Physical Theory Of Diffraction Research Articles

Far-field Pattern Analysis Based on Piecewise Aperture Field Integration for Leighton Chajnantor Telescope Antenna under Gravity and Wind Load

The Caltech Submillimeter Observatory telescope will be relocated from Mauna Kea, Hawaii to Chajnantor Plateau, Chile, refurbished there and renamed the Leighton Chajnantor Telescope (LCT). At the new site, the open-air environment, as well as the high altitude, will amplify the influence of gravity and wind load on structural deformation, thus affecting the antenna’s radiation characteristics, which can be characterized by a far-field pattern. To quickly and accurately compensate for the effect of reflector structural deformation on the far-field pattern of LCT’s antenna, we propose a far-field pattern quick calculation method (FPQCM) to analyze the antenna’s radiation characteristics under gravity and various wind loads, which combines the optical path difference calculation method on the aperture plane, the piecewise Zernike polynomial function, and the piecewise aperture field integration method. Through extensive experimental comparisons with the numerical method based on physical optics and physical theory of diffraction, it is validated that the proposed FPQCM significantly reduces the time by more than 100 times for acquiring the far-field patterns while maintaining the accuracy of the main figure of merits at the highest frequency (i.e., 856 GHz). In addition, we analyzed the far-field pattern of the antenna at different zenith angles, gravity, and winds of different strengths and directions by FPQCM, which provided guidance for performing more precise control through an active surface optimization system after LCT resumes operation, thus facilitating the acquisition of higher surface accuracy and better observation effect.

A high-resolution acoustic goniometer for characterizing sound diffuser reflections

Noise control engineering and architectural acoustics practice have widely applied diffusing elements and devices to create surface scattering and diffuse reflections. An acoustical goniometer in the form of a circular microphone array has been used to characterize scattered responses for various types of diffusing elements/devices. This research is also intended for experimental validation of diffraction simulations of diffusing devices based on the physical theory of diffraction (PTD). To cope with experimental challenges, particularly for the research in the physical theory of diffraction, an acoustic goniometer must achieve a high enough angular resolution in addition to fulfilling far-field requirements. This paper discusses practical implementations and experimental results of portable goniometers with a radius of up to five meters and an angular resolution of 1.25 degrees. The practical implementation is intended to be easily deployable in empty, indoor spaces of sufficiently large dimensions for scattered reflection characterization. This paper discusses an effort of increasing experimental efficiency of characterization procedures for oblique incidences.

Effect of Panel Misalignment Error Distribution on the Radiation Pattern of Leighton Chajnantor Telescope’s Antenna

The Leighton dish formerly at the Caltech Submillimeter Observatory will be reassembled to become the Leighton Chajnantor Telescope (LCT). It will be required to demonstrate high surface accuracy and controlled radiation patterns at high frequency, which are largely limited by surface error due to panel misalignment on the primary reflector. Not only the surface rms error but also the error distribution has effect on the radiation pattern of the antenna. Therefore, analyzing the effect of error distributions resulting from various panel misalignments on the radiation pattern of the antenna will facilitate better compensation of surface errors during the reassembly process. To acquire the radiation pattern of LCT’s antenna with panel misalignments, we first propose a simulation method based on physical optics and the physical theory of diffraction, which offers precise results but is time-consuming, especially at high frequencies. Then, we propose a rapid computation method that combines the method of calculating the optical path difference (OPD), the OPD fitting method, and the aperture integration method for segmented reflectors. Experimental results demonstrate that the rapid computation method is highly efficient and accurate compared to the simulation method. In order to show the effect of error distributions due to two typical panel misalignments (i.e., piston and tip-tilt) on radiation patterns, experiments are conducted using the two proposed methods for various error distributions. These experiments indicate that for the same surface rms error, smaller panel errors at smaller normalized aperture radii are more conducive to achieving improved characteristics of the radiation patterns, such as reduced peak gain losses and lower sidelobe levels. Additionally, comparison experiments also reveal that variations in piston error have a greater impact on the radiation patterns than variations in tip-tilt error under the same surface rms error.

