption and disturbance of turbulent seawater.

Closed-Form Expressions for InSAR Sample Statistics and Its Application to Non-Gaussian Data

Aim of this article is to analytically derive the statistics of the magnitude and phase of the complex sample correlation coefficient between two Gaussian synthetic aperture radar (SAR) acquisitions, the foundation of interferometric SAR (InSAR), and polarimetric SAR. In particular, several novel closed-form expressions containing only elementary functions for the probability density functions (pdf) and the central moments are derived when the complex sample coherence is averaged over an integer number of independent samples (multilooking). Based on these rather simple expressions, a promising way to overcome the assumption of an underlying normal distribution for the InSAR data is proposed. Jointly, these two approaches permit a physically sound, robust, and highly accurate description of the InSAR statistics of severely heterogeneous scenes, a crucial prerequisite to many applications.

Simultaneous Generation of Three OAM Modes by Using a RLSA Fed by a Waveguide Circuit for 60 GHz-band Radiative Near-field Region OAM Multiplexing

This article reports for the first time the design of a 60 GHz planar antenna system for radiative near-field region line-of-sight (LOS) link based on an orbital angular momentum (OAM) multiplexing. The antenna system is composed of a radial line slot array (RLSA) fed by a Butler network, made in post-wall waveguide technology, and located underneath the array. The network can launch different progressive phase states in the RLSA parallel-plate waveguide (PPW) to radiate three different OAM beams. To focalize each beam in the radiative near region, the use of a modified Laguerre–Gaussian aperture distribution is proposed to extend the range where the link is guaranteed. The design concept has been verified by prototyping and testing a 20 free-space wavelengths’ radius antenna. The measurements show that the proposed antenna can generate simultaneously the three OAM-mode states $n =0$ , −1, and +1.

Colour image encryption using Gaussian apertured real-preserving fractional Mellin transform in diffraction domain

A colour image encryption scheme based on Gaussian apertured real-preserving fractional Mellin transform (GARPFrMT) in diffraction domain and chaos permutation is proposed. Real-preserving fractional transform in diffraction domain using Gaussian aperture is constructed to ensure that the output is real, which is convenient for storage and communication. And the Gaussian aperture, as a soft aperture, can improve the intensity distributions of the output light, which contributes to prevent possible attacks for obtaining some useful information from the marginal leakage of light in the optical encryption systems. The colour space rotation transform is first used to convert the colour image from standard space to space. And then, the three new colour components are transformed by GARPFrMT with three different diffraction channels, respectively. A 3D-logistic map is utilized to further scramble the three-colour components. At last, a logistic-sine map is used to perform Xor operation with three components, respectively. Simulation results demonstrate that the proposed algorithm is feasible and robust to noise attack and data loss.

GO Synthesis of Offset Dual Reflector Antennas Using Local Axis-Displaced Confocal Quadrics

Abstract This work investigates an alternative numerical scheme for the solution of an exact formulation based on Geometrical Optics (GO) principles to synthesize offset dual reflector antennas. The technique is suited to solve a second-order nonlinear partial differential equation of the Monge-Ampere type as a boundary value problem. An iterative algorithm based on Newton's method was developed, using axis-displaced confocal quadrics to locally represent the subreflector surface, thus enabling an analytical description of the partial derivatives within the formulation. Such approach reduces discretization errors, as exact expressions for the mapping function and its derivatives are analytically determined. To check the robustness of the methodology, an offset dual-reflector Gregorian antenna was shaped to provide a Gaussian aperture field distribution with uniform phase within a superelliptical contour. The shaped surfaces were further interpolated by quintic pseudo-splines and analyzed by Physical Optics (PO) with equivalent edge currents to validate the synthesis procedure at 11,725 GHz.

Image encryption scheme based on a Gaussian apertured reality-preserving fractional Mellin transform

An image encryption scheme based on a Gaussian apertured reality-preserving fractional Mellin transform (GARPFrMT) is proposed. The GARPFrMT was realized in the diffraction domain. The Gaussian aperture, like a soft aperture, improved the amount of light that passed through the lens compared to a hard aperture and reduced the light leakage at the edge of the lens, assisting to some extent in resisting direct attacks. In the proposed scheme, the reality-preserving transform was constructed in the diffraction domain to ensure that the cipher-text is real. The GARPFrMT is a nonlinear transformation used for eliminating potential insecurity existing in the linear image encryption system. In order to further enhance the security of the encryption system, an Arnold transform, and a bitwise XOR operation were employed for permutation and scrambling in the encryption process. Simulation results and theoretical analysis show that the proposed algorithm is feasible and capable of withstanding several common attacks.

