With the corrections and developments on the theory of light scattering by spheroidal particles, we have computed the scattering parameters of both prolate and oblate spheroids with high aspect ratio 7:1 in dielectric and metallic cases. The theoretical results come out to be satisfactory if compared with our microwave measurements in P-Q plot form.

This paper shows that Sommerfeld's multiple-valued function image method for electrostatics and electromagnetic boundary value problems can be extended to both conducting and diel-ectric surfaces bounded by space curves of general shape. The latter are models of material flakes of essentially arbitrary shape.

When waves propagate in a medium containing a random distribution of randomly oriented nonspherical scatterers, the attenuation and the dispersion are independent of the direction of propagation due to the fact that the scattering medium is macroscopically or on the average isotropic. But, in many cases, the non-spherical particles are aligned, rendering the random medium effectively anisotropic. Previous approaches to the problem, depending on the concentration of scatterers, used either single scattering theory (an extension of Mie theory for a single scatterer) or multiple scattering theory by assuming spherical statistics for describing the spatial distribution of even nonspherical scatterers. Approximating the spatial distribution of aligned nonspherical scatterers using spherical statics will yield very different results which has been, recently, shown by the authors. In this paper, we wish to discuss the isotropic properties of randomly oriented nonspherical scatterers with a considerable concentration. In collaboration with Professor William A. Steele of Chemistry Department at Penn State, we have generated by Monte Carlo simulation the pair correlation function for randomly oriented spheroidal particles as a function of the their separation distance and the relative azimuthal and polar angles. The randomly oriented case is more complicated than that for the aligned one. The pair correlation function is then incorporated into the multiple scattering calculations and compared with those using spherical statistics. Numerical results are presented for the attenuation of electromagnetic waves versus freqency and concentration.

For a half space of small spherical scatterers illuminated by a plane wave at oblique incidence, the coherent field propagation is investigated by solving the Foldy-Twerskey Integral Equation. It is found that for a horizontally polarized incident wave, the coherent field is horizontally polarized with reflectivity and transmissivity agreeing with the Fresnel formula for an equivalent continuous effective medium. For a vertically polarized incident wave, both vertical and longitudinal wave have been obtained for the coherent field. Furthermore, the reflectivity and transmissivity do not agree with the Fresnel formula. In numerical illustrations for both the transverse and longitudinal waves, the effective wave number, the reflectivity and transmissivity show strong dependence on particle size, volume fraction, scatterer-dielectric constant and the incident wave number.

We present the characteristics of backscattering enhancement for different particle sizes. Type I and II backscattering enhancements are defined, and the observable conditions are discussed. Experimental results are given for different cases.

Recently, an interesting phenomenon has been reported as a result of a series of optical backscattering experiments conducted using collimated light sources (lasers). A locally high intensity maximum has been observed in the range of π-ε<θ<π + ε where e is of the order of milliradians and 0 = πit is the backscattering direction. Albeit similar phenomena found in backscattering from various random media, e.g., Anderson localization, light scattering from random rough surfaces, this is the first observation of enhanced backscattering from suspensions.

The physical mechanism of scattering of electromagnetic beams from a surface can be quantified by either differential scattering coefficient (0- ) or bidirectional reflectance distribution function (BRDF). The differential scattering coefficient is an extension of radar scattering cross section of targets, and the geometrical constraints inferred in its measurement at microwave frequencies are relatively easily satisfied. These same con-straints must also be met in the measurement of BRDF using coherent optical frequency beams and these may influence the geometrical configuration to obtain range-independent values. For a diffuse surface, u = 47BRDF cos G. cos Gr where and Gr are the incidence and reflected angles, respectively, from surface normal. Considerably more care in the design of the configuration is required for the measurement of surfaces entailing specular components than for diffuse surfaces.

Scattering problems in randomly irregular media are generally analyzed by using the parabolic wave equation when the random medium is continuous or the Foldy-Lax-Twersky formalism when the medium consists of discrete scatterers. In the former, moment equations can be derived by assuming (1) small local perturbations (the Markov approximation), (2) narrow-angle scatter, and 69) negligible backscatter. For discrete tenuous media, approximations involving the relation between the local effective fields and the average fields permit the derivation of moment equations that apply under similar conditions. This paper describes a spectral-domain method for computing the first-and second-order moments of scattered wavefields that can be applied to both discrete and continuous media as long as the local perturbations are small. The method fully accommodates multiple forward and backward scattering, and it makes minimal restrictions on angular extent. The scattering is characterized by incremental forward and backward scattering functions that can be computed from the constitutive properties of the medium or the particle scattering functions. The application of the method to scalar wavefields in continuous media is described in Rino The extension of the spectral-domain method to vector wavefields in discrete media is straightforward. General solutions for the coherent wavefield are obtained and compared to known results, which are recovered when the backscatter terms or the cross-polarization terms are neglected. The extensions of the theory to second-order moments give new insights into backscatter enhancements by showing that they depend on the correlation between scattered waves propagating in the forward and backward directions.

