M. A. Plonus

Optical beam propagation for a partially coherent source in the turbulent atmosphere

The extended Huygens-Fresnel principle is used to formulate general expressions of the mutual intensity function for a finite optical source with partial spatial coherence propagating in the weakly turbulent atmosphere. Formulations are developed for both the focused and collimated Gaussian beam. Generalized criterion for the effective far-field range is defined in terms of the source aperture, optical wave number, source coherence, and characteristic length associated with the atmospheric turbulence. Beam spread and lateral coherence length in the near and far field are investigated for a combination of parameter variations and the physical implications discussed. Finally, analytic results are calculated and plotted to illustrate the functional behavior of relevant physical parameters.

Receiver-aperture averaging effects for the intensity fluctuation of a beam wave in the turbulent atmosphere

Using a Gaussian weighting function for the receiver aperture, we obtain a closed-form representation for the receiver-aperture averaging effect for the intensity fluctuation of a beam wave in the turbulent atmosphere. It is shown that, unlike for the plane-wave case, the power scintillations do not always decrease when the receiver aperture is increased. The reasons are that (1) the intensity fluctuations on the axis for a coherent beam-wave source are smaller than these off the axis and (2) the averaging effect cannot show up when the total beam is within a coherent patch (i.e., the coherence length is larger than the beamwidth).

Radar cross section of curved plates using geometrical and physical diffraction techniques

Geometrical and physical optics techniques, supplemented by their respective extensions, i.e., geometrical and physical diffraction, are applied to the problem of finite cylindrically curved plates. Numerical calculations of the radar backscattering cross sections were made, and a graphical comparison of these methods with experimental results is made. Kellers and Ufimtsevs theories axe discussed and compared as they apply to this problem.

The diffracted field contribution to the scattering from a large dense dielectric sphere

In a previous paper we discussed the geometric optics contribution to the scattering from a large dense dielectric sphere. This is a sequel to this paper and treats the more important diffracted wave contribution. The problem of electromagnetic wave scattering by a lossless dielectric sphere is more involved than that for the perfectly conducting sphere, since waves existing within the sphere can contribute significantly. The geometrical optics method which is relatively straightforward has been widely used for solving the problems of large, with respect to wavelength, dielectric spheres. Approximate expressions based on this method have been derived and have indicated that the geometrical optics fields are the major contributor to the total backscattering. However, a rigorous approach [1] based on the Watson transformation which splits the Mie series into two terms, geometrical optics fields and diffracted fields, shows that the former contributes negligibly to the total backscattering in the range ka = 5 to 20 for relative refractive index m = 1.6 . In this paper we confine ourselves to the diffracted fields which give rise to surface waves. It is shown that the dominant contributions come from the surface waves rather than the geometrical optics fields in the particular range where the geometrical optics fields have been assumed to be the dominant contributor. Although a rigorous mathematical analysis associated with the Watson transformation for the scattering problems has been known fundamentally for many years, a complete numerical result based on this transformation has not been available, especially for a dielectric cylinder or sphere. Such results would serve to provide a sound basis for understanding the scattering mechanisms involved and also would serve to check the validity of approximate expressions obtained under a particular assumption. Complete numerical results are included and lead to several interesting conclusions.

Optical-Pulse Propagation in a Turbulent Medium

Based on the theory of the structure of atmospheric turbulence, the propagation of the optical pulses from a point source in the atmosphere, where the refractive index varies randomly, is studied by use of the Rytov method. The mean-square amplitude and phase fluctuations are evaluated for pulse lengths short compared with the time in which the refractive index varies significantly. The results are identical to Tatar-ski results for the continuous-spherical-wave (csw) case. Available data from continuous-wave (cw) and pulsed-laser experiments confirm this conclusion.

Intensity fluctuations due to a spatially partially coherent source in atmospheric turbulence as predicted by Rytov’s method

All the existing Rytov method solutions in atmospheric turbulence deal with coherent sources. In this paper we introduce the spatial partial coherence of a beam wave source to Rytov’s method and evaluate the intensity covariance and the scintillation index due to a spatially partially coherent beam wave source. The advantage of this solution is that in the calculation of the scintillations, the need for the use of the quadratic approximation for the medium structure functions is eliminated. The disadvantage is that, since it is a weak-fluctuation solution, we cannot extend the results to the incoherent source limit when (weak) turbulence is present.

Theoretical investigations of scattering from plastic foams

The use of cellular or foamed plastics in various microwave applications, such as supports at radar ranges, makes it desirable to know the back scattering properties of such materials. Since the cell structure is of a random nature with some predictable average properties such as cell size and density, it is modeled by an aggregate of randomly distributed spherical shells. Assemblies of scatterers will in general have a coherent and an incoherent scatter. Coherent scattering comes primarily from sudden particle density changes such as that at the boundaries of a particle system. Since coherent scattering comes only from the boundaries of a constant density material, it can sometimes be reduced by appropriate shaping. Incoherent scattering is the result of the contribution of all the particles in the system, i.e, a volume or an interior effect. It represents the irreducible scattering contribution to the total back scatter. As such it can be looked upon as the minimum cross section that can be obtained from a foam structure provided all coherent scatter has been removed. The magnitude of the incoherent scattering is illustrated by calculating radar cross sections for a cylinder made of styrofoam. Since the compressive strength of styrofoam is known, the maximum load that a styrofoam structure can support and the minimum achievable cross section from it can be easily calculated.

Two-source, two-frequency spherical wave structure functions in atmospheric turbulence: errata

Structure functions are derived for two spherical wave sources, separated by a distance sd, which operate at different frequencies k1 and k2. The observation is at two different points in the receiver plane which are separated by a distance pd. The two-frequency structure functions are presented in terms of one-frequency structure functions that have known solutions.

OPTICAL PULSES IN ATMOSPHERIC TURBULENCE.

Rytov’s method is generalized so that it can be applied to the time-dependent wave equation. The method is used to obtain an expression for a pulsed spherical wave that has propagated through atmospheric turbulence. The expression contains two terms. One term represents scattering by refractive-index inhomogeneities located on a direct line between the transmitter and receiver. The other term arises from the time-varying dimensions of the scattering volume of the pulsed wave and represents scattering by inhomogencities located on the surface of a prolate spheroid. Under appropriate conditions, the surface scattering can be neglected, so that if the pulse shape does not change significantly over times on the order of the period of the carrier frequency, the pulse shape will be preserved after transmission through the turbulence. In this case, the fluctuations depend upon only the carrier frequency. The statistics of the direct-line term are shown to be identical to the statistics for the monochromatic spherical wave. The surface and direct-line terms remain correlated for only a very short period during the beginning of the pulse.

Superresolved image reconstruction of images taken through the turbulent atmosphere

Superresolved image reconstruction is demonstrated by use of multiple images taken through atmospheric turbulence under photon-limited conditions. An iterative reconstruction algorithm applies estimate-maximize techniques to a series of short-exposure images of the desired object scene along with the corresponding image sequence of a guide star. Simulations show that estimates of the Fourier components both below and above the diffraction limit are improved at successive iterations. The estimated images give finer detail of the original object than does the diffraction-limited image. Effects of photon-noise levels on restoration performance are investigated, and a modification to the reconstruction algorithm is derived that accounts for the effects of CCD read noise.