Showing papers on "Physical optics published in 1980"

Applications of Laser Radiation Pressure

Abstract: Use of lasers has revolutionized the study and applications of radiation pressure. Light forces have been achieved which strongly affect the dynamics of individual small particles. It is now possible to optically accelerate, slow, stably trap, and manipulate micrometer-sized dielectric particles and atoms. This leads to a diversity of new scientific and practical applications in fields where small particles play a role, such as light scattering, cloud physics, aerosol science, atomic physics, quantum optics, and high-resolution spectroscopy.

Inverse scattering problems in optics

Abstract: 1. Progress in Inverse Optical Problems.- 1.1 Inverse Problems in Optics and Elsewhere.- 1.2 Survey of Recent Results.- 1.2.1 Phase, Uniqueness, and Estimation.- 1.2.2 Radiometry and Coherence.- 1.2.3 A Moment Problem.- 1.3 Construction of Lambertian Scatterers.- 1.3.1 Lambertian Source Correlation.- 1.3.2 Random Scatterer Models.- 1.4 Organization of this Volume.- References.- 2. The Inverse Scattering Problem in Structural Determinations.- 2.1 Philosophical Background.- 2.2 The Direct Scattering Problem.- 2.2.1 Description of the Medium.- 2.2.2 The Scattered Fields.- 2.2.3 Expression for the Intensity.- 2.3 Analytic Description and Properties of Scattered Fields.- 2.3.1 Entire Functions of the Exponential Type.- 2.3.2 Distributions of Zeros for Functions of Class E.- 2.3.3 Encoding of Information by Zeros.- 2.4 The Deterministic Problem.- 2.4.1 Limitations of Measurements.- 2.4.2 The Phase Problem.- 2.4.3 Solutions to the Zero Problem.- 2.4.4 Zero Location.- 2.4.5 Extensions of the Method.- 2.5 The Statistical Problem.- 2.5.1 Overall Characterization of the Medium.- 2.5.2 Analytical Properties of Overall Descriptors.- 2.5.3 Determination of Overall Descriptors from Finite Records.- 2.6 Conclusions.- References.- 3. Photon-Counting Statistics of Optical Scintillation.- 3.1 Introductory Remarks.- 3.2 Photon-Counting Statistics.- 3.2.1 Single-Interval Statistics.- 3.2.2 Photon-Correlation Spectroscopy.- 3.2.3 Instrumental Effects.- 3.2.4 Noise and Statistical Accuracy.- 3.3 Scattering Theory.- 3.3.1 Mechanisms and Theories for Strong Scattering.- 3.3.2 The "Discrete-Scatterer" Model.- 3.3.3 K Distributions.- 3.3.4 Correlation Functions.- 3.4 Limit Distributions in the Random Walk Problem.- 3.4.1 The Gaussian Limit.- 3.4.2 Negative Binomial Number Fluctuations.- 3.4.3 A Population Model.- 3.5 Experiments.- 3.5.1 Dynamic Scattering by Nematic Liquid Crystals.- 3.5.2 Hot-Air Phase Screen.- 3.5.3 Extended Atmospheric Turbulence.- 3.5.4 Other Experiments.- 3.6 Concluding Remarks.- References.- 4. Microscopic Models of Photodetection.- 4.1 Photoelectron and Photon Statistics.- 4.1.1 Definition of the Problem.- 4.1.2 Ideal and Real Detection.- 4.2 Models for Ideal Detection - a Review.- 4.2.1 Mandel's Formula.- 4.2.2 Perturbation Approach.- 4.2.3 Field Attenuation.- 4.2.4 Inversion Problem.- 4.3 Open-System Detection Scheme.- 4.3.1 Detector Model.- 4.3.2 Relation Between Atomic and Field Dynamics.- Field Dynamics.- Dynamics of the Atomic Moments.- 4.3.3 Photocounting Probability.- 4.4 Disturbing Effects.- 4.4.1 Dark Currents and Noise.- Photodetectors.- Noise in Photoconductive Detectors.- Noise in Photomultipliers.- PMT Statistics.- 4.4.2 Dead Time Effects.- 4.4.3 Coherence and Sampling Effects.- Time Effects.- Spatial Effects.- Sampling Effects.- Other Counting Experiments.- 4.5 Temperature Effects in Photodetection.- 4.5.1 Langevin Equations of Motion.- The Field Equation.- Connection Between Atomic and Field Dynamics.- 4.5.2 Photocounting Probability.- 4.5.3 Applications.- Numerical Examples and Discussion.- 4.6 Summary of Statistical Methods.- 4.6.1 Random Variables.- Examples.- 4.6.2 Stochastic Processes.- 4.6.3 The Statistical Description of the Radiation Field.- 4.7 The Statistical Description of Open Systems.- 4.7.1 Equation of Motion of the Reduced Density Matrix.- 4.7.2 Langevin Equations.- References.- 5. The Stability of Inverse Problems.- 5.1 Ill-Posedness in Inverse Problems.