Aperture Function Research Articles

Duct mode identification in a statistical model via the Iterative Bayesian Focusing

The measurements of aero-engine fan noise are crucial to engine-noise reduction and silent-turbofan design. The duct mode identification is adpoted to decompose inner duct noises into spinning modes from acoustic pressure measured by a microphone array. However, modes identification of the aero-engine fan are difficult cause the number of modes is usually much larger than the number of microphones and leading to an ill-posed problem during the inverse process. A mode identification method based on Iterative Bayesian Focusing is used to solve this problem. The in-duct sound field is described by a statistical model, and the inverse problem of mode identification is expressed in a Bayesian framework. The sparsity of the target acoustic modes is applied as a priori condition, and a Mode Aperture Function (MAF) is developed. The aperture width of the MAFis automatically updated and contracted through iterations, after which mode coefficients are contracted to a sparsest solution. The used mode identification method is firstly validated through numerical simulations, and the effects of the number of microphones and SNR on mode identification results are discussed. Then the Iterative Bayesian Focusing-based mode identification method is experimentally verified through a well designed Spinning Mode Synthesizer. Both numerical and experimentalresults indicate that target modes can be accurately identified when the number of microphones are much less than the number of all propagating modes.

Synthesis of the rotational blur kernel in a digital image using measurements of a triaxial gyroscope

A method for calculating of a blur kernel arising from the rotation of a digital camera is proposed. The rotation is measured with a three-axis gyroscope attached to the camera. Differential equations of a continuous trajectory of the rotational blur starting from a selected pixel are obtained. These equations are presented both in the form of an explicit system of differential equations for the blur curve in the focal plane and in the form of a matrix equation for the increment of the camera attitude. An expression is given for the integral of the energy illumination from a point light source along the continuous blur trajectory. The integral takes into account the point spread function and the aperture functions of individual photosensitive cells of the photodetector array. The calculation of the integral values for all photosensitive cells illuminated with the point source gives a discrete kernel of rotational blur starting at the selected pixel. Algorithms for the numerical integration of the blur equations are described. The analysis of the blur equations are carried out, characteristic features of the kernels are highlighted and their non-homogeneity is shown, with the kernels of rotational blur revealed not to coincide with each other for different pixels. An example of the synthesis of the blur kernels for given rotation parameters of the digital camera is given.

Model of spatial-temporal synthesis of the combined aperture function of spaced antenna arrays

Model of spatial-temporal synthesis of the combined aperture function of spaced antenna arrays

Predicting impact scenarios of a rimless wheel: a geometrical approach

The 2D motion of a rigid rimless wheel on an inclined plane has been widely studied as a first simple case of passive walker. Usually, it is modelled as a hybrid dynamical system alternating continuous smooth phases and discrete impact ones. As in other bipedal walkers, the related research is often devoted to the analysis of cyclic motions and assumes that the spoke-ground collision is a single-point one. This work focuses exclusively on the impact problem and explores the possibility of different transitions within the impact interval (single-point to double-point collisions, dynamic jamb, stick-slide transitions and sliding reversal) as a function of the spokes angular aperture, the wheel inertia, the wheel-ground friction coefficient, and the initial conditions. This analysis is done through an innovative geometrical approach based on the Percussion Centre.

Edge spin wave transmission through a vertex domain wall in triangular dots

Spin waves (SWs), being usually reflected by domain walls (DWs), could also be channeled along them. Edge SWs yield the interesting, and potentially applicable to real devices property of broadband spin wave confinement to the edges of the structure. Here, we investigate through numerical simulations the propagation of quasi one-dimensional spin waves in triangle-shaped amorphous YIG (Y3Fe5O12) micron sized ferromagnets as a function of the angle aperture. The edge spin waves (ESWs) have been propagated over the corner in triangles of 2 microns side with a fixed thickness of 85 nm. Parameters such as superior vertex angle (in the range of 40^circ –75^circ ) and applied magnetic field have been optimized in order to obtain a higher transmission coefficient of the ESWs over the triangle vertex. We observed that for a certain aperture angle for which dominated ESW frequency coincides with one of the localized DW modes, the transmission is maximized near one and the phase shift drops to pi /2 indicating resonant transmission of ESWs through the upper corner. We compare the obtained results with existing theoretical models. These results could contribute to the development of novel basic elements for spin wave computing.

