Wolfgang-M. Boerner

Polarization dependence in electromagnetic inverse problems

The complete description of electromagnetic scattering processes implies polarization since an electromagnetic scatterer acts like a polarization transformer. The main objective is to show that due to the vector nature of electromagnetic waves, electromagnetic remote sensing and inverse scattering techniques, if applied rigorously, require incorporation of polarization information into their formulation. By applying this approach to existing and some novel theories, remarkable improvements in quality and fidelity of the reconstructed profiles and/or images can be obtained. Thus there is ample justification for continuing efforts in developing methods and theories of vector inverse scattering for the electromagnetic polarization-dependent case or in the even more complicated seismic case of p - and s -wave interaction in elastic media as for example encountered in vertical seismic profiling.

On the polarimetric contrast optimization

The problem considered is one of finding the polarization state of an antenna such that a power ratio due to two different objects is optimized. It is reduced to an optimization problem of two Hermitian forms which can be simultaneously diagonalized using a well-known linear-algebraic construction. The corresponding polarization vectors are found. The calculations are performed directly on the expression for the energy density of the reflected wave as a function of the transmitter polarization and are, therefore, decoupled from the receiving antenna parameters. Such decoupling is particularly convenient in bistatic applications.

Optimal reception of partially polarized waves

Various aspects of the physics of partially polarized waves are discussed with applications to optical (lidar) reception problems. We focus on the issue of the optimal intensity reception of partially polarized waves scattered off a fluctuating object (ensemble of scatterers) of known polarization properties (measured Mueller matrix). Expressions for total available intensity and adjustable (polarization-dependent) intensity are derived in a clear and novel manner by using the coherency matrix approach. A general numerical technique is developed and illustrated for the optimization of adjustable intensity as a function of transmitted polarization. Closed-form expressions are derived for two important subcases, and numerical illustrations for the general case are discussed in detail, including the use of relevant experimental data.

Interpretation of the Polarimetric Co-Polarization Phase Tern in Radar Images Obtained with the JPL Airborne L-Band SAR System

The utilization of both polarimetric amplitude and relative phase terms of the polarization scattering matrix [S] given for each pixel, is pursued for polarimetric SAR imagery interpretation. The existing amplitude-only backscattering approaches hitherto used are extended and modified to accommodate the interpretation of information contained in the amplitude and/or phase terms. Both a vector radiative transfer model for surface versus volume scattering from rough terrain with and without vegetation canopy and a high-frequency electrical curvature model for perfectly conducting surfaces are examined to come up with theoretical models that out-perform other hitherto known approaches. The developed models agree with the excellent polarimetric SAR imagery recently obtained with the JPL CV-990 dual-polarization L-band (1.225 GHz) SAR system. Recommendations are made on how to further perfect the system for integration in the SIR-C and other future polarimetric SIR-SAR systems.

Introduction to the special issue on inverse methods in electromagnetics

Inverse methods have become a fundamental tool in the physical sciences for remotely sensing unknown objects and reconstructing their physical properties. The objective of this special issue is to present an overview of this important rapidly emerging discipline and to provide examples of the wide scope of methods used to investigate inverse problems in electromagnetics, ranging from purely theoretical considerations to some very practical problems.

Polarimetric SAR interferometry for forest canopy analysis by using the super-resolution method

In this paper, we propose an polarimetric SAR interferometry technique for interferometric phase extraction of each local scatterer of the forest region. The proposed method formulated for local scattering center extraction is based on the ESPRIT algorithm which is known for high-resolution capability of closely located incidences. The method shows high-resolution performance when local scattered waves are uncorrelated and have different polarization characteristics. Using the method, the number of dominant local scattered waves and their interferometric phases in each image patch can be estimated directly. Validity of the algorithm is demonstrated by using examples derived from SIR-C data.