- 5.1.1 Well-Posed and Ill-Posed Problems.- 5.1.2 Ill-Posedness and Numerical Instability.- 5.1.3 General Formulation of Linear Inverse Problems.- 5.1.4 Prior Knowledge as a Remedy to Ill-Posedness.- 5.1.5 Holder and Logarithmic Continuity.- 5.2 Regularization Theory.- 5.2.1 An Outline of Miller's Theory.- 5.2.2 Eigenfunction Expansions and Numerical Filtering.- 5.2.3 Tikhonov Regularization Method.- 5.2.4 Stability Estimates.- 5.3 Optimum Filtering.- 5.3.1 Random Variables in a Hilbert Space.- 5.3.2 Best Linear Estimates.- 5.3.3 Mean-Square Errors.- 5.3.4 Comparison with Miller's Regularization Method.- 5.4 Linear Inverse Problems in Optics.- 5.4.1 Inverse Problems in Fourier Optics.- Prolate Spheroidal Wave Functions (PSWF).- Perfect Lowpass Filter.- Bandwidth Extrapolation.- 5.4.2 Inverse Diffraction.- Inverse Diffraction from Plane to Plane.- Inverse Diffraction for Cylindrical Waves.- Inverse Diffraction from Far-Field Data.- 5.4.3 An Inverse Scattering Problem for Perfectly Conducting Bodies.- 5.4.4 Inverse Scattering Problems in the Born Approximation.- 5.4.5 Object Reconstruction from Projections and Abel Equation.- 5.4.6 Concluding Remarks and Open Problems.- References.- 6. Combustion Diagnostics by Multiangular Absorption.- 6.1 Absorption in Homogeneous Media.- 6.2 Multiangular Scanning.- 6.2.1 Basic Equation.- 6.2.2 Two-Dimensional Fourier Transform.- 6.2.3 Linear Superposition Techniques.- 6.2.4 Algebraic Reconstruction Techniques (ART).- 6.2.5 Applications and Results.- 6.3 The Reconstruction Procedure.- 6.3.1 Reconstruction Errors.- 6.3.2 An Observation of the Oversampling Requirement of Reconstruction.- 6.3.3 Number of Measurements M x N in Combustion Application.- 6.3.4 The Convolution Algorithm.- 6.3.5 Simulated Test Functions and Results.- 6.3.6 Algebraic Reconstruction.- 6.3.7 Benefits of Additional Digital Signal Processing.- 6.3.8 Conclusion.- 6.4 Experimental Aspects.- References.- 7. Polarization Utilization in Electromagnetic Inverse Scattering.- 7.1 Scope.- 7.1.1 Definitions of the Electromagnetic Inverse Problem.- 7.1.2 Definitions of Exact, Unique, and Approximate Methods.- 7.1.3 Incompleteness and A Priori Knowledge, Data Limitedness and Self-Consistency.- 7.2 The Vector Diffraction Integral, Its Far-Field Approximations, and Some Tauberian Relations.- 7.2.1 Basic Scattering Phenomena, Nomenclature, and Radar Definitions.- 7.2.2 The Stratton-Chu Vector Diffraction Integral and the Vector-Current Integral Equations.- 7.2.3 Far Scattered Fields in the Physical Optics Limit and Their Vector Corrections.- 7.2.4 Time-Domain Target Modeling: Utilization of Some Tauberian Theorems.- 7.3 The Radar Scattering and Target Polarization Matrices.- 7.3.1 Basic Electromagnetic Polarization Descriptors.- 7.3.2 Radar Scattering Matrices and Radar Measurables.- 7.3.3 Kennaugh's Optimum Polarization Pairs.- 7.3.4 Radar Target and Clutter Characteristic Operators.- Single Radar Target Classification.- The Time-Varying Distributed Target.- Synthetic Aperture Imagery.- 7.4 Inverse Scattering Theories in Various Electromagnetic Frequency Regimes.- 7.4.1 The Low Frequency Regime: Rayleigh-Gans Theory.- 7.4.2 The Resonant Frequency Regime: Natural Frequency Expansion.- 7.4.3 Physical Optics Far-Field Inverse Scattering Theories: Broad-Band Approach.- Fourier Transform Method of Physical Optics.- POFFIS in Time, Frequency, and Projection Domain.- The Limited Aperture Problem.- Polarizational Correction.- 7.4.4 Geometrical Optics Inverse Scattering Asymptotic Theories.- GOIS and the Minkowski Problem.- Vector Extension of GO Equivalent Curvature Inverse Method.- Scattering Center Discrimination: Kell's Monostatic-Bistatic Equivalence Theorem.- 7.5 Vector Holography and Polarization Utilization.- 7.5.1 Vector Wavefront Reconstruction and Interferometry.- 7.5.2 Polarization Dependence in Millimeter and Microwave Holography.- 7.5.3 The Postulate of Inverse Boundary Conditions.- 7.5.4 Near-Field Approach to Vector Inverse Scattering.- 7.6 Conclusions.- 7.6.1 Summary.- 7.6.2 Unresolved Vector Inverse Problems.- 7.6.3 Limitations and Omissions.- 7.6.4 Recommendations.- References.- Additional References with Titles.

