Showing papers on "Physical optics published in 1987"

Backscatter analysis of dihedral corner reflectors using physical optics and the physical theory of diffraction

Abstract: Physical optics (PO) and the physical theory of diffraction (PTD) are used to determine the backscatter cross sections of dihedral corner reflectors in the azimuthal plane for the vertical and horizontal polarizations. The analysis incorporates single, double, and triple reflections; single diffractions; and reflection-diffractions. Two techniques for analyzing these backscatter mechanisms are contrasted. In the first method, geometrical optics (GO) is used in place of physical optics at initial reflections to maintain the planar nature of the reflected wave and subsequently reduce the complexity of the analysis. The objective is to avoid any surface integrations which cannot be performed in closed form. This technique is popular because it is inherently simple and is readily amenable to computer solutions. In the second method, physical optics is used at nearly every reflection to maximize the accuracy of the PTD solution at the expense of a rapid increase in complexity. In this technique, many of the integrations cannot be easily performed, and numerical techniques must be utilized. However, this technique can yield significant improvements in accuracy. In this paper, the induced surface current densities and the resulting cross section patterns are illustrated for these two methods. Experimental measurements confirm the accuracy of the analytical calculations for dihedral corner reflectors with right, acute, and obtuse interior angles.

Measuring and modeling the backscattering cross section of a leaf

Abstract: Leaves are a significant feature of any vegetation canopy, and for remote sensing purposes it is important to develop an effective model for predicting the scattering from a leaf. From measurements of the X band backscattering cross section of a coleus leaf in varying stages of dryness, it is shown that a uniform resistive sheet constitutes such a model for a planar leaf. The scattering is determined by the (complex) resistivity which is, in turn, entirely specified by the gravimetric moisture content of the leaf. Using an available asymptotic expression for the scattering from a rectangular resistive plate which includes, as a special case, a metallic plate whose resistivity is zero, the computed backscattering cross sections for both principal polarizations are found to be in excellent agreement with data measured for rectangular sections of leaves with different moisture contents. If the resistivity is sufficiently large, the asymptotic expressions do not differ significantly from the physical optics ones, and for naturally shaped leaves as well as rectangular sections, the physical optics approximation in conjunction with the resistive sheet model faithfully reproduces the dominant feataures of the scattering patterns under all moisture conditions.

Quantum theory of light propagation: Linear medium

Abstract: We have developed a quantum-mechanical formalism which permits the treatment of light propagation within the conceptual framework of quantum optics. The formalism rests on the calculation of the momentum operator for the radiation field, and yields directly a description for the spatial progression of the electromagnetic waves. In this paper we give a quantum-mechanical treatment for refraction and reflection by applying our formalism to propagation through a linear dielectric. The fidelity with which this formalism reproduces all results known from classical optics demonstrates its validity.

Synthesis of tapered resistive strips

Abstract: A technique for synthesizing a resistive taper that generates desired bistatic scattering and backscattering patterns from a strip is outlined. Antenna synthesis techniques relate the scattered field to the induced surface current density. Physical optics approximations then relate the induced current to the resistivity. The taper is checked by computing the surface current density and scattered fields of the tapered resistive strip using the integral equation formulation and comparing with the physical optics results.

Review of the full wave solutions for rough surface scattering and depolarization: Comparisons with geometric and physical optics, perturbation, and two-scale hybrid solutions

Abstract: In this review paper, the principal steps in the derivation of the full wave solutions to problems of scattering and depolarization by irregular layered media are presented. Special consideration is given to scattering by two-dimensional random rough surfaces of finite conductivity. The full wave solutions are compared with the high-frequency/geometric optics and physical optics solutions as well as the low-frequency/perturbation solutions. Since the full wave approach accounts for both specular point scattering as well as diffuse/Bragg scattering in a unified. self-consistent manner, it resolves the discrepancies between the physical optics and perturbation solutions and bridges the wide gap between them. Thus on applying the full wave approach to scattering by composite rough surfaces, it is not necessary to adopt a two-scale model of the rough surface. The full wave solutions are also compared with hybrid perturbation and physical optics solutions which are based on the artificial decomposition of the composite rough surface into a large- and a small-scale rough surface. The full wave solutions satisfy duality, reciprocity, and realizability relationships in electromagnetic theory, and the results are invariant to coordinate transformations. The full wave approach also accounts for coupling between the radiation fields, the lateral waves, and the surface waves that constitute the complete field expansions, and it can be applied to problems of scattering at near-grazing angles. A recent review of the full wave approach is also discussed in detail.