The acoustic inverse problem in the inhomogeneous medium by iterative Bayesian focusing algorithm

A random inhomogeneous sound propagation medium is considered in acoustic imaging, which is modeled by a random function of the spatial medium. The inhomogeneity of the sound propagation environment can cause large errors in the modeling and measurement of acoustic imaging. Since the wave equation contains random variables, Green’s function no longer has a specific analytical solution. The main work of this paper is as follows: (1) The acoustic inverse problem is considered in the inhomogeneous sound field, which is expressed according to predefined statistical information; (2) Karhunen-Loève expansion is used to simplify the proposed inhomogeneous propagation sound field, and the numerical solution of Green’s function is used instead of the original analytical solution; (3) A dual-driven (including data-driven and knowledge-driven) algorithm based on the Bayesian framework is developed to achieve acoustic imaging, which is implemented through the joint estimation of the aperture function and the sparse prior. Finally, the proposed model and algorithm are verified by a numerical simulation. The proposed algorithm is compared with conventional beamforming in terms of localization accuracy and sound power quantization. The simulation results show that the inhomogeneous sound field can be represented by a small number of random variables, and the proposed dual-drive algorithm can accurately achieve acoustic imaging in the inhomogeneous propagation environment.

Three-dimensional echo distribution analysis of multi-band and oblique Gaussian beams propagating through cat-eye optical system

The cat-eye effect in optical systems enables active laser detection at long distances and high orientation precision. However, few studies focus on the influence of a multi-band laser with a large incident angle on the echo distribution. This study proposes a three-dimensional echo distribution calculation model of an obliquely incident multi-band laser based on the Collins diffraction integral formula and aperture function expansion as the sum of complex Gaussian functions. The echo distributions for different detection ranges are calculated by coupling the size of the detector in a cat-eye optical system into the model. In the numerical simulation, the influences of laser wavelength, incident angle, and target detector parameter are quantitatively analysed by introducing a target-missing quantity of echo spot and peak light intensity. The results show that the peak light intensity decreases with an increase in incident laser wavelength. When the incident angle increases to a particular value, the peak light intensity decreases sharply, and the target-missing quantity of the echo spot centroid is positively correlated with the incident angle. We can effectively extract important information, such as the working band and detector size, from the cat-eye target echo using this model and provide a trajectory prediction theory for the active detection of a cat-eye target moving at high speed.

Increased Azimuth Resolution by Extrapolating the Antenna Array Aperture Function by Least Squares Linear Prediction Estimation Using Autoregressive Model Coefficients

Introduction. Short-wave stations for detecting airborne objects of the ionospheric type have a number of limited technical characteristics, one of which is their low azimuth resolution. This limitation is manifested in the impossibility to separately observe air objects in a group, the distance between which is less than 30 km (at an observation range of 2000 km). The technical characteristics under consideration can be improved by making changes to the dimensions of the receiving antenna array (AA); however, such changes lead, as a rule, to unjustified engineering and financial costs. In practice, space-time signal processing is carried out using conventional superresolution methods, which, although increasing the resolution of the station, decrease the rate of delivery of observation results to the operator due to an additional computational load. It is necessary to find a compromise between the maximum possible resolution indicator and the acceptable load on the system during signal processing.Aim. Analysis of the phase distribution of the incident wave scattered by objects at the AA aperture, as well as the azimuthal images of these objects when performing spacetime signal processing after extrapolating the AA aperture function by evaluating linear prediction using the least-squares method using autoregressive model coefficients.Materials and methods. Modelling of phase distributions at the AA aperture and azimuthal images of the observed objects was conducted in the MATLAB environment.Results. It is shown that the problem of increasing the azimuth resolution of a short-wave station for detecting air objects can be successfully solved using linear prediction based on the least-squares method using autoregressive model coefficients for the extrapolation of the AA aperture function. The results obtained during modelling were analysed using the example of group observation of air objects.Conclusion. The proposed approach for extrapolation of the AA aperture function for short-wave stations with large receiving AAs proved its relevance. The method proposed for increasing the resolution is characterized by a lower computational load, thereby being promising for practical application.

