Showing papers on "Physical optics published in 1974"

A numerical study of electromagnetic scattering from ocean-like surfaces

Abstract: The integral equations describing electromagnetic scattering from cylindrical, perfectly conducting surfaces are formulated and numerical results are presented. The results are compared with those obtained using approximate methods such as physical optics, geometrical optics, and perturbation theory. The integral equation solutions show that the surface radius of curvature must be greater than 2.5 wavelengths for either the physical optics or geometrical optics to give satisfactory results. It has also been shown that perturbation theory agrees with the exact fields as long as the root-mean-square surface roughness is less than one tenth of a wavelength.

Integral equation solution and RCS computation of a thin rectangular plate

Abstract: In this work, a new integral equation is employed to calculate the current distribution on a rectangular plate which is illuminated by a plane wave. Numerical results are also obtained for the radar cross section (RCS) of the plate for different angles of incidence and different dimensions of the plate. These results are compared with other RCS computations using geometrical theory of diffraction, physical optics, and variational methods.

Illumination of multimode optical fibresleaky ray analysis

Abstract: The power transmitted within multimode circular optical fibres illuminated at one end by either coherent or incoherent light is determined. In general, a significant portion of this power is due to the radiation field even kilometres from the source. Thus an analysis in terms of bound modes alone is inadequate and so is geometric optics using Fresnel's lawS. Instead, we use a modified form of geometric optics in which the rays are appropriately weighted to account for the leakage (radiation) from the fibre not included by Fresnel's laws. Extensive numerical results are given.

Geometrical optics and the corner problem

Abstract: : The mixed problem for strictly hyperbolic first order systems in regions containing a multiple corner is considered. Geometric optics approximations are studied and in certain cases are used to construct counter-examples. (Author)

Image Transmission by an Optical System with a Lens-like Medium

Abstract: Image transmission by an optical system with a lens-like medium which has a square-law distribution of dielectric constant was investigated both theoretically and experimentally to see if this system could be applied to coherent optics. The equation describing the field transformed by this system was obtained on the basis of wave optics. It became apparent that not only an imaging condition but also a Fourier transform condition are derived from this equation. Some experiments performed on the image transmission and Fourier transform using SELFOC fibers, and measured results were compared with theoretical ones. The limits on the pass band of spatial frequencies were obtained in terms of off-axis point images in cases, in which the diameter of a medium was finite, and in other cases where a medium had square-law absorption.

Alternative to Holography for Determining Phase from Image Intensity Measurements in Optics

Abstract: IN light optics and electron optics one normally measures the image intensity and attempts to infer from these measurements the object structure In light optics these intensity measurements are insufficient to evaluate the detailed structure of the object and information on the phase of the transmitted light is of prime importance1; the interaction of the light or electrons in transmission through the object can be only satisfactorily explained by wave optics The phase problem in optics is analogous to the X-ray diffraction phase problem, that is, whereas an object can be reconstructed from the phase information (even with incorrect amplitudes), it is not possible to define an object from amplitude measurements only1 We suggest here how a normal optical system can be used to determine both the amplitude and phase from image intensity measurements in bright-field optics In bright-field optics, where the main (on-axis) beam is allowed to interfere with the scattered wave, the transmitted object wavefunction Ψ0(r0) can be written as where Ψs(r0) represents the effect of the object on the incident light or electron wave at the point r0 = (x0, y0) in the object plane; Φs carries information not only on the amplitude attenuation of the wave but also phase shifts introduced by refractive index differences (potential differences in electron optics) across the object The 1 represents the amplitude of the transmitted wave that is not scattered in the object, and this unscattered contribution will give a background in the image The wavefunction Φ0(r0) transmitted by the object may be subsequently affected by lens defects and restricting apertures in the optical system, particularly in electron optics, but for simplicity we shall assume that the wave at the image plane Φi(ri) is equivalent to Φ0(r0) We record not Φi(ri) but the image intensity ∣Φi(ri)∣2 ≡∣Φ0(r0)∣2; the image intensity is from equation (1) where Re and Im denote the real and imaginary parts of Φs At best, if the interaction between the light or electron wave and the object is small and the squared terms in equation (2) can be neglected, we can only determine the real part of Φs from image intensity measurements, and there is no direct way of evaluating the imaginary part of Φs, hence determining both the amplitude and phase But instead of using a normal circular aperture in the back focal plane (Fourier plane) of the objective lens, we can use a semicircular (half-plane) aperture to cut off one-half of the Fourier plane of the object wave-function The Fourier plane, which corresponds to the diffraction or scattering plane, displays the spatial frequencies of the object structure, and the idea is to eliminate initially one-half of the object frequencies from the image Now there is an explicit relationship between the real and imaginary parts of Φs We maintain the bright-field situation by having a small centre section cut out from the aperture to allow the main beam through to interfere with the scattered wave—this is strictly necessary in electron optics to avoid electrical charging problems Suppose we omit the negative half of the Fourier plane (spatial frequencies νx<0), but allow all positive frequencies to contribute to the image; then the image intensity corresponding to this situation (Fig 1a) is, omitting subscripts i, The idea of using a half-plane aperture is not new2, but the important relationship between and has not been given The relationship between the real and imaginary parts of can be derived from standard Fourier theory3 and the analyticity of Φs4, and in order to avoid detailed mathematics, we state the result that the imaginary part of is a one-dimensional Hilbert transform of the real part; that is, taking the Cauchy principal value of the integral From an image recorded using a semicircular or half-plane aperture we have an explicit relation between and But the squared terms in equation (3) prevent a direct calculation of from the image intensity We have solved this problem by initially neglecting these squared terms and we calculate from ½( >0−1); using this approximation to we evaluate using a form of equation (4) which avoids the problem of the singularity at z=x and also takes account of the finite extent of the actual image; again this is a mathematical detail We now have values for both the real and imaginary parts of and a correction is applied to equation (3) for the squared terms, Re2+Im2; it may be necessary to apply this correction several times, depending on the relative contributions of the squared and linear terms to the image intensity In numerical tests, contributions from these squared terms pf 25% of the value of can be systematically corrected in 1–5 iterations This magnitude for the correction is well within the normal conditions of electron microscopy, where image contrast is only 20% (of which squared terms contribute 10%); Re2+Im2 = 025 (relative to the unity of the unscattered beam) would correspond to a very thick object with a strong interaction between the incident wave and the object, corresponding to about 25% scattering from the incident beam

