Physical Optics Method Research Articles

Comprehensive optimization of aerodynamic noise and radar stealth for helicopter rotor based on Pareto solution

To reduce the aerodynamic noise and radar cross section (RCS) of the helicopter rotor without sacrificing its aerodynamic characteristic, a comprehensive optimization method (COM) based on Pareto solutions is presented. An initial model of the rotor is created by full factorial design (FFD) and meshed by unstructured grid techniques to participate in the calculation and analysis of flow field and electromagnetic scattering field. The aerodynamic characteristics of the rotor flow field are simulated by computational fluid dynamics (CFD) method based on Navier–Stokes (N–S) equations and k–ε standard viscous model. According to the aerodynamic performance constraints of not reducing rotor lift, the thickness noise and the loading noise solved by Farassat 1A formula and the RCS value calculated by physical optics (PO) method and physical theory of diffraction (PTD) are designed as the comprehensive optimization goals. With the progress of the comprehensive balance analysis of these stealth indicators for the rotor models to be optimized, an excellent model with high comprehensive stealth performance and aerodynamic characteristic is generated by the proposed optimization method based on Pareto solutions. In addition, the effects of the models and parameters of each part of the rotor on these characteristics including aerodynamic lift, RCS, thickness noise and loading noise are analyzed in detail. It is effective and impactful of the comprehensive optimization method to deal with the multidisciplinary optimization problems of aerodynamic noise and radar stealth for helicopter rotor.

Discussion of a physical optics method and its application to absorbing smooth and slightly rough hexagonal prisms

Three different mathematical solutions of a physical optics model for far field diffraction by an aperture due to Karczewski and Wolf are discussed. Only one of them properly describes diffraction by an aperture and can, by applying Babinet's principle, be used to model diffraction by the corresponding plane obstacle, and by further approximation, diffraction by a particle. Studying absorbing scatterers allows a closer investigation of the external diffraction component because transmission is negligible. The physical optics model has been improved on two aspects: (i) To apply the diffraction model based on two-dimensional apertures more accurately to three-dimensional objects, a size parameter dependent volume obliquity factor is introduced, thus reducing the slightly overestimated side scattering computed for three-dimensional objects. (ii) To compensate simplifications in the underlying physical optics diffraction model for two-dimensional apertures [26] a size parameter dependent cross polarisation factor is implemented. It improves cross polarisation for diffraction and reflection by small particle facets. 2D patterns of P11, –P12/P11 and P22/P11 and their azimuthal averages for slightly rough absorbing hexagonal prisms in fixed orientation are obtained and compared with results from the discrete dipole approximation. For particle orientations where shadowing is not negligible, improved phase functions are obtained by using a new method where the incident beam is divided into sub-beams with small triangular cross sections. The intersection points of the three sub-beam edges with the prism define the vertices of a triangle, which is treated by the beam tracer as an incidence-facing facet. This ensures that incident facing but shadowed crystal facets or regions thereof do not contribute to the phase functions. The method captures much of the fine detail contained in 2D scattering patterns obtained with DDA. This is important as speckle can be used for characterizing the size and roughness of small particles such as ice crystals.

Range Distance Requirements for Large Antenna Measurements for Square Aperture With Uniform Field Distribution

Frequency dependences of the field for constant angle of observation measured by different probes at different distances are discussed. We consider the case of the square aperture antenna with the uniform field distribution. The analysis is based on time-domain physical optics method of field calculation. We show and explain the effect of sidelobe reduction when a big square probe is placed at a finite distance from square aperture antenna. Errors of the sidelobe levels of the antenna radiation pattern (ARP) in the cases of different sizes of the probe placed at different distances are shown. We show an optimal probe size and an optimal measurement distance between antennas. We also show and explain the effect of a large distortion of the ARP first zero, measured by the big probe at the finite distance.

Modified theory of physical optics and the correction terms of the physical theory of diffraction

The methods of physical optics and physical theory of diffraction are reviewed for electromagnetic waves. The Fermat principle and its’ modified version are investigated and the necessity of the introduction of a variable unit vector is put forth. The scattering integrals of modified theory of physical optics are reviewed in this context. Recent comments on the modified theory of physical optics are discussed and refuted clearly. A proof is given on the nature of the physical theory of diffraction’s correction terms. The proof is visualized with some numerical simulations.