Elastic Wave Velocity Changes Due to the Fracture Aperture and Density, and Direct Correlation With Permeability: An Energetic Approach to Mated Rock Fractures

AbstractIn an effort to reveal the subsurface hydraulic changes in fractures by seismic monitoring, aperture‐related velocity changes need to be investigated. We developed a numerical approach for calculating changes in elastic wave velocity with fracture aperture opening by determining the internal energy of a digitized fracture model based on natural rough surfaces. The simulated local elastic energy revealed that the interaction energy converged within 1.5 mm of the mean fracture position, and was insignificant unless the fractures intersected. This energetic approach clarified the aperture‐velocity relationship and reproduced the experimental results. Further calculations using digital fractures with various sizes and densities demonstrated that the velocity can be accounted for by the superposition of a linear function of fracture density and quadratic function of aperture, and is insensitive to the fracture size. Although the relationship between fracture permeability and elastic wave velocity (i.e., the k‐V relationship) depends on the fracture density, the offset‐normalized k‐V relationship shows clear linearity with the fracture density. The proposed k‐V relationship as a function of the aperture and fracture density indicates that laboratory‐scale fracture properties of a single fracture can be applied to multiple fractures on a larger scale. Our findings can be used to interpret temporal changes in seismic observations and to monitor fluid flow in fractures.

ISAR Imaging Algorithm for Maneuvering Targets Based on Fourier Ptychographic Microscopy

Aiming at the problems of low resolution and poor noise suppression for maneuvering targets with traditional inverse synthetic aperture radar (ISAR) imaging algorithms, we propose a motion compensation-driven high-resolution imaging algorithm based on Fourier ptychographic microscopy (FPM) technology. FPM is a phase retrieval technology that uses the concept of synthetic aperture to obtain the high-resolution image of the target. The process of FPM imaging is composed of the enhancement of the known target information in the spatial domain and some fixed restricted alternating iteration in the frequency domain. This article analyzes the mathematical model of maneuvering target echo and then studies the rationality of applying the FPM phase retrieval algorithm to ISAR maneuvering target imaging. The proposed algorithm mainly includes two steps. First, a series of low-resolution ISAR images are generated by sampling echo data through an aperture function. Second, the FPM phase retrieval technology is applied to splice and reconstruct the spectrum of the low-resolution images to achieve the focused ISAR image. The effectiveness of the proposed algorithm is verified by using multiple groups of simulation data and real radar data.

Sensitivity of an infinite-strip-shaped polyvinylidene fluoride film in an underwater plane sound field

The sensitivity of an infinite-strip-shaped polyvinylidene fluoride (PVDF) film in an underwater plane sound field is analyzed in this paper. The high-frequency sensitivity is characterized by the resonances of the symmetrical in-plane stress modes with traction-free boundary conditions at the ends of the film and by the anti-resonances due to the superposition of the stress components. The low-frequency sensitivity exhibits a simple hydrostatic response. The directional property of the in-plane stress component, generated by the incident sound across the thickness, has two contributions. The first is from the aperture and dipolar functions of the incident sound pressure over the PVDF surfaces and at the two ends of the film. The second is from an amplitude modulation by an angle-dependent gain. The directional property of the in-plane stress component by the sound pressure at the two ends of the film is only controlled by the dipolar function, and that of the stress component in the thickness direction is only determined by the aperture function. The illustration of the frequency and directional features of the PVDF film may advance understanding of the mechanisms involved in generating the voltage output of PVDF by an incident sound field.

Particle size distributions following chewing: Transformation of two-dimensional outcome from optical scanning to volume outcome from sieving

Following chewing, the particle size distribution (PSD) by cumulative volume is characterized by X 50 , and b . Volume data are lacking when using less time-consuming optical scanning instead of sieving for characterizing PSDs. The aim was to transform 2D scanning data to 3D ones. Optosil® and almond were used as artificial and real solid foods, and minimal Feret-diameter (min-FD) as a measure of particle size. Border min-FDs were calibrated as a function of sieve aperture to determine size classes. Flakes produced by chewing were considered as ellipsoids. The ratio between the largest and the intermediate ellipsoid's radius was known by scanning. The ratio between the smallest and the intermediate radius was adjusted with Solver of Excel® to minimize the difference between the estimated total volume of the particles, and the known total volume. Estimated values of X 50 and b from scanning closely approached those from sieving, the ‘gold standard’. • Analysis of particle size distributions (PSDs) of a chewed solid artificial food. • PSDs by weight (volume) are usually obtained by labour and time consuming sieving. • Transformation of 2D optical scanning data to 3D volumes can replace sieving data. • Mathematical basis of 2D-3D transformation, assuming an ellipsoid particle shape. • The solution for 2D-3D transformation is also effective for real solid food (almond).