Image encryption scheme based on a Gaussian apertured reality-preserving fractional Mellin transform

An image encryption scheme based on a Gaussian apertured reality-preserving fractional Mellin transform (GARPFrMT) is proposed. The GARPFrMT was realized in the diffraction domain. The Gaussian aperture, like a soft aperture, improved the amount of light that passed through the lens compared to a hard aperture and reduced the light leakage at the edge of the lens, assisting to some extent in resisting direct attacks. In the proposed scheme, the reality-preserving transform was constructed in the diffraction domain to ensure that the cipher-text is real. The GARPFrMT is a nonlinear transformation used for eliminating potential insecurity existing in the linear image encryption system. In order to further enhance the security of the encryption system, an Arnold transform, and a bitwise XOR operation were employed for permutation and scrambling in the encryption process. Simulation results and theoretical analysis show that the proposed algorithm is feasible and capable of withstanding several common attacks.

Research on beam quality improvement method of LD side-pumped acousto-optic Q-Switched anisotropic Nd:YLF laser

In order to achieve a high beam quality for acousto-optic Q-switched anisotropic Nd:YLF quasi-continuous lasers, the influence factors of Nd:YLF laser beam quality is studied. The thermal strain distribution of an anisotropic Nd:YLF laser is simulated by finite element method in steady state, the laser beam is optimized by inserting a Gaussian aperture into the resonator cavity, and the distribution of the light field in the resonator is analyzed according to the Collins theory. The beam quality with or without a Gaussian aperture in the resonant cavity is experimentally compared. Experiments show that inserting a Gaussian aperture in the resonant cavity can effectively improve the output beam quality for anisotropic Nd:YLF lasers.

Theory of diffraction of vortex beams from structured apertures and generation of elegant elliptical vortex Hermite-Gaussian beams.

In this work, a comprehensive analytic study of the diffraction of vortex beams from structured apertures is presented. We formulate the near- and far-field diffraction of a vortex beam from an aperture having an arbitrary functionality in the Cartesian coordinates by two general and different approaches. We show that each of the resulting diffraction patterns can be determined by a number of successive derivatives of the 2D Fourier transform of the corresponding hypothetical aperture function or equally can be obtained by a summation of 2D Fourier transforms of the corresponding modified aperture function. We implement both introduced analytic approaches in predicting the diffraction of a vortex beam from an elliptic Gaussian aperture, an elliptic Gaussian phase mask, and a hyperbolic Gaussian phase mask in the near- and far-field regimes. It is shown that the predicted diffraction patterns by both these approaches are exactly the same. It is shown that the diffraction of a vortex beam from an elliptic Gaussian aperture at the far-field regime forms a light beam that belongs to a family of light beams we call elegant elliptical vortex Hermite-Gaussian beams. In addition, the diffractions of a vortex beam from a Fresnel zone plate in general form for the on- and off-axis situations are formulated, and sinusoidal and binary zone plates are investigated in detail. Our general analytic formula can be used for a large variety of apertures including off-center situations and asymmetrical cases.

Study of high beam quality side-pumped Nd:YLF laser with intracavity Gaussian aperture

In order to obtain a 1053 nm output laser with a high beam quality, the mode distribution of the YLF solid laser with a plane-plane resonator is studied. According to the Collins theory, the influences of the position and size parameters of a Gaussian aperture on the mode of the output beam is simulated and analyzed. Compared with the simulation results without a Gaussian aperture, the Gaussian aperture in the cavity can significantly improve the quality of the output laser. Based on the theoretical simulations, a laser with optimal structural parameters is built. The profiles and mode distributions of the laser output beams with a Gaussian aperture and without a Gaussian aperture in the cavity are measured, respectively. When the radius of the light spot on the film of the Gaussian aperture is 4 mm and the distance between the Gaussian aperture and total-reflection mirror is 30 mm, a 1053 nm laser output with the values of M2 in the x and y directions of 1.9 and 1.8, and maximum output power of 9.7 W is obtained. The experimental results demonstrate that the Gaussian aperture in the cavity can improve the mode distribution of the cavity and obtain the laser output with a higher beam quality, which is basically consistent with the results of theoretical simulations.