We present experimental studies of the imaging of an object behind randomly distributed spherical particles using coherent illumination. The object which has black stripes on white diffuse paper with different spatial wavelengths is placed behind a scattering cell and illuminated by an expanded HeNe laser beam. Results are obtained for different particle sizes and optical distances. The differences between the front and back illumination are studied. The diffusion approximation is used to calculate the modulation transfer function for the front illumination.

A finite-difference, two-step scheme with a convex parameter is investigated. The scheme is applied to a system of partial differential equations containing a source term describing the propagation of a small amplitude wave. For an initially exponentially decaying pulse or a triangular pulse, a network of front-ray coordinates is used to transform the PDEs into non-dimensional form. The finite-difference scheme for these PDEs is written and the stability condition for the scheme and the stability of the boundary condition are discussed. Since these PDEs can be used to describe water waves at large distances, we investigate the diffraction of a plane wave around a smooth convex wall and a convex wall with a sharp corner. The numerical results using the above scheme are compared with those given by Lighthill and Whitham. It is shown that the change in the Mach number along the wall is asymptotically proportional to square-root of the media nonlinearity parameter and the initial Mach number. This change also depends on the limiting value of the angle of the wall at large distances. The propagation of an initially curved front is also investigated and it is shown that the center of hump moves faster for a smaller parameter value of the media nonlinearity, than with a larger value of the parameter. These comparisons are done for atmosphere, distilled water and water with 35% salinity.

In this paper, we consider the problem of electromagnetic propagation in plane-parallel random media under rather general conditions and obtain solutions for the scattered polarized fields using radiative transport and the Stokes vector representation. More specifically, the plane-parallel medium is inhomogeneous, scatters radiation anisotropically, and has arbitrary boundary conditions. No restriction is placed on the radiative source as to its spatial and directional profiles. A uniform, unidirectional radiation beam incident on the medium from outside constitutes a special case. The formulation is based on the development of the Green's matrix for the scattering medium. The source matrices of this problem satisfy Fredholm integral equations of the second kind. The invariant imbedding technique developed by R. Bellman and co-workers is used to replace these integral equations with the equivalent Cauchy initial-value problems which can be solved using an appropriate quadrature formula and integration scheme. Various applicable symmetry relations for the scattered polarized fields are derived, and their utility in the solution of the initial-value problems is discussed. The Green's matrix approach is particularly useful in remote sensing applications, since it decouples the radiative sources and boundary conditions from media properties. For example, the temperature profile in a snow pack may be inferred by comparing the observed radiative field with the radiative field obtained by convoluting the Green's matrix solution with various trial temperature profiles.

To obtain the scattering cross sections for rough surfaces with different roughness scales a full wave approach (based on the complete expansion of the electromagnetic fields and the imposition of exact boundary conditions) has been used to convert Maxwell's equations into rigorous sets of generalized telegraphists' equations for the forward and back-ward scattered wave amplitudes. The full wave approach accounts for specular point scattering as well as diffuse scattering in a self-consistent unified manner. Thus in order to determine the like and cross polarized cross sections of rough surfaces it is not necessary to decompose the composite surface into surfaces with large and small roughness scales. The single scatter approximations of the rigorous full wave solutions indicate that the enhanced like and cross polarized backscatter is a first order effect. Furthermore, for normal incidence the full wave solutions for the bistatic like and cross polarized cross sections exhibit the observed fourfold symmetry about the backscatter direction.