PO calculation for reduction in radar cross section of hypersonic targets using RAM

The radar cross section (RCS) reduction of hypersonic targets by radar absorbing materials (RAM) coating under different reentry cases is analyzed in the C and X bands frequency range normally used for radar detection. The physical optics method is extended to both the inhomogeneous plasma sheath and RAM layer present simultaneously. The simulation results show that the absorbing coating can reduce the RCS of the plasma cloaking system and its effectiveness is related to the maximum plasma frequency. Moreover, the amount of the RCS decrease, its maxima, and the corresponding optimal RAM thickness depend on the non-uniformity and parameters of the plasma sheath. In addition, the backward RCS of the flight vehicle shrouded by plasma shielding and man-made absorber is calculated and compared to the bare cone.

MLFMM-based, fast multiple-reflection physical optics for large-scale electromagnetic scattering analysis

The asymptotic, physical optics (PO) approximation is applicable to electromagnetic scattering analysis of electrically large, conducting objects, which is important for various applications, such as radar cross-section (RCS) calculations. It relates the incident magnetic field to the induced surface current at points on a scatterer's surface with line-of-sight visibility to the source. Here, the focus is on mesh-based PO, using a triangle element mesh with standard Rao–Wilton–Glisson basis functions to represent the surface current density. The multiple-reflection PO (MRPO) method involves applying the PO approximation to the field radiated by the present current solution towards the scatterer itself, to account for successive internal reflections. The visibility status between every pair of basis functions is required, taking into account all geometry. In a conventional implementation, internal reflected field calculation and internal shadowing determination runtimes both scale as O(N2); N denotes the number of mesh elements. In this paper an accelerated version of the mesh-based MRPO method is presented: fast MRPO (FMRPO). The multi-level, fast multipole method (MLFMM) is used to accelerate internal reflected field calculation. The key aspect to achieving acceleration for general geometries, is to incorporate internal shadowing into the MLFMM interaction tree. This requires an alteration to the inter-group interaction criterion of the MLFMM, as well as efficient evaluation of inter-group shadowing status flags, to preserve the beneficial cost-scaling property of the MLFMM. Algorithmic parameters are introduced, which control the accuracy of internal shadowing determination. The FMRPO runtime scales as O(NlogN), in the high-frequency limit. Numerical results are presented, demonstrating accuracy and efficiency for general scattering objects.

A Bi-Iterative Model for Electromagnetic Scattering From a PEC Object Partially Buried in Rough Sea Surface

A bi-iterative physical optics (PO) method is presented in this letter to investigate the composite scattering from a perfectly electric conducting object partially buried in the dielectric rough sea surface. In the present method, both the scatterings of a partially buried object and the underlying sea surface are calculated by the PO method. And a bi-iterative strategy is considered, including the mutual interaction among points on the object in direct scattering and the mutual interaction between the object and the sea surface in coupling scattering. In addition, the coupling interaction between the partially buried object and the sea surface contains two parts: 1) the upper surface of the sea surface and the upper part of the object and 2) the lower surface of sea surface and the lower part of the object. In numerical simulations, the bistatic normalized radar cross sections of the composite model are computed by the bi-iterative PO method and are compared with those by the conventional method of moments for different object types and polarizations. The results show that the proposed method has a good accuracy and can greatly reduce the computational time and memory requirement.

Protecting Distance between Radar Stations and UHV Power Transmission Lines

With the construction of UHV (Ultra-High Voltage) transmission lines and radar stations, the interference of UHV transmission lines to air intelligence radar stations has become increasingly prominent. Aiming at the problem that it is difficult to solve the loss of radar detection range caused by UHV transmission lines, the idea of using RCS (Radar Cross Section) of UHV transmission towers as an intermediate parameter to solve the radar detection range loss is proposed. In order to solve the problem of accuracy when using Physical Optics (PO) to solve such electromagnetic scattering problems of complex structures, the traditional PO method needs to be improved when used in the calculation of the large-size’s scattering field like the UHV tower. It is proposed to use Incremental Length Diffraction Coefficient (ILDC) to revise the diffraction of the edge of the tower, and to study the coupling conditions with the PO method, so as to solve the scattering field of the complex structure of the tower. Based on this, 5 UHV transmission towers’ model is established to simulate the UHV transmission lines, and the regular variation of radar detection loss with the distance between the two systems is studied. These results show that when the distance between the UHV transmission lines and the radar station is more than 2200 m, the loss can reach within 0.9 dB of the standard, which is in line with the standard for the construction around the air intelligence radar station.