Electromagnetic scattering and imaging simulation of extremely large-scale sea-ship scene based on GPU parallel technology

Aiming to solve the bottleneck problem of electromagnetic scattering simulation in the scenes of extremely large-scale seas and ships, a high-frequency method by using graphics processing unit (GPU) parallel acceleration technique is proposed. For the implementation of different electromagnetic methods of physical optics (PO), shooting and bouncing ray (SBR) and physical theory of diffraction (PTD), a parallel computing scheme based on the central processing unit (CPU)-GPU parallel computing scheme is realized to balance computing tasks. Finally, a multi-GPU framework is further proposed to solve the computational difficulty caused by the massive number of ray tubes in the ray tracing process. By using the established simulation platform, signals of ships at different seas are simulated and their images are achieved as well. It is shown that the higher sea states degrade the averaged peak signal-to-noise ratio (PSNR) of radar image.

Accelerating the shooting and bouncing ray based electromagnetic scattering calculations via CPU and GPU Implementations: Application to PREDICS tool

In this paper, we present the parallel computation of physical electromagnetic (EM) solvers, namely physical optics (PO), shooting and bouncing rays (SBR), and the physical theory of diffraction (PTD), which are used for EM scattering/diffraction calculations. The accelerated solvers have been tested on CPU and GPU kernels for significantly faster calculation times. As an application, the developed implementation is employed to recently developed tool of PREDICS that uses combined techniques PO, SBR, and PTD for the calculation of EM scattering/diffraction and radar cross section (RCS) from electrically large, complex objects. First, the CPU parallelization of these three combined techniques on the PREDICS code is explained. The parallelization implementation is specially tailored for the nature of SBR technique such that the CPU iteration loop is accomplished over triangular facets of the CAD file by employing a read/write spin lock task dispatching technique. Next, a lock-free implementation of the PO, SBR, and PTD techniques on the GPU threads is presented. Thanks to availability of many GPU cores, the parallelization procedure is widened such that triangular facets, observation angles of elevation and azimuth are used for a much faster calculation set-up. Numerical examples for the EM/RCS calculation of simple canonical and electrically big, complex objects are shared to demonstrate the effectiveness, accuracy and the computational acceleration based on the multi-CPU and multi-GPU implementations. The key metric of the contribution of the study is the speed-up value of the implementations. The acceleration gained via multi-CPU realization yielded directly in parallel with the number of available CPU cores. On the other hand, the acceleration factor can reach to hundreds when multi-GPUs are used. In fact, the acceleration factor has reached to 4.7 for a machine with 4 Core 8 Thread CPU processor, and 141.3 for a 2560 CUDA GPU Core system.

A Quick Calculation Method for Radiation Pattern of Submillimeter Telescope with Deformation and Displacement

Radiation pattern captures the electromagnetic performance of reflector antennas, which is significantly affected by the deformation of the primary reflector due to gravity and the displacement of the secondary reflector. During the design process of large reflector antennas, a substantial amount of time is often dedicated to iteratively adjusting structural parameters and validating electromagnetic performance. To improve the efficiency of the design process, we first propose an approximate calculation method of optical path difference (OPD) for the deformation of the primary reflector under gravity and the displacement of the secondary reflector. Then an OPD fitting function based on the modified Zernike polynomials is proposed to capture the phase difference of radiation over the aperture plane, based on which the radiation pattern will be obtained quickly by the aperture field integration method. Numerical experiments demonstrate the effectiveness of the proposed quick calculation method for analyzing the radiation pattern of a 10.4 m submillimeter telescope antenna at its highest operating frequency of 856 GHz. In comparison with the numerical simulation method based on GRASP (which is an antenna electromagnetic analysis tool combining physical optics (PO) and physical theory of diffraction (PTD)), the quick calculation method reduces the time for radiation pattern analysis from more than one hour to less than two minutes. Furthermore, the quick calculation method exhibits excellent accuracy for the figure of merit (FOM) of the radiation pattern. Therefore, the proposed quick calculation method can obtain the radiation pattern with high speed and accuracy. Compared to the time-consuming numerical simulation method (PO and PTD), it can be employed for quick analysis of the radiation pattern for the lateral displacement of the secondary reflector and the deformation of the primary reflector under gravity in the design process of a reflector antenna.

