Michael J. Havrilla

A geometrical optics polarimetric bidirectional reflectance distribution function for dielectric and metallic surfaces

A polarimetric bidirectional reflectance distribution function (pBRDF), based on geometrical optics, is presented. The pBRDF incorporates a visibility (shadowing/masking) function and a Lambertian (diffuse) component which distinguishes it from other geometrical optics pBRDFs in literature. It is shown that these additions keep the pBRDF bounded (and thus a more realistic physical model) as the angle of incidence or observation approaches grazing and better able to model the behavior of light scattered from rough, reflective surfaces. In this paper, the theoretical development of the pBRDF is shown and discussed. Simulation results of a rough, perfect reflecting surface obtained using an exact, electromagnetic solution and experimental Mueller matrix results of two, rough metallic samples are presented to validate the pBRDF.

Electromagnetic Material Characterization using a Partially-Filled Rectangular Waveguide

Electromagnetic material characterization measurements are an important aspect of modern design. Rectangular waveguides are often used in the material characterization process to facilitate measurement since they are readily available and because rectangular samples can be easily machined and placed in the cross-sectional plane of the waveguide for reflection and transmission testing and subsequently analyzed using a simple theory [1, 2]. However, this technique can produce unacceptably large errors for high loss or highly reflecting samples due to a poor signal-to-noise ratio (SNR) for the transmission measurement.In this paper, a partially-filled waveguide method is presented that enhances transmission quality and accuracy in electromagnetic material characterization measurements. The partially-filled waveguide geometry improves transmission but leads to the excitation of higher-order modes. A mode-matching technique is developed here to accommodate the resulting waveguide discontinuity and a Newton root search method is utilized to subsequently extract the electromagnetic properties of the test sample. Experimental measurements for several materials will be presented at X-band frequencies (8–12 GHz) to verify the theoretical analysis.

Electromagnetic Characterization of a Magnetic Material Using an Open-ended Waveguide Probe and a Rigorous Full-wave Multimode Model

In this paper a material characterization technique employing a flanged opened-ended rectangular waveguide probe is presented that now allows extraction of both permittivity and permeability from a conductor-backed lossy shielding material. As an added benefit, this non-destructive technique reduces sample preparation time leading to rapid measurement. Calculation of both material parameters is accomplished using experimental reflection measurements from two different thicknesses of a given material sample. A theoretical solution to the reflection coefficients is developed through a rigorous magnetic field integral equation (MFIE) formulation. The double integral that results from the spectral domain analysis is reduced to a single integral through careful application of Cauchys Integral Theorem leading to improved convergence and is an additional contribution that is believed to be new for this particular structure. A comparison between the theoretical and experimental reflection coefficients allows extraction of the material parameters using a two-dimensional Newton root search algorithm. Parameter extraction results incorporating dominant and higher-order modes are presented and compared to results from traditional waveguide material characterization techniques. An uncertainty analysis is also performed to determine sensitivity to errors in sample and probe flange thickness.

A NONDESTRUCTIVE TECHNIQUE FOR DETERMINING COMPLEX PERMITTIVITY AND PERMEABILITY OF MAGNETIC SHEET MATERIALS USING TWO FLANGED RECTANGULAR WAVEGUIDES

In this paper,a nondestructive technique for determining the complex permittivity and permeability of magnetic sheet materials using two flanged rectangular waveguides is presented. The technique extends existing single probe methods by its ability to simultaneously measure reflection and transmission coefficients imperative for extracting both permittivity and permeability over all frequencies. Using Loves Equivalence Principle,a system of coupled magnetic field integral equations (MFIEs) is formed. Evaluation of one of the two resulting spectral domain integrals via complex plane integration is discussed. The system,solved via the Method of Moments (MoM),yields theoretical values for the reflection and transmission coefficients. These values are compared to measured values and the error minimized using nonlinear least squares to find the complex permittivity and permeability of a material. Measurement results for two magnetic materials are presented and compared to traditional methods for the purpose of validating the new technique. The techniques sensitivity to uncertainties in material thickness and waveguide alignment is also examined.

Error analysis of a two-layer method for the electromagnetic characterization of conductor-backed absorbing material using an open-ended waveguide probe

A two-layer nondestructive method for characterizing the electric and magnetic properties of lossy conductor-backed magnetic materials using a ∞anged rectangular-waveguide probe is examined. The two re∞ection measurements necessary to determine both permittivity and permeability are made by flrst applying the probe to the material under test and then applying the probe to a known-material layer placed on top of the material under test. The theoretical re∞ection coe-cient is obtained using a rigorous full-wave solution, and an extrapolation scheme is used to minimize the error due to truncating the modal expansion of the waveguide flelds. An error analysis is performed to compare the performance of the technique to the two-thickness method, which utilizes two difierent thicknesses of the material under test. The properties of the known material layer that result in the least error due to network analyzer uncertainty are determined. The sensitivity of the two-layer method is also explored and discussed.