Adaptive Sampling of Physical Optics Currents Based on EFIE Error Prediction

Simple and efficient method for a numerical analysis of an electromagnetic scattering problem is developed by converting the electric field integral equation (EFIE) into a simple integral equation with known variables. Regarding electrically large conducting objects, the surface current density can be easily approximated by the physical equivalent principle. The combination of the equivalent surface current and the EFIE generates unexpected tangential field component right on the perfectly conducting surface, which is against the boundary condition for electric field. The unexpected tangential field component which is against the physical behavior of electric field can be used to define numerical error that represents abnormality of the object. Instead of taking more samples over the entire surface, focusing on the abnormal surfaces by subdividing adaptively according to predefined error can improve the computation efficiency. In this paper, an adaptive sampling of physical optics (PO) currents is performed based on the error prediction by EFIE. Furthermore, the proposed method is applied to the conventional iterative PO algorithm in order to increase the calculation efficiency by adaptively meshing the target domain. The resulting radar cross section is compared to the results from the method of moments as well as the general PO method.

Physical Optics Methods of Recording Weak Structural Responses of Dispersed Clay Systems to the Effect of Microwave Radiation

A complex of physical optics methods that includes x-ray phase analysis, colorimetry, and wavelet analysis is proposed. Weak structural responses of dispersed clay systems to the effect of microwave radiation are recorded by means of the complex. Through the use of a combination of x-ray phase analysis and colorimetric gradation, it is possible to establish phase and polymorphic conversions, and with the use of wavelet analysis, the evolution of the morphology of dispersed particles. The efficiency of the proposed complex of physical optics methods for studying secondary phase morphologies in the millimeter, micrometric, and submicrometric scales is demonstrated.

Shadow Radiation Iterative Physical Optics Method for High-Frequency Scattering

A shadow-radiation-based fast iterative physical optics (IPO) scheme, for the analysis of the scattering from large complex geometries involving multiple reflection and occlusion effects, is proposed. By employing a “shadow-radiation” mechanism, the scheme alleviates the need for expensive computation and storage of a geometric visibility function. In a nested fashion, shadow radiation iterations are performed for each “bounce” in the conventional multiple reflection IPO scheme. The resulting method makes use of simple field integrals which are all accelerable using a multilevel nonuniform grid-based field evaluation algorithm, with a modification tailored to the scheme’s integral kernels. The proposed scheme is also shown analytically to be a more stable (faster converging) equivalent of existing IPO schemes. The method is studied in terms of accuracy and performance for representative examples and compared with alternative physical optics and numerically exact solution techniques.

Characteristics Analysis and Image Processing for Full-Polarization Synthetic Aperture Radar Based on Electromagnetic Scattering From Flat Horizontal Perfect Electric Conducting Reflector

In this paper, the physical optics method is employed to study the problem of characteristics analysis and image processing for full-polarization synthetic aperture radar (SAR), where electromagnetic scattering from a flat horizontal perfect electric conducting (PEC) reflector is involved. The model of the full-polarization SAR echo from a small region of flat horizontal PEC reflector is deduced based on the dyadic Green’s function theory. With the available echo model, image processing and results are presented for the full-polarization SAR. For the horizontal co-polarization channel, the amplitude of imaging result descends with the squint angle, where the well-focused imaging result can always be obtained. On the contrary, the amplitude of cross-polarization channel imaging results is increased with the squint angle. When the radar works in the side-looking mode or low-squint mode, the cross-polarization channel echo cannot be well focused. For the high-squint mode, it can be well focused. For the horizontal co-polarization channel, the amplitude of well-focused result can be approximately regarded as a constant for all squint angles. The effectiveness of the characteristics analysis results is demonstrated via simulated and real measured Ka-band airborne full-polarization SAR data.

A Facet-Based Simulation of the Multipath Effect on the EM Scattering and Doppler Spectrum of a Low-Flying Target at Maritime Scene

A hybrid facet-based electromagnetic scheme is developed in this letter to investigate the multipath effect on the electromagnetic scattering and the Doppler spectrum of a low-flying target at maritime scene. In the scheme, the target and sea surface are both facetized. The facet-based small slope approximation method is developed to calculate the scattering upon the sea facet, which involves the composite scattering mechanisms upon both the long wave and short wave structures. The geometrical optics and physical optics method are combined with the fast ray-tracing technique in consideration of the multipath scattering. The equivalent edge current method is used to consider the scattering from the edged structures on the target. The tapered wave is used in the calculation process to eliminate the nonphysical edge diffractions. Numerical simulations present the multipath effect on the radar scattering characteristics of a low flying missile-like target above the sea surface. The Doppler spectra of the multipath scattering from the target flying at the time-evolving maritime scene are eventually simulated. The multipath effect is also investigated in the Doppler domain.