Experimental characterization of scattered reflections of sound diffusers using a portable high-resolution acoustic goniometer

Surface scattering and diffuse reflections from acoustic diffusers have recently become a significant topic of research for room acoustics. An acoustical goniometer can be implemented in the form of a circular microphone array to characterize scattered responses for various types of diffusing elements/devices. This research is also intended for experimental validation of diffraction simulations of finite-sized diffusing devices using the physical theory of diffraction (PTD). To cope with experimental challenges, an acoustic goniometer must achieve a fine enough angular resolution in addition to fulfilling far-field requirements. This paper will discuss pragmatic implementations and experimental results of portable goniometers with a radius of up to five meters and an angular resolution of 1.25 degrees. The pragmatic implementation is intended to be easily deployable in empty, indoor spaces of sufficiently large dimensions for scattered reflection characterization. This paper highlights an effort of increasing experimental efficiency of measurement routines for oblique incident characterization and challenges of characterizing full angular ranges of scattered reflections.

Facilitating learning adaptive V-tail of a supersonic missile for radar cross-section reduction during interval flight

To study the V-tail inclination of a supersonic missile that meet the requirements of low electromagnetic scattering characteristics in interval flight, an automatic tilt scheme is presented. The improved annealing algorithm is used to determine the optimal solution of the V-tail tilt angle, where multiple scattering of the physical optics plus physical theory of diffraction is used to calculate the radar cross section (RCS) of the target. The results show that the optimal solutions of V-tail inclination are different in various flight intervals of the horizontal observation field. In the forward side flight interval, changing the initial azimuth has less influence on the optimal solution of V-tail tilt angle, while more influence on the missile RCS indicator. In the side tail flight interval, the RCS level of the missile is low, and there is an optimal solution and a few feasible solutions for the V-tail inclination. The feasible solution of V-tail tilt angle in the lateral flight interval is obviously increased. The presented automatic tilt scheme is effective for studying the low scattering performance of the supersonic missile V-tail.

Theoretical Verification of Single-Reflector Compact Antenna Test Range With High Aperture Usage

In the reflector-based compact antenna test range (CATR), the aperture usage is one of our most concerned problems. Higher aperture usage means that in a CATR with the same aperture reflector, a larger quiet zone (QZ) can be generated to measure a larger aperture antenna. In this work, we theoretically derive a method to design a single-reflector CATR with high aperture usage. Specifically, the radiation function of the ideal feed for the offset-fed CATR is deduced. An offset-fed parabolic reflector CATR with this ideal feed can generate a QZ with 100% aperture usage analyzed by geometrical optics (GO). An offset-fed CATR with a 3 m side-length rectangular aperture parabolic reflector is designed and simulated by physical optics (PO) and physical theory of diffraction (PTD) in GRASP10. With the proposed feed, the aperture efficiency can reach about 74% at 100 GHz and over 86% from 200 to 500 GHz. The simulation results of the QZ field distribution in the system with an ideal feed and a manufactured coaxial cavity horn feed are presented and analyzed. Besides, we also summarize amplitude ripple, phase ripple, and cross-polarization isolation in the QZ to illustrate the performance of the single-reflector CATR.