Numerical Calculation of Fracture Seepage in Rough Rock and Analysis of Local Pressure Drop

The seepage performance of a rock mass mainly depends on the rock fractures developed in it. Numerical calculation method is a common method to study the permeability properties of fractures. Seepage in rock fractures is affected by various factors such as fracture aperture, roughness, and filling, among which aperture and roughness are the two most widely influenced factors. The Navier-Stokes (NS) equation can be solved directly for the seepage flow in rock fractures with good accuracy, but there are problems of large computational volume and slow solution speed. In this paper, the fracture aperture space data is substituted into the local cubic law as an aperture function to form a numerical calculation method for seepage in rough rock fractures, namely, the aperture function method (AFM). Comparing with the physical seepage experiments of rock fractures, the calculation results of AFM will produce a small amount of error under the low Reynolds number condition, but it can greatly improve the calculation efficiency. The high efficiency of calculation makes it possible to apply AFM to the calculation of large-scale 3D rough fracture network models. The pressure drop of fluid in the fracture has viscous pressure drop (VPD) and local pressure drop (LPD). VPD can be calculated using the AFM. After analyzing the results of solving the NS equation for fracture seepage, it is concluded that the LPD includes the pressure drop caused by area crowding in the recirculation zone (RZ), kinetic energy loss in the RZ, kinetic energy loss in the vortices, and other reasons.

Algorithm for synthesizing virtual antenna array aperture by extrapolating the aperture function based on sequential signal processing

Algorithm for synthesizing virtual antenna array aperture by extrapolating the aperture function based on sequential signal processing

Numerical calculation method of aperture function for rough rock fracture flow

Fracture is the main path of rock seepage and plays a decisive role in the permeability of rock masses. The method of solving Navier-Stokes (NS) equation directly to study the fracture seepage flow has high accuracy and can well reflect the nonlinear flow characteristics in the fracture, but there is also the problem of excessive calculation. In this paper, the fracture aperture spatial data is substituted into the local cubic law as an aperture function to form a numerical calculation method for seepage in rough rock fractures, namely, the aperture function method(AFM). After comparing with the experimental calculation results of fracture seepage, it is found that the AFM calculation results are in good agreement. Using the method of solving the NS equation, the seepage calculations were performed for two typical fracture models with multiple boundary conditions. After comparison and analysis, a) the nonlinear term in the rough fracture flow mainly originates from the local pressure drop (LPD), and the generation of the recirculation zone(RZ) is the main reason for the formation of the LPD. b)The AFM calculation results are compared with the NS method under low hydraulic gradient conditions and its error is not significant (i. e., 0.21%, 0.81%). AFM is an excellent numerical calculation method when the condition of neglecting the effect of nonlinear items in fracture flow is allowed. c) The main advantage of AFM is that it has a very high numerical calculation efficiency, which makes the method available for seepage calculations in large-scale rough fractures.

Multiplexing Tensor Holographic Metasurface with Surface Impedance Superposition for Manipulating Multibeams with Multimodes

AbstractMultimode multibeams are widely investigated, but are mostly generated by 3D bulky configuration or partitioned aperture for each beam. This paper proposes and analyzes a method to generate multimode multibeams using a planar single‐layer metasurface with shared aperture. The underlying principle is multiplexing tensor holographic metasurface with a superposition of modulated impedance surface. The multiplexed metasurface is an interference pattern of objective radiation and reference current to generate each beam. To validate the proposed method, this paper presents a multiplexed metasurface shared for two different beams. These two beams are with different modes, i.e., different beam types, different frequencies, different polarizations, and different focal depths. This multiplexed tensor holographic metasurface is theoretically analyzed, fabricated, and validated with matched results in simulation and measurement. The proposed method is promising to realize multiplexed tensor holographic metasurface for emerging wireless communication and radar front‐ends with compact aperture, low profile, light weight, and multiple functions.

Computer Simulation for the Effects of Optical Aberrations on Solar Images Using Karhunen-Loeve polynomials

Numerical simulations were carried out to evaluate the effects of different aberrations modes on the performance of optical system, when observing and imaging the solar surface. Karhunen-Loeve aberrations modes were simulated as a wave front error in the aperture function of the optical system. To identify and apply the appropriate rectification that removes or reduces various types of aberration, their attribute must be firstly determined and quantitatively described. Wave aberration function is well suitable for this purpose because it fully characterizes the progressive effect of the optical system on the wave front passing through the aperture. The Karhunen-Loeve polynomials for circular aperture were used to describe wave front deviations and to predict the initial state of adaptive optics corrections. The results showed that increasing the aberration modes causes an increase in the blurring of the observed image. Also, we conclude that the optical phase error is increased significantly when aperture’s radii are increased.