Shaped reflector antenna analysis using the Jacobi-Bessel series

Abstract: The physical optics approximation is employed to derive the radiation integral for a doubly curved offset reflector antenna illuminated by an arbitrary source. A novel procedure is presented for expressing the radiation integral in terms of a summation of Fourier transforms of an "effective" aperture distribution which includes the effect of the curvature of the surface. The Jacobi-Bessel series is used to evaluate the Fourier transforms. The vector nature of the far-field pattern is studied by evaluating its three Cartesian components in a unified fashion. The rapid numerical evaluations of the expressions obtained are demonstrated via extensive test cases. In particular, the scattering characteristics of symmetric and offset parabolic, spherical, and shaped reflectors are studied in detail, and comparisons are made with other available data.

Backscattering in single-mode fibres

Abstract: The scattering process in single-mode optical fibres is considered in terms of wave optics rather than geometrical optics, which is inadequate in this case. Surprisingly, however, the result for the backscattering signal at the input end of the fibre is nearly the same as for multimode fibres.

Theory for gradient-index imaging.

Abstract: Results of wave optics and ray optics are summarized to make a convenient and self-consistent expression for gradient-index imaging. By applying the theory, a limit of the transmitted spatial frequency and focused spot is obtained. An optimum design of a light focuser for a video disk is demonstrated.

Fast analysis of large antennas--A new computational philosophy

Abstract: A new computational approach is presented which allows a fast analysis of radiation properties of large antennas. The radiated field is first computed using conventional techniques, e.g., physical optics and geometrical theory of diffraction, in prescribed sampled space directions, roughly one direction per lobe. Then sampling theory is used to reconstruct the complete radiation diagram. Numerical experiments are presented in the last part of the paper, showing the excellent performance of the method.