FDTD analysis of a new leaky traveling wave antenna

A new antenna is proposed based on a structure first constructed by Menzel (1979) that utilizes the leaky wave phenomena of the first higher order mode. This work seeks to determine the effect on performance of the antenna due to varying geometries. Standard antenna range far-field and near-field measurements are not sensitive enough to extract the propagation constant. A numerical simulation was thus developed using the finite difference time domain (FDTD) method to extract the propagation constant. The simulation was validated with published analytical data as well as measured data.

Material Classification of an Unknown Object Using Turbulence-Degraded Polarimetric Imagery

In this paper, a material-classification technique using polarimetric imagery degraded by atmospheric turbulence is presented. The classification technique described here determines whether an object is composed of dielectric or metallic materials. The technique implements a modified version of the LeMaster and Cain polarimetric maximum-likelihood blind-deconvolution algorithm in order to remove atmospheric distortion and correctly classify the unknown object. The dielectric/metal classification decision is based on degree-of-linear-polarization (DOLP) maximum-likelihood estimates provided by two novel DOLP priors (one being representative of dielectric materials and the other being representative of metallic materials) developed in this paper. The DOLP estimate, which maximizes the log-likelihood function, determines the image pixels classification. Included in this paper is the review and modification of the LeMaster and Cain deconvolution algorithm. Also provided is the development of the novel DOLP priors, including their mathematical forms and the physical insight underlying their formulation. Lastly, the experimental results of two dielectric and metallic samples are provided to validate the proposed classification technique.

A Novel Method for Determining the R-Card Sheet Impedance Using the Transmission Coefficient Measured in Free-Space or Waveguide Systems

Free-space and rectangular waveguide techniques for determining the effective complex permittivity and, ultimately, the effective sheet impedance of an R-card using the forward transmission coefficient are presented. The advantage of using a transmission coefficient method instead of a more traditional reflection-based technique is discussed. The exact transcendental expressions relating the transmission coefficient and effective complex permittivity are derived and approximated using the Maclaurin series for sine and cosine. It is shown that the Maclaurin series expansion leads to simple closed-form solutions to the effective complex permittivity and avoids the use of sensitive and often unstable root search algorithms, which are necessary to solve transcendental equations. The accuracy of the approximations is directly related to the R-cards thickness and wavenumber. Free-space (4-16 GHz) and waveguide (8.2-12.4 GHz) measurements are made using two R-cards of differing thicknesses and impedances to demonstrate the method and regimes of validity. An uncertainty analysis is also performed to demonstrate the robustness of the technique.

Natural Resonance Representation of the Transient Field Reflected by a Conductor-Backed Lossy Layer

The impulse response of a conductor-backed lossy slab is evaluated analytically. It is shown that the impulse response consists of a specular reflection from the interface between free-space and the dielectric slab during the early-time period, and a natural mode series, which is a pure sum of damped sinusoids whose frequencies are determined by the poles of the complex S-plane reflection coefficient, during the late-time period. Time-domain responses using a truncated Gaussian pulse as an input with an arbitrary incident angle and with parallel or perpendicular polarization are compared to responses found via the inverse fast Fourier transform. The results may be applied to material characterization using the E-pulse method, and also give physical insight into the nature of transient scattering by a layered medium.

Two-Iris Method for the Electromagnetic Characterization of Conductor-Backed Absorbing Materials Using an Open-Ended Waveguide Probe

A two-iris waveguide-probe technique is introduced for measuring the electromagnetic properties of a lossy conductor-backed material layer. A flanged open-ended rectangular waveguide is applied to the material under test, and the reflected signal is measured under two conditions. The reflection is first measured when the aperture of the waveguide is unobstructed; then, the reflection is measured with an iris placed in the aperture of the guide. These two measurements allow the extraction of both the permittivity and permeability of the material. The theoretical reflection coefficient necessary to perform the extraction is obtained using a rigorous full-wave approach combining a modal expansion in the waveguide and iris regions with a magnetic-field integral equation formed using equivalent currents at the waveguide aperture. The optimum iris size is determined by minimizing the propagated error due to instrumentation uncertainty and by comparing the extracted parameters to those found using a two-thickness method. Measurements of a commercially available magnetic radar-absorbing material demonstrate the feasibility of the two-iris approach.