An Accelerated Hybrid Method for Electromagnetic Scattering of a Composite Target–Ground Model and Its Spotlight SAR Image

In this paper, an accelerated hybrid method of physical optics (PO) shooting and bouncing ray (SBR)–physical theory of diffraction (PTD) is proposed to deal with the electromagnetic scattering of a complex target on rough ground. To accelerate the ray tracing progress, the ray marching technique based on octree structure is employed. In this technique, only the nodes passed by the ray are detected successively until the first facet intersected by ray is found or the ray passes through the bounding box, which greatly decreases the intersection test. Then, based on the accelerated PO-SBR-PTD method, the spotlight synthetic aperture radar (SAR) echo data of the composite target–ground model is obtained by the vector superposition of the echo on each meshed patch. Furthermore, the spotlight SAR image of the composite model is simulated by the polar format algorithm (PFA). In numerical simulations, both the EM scattering of the target and composite model are calculated and evaluated by comparing with the multilevel fast multipole method (MLFMM) in FEKO software. Meanwhile the spotlight SAR image of the composite target–ground model is also compared with the real image in MSTAR data, and a satisfactory similarity between them is obtained. In addition, the SAR images of two targets on rough ground for different pose angles are also presented and analyzed.

A Dynamic RCS and Noise Prediction and Reduction Method of Coaxial Tilt-Rotor Aircraft Based on Phase Modulation.

For tilt-rotor aircraft with coaxial rotors (coaxial rotor aircraft), reduction of radar cross section as well as acoustic noise can be essential for stealth design, and the rotation of the coaxial rotors can have an influence on noise and dynamic radar cross section (RCS) characteristics. In this paper, an approach to the prediction of both the sound pressure level (SPL) of noise and the dynamic RCS of coaxial-tilt aircraft is carried out, based on the theories of the FW-H equation, the physics optics method (PO) and the physical theory of diffraction (PTD) method. In order to deal with the rotating parts (mainly including coaxial rotors), a generated rotation matrix (GRM) is raised, aiming at giving a universal formula for the time-domain grid coordinate transformation of all kinds of rotation parts with arbitrary rotation centers and rotation axis directions. Moreover, a compass-scissors model (CSM) reflecting the phase characteristics of coaxial rotors is established, and a method of noise reduction and RCS reduction based on the phase modulation method is put forward in this paper. The simulation results show that with proper CSM parameter combinations, the reduction of noise SPL can reach approximately 3~15 dB and the reduction of dynamic RCS can reach 1.6 dBsm at most. The dynamic RCS and noise prediction and reduction method can be meaningful for the radar-acoustic stealth design of coaxial tilt-rotor aircrafts.

An Improved GO-PO/PTD Hybrid Method for EM Scattering From Electrically Large Complex Targets

The accuracy and the efficiency of hybrid methods that combine geometrical optics (GO) and physical optics (PO), and physical theory of diffraction (PTD), have been improved by the use of backward-ray-tracing technique and Gordon’s integral algorithm. However, the overall accuracy of the method is still limited by the errors in the process of backward ray tracing. In this study, both the advantages and the disadvantages of the two techniques, namely, backward ray tracing and forward ray tracing, are compared. Also, the reasons for the errors in the backward ray tracing are explored in detail. On this basis, an improved ray-tracing technique is presented, called the two-scale division method (TSDM). This technique combines the advantages of forward and backward tracing, and it improves the accuracy of the GO-PO/PTD hybrid method. Meanwhile, the efficiency of the ray tracing is improved by using two-scale facets to structure the targets’ geometric model. The implementation principle of this method will be comprehensively discussed and it is validated by comparing the simulation results from FEKO-Multilevel fast multipole method (MLFMM), FEKO-ray launching GO (FEKO-RL-GO), and those from an unoptimized method.