The physical optics method in electromagnetic scattering

Abstract: The purpose of this work is to analyze the physical optics method as applied to electromagnetic scattering theory and to point out its physical and mathematical drawbacks. The main conclusions are (1) that the boundary values assumed by physical optics lead to electromagnetic fields that do not satisfy the finiteness of energy condition and, as a consequence, that integral representations of these fields cannot be obtained via the divergence theorem; (2) that the commonly accepted representations are not solutions of the physical optics problem because they fail to reproduce the assumed discontinuities of the fields on the scatterer. Despite the above conclusions, the present work should not be construed as an attempt to discredit the method but rather as an effort toward a better understanding of it. As it is well known, there have been a number of occasions in which physical optics has yielded quite satisfactory results.

Geometric optics in plasmas characterized by non-Hermitian dielectric tensors

Abstract: This paper presents a generalization of the theory of geometric optics in plasmas where the local dielectric tensor epsilon(k,..omega..;r,t) is not almost Hermitian, as heretofore assumed. It is shown that for general epsilon one can construct the formalism so that the new theory is characterized by the same equations determining the rays, and the equation for the amplitude of the wave along the rays is unmodified in structure. The theory uses the quasidispersion relation det)epsilon(k,..omega..+i..nu..;r,t)x(epsilon(k,..omega..-i..nu..;r,t))*)=0 to find the complex roots ..omega..+i..nu.., where when the approximation of short wavelength compared with the scale length underlying geometric optics holds, the real part ..omega.. serves to generate the rays via r=..omega../sub k/, and the imaginary part i..nu.. enters the transport equation for the amplitude.

Incoherent Optical Processing

Abstract: In this chapter we have analyzed the basic characteristics of incoherent optical processing, considering three major classes of systems: (1) systems that rely on diffraction; (2) systems that rely on plane-to-plane imaging in the geometrical optics sense; and (3) systems that rely on diffractionless geometrical optics “shadow casting” for their operation. Incoherent systems are often characterized by a redundancy and immunity to noise not associated with coherent optical systems. However, the non-negative real nature of the information-bearing irradiance distributions precludes direct implementation of incoherent systems in many signal processing applications, and various tricks must be employed. Dynamic range limitations with incoherent systems are an area of active study, and the relative advantages of incoherent systems over coherent systems are not known conclusively.

Phase matrix and cross sections for single scattering by circular cylinders: a comparison of ray optics and wave theory.

Abstract: The phase matrix and several quantities for single scattering by an arbitrarily oriented circular cylinder are formulated by using the approximation of ray optics, which includes geometrical reflection and refraction plus Fraunhofer diffraction; then the effects of polarization are considered. Computations were made using electromagnetic wave theory and ray optics approximations for m = 1.31–0.0i and 1.31–0.1i. Results by these methods approach one another as the ratio of the cylinder's circumference to the incident wavelength increases. One of two ray optics approximations proposed requires less computation time than wave theory. The applicability of the ray optics approximation is dependent on the orientation of the cylinder relative to the incident light as well as the size parameter and, moreover, dependent on what quantity for single scattering is compared.

High-resolution electrooptic surface prism waveguide Deflector: an analysis.

Abstract: A surface waveguide electrooptic deflector as described in the literature is analyzed in terms of a simple 2-D prism model. The model is treated by geometric as well as physical optics, and the far-field interference pattern is calculated. The results of this analysis are used to predict an upper limit to the ultimate resolvability of such a device. The maximum number of resolvable spots per centimeter of beamwidth, assuming ±500-V drive, 50-μm prism aperture, and diffraction-limited operation, is shown to be on the order of 103. It is also shown that this ultimate resolution can be obtained only if the far-field interference pattern generated by the periodicity of the deflector array is overcome.