Transmission properties of tapered optical fibres: Simulations and experimental measurements

We measured the transmission of tapered and untapered optical fibres as a function of input beam numerical aperture at 635nm. The tapered fibres were fabricated with an adiabatic tapering process from graded and step-index fibres with 50μm core diameters to form a 100mm long taper with 5:1 taper ratio. We tested tapered graded-index and step-index fibres fabricated from commercial Thorlabs products and a custom graded-index taper. The 5:1 tapered graded-index fibre can give a transmission greater than 0.4 for Thorlabs and 0.6 for the custom taper. We simulated the transmission of the tapered fibres and found reasonable agreement with the measured graded-index tapered fibre results across the numerical aperture range of interest. Experimentally, step-index tapered fibres performed relative poorly and considerably below modelling expectations. Based on our examinations this arises because the properties of step-index fibre were not robust to the tapering process. Suitably tapered graded-index fibres may offer a new route for efficient focal ratio reduction of fibre optic signals, e.g., in fibre-fed spectrographs, though we stress that our measurements have been limited to monochromatic light in this work.

Fundamental limit of single-mode integral-field spectroscopy

There are several high-performance adaptive optics systems that deliver diffraction-limited imaging on ground-based telescopes, which has renewed interest in single-mode fiber (SMF) spectroscopy for exoplanet characterization. However, the fundamental mode of a telescope is not well matched to those of conventional SMFs. With the recent progress in asphere manufacturing techniques, it may be possible to reshape the fundamental mode of a SMF into any arbitrary distribution. An optimization problem is set up to investigate what the optimal mode field distribution is and what the fundamental throughput limit is for SMF spectroscopy. Both single-object spectrographs and integral-field spectrographs are investigated. The optimal mode for single-object spectrographs is found to be the aperture function of the exit pupil; for integral-field spectrographs, the optimal mode depends on the spatial sampling of the focal plane. For dense sampling, a uniform mode is optimal; for sparse sampling, the mode of a conventional SMF is near optimal. With the optimal fiber mode, a high throughput ( > 80 % ) can be achieved when the focal plane is (super) Nyquist sampled. For Nyquist sampled cases, the optimal mode has almost 20% more throughput than a conventional SMF.

High angular resolution polarimetric imaging of the nucleus of NGC 1068

Context. Polarisation is a decisive method to study the inner region of active galactic nuclei (AGNs) since, unlike classical imaging, it is not affected by contrast issues. When coupled with high angular resolution (HAR), polarisation can help to disentangle the location of the different polarising mechanisms and then give insight into the physics taking place in the core of AGNs. Aims. We obtained a new data set of HAR polarimetric images of the archetypal Seyfert 2 nucleus of NGC 1068 observed with SPHERE/VLT. We aim in this paper to present the polarisation maps and to spatially separate the location of the polarising mechanisms, thereby deriving constraints on the organisation of the dust material in the inner region of this AGN. Methods. With four new narrow-band images between the visible and the near-infrared combined with older broad-band observations, we studied the wavelength dependence of the polarisation properties from 0.7 to 2.2 μm of three selected regions within the inner 2″ surrounding the central engine. We then compared these measurements to radiative transfer simulations of scattering and dichroic absorption processes, using the Monte Carlo code MontAGN. Results. We establish a detailed table of the relative importance of the polarising mechanism as a function of aperture and wavelength. We are able to separate the dominant polarising mechanisms in the three regions of the ionisation cone, the extended envelope of the torus, and the very central bright source of the AGN. Thus, we estimate the contribution of the different polarisation mechanisms to the observed polarisation flux in these regions. Dichroic absorption is estimated to be responsible for about 99% of the polarised flux coming from the photo-centre. However, this contribution would only be restricted to this location because the double-scattering process would be the most important contributor to polarisation in the equatorial plane of the AGN and single scattering is dominant in the polar outflow bi-cone. Conclusions. Even though results are in good agreement with larger apertures measurements, the variety of situations with different mechanisms at play highlights the importance of spatial resolution for the interpretation of polarisation measurements. We also refine the estimation of the integrated optical depth in the visible of the obscuring structure to a range of 20−100, constraining the geometry of the inner region of this AGN.