An analysis is made of anomalous resonance effects on multilayer-overcoated, low-efficiency gratings using the extinction theorem technique for various degrees of grating replication at overlayer interfaces. For wavelength-to-grating-period ratios such that only the specular and -1 order are reflected from the grating, an enhancement of the 2% nominal efficiency in the -1 order can be realized. Anomalously high diffraction efficiency at resonance, which may exceed 50% in the -1 order, results from the coupling of the incident beam into guided waves supported by the multilayer assembly. Previously, resonance effects were studied assuming perfect replication of the substrate grating profile at each film interface. However, perfect transfer of the grating relief to the film boundaries does not occur in all instances; it depends on the grating and film characteristics as well as the conditions during deposition. In this paper, we investigate the effect of nonreplication of the grating profile at film interfaces on anomalous diffraction, while assuming a transition from trapezoidal profile at the grating substrate to a rounded relief at the top surface of the multilayer structure.

The scattering of electromagnetic waves from a randomly perturbed periodic surface is formulated by the Extended Boundary Condition (EBC) method and solved by the small perturbation method (SPM). The scattering from periodic surface is solved exactly and this solution is used in the SPM to solve for the surface currents and scattered fields up to the second order. The random perturbation is modeled as a Gaussian random process. The theoretical results are illustrated by calculating the bistatic and backscattering coefficients. It is shown that as the correlation length of the random roughness increases, the bistatic scattering pattern of the scattered fields show several beams associated with each Bragg diffraction direction of the periodic surface. When the correlation length becomes smaller, then the shape of the beams become broader. The results obtained using the EBC/SPM method is also compared with the results obtained using the Kirchhoff approximation. It is shown that the Kirchhoff approximation results show quite a good agreement with EBC/SPM method results for the hh and vv polarized backscattering coefficients for small angles of incidence. However, the Kirchhoff approximation does not give depolarized returns in the backscattering direction whereas the results obtained using the EBC ,'SPM method give significiant depolarized returns when the incident direction is not perpendicular to the row direction of the periodic surface.

The relative potential of higher order perturbation theory, its extensions based on Pade approximants, and its modification by means of Wiener-Hermite functional expansion to describe scattering of electromagnetic waves by rough surfaces are examined in the limit of infinite correlation length, for which the exact solution is well known.

Remote imaging in varied media is strikingly similar to a number of other application areas, including underwater exploration using the shallow seismic technique. As a result, techniques available for marine geophysical signal processing using underwater acoustic methods for seismic signal analysis and interpretation on the basis of reflections and multiple reflections from the sea-bed and the underlying media are described in the paper. This is done with a view to possible transfer of some useful procedures to the remote imaging area. The main problem of marine seismic exploration is briefly described. We focus our attention on model for the case involving attenuation effects. We present a frequency domain model and discuss an iterative technique for extracting the parameters of the model of the process. The process of relating signal model parameters to physical properties of the media traversed is discussed. Emphasis is given to the role of peak detection and parameter estimation in enhancing the identification process. A number of information extraction algorithms that are central to the interpretation process are presented. In particular, we treat delay and amplitude parameter estimation using two methods. In the first, a combined cross-correlation minimum variance filter is employed. In the second a linearized recursive estimation process is useful in the parameter estimation task.

First-order vector perturbation theory is applied to calculate angle-resolved scattering (ARS) from a semi-infinite medium with interface roughness and an inhomogeneous dielectric permittivity. Two distinct physical situations are considered: ARS of a (1) beam incident on the surface and (2) surface plasmon propagating along the surface. The dielectric perturbation is assumed to fluctuate randomly in the plane parallel to the surface and decay exponentially with depth into the surface. Both the roughness and dielectric permittivity perturbations, which are treated as random variables, can independently cause scattering, and generally there i s interference between the two scattered fields. The scattered fields usually depend on the autocovariance functions of the surface roughnes s and dielectric fluctuations as well as the cross-correlation properties between them. For this reason, the polarization ratio of the p- and s-scattered fields depends on the autocovariance and cross-correlation statistical properties. This result is unlike the calculation of scattered fields caused by roughness or dielectric perturbations alone, since in this case the polarization ratios of the scattered fields do not depend on the statistical properties of the perturbation.