Consequences of nonorthogonality on the scattering properties of dihedral reflectors

Abstract: Small deviations from orthogonality can reduce drastically the backscattering radar cross section (RCS) of dihedral corner reflectors. The method of physical optics is used to calculate the magnitude of the reductions in RCS which result from modest departures from orthogonality. The theoretical results are then compared with experimental measurements which are found to be in very good agreement.

Scattering by a ferrite-coated conducting sphere

Abstract: The theory for scattering by a perfectly conducting sphere with a coating of lossy, homogeneous, isotropic ferrite material is presented. In addition to the rigorous eigenfunction formulation, the physical optics (PO) and geometrical optics (GO) approximations are also included. Numerical results are shown in graphical form to illustrate the backscatter echo area versus the radius of the sphere, as well as the bistatic scattering patterns.

A physical optics correction for backscattering from curved surfaces

Abstract: The conventional physical optics (PO) approximation used to calculate the scattered fields from a conducting body leads to incorrect scattered fields even in the specular reflection region. This is true even when all other subdominant terms are assumed to be absent. The inaccuracy stems from the fact that the surface currents used in the PO approximation suddenly truncate at the shadow boundary of curved surfaces resulting in an erroneous contribution. Expressions for these shadow boundary (end point) contributions are presented in this paper. It is shown that if these end point contributions are subtracted from the conventional PO results, one obtains a better representation of the true scattered field. For illustration, backscattered fields from various conducting bodies are computed using the corrected PO solution and are compared with the exact scattered fields.

Geometrical optics approach to the nematic liquid crystal grating: numerical results.

Abstract: The problem of the grating action of a periodically distorted nematic liquid crystal layer, in the geometrical optics ray approximation is considered, and a theory for the calculation of the fringe powers is proposed. A nonabsorbing nematic phase is assumed, and the direction of incidence is taken to be normal to the layer. The powers of the resulting diffraction fringes are related to the spatial and angular deviation of the rays propagating across the layer and to the perturbation of the phase of the wave associated with the ray. The theory is applied to the simple case of a harmonically distorted nematic layer. In the case of a weakly distorted nematic layer the results agree with the predictions of Carroll's model, where only even-order fringes are important. As the distortion becomes larger, odd-order fringes (with the exception of the first order) become equally important, and particularly those at relatively large orders (e.g., seven and nine) exhibit maxima greater than that of the even-order neighbors. Finally, the dependence of the powers of odd-order fringes on the distortion angle is quite different from that of the even-order fringes.

The Ultrasound Examination of the Hip

Abstract: The physical properties of ultrasound can be explained using the physical concepts of wave optics. The ultrasound wave propagates in the body along a straight path, similar to a beam of light. As in optics, the ultrasound wave is subject to processes of refraction and interference. Unlike light, sound requires a medium in which to propagate. It does so as a periodic fluctuation of density in the form of longitudinal waves; transverse waves also can occur in solid materials. The number of vibrations per second is measured in Hertz (Hz). Sound vibrating at frequencies up to 16 Hz is called infrasound. This range of frequencies is inaudible to the human ear, which can perceive frequencies only in the 16–20 Hz range. Frequencies above 20 Hz are called ultrasound. The velocity of sound in air is 0.3 km/s. Sound velocity increases in media of greater acoustic density, ranging from 1500 m/s in water to as much as 6000 m/s in iron.

Numerical computation of diffraction coefficients

Abstract: Direct numerical methods are explored for the computation of diffraction coefficients for a wide class of canonical structures. Although these canonical structures are infinite or semi-infinite, the initial computations are performed on finite bodies. Extraction of the desired coefficient therefore necessitates the elimination of radiation from extraneous diffraction centers. This is accomplished by a variety of techniques including current windowing, tapered resistivity, and screening by conducting shields. Singularities at shadow boundaries are derived via physical optics (PO). The procedure is elucidated through a number of examples for which analytic results are available for comparison. These include the perfectly conducting half-plane, wedge, rounded wedge, and grooves in a ground plane. Computed diffraction coefficients for lossy dielectric wedges are applied within the context of geometrical theory of diffraction (GTD) to the computation of diffraction from a triangular prism and the results are in satisfactory agreement with those of the method of moments (MM).