Signal-to-noise ratio reduction due to oceanic turbulence in oceanic wireless optical communication links

The effect of oceanic turbulence on the signal-to-noise ratio (SNR) at the receiver of an oceanic wireless optical communication (OWOC) link is studied. To quantify such effect, the metric employed is the reduction in the SNR when oceanic turbulence is present. SNR reduction due to oceanic turbulence is formulated by subtracting the 10 log (SNR) evaluated at the receiver in the presence of turbulence from the 10 log (SNR) evaluated at the receiver in the absence of turbulence. Classical SNR formula which is function of the received optical power, noise and optical detector parameters is utilized. As the average received power, our earlier result that uses a Gaussian optical source field and a finite Gaussian receiver aperture in atmospheric turbulence is adapted for oceanic turbulence and such found average received power is inserted in the SNR expression. OWOC links that use collimated Gaussian optical sources at the transmitter and PIN photodiode, avalanche photodiode (APD) at the receiver, are analyzed. Results that present the variations of the SNR reduction due to oceanic turbulence against the changes in the source, oceanic turbulence and the optical receiver parameters are reported.

Investigation on beam collection efficiency in microwave wireless power transmission

The beam collection efficiency (BCE), which defined as the microwave power transfer efficiency between the transmitting and receiving aperture, plays a key role in the overall transmission efficiency of the microwave wireless power transmission (MWPT) system. However, due to many long distance MWPT applications are near-field microwave power transmission and transmitting antennas are not designed with optimal Gaussian aperture field distributions, widely used Friis formula and Gouban formula may result in considerably errors. This work explores evaluating the BCE using a numerical integration method that is based on the transmitting antenna’s three-dimensional (3D) radiation pattern. Furthermore to facilitate engineering applications of MWPT, a revised formula is proposed, which is based on the numerical integration results and modified from the Gaubau formula. Moreover, a MWPT system working at X band (10 GHz) is designed and its BCE under various transmission distances is measured. Through a comparative analysis, the accuracy of the proposed numerical integration method and modified formula is validated.

Two-phase flow properties in aperture-based fractures under normal deformation conditions: Analytical approach and numerical simulation

A systematic method has been proposed to estimate the two-phase flow properties of horizontal fractures under normal deformation condition. Based on Gaussian aperture distributions and the assumption of local parallel plate model, a simple model was obtained in closed form to predict the capillary pressure-saturation relationships for both wetting and non-wetting phases. Three conceptual models were also developed to characterize the relative permeability behaviors. In order to investigate the effect of normal deformation on two-phase flow properties, the normal deformation could be represented with the maximum void space closure on the basis of penetration model. A rigorous successive random addition (SRA) method was used to generate the aperture-based fractures and a numerical approach based on invasion percolation (IP) model was employed to model capillary-dominated displacements between wetting and non-wetting phases. The proposed models were partially verified by a laboratory dataset and numerical calculations without consideration of deformation. Under large normal deformations, it was found that the macroscopic model is in better agreement with simulated observations. The simulation results demonstrated that the two-phase flow properties including the relationships between capillary pressure, relative permeability and saturation, phase interference, phase structures, residual-saturation-rated parameters and tortuosity factor, were highly sensitive to the spatial correlation of aperture distribution and normal deformation.

Improved extension of depth-of-field performance by apodized wavefront coding

Wavefront coding (WFC) is a popular technique for extending the depth of field (DOF), where the DOF is extended by the phase modulation of the pupil function using a phase mask and digital processing using a deconvolution filter. We previously proposed an apodized WFC system with a Gaussian aperture that extends the DOF while suppressing artifacts in the reconstructed image. In this study, the influence of aberrations on the proposed WFC system was examined in detail by computer simulation. Then, the image quality was experimentally examined to confirm the effectiveness of the apodized WFC system. In addition, we proposed a new type of aperture, i.e., a generalized Gaussian aperture, to prevent the significant reduction in transmitted light intensity due to apodization, the effectiveness of which was confirmed by computer simulation.