Harold Mott

The characteristic polarization states and the equi-power curves

Characteristic polarization state theory is restudied for the symmetric coherent Sinclair scattering matrix case. First, the geometric relations of the characteristic polarization states on the Poincare sphere are derived. Based on these relations, simple formulas are given for all of the characteristic polarization states of this Sinclair matrix in Stokes vector form. From the formulation, it is clear that the CO-POL Nulls are fundamental characteristic polarization states for the symmetric coherent Sinclair scattering matrix case, in that the others can straightforwardly be obtained from the Stokes vectors of the CO-POL Nulls. For further study of the characteristic polarization state and the distribution of the received powers on the Poincare sphere, the authors introduce the concept of the equi-power curve. It is defined as the curve on the Poincare sphere on which the received powers in some defined channel have the same value. They deal with the characteristics of the equi-power curves for various special cases. In addition, they show how the characteristic polarization states are generated by the equi-power curves. It is demonstrated that the characteristic polarization states can usually be regarded as the points of contact of the Poincare sphere and a conicoid representing a power-related quadratic form. This leads to a new method to introduce the characteristic polarization states.

On charge relaxation in good conductors

The charge relaxation in a good conductor is reexamined. It is shown that the fallacy in the prediction of the very rapid decay of free charge implanted in a metal lies in the use of the dc conductivity. The corrected decay time is some six orders of magnitude greater than that predicted on a dc theory.

Polarimetric contrast enhancement coefficients for perfecting high-resolution POL-SAR/SAL image feature extraction

In microwave remote sensing, it is desirable to select radar antenna polarizations that maximize the contrast between two classes of scatterers or scatterer ensembles. A polarimetric radar measures complete polarization properties of a target and then provides a vector description of the resulting scattered wave through various target matrices. Several optimization procedures for the completely and partially polarized cases have been proposed based on the theory of radar polarimetry. It is the purpose of this paper to present optimization procedures for the enhancement of polarimetric contrast between two time-varying targets and to extend the procedure to two spatially incoherent image pixel targets. The targets are now characterized by the time-averaged or spatially-averaged Kronecker matrices, from which one can obtain the associated Graves and Kennaugh matrices. The Graves matrices of the targets are used to find a transmitter polarization to maximize the ratio of scattered power densities at the receiver. Using the Lagrange multiplier method, the maximization problem is cast into the form of a generalized Balois eigenvalue equation. The largest eigenvalue of the equation equals the maximal power ratio, and the optimal effective length of the transmitting antenna is proportional to the corresponding eigenvector. The Kennaugh matrices of the targets are employed to obtain the Kennaugh vectors of partially polarized scattered waves from the two targets. Each of the scattered Kennaugh vectors is decomposed into a completely polarized and an unpolarized part. It is well known that the power received from the unpolarized part is independent of the polarization characteristics of the receiving antenna. Then a receiver polarization is selected to maximize or minimize the completely polarized part scattered from the desired or the undesired target. As a numerical example, the optimal Stokes vectors of transmitting and receiving antennas are given to show the validity of the optimization procedures and how it can be applied to perfecting high resolution POL-SAR/SAL Image Feature Extraction.

Operations on power series and polynomials

Abstract When an operation is carried out on polynomials or power series the result is usually a new power series. The general term of the series is the product of a multiplier which depends on the operation being performed and another factor which is common to the power series being operated on. In this paper equations are developed for the general term of the resultant series when certain operations are carried out on a series or on several series. Convenient equations are given for obtaining those factors common to a given series, and the lower order factors are tabulated. Several useful examples are given.

Depolarization of an Uncollimated Laser Beam in a Turbulent Medium

Abstract The depolarization of a beam wave, with Gaussian intensity distribution and arbitrary divergence, propagating in a turbulent medium is considered. The correlation function of the depolarized component of the beam is determined. The mean-square depolarization fluctuation is then determined for a medium characterized by a Kolmogorov spectrum. If the beam is assumed to be collimated, this expression reduces to that of Collett and Alferness; if the plane-wave limiting case of the Gaussian beam is taken, the results in this paper agree with those of Strohbehn. The results show that off the beam axis the depolarization can be greater than for the plane wave, and that near the beam focal point the depolarization may decrease by orders of magnitude.

On circular array pattern synthesis using a digital computer

A method is presented for synthesizing patterns by a circular array which is useful for a digital computer. The method involves an integration of the pattern which leads to a matrix equation so well-behaved that it can be handled with greater facility than a general matrix equation.

Definitions of Polarization in Radar

A review of definitions and methods used in the polarization-dependent analysis of radar is presented. Careful attention is given to coordinate systems used in the definitions of polarization descriptors. Deficiencies in the IEEE Standards for antennas are pointed out.

The fields of an electric dipole in motion

Abstract The retarded potentials and fields of an oscillating electric dipole undergoing accelerated relativistic motions are developed. Radiation patterns for typical dipole motions are given. The simultaneous fields of the dipole are derived. A four-vector form for the dipole potential is developed. It is assumed that the dipole motion is “a priori” known and that the path dimensions are macroscopically measurable in order that the classical field theory be valid. The resulting equations are verified by showing that for restricted motions the fields reduce to less general forms found in the literature.

The reproducibility of a source distribution from the pattern amplitude

Source distribution determination from radiation pattern and field amplitudes expressed as Fourier transform pair

Diffusion-free charge relaxation in a conducting medium

The commonly used two-term relaxation equation can lead to inconsistencies, which researchers have sought to resolve by introducing diffusion and scattering-time effects. It is shown here that the complete equation ∂n^~/∂t + σ/ε n^~+ E^→ċ grad^→(nµ) = 0 is sufficient to account for charge flow, propagation effects and surface-charge induction, as well as instabilities in negative-differential-conductivity materials.