Computer Simulation of Synthetic Aperture Radar Images of Three-Dimensional Objects

Abstract: A digital simulation of coherent synthetic aperture radar (SAR) images of three-dimensional objects is described. The simulation is intended to produce representative SAR images that would be suitable for image analysis and pattern recognition studies. The procedure involves a modeling of the object using a combination of three-dimensional quadratic shapes yielding a smooth surface representation. The radar images of these models are then computed using physical optics scattering theory. Finite resolution both in range and cross-range direction is incorporated via a theoretical analysis which results in a simple Fourier transform representation of an equivalent "offset" window filter. Examples of the computer simulation for both infinite resolution and blurred or finite resolution are given for a KC-135 aircraft model.

Scattering by Non-Spherical Particles of Size Comparable to a Wavelength: A New Semi-Empirical Theory

Abstract: We propose an approximate method for evaluating the interaction of randomly oriented, non-spherical particles with the total intensity component of electromagnetic radiation When the particle size parameter, x, the ratio of particle circumference to wavelength, is less than some upper bound xo (~5), Mie theory is used For x > xo, the interaction is divided into three components: diffraction, external reflection, and transmission Physical optics theory is used to obtain the first of these components; geometrical optics theory is applied to the second; and a simple parameterization is employed for the third The predictions of this theory are found to be in very good agreement with laboratory measurements for a wide variety of particle shapes, sizes, and refractive indexes Limitations of the theory are also noted

Rigorous theory of scattering by perfectly conducting periodic surfaces with trapezoidal height profile, TE and TM polarization

Abstract: A rigorous method for analyzing plane-wave scattering from perfectly conducting periodic surfaces is examined and applied to trapezoidal profiles. Both TE and TM polarizations of the incident plane wave are considered. An integral equation for the unknown current distribution in the scatter surface is formulated by invoking the extended boundary condition. Upon expressing the current density in terms of its physical optics approximation multiplied by a Fourier series, the integral equation reduces to a linear system of equations. For the case of a piecewise linear surface profile, the coefficient matrix of this system is amenable to efficient computer evaluation, which furnishes the Fourier coefficients of the current distribution. The method is applied to trapezoidal scatterers for which little data is available in the literature, and, by using appropriate limiting procedures, to triangular and rectangular profiles. Scatter fields and surface current densities are calculated. The accuracy of the method, its range, and its limitations, are investigated and comparisons are made with the results of others. The method has given accurate results for surface groove depths of less than half a wavelength and for surface periods of greater than a wavelength at minimal computational cost.

General Geometric Optics Formalism in Plasmas

Abstract: This paper exploits a general approach to geometric optics in inhomogeneous plasmas based on the properties of the local dielectric tensor ?. We express ? in terms of its eigenvalues ?j and eigenvectors ?. Then to zeroth order in the geometric optics approximation the determinant D = ?1?2?3 vanishes and the elements ?j vanish separately in pairs or simultaneously. It is shown that this branching in the dispersion relation changes the formulation of the geometric optics equations. The ray tracing and the transport of the amplitude of the wave in both degenerate and nondegenerate cases is described. The general procedure for transition through a boundary between degenerate and nondegenerate regions, where the rays split into two parts each following a different branch of the dispersion relation is also presented in this paper. We demonstrate our general method in a case, where radiation from a vacuum region enters an inhomogeneous magnetized plasma layer.

A time domain synthesis of electromagnetic backscattering by conducting ellipsoids

Abstract: A synthesis technique is presented which produces the backscatter impulse response of a conducting ellipsoid, for arbitrary direction of incidence and polarization. The basic features of the response waveform are determined by using the laws of physical optics and the time domain interpretation of the creeping wave mechanism. The above waveform is further refined by forcing it to satisfy five (namely zeroth- to fourth-order) moment conditions through the use of nonlinear optimization. Numerical results and their verification are presented.

EM scattering by an array of perfectly conducting strips by a physical optics approximation

Abstract: The scattering of electromagnetic waves by planar arrays of perfectly conducting strips is analyzed by a simple method based on physical optics. The induced current as determined by physical optics is used in simple hand computation to obtain the amplitudes of various propagating space harmonics. Results are compared against some exact results available in the literature to show the accuracy of the proposed approximate method.