The concept of two-dimensional digital filtering is used to generate three-dimensional random surfaces with specified autocorrelation function. The unknown filter weights is found to be the inverse Fourier transform of the square root of the Fourier transform of the surface autocorrelation function (or the square root of the roughness spectrum). To generate the sea -like random surfaces with specification up to the second moment, ie., the correlation , accurate estimate of the two-dimensional anisotropic sea roughness spectrum must be known. A patch of sea surface with 300x300 data points obtained from stereo photography by Ocean Research and Engineering was used to estimate the sea surface autocorrelation function and roughness spectrum. The effect of both the sizes of the surface patch and the averaging of several patches on the estimate of the autocorrelation function was examined for a numerically generated surface with Gaussian correlation function . It is found that averaging different patches alone does not help in the estimation of the correlation function. However, averaging does help in the accuracy of the estimate of the correlation if the size of each patch is at least 20 times the correlation length. It is recommended that the estimation of autocorrelation function being handled in the following steps. First using the total data to estimate the correlation length of the surface. Secondly the correlation function is estimated by averaging estimates from smaller patches each with at least 20 times the correlation length in size. A sea-like random surface is generated following the above algorithm. The statistics calculated from the generated surface are in good agreement with the specifications.

The paper presents the results of a series of measurements acquired with a novel bi-static polarimetric radar cross section facility. The system operates from 2 to 18 Ghz with full phase amplitude measurement capability. In addition the facility is supported in a capability to construct distributed target model that resemble natural structures such as rough surfaces, vegetation and other volumetric targets. This paper describes measurements from a vegetation like structure, a dense vertically structured media and measurements of simple geometric components. The measurements from the vegetation like media were used to evaluate the effect of the backscatter as a function of leaf angle distribution and leaf shape three leaf types circular, elliptic and needle shape. Because of the artificial nature of the canopy the same distributions and densities could be implemented for all three leaf types. In addition the so called ground truth of the target is well known for comparison to the analytical models. The vertically structured dense media was constructed to test the scattering behavior for media with densities over 10% to 22 %. The cylindrical structure was chosen to investigate the polarization and phase behavior of the like polarized linear scattering coefficients as a function of density. The measurements of simple scattering structures consisted of bistatic measurements for circular and elliptic disks with two permittivities (conductive and er = 28). Measurements were acquired over the 4 to 12 Ghz band for incident angle of 0 and 45 degrees. Both monostatic and bistatic angles in the forward scatter direction were measured.

The wave number spectrum of a well developed sea includes a broad range of wavenumbers (the equilibrium range) where the spectral density is governed by a power law k P. In the approximation of a Causaussian surface, the exponent p is related to the Hausdorff dimension by DH =(8-p)/2 For p < 4, Dh exceeds 2, and the surface is character-ized by an increased number of steep and breaking wavelets and by an increased number of specular points at near vertical incidence. The former results in the so-called spike component in the total return at oblique incidence, whereas the latter leads to an increased backscatter at nadir and near-nadir angles. Theory for both cases is reviewed and implications for satellite scatterorneter and altimeter measurements of surface winds are discussed.

With a simplified statistical model,the relation between the light energy and the surface roughness is deduced for the case that a laser (or incoherent) beam incidents on a rough surface, wherefrom a rather simple method for surface roughness measurement is presented.

A laboratory facility has been established at NASA/Goddard Space Flight Center to measure and model light scattered by soil samples and by individual plant leaves. Two goniometers have been built for this laboratory, one to measure directional reflectance and transmittance from vertically mounted samples such as leaves, the other to measure directional reflectance from horizontal, semi-infinite particulate surfaces such as soil samples. The design and operation of these two devices are discussed. Goniometric observations of various soil minerals and plant leaves are also presented. Level, semi-infinite surfaces consisting of quartz particles, for example, are shown to reflect red light diffusely when illuminated from zenith angles of less than 45 degrees. As an example of leaf observations, the magnitudes of oak leaf reflectance and transmittance are shown to depend upon leaf color. The goniometric measurements are compared to a model of reflectance from particulate surfaces or to a ray-tracing model of leaf reflectance and transmittance.

A rough surface may be described by its statistical moments. The second order one, which is called the autocovariance function, is significant in that it makes it possible to describe a rough surface by means of two parameters, namely the root-mean-square surface roughness height and the autocovariance length. It is shown that some complications arise when the definition of the autocovariance length for not perfectly randon surfaces is considered. Solutions are proposed to overcome them. At the present time the knowledge of higher moments is needed in the framework of theories about surface plasmons and polaritons. The problem of the determination of third and fourth order moments is considered for rough surfaces. Results are compared to what has to be expected for a gaussian process (in this case the third order moment is zero and the fourth order moment satisfies the standard relation involving the sum of products of second order moment taken two-by-two different in all possible ways. At last it is shown that other approaches exist that enable us to characterize random rough surfaces. In particular the minimal spanning tree, which is a graph constructed on the set of points representing the position of features on a surface, turns out to be a powerful tool to statistically study order and disorder in the distribution of these features.