Radar cross section of a rectangular conducting plate by wire mesh modeling

Abstract: Radar cross section of a conducting rectangular plate is investigated numerically and experimentally by a wire mesh model as a function of plate size and incidence angle. Numerical examples also include the edge-on incidence where physical optics and the geometrical theory of diffraction fail.

A comparison of geometrical and integral fields from high-frequency reflectors

Abstract: Various comparisons are made between geometrical optics, integrated physical optics, asymptotic physical optic, the geometrical theory of diffraction, and experimental data for fields from high-frequency paraboloidal and hyperboloidal reflectors.

Recently developed formulations of the inverse problem in acoustics and electromagnetics

Abstract: : Recently developed formulations of the inverse problems in acoustics and electromagnetics are described. There are two types of formulations, one in the geometrical optics limit and the other, an exact formulation for the inverse source problem. Both basic formulations are extended to include the realistic problem of a 'limited aperture' of observations. It is also shown that the inverse source formulation can be applied to the problem of reconstruction of media inhomogeneities from remotely sensed field data. The basic physical optics result is that the characteristic function of the scattering obstacle and the phase and range normalized scattering amplitude are a Fourier transform pair. All other formulations lead to Fredholm integral equations of the first kind.

Rays and modes in optical fibres

Abstract: Difficulties have recently been noted in the application of geometric optics to modal propagation and cutoff in optical fibres. It is shown here that geometric optics is adequate, provided that it treats collectively the congruence of modal rays.

Directional spectra of ocean waves from microwave backscatter

Abstract: The paper presents an analysis of two proposed microwave radar techniques for measuring ocean wave directional spectra. Tomiyasu's (1971) short pulse idea and Barrick's (1972) two-frequency correlation idea are regarded - independent of transmitted waveform - as essentially two alternative detection systems for modulated noise. Together, the two systems constitute a general detection system for modulated noise described some years ago by Parzen and Shiren (1956). A frequency domain analysis for backscatter on arbitrary incident waveform is given, and an interesting physical optics solution for the generalized fourth-order moments of the scattering matrix is obtained. It is shown that the present narrowband version of Barrick's two-frequency idea is impractical, and that the proper application of Barrick's idea is to wide band signals.

High‐frequency backscattering from an elliptic metal plate

Abstract: The high‐frequency backscattered field produced by a plane, linearly polarized electromagnetic wave obliquely incident on a perfectly conducting disk of elliptical shape, is considered. The leading term of the asymptotic expansion is obtained by means of the geometrical theory of diffraction, and it is matched to the physical optics result for normal incidence via Bessel functions. The formula thus obtained is uniformly valid for all directions of incidence and polarization; it reduces to the known result for a circular disk in the case of zero eccentricity. Numerical results are presented for direct‐ and cross‐polarized monostatic cross sections. The difficulties encountered in obtaining higher‐order terms of the asymptotic expansion are discussed in detail.

On the Evaluation of Image Region Fields for Dual Reflector Scanning Antennas

Abstract: Evaluation of the field from dual reflector scanning antennas using the physical optics approximation is impractical when the main reflector is large. Asymptotically evaluating the physical optics integral yields the geometrical optics field as the first term in the solution. This approximation is not always sufficient as it does not account for diffraction. The next higher order term in the asymptotic expansion yields diffraction effects. This is compared with the geometrical theory of diffraction (GTD). These methods are applied to a practical dual reflector scanning antenna. It is shown that the physical optics and GTD approaches are complementary allowing rapid evaluation of the field.

A Modified Physical Optics Technique for Obtaining Electromagnetic Signatures of Objects with Edges Totally Immersed in the Ocean

Abstract: The objective of this study was to develop an approximate method for predicting, with acceptable accuracy, the electromagnetic field scattered by perfectly conducting bodies of complex shape immersed in a lossy medium, i.e. the ocean, when subjected to the field of an oscillating magnetic dipole source.