Radar absorbing photonic-crystal structure containing magnetic [formula omitted] ferrite nanocomposite and dielectric materials

In this paper, a one-dimensional absorptive multilayer photonic-crystal structure has been designed and simulated using the physical theory of diffraction (PTD), transmission line modeling (TLM), and the transfer matrix method (TMM) in order to less visible fighter planes from radar signals. The periodic structure is comprised of Quartz glasses as dielectric materials and a particular kind of magnetic cobalt ferrite nanocomposite known as synthesized Co0.9Fe2.1O4 at 200 °C whose optical data was extracted from experimental work. Totally, the results illustrated a high absorption rate at the angles of incidence from 0° to 90° for TM and TE polarizations about 80 % and 51 % without any sublayer on average within X-band radar frequency from 8 GHz to 12 GHz. More significantly, the electric field profile and magnetic field distribution showed that this structure attenuated electromagnetic field along propagation vector integrally as well as reflected power is negligible up to about 21 % across all components of the field respectively. Manufacturing tolerance calculations have been carried out to consider production errors practically as an engineering technique to increase the performance of such photonic-crystal composition in the industry. In this designation, the device also is protected from environmental impacts by dielectric materials.

Strip SAR image simulation of a composite vehicle-ground model.

In this paper, the strip synthetic aperture radar (SAR) image of a composite vehicle-ground model is simulated by combining the electromagnetic scattering algorithm and radar imaging algorithm. A linear frequency modulated wave is incident on the composite model, which is partitioned into a mass of triangular patches. In the "stop-and-go" radar mode, for each patch, the amplitude of scattered echo in the frequency domain is solved by a hybrid method of physical optics (PO)-shooting and bouncing ray (SBR)-physical theory of diffraction (PTD). For the composite model, the total scattered echo in terms of range frequency and azimuth time is obtained by the vector superposition of echo on patches. Then the SAR image of the composite model is generated by the range-Doppler algorithm. In numerical simulations, both the electromagnetic scattering of a target by the SBR-PTD method and composite scattering by the PO-SBR-PTD method are validated and evaluated by comparing with the multilevel fast multipole method (MLFMM) in FEKO software. Moreover, the SAR image of the composite vehicle-ground model is also compared with the real image in Moving and Stationary Target Acquisition and Recognition database, which verifies the feasibility of the proposed method. SAR images of the composite model for different incident angles are also presented and analyzed.

Radar Cross Section Prediction Using Iterative Physical Optics With Physical Theory of Diffraction

A new approach is presented to predict radar cross section (RCS) of electrically large conducting geometries using iterative physical optics (IPO) in conjunction with physical theory of diffraction (PTD). IPO is based on iterative refinement of physical optics (PO) currents to include multiple reflections. However, IPO does not yield sufficient accuracy in diffraction dominant regions since it does not properly include effects of edge diffractions. Hence, the proposed approach includes diffraction effects using PTD, which introduces edge currents. Diffracted fields due to these edge currents are radiated on triangular facets to modify the PO currents before IPO iterations. Scattered fields are computed from converged IPO surface currents and PTD edge currents. A new set of PTD edge currents excited by the fields due to the IPO currents are also found and the fields radiated by these PTD edge currents are added to the scattered fields. Therefore, interactions between the surface and edge currents are included. Computations are accelerated by parallel processing using message passing interface (MPI). Monostatic and bistatic RCS are predicted using the proposed approach for tail-wing and trihedral corner reflector geometries. The IPO-PTD results are compared with method of moments (MoM) and multilevel fast multipole method results obtained using field calculations involving bodies of arbitrary shape (FEKO) commercial electromagnetic simulation software for validation.

An Experimental and Theoretical Comparison of 3D Models for Ultrasonic Non-Destructive Testing of Cracks: Part I, Embedded Cracks

Ultrasonic Non-Destructive Testing (NDT) methods are broadly used for detection and characterization/imaging of cracks. Simulation is of great interest for designing such NDT methods. To model the ultrasonic 3D response of a crack, ultrasonic high frequency asymptotic (semi-analytical) models (such as the Physical Theory of Diffraction—PTD) are known to provide accurate predictions for most classical NDT configurations, and 3D numerical models have also emerged more recently. The aim of this paper is to carry out for the first time an experimental and theoretical comparison of 3D models for ultrasonic NDT of embedded cracks in 3D configurations. Semi-analytical models and a hybrid 3D FEM strategy—combining high-order spectral Finite Elements Method (FEM) for flaw scattering and an asymptotic ray model for beam propagation—have been compared. Both numerical validations and comparisons between simulation and experiments prove the effectiveness of PTD in numerous configurations but validate and demonstrate the improvement provided by the 3D hybrid code, notably for small flaws compared to the wavelength and for shear waves.