Analytic Physical Optics Solution to Bistatic 3D Scattering From Separated Dihedral

Constructing the mapping between the geometric object and its corresponding 3D scattering response is a fundamental but challenging task in the domain of electromagnetic scattering, which is crucial for radar target recognition and the 3D structure interpretation. In recent years, the analytic physical optics, as a typical analytic solution, has been successfully utilized to produce the parsimonious, physically relevant 3D bistatic scattering models for standard dihedral and obtuse dihedral. In this paper, the scattering mechanism of separated dihedral, as a canonical structure that often appears in the actual targets, is investigated and its corresponding bistatic 3D scattering model is derived and established by the combination of geometric optics and physical optics method. First, the single and double-bounce reflection, as well as the occlusion occurred under different incident wave angles for the separated dihedral are analyzed in detail. Consecutively, the bistatic 3D scattering responses for different reflection cases are derived by the physical optical integration. Finally, the closed-form solution to bistatic 3D scattering model of separated dihedral is presented. The experiments with the two state-of-the-art electromagnetic calculation methods, shooting and bouncing rays and method of moments, validate the effectiveness of the proposed model. Especially, the experimental results also manifest that the standard dihedral is the specific case of the proposed model.

About modeling the waves scattering on the complex shape objects

Background: Reducing the detection probability by radar stations for military or civil complex shape objects is very important problem of modern radar theory. The solution to this problem is impossible without numerous estimates of the effective scattering surface (RCS) of the investigated object. Objectives: The purpose of the work was to analyze and improve the efficiency of methods for modeling electromagnetic scattering on objects of complex shape. The process of constructing a facet model of an complex shape object for modeling electromagnetic scattering and an algorithm to simplify the geometric model of an object to reduce the time required for modeling is considered. Materials and methods: As the main method for calculating the RCS, we chose the method of rays that fall and reflect (in the English language literature “Shooting and Bouncing Rays” SBR). Wherein the modeling electromagnetic scattering on an complex shape object is based on the methods of physical and geometric optics. Object is represented in the form of a geometric model which takes into account the shape of the object and its electrodynamic properties (reflection coefficient, dielectric and magnetic permeability of the surface, conductivity, etc.). Results: The general steps of the SBR method are discussed, and the efficient of using the surface mesh method to launch the rays is shown. Effective approaches to simplify the calculation for complex shape objects are proposed, in particular, the use of Raytressing and k-d tree is considered. The using of large facets for modeling surface flat sections of complex shape object is proposed. To assess the effect of the facet size on the accuracy of RCS calculations, we simulated electromagnetic scattering for a triangular plate, the surface of which is represented using different numbers of facets. A comparison with the well-known expressions for a triangular plate RCS is made. Conclusions: The accelerating possibilities of the process of electromagnetic wave diffraction calculation on complex shape objects are offered. The efficiency of the created algorithms is tested numerically.

The Fast Solver for Calculating the Scattered Fields From the Multiscale Scatterers

In this paper, the efficient methods for calculating the scattered fields from the electrically large scatterers and multiscale scatterers are discussed. The method of moment physical optics (MoM-PO) method is introduced to obtain the scattered fields from the multiscale scatterers. Due to the highly oscillatory behavior of the PO integrals, the numerical contour deformation technique is proposed to calculate the PO scattered fields. The z buffer acceleration technique based on General Public Utilities is adopted to distinguish between the lit and shadow regions of the surfaces. Numerical examples from the electrically large and multiscale scatterers are provided to benchmark the efficiency of the proposed method.

Comparison of Three Different Styles of Submarine Sails on Electromagnetic Scattering under the Detection of Airborne Radar

This paper studies radar cross section of submarine sails on the water. Under the detection of the enemy’s airborne radar, considering the motion of the submarine, the sail model of radar pitch angle incidence range analysis is established. By using CATIA software, the 3D models of AKULA sail, SUBOFF sail and VICTOR sail are built. On the basis of the physical optics method and the equivalent currents method, the scattering characteristics of sails RCS(radar cross section) are simulated under X radar band. Through the microwave anechoic chamber test, this paper verifies the accuracy of the combination of the physical optics method and the equivalent electromagnetic flow method. The influence of the distance from the airborne radar to the sail on the pitch angle of the electromagnetic wave is discussed, with the elevation angle of the radar antenna varies. Then, we illustrate the characteristics of circumferential direction RCS of the sail under different pitch angles. Finally, the mean RCS of the sail at a given pitch angle is simulated. The results show that the AKULA sail is considerably superior to SUBOFF sail and VICTOR sail on stealth performance with the pitch angle less than 4° . But when the pitch angle exceeds 10°, the SUBOFF sail can be given priority.