Geometric Optics of Lower Hybrid Waves in Nonuniform Plasmas

Abstract: The propagation of lower hybrid waves in the presence of strong density and field gradient-produced refractive effects is studied in the geometric optics limit. Attention is focused on the electrostatic wave and the modification of the parallel wavenumber k? due to gradients. It is found that in cases where the gradients occur along the direction of the magnetic field the resulting decrease of k? gives rise to a cusp or reflection of the ray at the resonance layer. An asymptotic series for the field amplitudes is developed which is valid in the short wavelength limit everywhere except near the cusp point. It is found that the cusp represents a singularity where the geometric optics assumption is invalid; however, the inclusion of thermal effects removes the singularity by linear mode conversion (LMC). The analysis is applied to toroidal geometry and is extended to include distributed sources.

A Theory of Polarization-dependent Off-specular Peaks of Light Scattered from Rough Surfaces

Abstract: When light is scattered from a rough surface, the power distribution of the co- and cross-polarized components will in general not be peaked in the specular direction. A theory based on physical optics under the tangent-plane approximation describing this angular deviation is developed. The theory applies to scattering in the plane of incidence for incident light polarized at any angle to the plane of incidence. From the resulting closed-form expressions, plots of the angular shift versus angle of incidence and versus surface r.m.s. slope are presented. Comparisons with experimental results for the co-polarized component seem to support the validity of the theory.

The resolution limits of the imaging of conducting bodies using multistatic scattering

Abstract: The well-known inverse scattering problem is discussed for the multistatic case. With physical optics a reconstruction of the equivalent sources of the scattered field is proposed giving the location of the scatterer's surface as well as its inclination. The resulting multidimensional Fourier transform relationships can be discussed regarding resolution, which can be achieved provided the range of aspects and the available frequency band are limited. When the object domain is given the application of the sampling theorem ensures the minimum possible number of measurements without degradation of the results.

Kirchhoff approximation and closed-form expressions for atom-surface scattering

Abstract: In this paper an approximate solution for atom-surface scattering is presented beyond the physical optics approximation. The potential is well represented by a hard corrugated surface but includes an attractive tail in front. The calculation is carried out analytically by two different methods, and the limit of validity of our formulas is well established in the text. In contrast with other workers, I find those expressions to be exact in both limits of small (Rayleigh region) and large momenta (classical region), with the correct behavior at the threshold. The result is attained through a particular use of the extinction theorem in writing the scattered amplitudes, hitherto not employed, and not for particular boundary values of the field. An explicit evaluation of the field on the surface shows in fact the present formulas to be simply related to the well known Kirchhoff approximation (KA) or more generally to an ''extended'' KA fit to the potential model above. A possible application of the theory to treat strong resonance-overlapping effects is suggested in the last part of the work.

Conjugation of space and time variables in optics

Abstract: A review of the main landmarks which proceed the fundamentals of space‐time optics is given. It includes a comparison of the roles of space and time variables in optics as far as information transfer is concerned. Illustrations deal with interference and diffraction phenomena, the light beam being considered as a carrier whose capacity is linked to the width of the spectral band. Experimental examples are reported in metrology, information processing, spectral analysis and wavelength coding, holography, transmission by spectral modulation, etc.

Edge-diffraction by right-angled dielectric wedge

Abstract: Rigorous asymptotic diffracted fields from a right-angled dielectric wedge are obtained for plane wave incidence. A correction field to the physical optics approximation is derived from a dual series equation amenable to simple numerical calculation. The edge-diffracted cylindrical wave pattern is calculated and shown.

Nonlinear optics in gases

Abstract: Nonlinear Optics of Free Atoms and Molecules. By D.C. Hanna, M.A. Yuratich and D. Cotter. Pp.351. (Springer: Heidelberg and New York, 1979.) DM 79, $44.30.