Analysis of physical optics far field inverse scattering for the limited data case using radon theory and polarization information

Abstract In the inverse scattering problem for perfectly conducting objects, the reconstruction of the shape and size of a convex body from its cross-sectional areas has been formulated as a Radon problem of shape reconstruction from projections. It is shown here that the Physical Optics Inverse Scattering time-domain and frequency-domain identities form a Radon-Fourier transform pair, and the problem of target reconstruction from incomplete data is common to both. The mathematical aspects of reconstruction from projections are examined using concepts of Radons theory, and the sparse data problemis analyzed. The limited aperture problem is solved via the Radon transform approach utilizing properties of Ludwigs theorems on support. In order to obtain more accurate cross-sectional areas for reconstruction, polarization utilization is investigated to correct the polarization-independent deficiency in the Physical Optics approximation. The technique is applied to the case of a sphere-capped cylinder and the results show substantial improvement over previous scalar approaches.

Long-term ELF background noise measurements, the existence of window regions, and applications to earthquake precursor emission studies

Abstract A Low Frequency Monitoring Network has been under development at Naval Command, Control and Ocean Surveillance Center (NCCOSC), Research, Development, Test and Evaluation Division (RDT & E), San Diego, CA, for the last 2 years. Originally developed to monitor space vehicle induced signatures in the 5–12 Hz region, the network now includes monitoring of anomolous broadband signals in the 0.1–20 Hz region that often precede the occurrence of nearby earthquakes. Observations of such events have led to a hypothesis that geological signals are normally present in the ULF (ultra-low frequency, less than 3 Hz) and ELF (extremely low frequency, 3–3000 Hz) bands in addition to the generally accepted signals from micropulsations and lightning discharges. In Southern California, the geological signals are best observed in the ‘polarimetric window’ regions of (i) 2–5 Hz using horizontally oriented magnetic sensors and, (ii) 2–20 Hz using vertically oriented magnetic sensors. To determine the significance of anomalous events, we conducted a statistical study of the background noise levels. Observations of daily records over a span of several months indicated that the background level in the 1–20 Hz region is stationary. Stationarity is not true below 1 Hz. The APD (amplitude probability density) of 2–12 Hz signals was found to be surprisingly close to a Gaussian distribution. These two results indicated that a determination of long-term averages and variances would be meaningful. Long-term averages and variances were obtained and were used to develop alert-level criteria. Typical deviations over the course of several hours are 1 to 2 dB. The alert-level criteria are used as input parameters in our Automated Monitoring System (AMS), a computerized monitoring and real-time analysis system. The alert levels warn the operator when unusual events are occurring. High alert-levels in conjunction with the fulfilment of several other conditions often presage the occurrence of an earthquake. These other conditions include: (i) persistence of the elevation of the signals; (ii) the existence of resonance lines in the window region of the power spectrum; (iii) the Schumann peaks remaining relatively normal. Several examples of broadband precursor emissions are shown as well as a table listing all nearby moderate/large quakes that occurred during the research period and the correlation with our data base. The table showed that the periods preceding nearby quakes are usually associated with higher than average background levels in the 3–4 Hz region. The general conclusions are that more systematic research is needed, many more monitoring stations are needed, and full tri-axial electric and magnetic monitoring are required.

Basic Concepts of Radar Polarimetry

A comprehensive overview of the basic principles of radar polarimetry is presented. The relevant fundamental field equations are first provided in order to introduce the polarization state formulations of electromagnetic waves in the frequency domain, including the Jones and the Stokes vector formalism and its presentation on the Poincare sphere and on relevant map projections. In a next step, the scattering matrices [S] and [M] are given together with change of polarization bases transformation operators, where upon the optimal (characteristic) polarization states are determined for the coherent and partially coherent cases, respectively. This chapter is concluded with a set of simple examples.

A validation analysis of Huynen's target-descriptor interpretations of the Mueller matrix elements in polarimetric radar returns using Kennaugh's physical optics impulse response formulation

By applying correction to Kennaughs impulse response formulation for smooth, convex targets, Huynens descriptors have been shown to relate to specular geometry at high frequencies. A time-gating technique has been developed to separate the specular signature from the creeping wave contribution in the total backscattered return. This enables approximately equivalent high frequency data to be extracted from bandlimited scattering measurements. It is shown that the validation of the target-descriptor interpretations of the Mueller matrix elements with the isolated specular contribution data is acceptable, whereas the validation of these interpretations with the total backscattered data seems doubtful.