A Fast and Efficient Method for the Composite Scattering of a Coated Object Above 3D Random Rough Surfaces

This paper presents a fast and efficient method that combines physical optics with physical optics to solve the composite scattering problem of a coated object above 3-D random rough surfaces. The object coated with lossy electric or magnetic radar absorbing materials is modeled as a stratified structure, and 3-D random rough surfaces are generated using Monte Carlo method with Gaussian spectrum. The proposed method utilizes fast and efficient physical optics as a solution for the coated object and the underlying random rough surface. Then a reradiation physical optics method based on Huyghens’ principle is used as a solution for coupling scattering between the coated object and the underlying rough surface. The proposed method is numerically validated by comparing it with the commercial software FEKO and a multihybrid Kirchhoff approximation with the hybrid finite element-boundary integral algorithm. Runtime and memory consumption are also compared. Our method is found to reduce considerable time and memory while maintaining sufficient accuracy. The difference scattering radar cross section of a coated sphere above a 3-D perfectly electric conductor rough surface is numerically simulated. Furthermore, the dependence of difference scattering characteristic on the object coating parameters and the underlying rough surface parameters under different polarizations is discussed.

A hybrid EM scheme for the composite scattering and the SAR imaging of a low-altitude target above the electrically large and multi-scale sea surface

ABSTRACTThis article has developed a feasible hybrid electromagnetic scheme to evaluate the composite scattering and the Synthetic Aperture Radar(SAR) image characteristics of a low altitude perfect electric conductor (PEC) target above the sea surface at the high microwave frequency bands. In this method, the scattering upon the target surface is calculated by the Physical Optics (PO) method; the sea surface scattering is evaluated by a Bragg Modified Small Scale Approximation (BMSSA) method; the coupling components are considered by the Geometrical Optics (GO) method with efficient ray tracing techniques; finally, the diffractions from the edged structures are considered by the Equivalent Edge Current (EEC) method. The hybrid method can give a physical insight of the composite scattering mechanisms, and it can overcome the difficulties in accurately evaluating the composite scattering characteristics of a target above the electrically large and multi-scale sea surface in the real scene. The computation model and method is validated by the exact numerical solver. Numerical results compare the scattering characteristics of a missile-like target above the electrically large sea surface in the conditions of different incident frequencies, incident angles and sea states. Finally, SAR image characteristics at different sea states are presented, with the target scattering, sea scattering and coupling scattering characteristics further discussed in details.

The applicability of physical optics in the millimetre and sub-millimetre spectral region. Part II: Application to a three-component model of ice cloud and its evaluation against the bulk single-scattering properties of various other aggregate models

The bulk single-scattering properties of various randomly oriented aggregate ice crystal models are compared and contrasted at a number of frequencies between 89 and 874 GHz. The model ice particles consist of the ten-branched plate aggregate, five-branched plate aggregate, eight-branched hexagonal aggregate, Voronoi ice aggregate, six-branched hollow bullet rosette, hexagonal column of aspect ratio unity, and the ten-branched hexagonal aggregate. The bulk single-scattering properties of the latter two ice particle models have been calculated using the light scattering methods described in Part I, which represent the two most extreme members of an ensemble model of cirrus ice crystals. In Part I, it was shown that the method of physical optics could be combined with the T-matrix at a size parameter of about 18 to compute the bulk integral ice optical properties and the phase function in the microwave to sufficient accuracy to be of practical value. Here, the bulk single-scattering properties predicted by the two ensemble model members and the Voronoi model are shown to generally bound those of all other models at frequencies between 89 and 874 GHz, thus representing a three-component model of ice cloud that can be generally applied to the microwave, rather than using many differing ice particle models. Moreover, the Voronoi model and hollow bullet rosette scatter similarly to each other in the microwave. Furthermore, from the various comparisons, the importance of assumed shapes of the particle size distribution as well as cm-sized ice aggregates is demonstrated.