In testing a holographic particle track recording system for the Fermilab 15 foot bubble chamber, it was shown that the peak power of Q-switched laser pulses (50ns duration) at the required energy gave rise to boiling during the chamber expansion. A pulse stretching technique is described which was developed to reduce the peak power. Applied to a ruby laser (oscillator and three amplifiers) with a maximum Q-switched output of 30J, pulses of up to 10-μs duration with coherence up to and exceeding 11 m at 2.5μs were produced. The considerably increased coherence length will find applications in many fields of pulsed holography, and its use with fiber optics is particularly promising.

A simple approximation for the A and B Mie coefficients has been derived for a coated sphere subject to the conditions that the shell is electromagnetically reactive but that the field can penentrate the shell and interact with the core. The approximation is for kshellb greater than 10 for the shell and kcorea less than 1/2 for the core, where k is the propagation constant and a is the inner radius and b is the outer radius of the coating.

X-rays present designers of optics with unfamiliar problems which are currently being solved in novel ways. Multilayer diffractors are an important new class of x-ray optics. Their advantages and limitations are discussed and a rational method for their design is presented.

Tiny conducting loops are shown to be effective absorbers of microwave radiation. Theory for a single loop is presented. Two theoretical methods are developed for a collection of loops. The first method is an effective medium approach and accounts for particle-particle interactions; a collection of loops is shown to behave as a diamagnetic medium. The second method is only applicable to loops which are relatively far apart and for which interactions are negligible. Both methods are applied to a low density loop chaff cloud and are shown to give essentially the same results. For such clouds the second method is preferred since it is computationally simpler. The first method should be useful for computation of denser compactions of loops. The chaff calculations indicate that a 30 m thick cloud of the specified loops should give more than 15 dB attenuation at 3 GHz (double microwave beam pass through the cloud as would be required for detection of a flat metal plate behind the cloud).

In many applications involving electromagnetic as well as optical waves, it is desirable to design materials that will have prescribed reflection and transmission characteristics as a function of frequency (narrow or wide band) and at the same time conform to restrictions on weight, structural properties, thickness, etc. Composite materials that contain a distribution of inclusions of specific concentration, distribution, geometry and material properties can often achieve such goals. Since the actual response of electronic and optical composite materials to the incident wave of low GHz to infrared frequency is quite diverse, it becomes very expensive and time consuming to actually prepare samples of such materials and test them experimentally. However, an optimal design through theoretical analysis of such materials is relatively efficient and the parameters involved are tractable. In this study, the damping characteristics of composites consisting of ferrite or chiral polymer inclusions embedded in a polymer matrix is examined. The reflection and transmission characteristics for a layer of such materials in response to incident millimeter-waves and microwaves will be presented with and without a conducting plate as a substrate.

A metallic cylinder of arbitrary cross section is surrounded by an anisotropic material characterized by tensors F and 5, which are seen to be homogeneous in a local orthogonal system conformal with the cylinder. Here we deal with tensors that remain invariant under a rotation about the cylinder axes i. A simple field representation is obtained that allows us to formulate the scattering problem in terms of field quantities at the material boundaries. Only normal incidence and H polarization are discussed here.

Composite materials consisting of liquid crystal droplets dispersed in a polymer binder may be switched from an opaque scattering state to a clear transparent state by application of a d.c. or low frequency a.c. electric field.1-3 This optoelectronic response is the result of the effect of the external field on the birefringence of the liquid crystal contained in the droplets. The applied electric field serves to align the liquid crystal in an orientation such that the refractive index of the droplet is matched with that of the polymer binder. In this paper we report observations of a nonlinear scattering mechanism in polymer dispersed liquid crystal films due to reorientation of the liquid crystal molecules by the optical field of a CW argon ion laser. Preliminary observations show an 80% reduction in the transmittance of these materials due to laser induced scattering.

A quasi-optical technique is developed to investigate random surface and volume scattering of guided waves in planar waveguides. Through the use of quasi-optics, the guide extinction coefficient is calculated in a simple manner by following a zigzagging ray in the guide. The analysis demonstrates that the scattering losses resulting from random surface roughness depend more strongly on optical wavelength than the index inhomogeneity-induced losses. For a typical correlation length both surface and volume scattering losses increase at shorter wavelengths. The surface roughness-induced losses are larger for low order TM modes than the TE modes of the same order but the differences between the polarizations decrease with increased wavelength and mode order.