Analysis of Radome Cross Section of an Aircraft Equipped With a FSS Radome

We study the radar cross section (RCS) property of an aircraft considering the electromagnetic (EM) characteristics of a frequency selective surface (FSS) radome, mounted on the aircraft. Instead of full-wave methods, we utilize high-frequency methods, such as the shooting and bouncing rays (SBR), physical theory of diffraction (PTD), and flat model, taking a significant computational efficiency. Based on the developed algorithm, we analyze monostatic and bistatic RCSs of the aircraft equipped with either single- and multi-layer dielectric, FSS, or PEC radomes in terms of frequency and polarization. Our calculations are validated by comparing with those of the commercial EM simulator with significant computational efficiency. The present numerical study indicates that including the radome EM characteristics into the overall aircraft RCS study is crucial for the accurate RCS estimate

Electromagnetic Scattering Analysis of the Sea Surface with Single Breaking Waves

A new electromagnetic (EM) scattering model of the sea surface with single breaking waves is proposed based on the high-frequency method in this paper. At first, realistic breaking wave sequences are obtained by solving the fluid equations which are simplified. Then, the rough sea surface is established using the linear filtering method. A new wave model is obtained by combining breaking waves with rough sea surface using a 3D coordinate transformation. Finally, the EM scattering features of the sea surface with breaking waves are studied by using shooting and bouncing rays and the physical theory of diffraction (SBR-PTD). It is found that the structure that is similar to a dihedral corner reflector between the breaking wave and rough sea surface exhibits multiple scattering, which leads to the sea-spike phenomenon that the scattering result of horizontal (HH) polarization is larger than that of vertical (VV) polarization, especially at low-grazing-angle (LGA) incidents with upwind. The sea-spike phenomenon is also closely related to the location of strong scattering.

Study of RCS characteristics of tilt-rotor aircraft based on dynamic calculation approach

To study the Radar Cross-Section (RCS) characteristics of the tilt-rotor aircraft, a dynamic calculation approach that takes into account rotor rotation and nacelle tilt is presented. Physical optics and physical theory of diffraction are used to deal with the instantaneous electromagnetic scattering of the target. The RCS of the aircraft in the helicopter mode, fixed-wing mode and transition mode is analyzed. The results show that in the fixed-wing mode, the blade has a weaker deflection effect on the head incident wave in the horizontal plane. The helicopter mode improves the scattering of the rotor in the horizontal plane, while it increases the scattering source on the surface of the nacelle. At a fixed tilt angle, the RCS of the aircraft under a given azimuth angle still shows obvious dynamic characteristics. Dynamic tilting significantly changes the scattering effects of blades, hubs, nacelles and wingtips. The proposed approach is shown to be feasible and effective to learn the electromagnetic scattering characteristics of the tilt rotor aircraft.

증분 회절이론을 이용한 완전도체 산란체의 레이다 단면적 해석

This paper presents the calculation of the radar cross-section (RCS) of an arbitrary scatterer with a perfect electric conductor by using the incremental theory of diffraction (ITD), a high-frequency technique. The reflected field at the surface of the scatterer is calculated using conventional shooting and bouncing rays (SBR), and the diffracted field at the edge is calculated using the ITD. The proposed method is verified by calculating the monostatic and bistatic RCS of a scatterer composed of two cubes of different sizes and comparing it with the simulation results from CST Microwave Studio. Furthermore, it is demonstrated by calculating the bistatic RCS for a simplified ship that the divergence problem in the physical theory of diffraction can be solved using the proposed method.