External self-focusing, self-bending and optical limiting with thin non-linear media

Abstract: Analytic solutions are presented for a simple model describing situations where self-focusing and self-bonding of intense optical beams by thin non-linearly refracting media can occur. Physical optics is employed to study effects arising when a non-linear medium is placed in contact with an aperture stop. The feasibility of constructing an optical power limiter by utilizing either external self-focusing or self-bending is discussed.

An efficient method to compute spurious end point contributions in PO solutions. [Physical Optics

Abstract: A method is given to compute the spurious end point contributions in the physical optics (PO) solution for electromagnetic scattering from conducting bodies. The method is applicable to general three-dimensional structures. The only information required to use the method is the radius of curvature of the body at the shadow boundary. Thus, the method is very efficient for numerical computations. As an illustration, the method is applied to several bodies of revolution to compute the end point contributions for backscattering in the case of axial incidence. It is shown that in high frequency situations, the end point contributions obtained using the method are equal to the true end point contributions.

Models for electromagnetic scattering from the sea at extremely low grazing angles

Abstract: : The present state of understanding in the field of low-grazing-angle sea scatter is reviewed and extended. The important concept of shadowing is approached from the point of view of diffraction theory, and limits in wind speed and radar frequency are found for the application of shadowing theories based on geometrical optics. The implications of shadowing function based on 'illumination thresholding' are shown to compare favorably with a variety of experimental results. Scattering from the exposed surface peaks is treated by a composite-surface Bragg model, and by wedge models using both physical optics an the method of equivalent currents. Curiously, the scattering levels predicted by these widely different approximations are all in fairly good agreement with experimental values for moderately low grazing angles (about 5 deg), with the physical optics wedge model being superior at 1 deg. A new scattering feature, the 'slosh', is introduced, with scattering behavior that resembles the temporal and polarization dependence of observed low angle returns from 'calm' water. The 'plume' model of scattering from breaking waves (from earlier work) is discussed as a source of high-intensity Sea Spikes. It is emphasized that the prediction of low angle scattering from the sea will require considerably more information about the shape, size, and distribution of the actual scattering features. Keywords: Radar clutter, Rough surface, Backscattering, Sea clutter, Diffraction theory, Bragg scattering.

A polarimetric model for the recovery of the high-frequency scattering centers from bistatic-monostatic scattering matrix data

Abstract: The objective of this investigation is to develop multistatic electromagnetic identification/discrimination algorithms using the complete polarimetric scattering data. At high frequencies the electromagnetic scattering from a complex object is modeled by certain scattering centers. The high-frequency (physical optics) bistatic and monostatic scattering matrix properties of a flat plate model of such a scattering center are developed in detail. For the complex target representations, the single scattering center results can be extended to two and three scattering center models. It is suggested that the knowledge of the locations and the local geometries of these scattering centers can be useful in developing identification and pattern recognition algorithms.

The physical optics radar cross section of an elliptic cone

Abstract: The physical optics approximation is used to evaluate the backseattering radar cross section of a semi-infinite metallic elliptic cone. The resulting formula can be directly interpreted as a generalization Of the well-known formula for the baekscattering cross section of a circular cone. In addition the bistatic radar cross section of the elliptic cone is calculated.

The SNFGTD method and its accuracy

Abstract: The spherical near-field geometrical theory of diffraction (SNFGTD) method is an extended aperture method by which the near field from an antenna is computed on a spherical surface enclosing the antenna using the geometrical theory of diffraction. The far field is subsequently found by means of a spherical near-field to far-field transformation based on a spherical wave expansion of the near field. Due to the properties of the SNF-transformation, the total far field may be obtained as a sum of transformed contributions which facilitates analysis of collimated beams. It is demonstrated that the method possesses some advantages Over traditional methods of pattern prediction, but also that the accuracy of the method is determined by the quasioptical methods used to calculate the near field.

New main reflector, subreflector and dual chamber concepts for compact range applications

Abstract: A compact range is a facility used for the measurement of antenna radiation and target scattering problems. Most presently available parabolic reflectors do not produce ideal uniform plane waves in the target zone. Design improvements are suggested to reduce the amplitude taper, ripple and cross polarization errors. The ripple caused by diffractions from the reflector edges can be reduced by adding blended rolled edges and shaping the edge contour. Since the reflected edge continues smoothly from the parabola onto the rolled surface, rather than being abruptly terminated, the discontinuity in the reflected field is reduced which results in weaker diffracted fields. This is done by blending the rolled edges from the parabola into an ellipse. An algorithm which enables one to design optimum blended rolled edges was developed that is based on an analysis of the continuity of the surface radius of curvature and its derivatives across the junction. Futhermore, a concave edge contour results in a divergent diffracted ray pattern and hence less stray energy in the target zone. Design equations for three-dimensional reflectors are given. Various examples were analyzed using a new physical optics method which eliminates the effects of the false scattering centers on the incident shadow boundaries. A Gregorian subreflector system, in which both the subreflector and feed axes are tilted, results in a substantial reduction in the amplitude taper and cross polarization errors. A dual chamber configuration is proposed to eliminate the effects of diffraction from the subreflector and spillover from the feed. A computationally efficient technique, based on ray tracing and aperture integration, was developed to analyze the scattering from a lossy dielectric slab with a wedge termination.

Comparison of induced current and aperture field integrations for an offset parabolic reflector

Abstract: The fields predicted by integration of the physical optics induced currents on the reflector (ICM) and the geometrical optics aperture fields (AFM) on the surface that caps the reflector are compared numerically for offset parabolic reflectors. It is found that the AFM solutions are very close to ICM solutions for the main beam and the first few sidelobes but discrepancy remains for the far-out sidelobes. This discrepancy is found to come mainly from the difference of polarization matrix for each method.

Brightness and coherence of radiation from undulators and high-gain free electron lasers

Abstract: The purpose of this paper is to review the radiation characteristics of undulators and high-gain free electron lasers (FELs) The topics covered are: a phase-space method in wave optics and synchrotron radiation, coherence from the phase-space point of view, discussions of undulator performances in next-generation synchrotron radiation facility and the characteristics of the high-gain FELs and their performances (LSP)

Experiments with nondiffracting needle beams

Abstract: We present a method for generating the nondiffracting beams predicted by Durnin 1 as well as the results of recent experiments with these beams

Computer‐assisted teaching of optics

Abstract: This article introduces ideas for the teaching of an undergraduate optics course using personal computers. It covers five topics with three on geometric optics and two on physical optics. They are (1) image formation of spherical mirrors, (2) spherical aberration of a lens, (3) chromatic aberration of lenses, (4) computer generated hologram, and (5) Fourier transforms and information processing.

Terrain modelling of glideslope for instrument landing system

Abstract: The paper makes a contribution to the evaluation of irregularities introduced in electronically defined glideslopes of UHF instrument landing systems (ILS) by the unevenness of the terrain around the glideslope antenna. Various methods of physical and geometric optics have been applied in recent years to model and estimate the glideslope aberration at given locations prior to actual installation. A systematic study of various methods is made in the paper. A general treatment is evolved, which is capable of exhaustively handling arbitrary ray order effects and topography. The uniform asymptotic theory has been applied to the ILS problem and results compared with the uniform theory of diffraction. The results of actual case studies are presented.

Incremental Diffraction Coefficients for Planar Surfaces. Part 1. Theory

Abstract: : Exact expressions for incremental diffraction coefficients at arbitrary angles of incidence and scattering are derived directly in terms of the corresponding two-dimensional, cylindrical diffraction coefficients. Specifically, if one can supply an expression for the conventional diffraction coefficients of a two-dimensional planar scatterer, one can immediately find the incremental diffraction coefficients of a two-dimensional planar scatterer, one can immediately find the incremental diffraction coefficients through direct substitution. No integration, differentiation, or specific knowledge of the current is required. The derivation is limited to perfectly conducting scatters that consist of planar surfaces, such as the wedge, the slit in an infinite plane, the strip, parallel or skewed planes, polygonal cylinders, or any combination thereof; and requires a known expression (whether exact or approximate) for the two-dimensional diffraction coefficients produced by the current on each different plane. Special attention is given to defining unambiguously all real angles and their analytic continuation into the imaginary values required by the incremental diffraction coefficients. The physical theory of diffraction, geometrical theory of diffraction, and physical optics incremental diffraction coefficients agree in the case of the infinite wedge. The two dimensional diffraction coefficients are recovered when the general expressions for the incremental diffraction coefficients are integrated over an infinite straight line. The general method is used to obtain, for the first time, the incremental diffraction coefficients for the infinitely long, narrow strip and slit.

Applied Classical Electrodynamics. Volume 2. Nonlinear Optics

Abstract: (1987) Applied Classical Electrodynamics Volume 2 Nonlinear Optics Journal of Modern Optics: Vol 34, No 4, pp 480-481