On-grid compressive sampling for spherical field measurements in acoustics.

We derive a compressive sampling method for acoustic field reconstruction using field measurements on a pre-defined spherical grid that has theoretically guaranteed relations between signal sparsity, measurement number, and reconstruction accuracy. This method can be used to reconstruct band limited spherical harmonic or Wigner D-function series (spherical harmonic series are a special case) with sparse coefficients. Contrasting typical compressive sampling methods for Wigner D-function series that use arbitrary random measurements, the new method samples randomly on an equiangular grid, a practical and commonly used sampling pattern. Using its periodic extension, we transform the reconstruction of a Wigner D-function series into a multi-dimensional Fourier domain reconstruction problem. We establish that this transformation has a bounded effect on sparsity level and provide numerical studies of this effect. We also compare the reconstruction performance of the new approach to classical Nyquist sampling and existing compressive sampling methods. In our tests, the new compressive sampling approach performs comparably to other guaranteed compressive sampling approaches and needs a fraction of the measurements dictated by the Nyquist sampling theorem. Moreover, using one-third of the measurements or less, the new compressive sampling method can provide over 20 dB better de-noising capability than oversampling with classical Fourier theory.

Vectorizing Green's identities.

Green's theorem and Green's identities are well-known and their uses span almost every branch of science and mathematics. In this paper, we derive a vector analogue of Green's three scalar identities and consider some of their uses. We also offer a number of historical tidbits in connection to the work of George Green.

Field-only surface integral equations: scattering from a perfect electric conductor.

A field-only boundary integral formulation of electromagnetics is derived without the use of surface currents that appear in the Stratton-Chu formulation. For scattering by a perfect electrical conductor (PEC), the components of the electric field are obtained directly from surface integral equation solutions of three scalar Helmholtz equations for the field components. The divergence-free condition is enforced via a boundary condition on the normal component of the field and its normal derivative. Field values and their normal derivatives at the surface of the PEC are obtained directly from surface integral equations that do not contain divergent kernels. Consequently, high-order elements with fewer degrees of freedom can be used to represent surface features to a higher precision than the traditional planar elements. This theoretical framework is illustrated with numerical examples that provide further physical insight into the role of the surface curvature in scattering problems.

Field-only surface integral equations: scattering from a dielectric body.

An efficient field-only nonsingular surface integral method to solve Maxwell's equations for the components of the electric field on the surface of a dielectric scatterer is introduced. In this method, both the vector wave equation and the divergence-free constraint are satisfied inside and outside the scatterer. The divergence-free condition is replaced by an equivalent boundary condition that relates the normal derivatives of the electric field across the surface of the scatterer. Also, the continuity and jump conditions on the electric and magnetic fields are expressed in terms of the electric field across the surface of the scatterer. Together with these boundary conditions, the scalar Helmholtz equation for the components of the electric field inside and outside the scatterer is solved by a fully desingularized surface integral method. Compared with the most popular surface integral methods based on the Stratton-Chu formulation or the Poggio-Miller-Chew-Harrington-Wu-Tsai (PMCHWT) formulation, our method is conceptually simpler and numerically straightforward because there is no need to introduce intermediate quantities such as surface currents, and the use of complicated vector basis functions can be avoided altogether. Also, our method is not affected by numerical issues such as the zero-frequency catastrophe and does not contain integrals with (strong) singularities. To illustrate the robustness and versatility of our method, we show examples in the Rayleigh, Mie, and geometrical optics scattering regimes. Given the symmetry between the electric field and the magnetic field, our theoretical framework can also be used to solve for the magnetic field.

Measurement of back-scattering patterns from single laser trapped aerosol particles in air.

We demonstrate a method for measuring elastic back-scattering patterns from single laser trapped micron-sized particles, spanning the scattering angle range of θ=167.7°-180° and φ=0°-360° in spherical coordinates. We calibrated the apparatus by capturing light-scattering patterns of 10 µm diameter borosilicate glass microspheres and comparing their scattered intensities with Lorenz-Mie theory. Back-scattering patterns are also presented from a single trapped Johnson grass spore, two attached Johnson grass spores, and a cluster of Johnson grass spores. The method has potential use in characterizing airborne aerosol particles, and may be used to provide back-scattering data for lidar applications.

Phase-ratio imaging as applied to desert sands for tracking human presence.

The phase function is a measure of the light-scattered intensity, or radiance, as a function of scattering angle θ. A phase ratio is the ratio of two values of the phase function measured at different scattering angles and relates to the slope of the phase function. By taking the ratio of two images acquired at different illumination or observation conditions, a phase-ratio image can be constructed. Such images accentuate differences in the phase curves, rather than their intensities, and are more sensitive to microtopography than to material properties. We produce phase-ratio images from intensity images acquired at different observation times and locations in the desert environment of White Sands National Monument. Because of the lack of surface features, coregistration of the images is challenging, especially for images acquired from different observation locations. However, we do demonstrate that phase-ratio images can be used to identify disturbed sands. We also produce polarimetric and color-ratio images. These latter images do not suggest the possibility of identifying topographical differences due to human presence.

Effects of surface materials on polarimetric-thermal measurements: applications to face recognition.

Materials, such as cosmetics, applied to the face can severely inhibit biometric face-recognition systems operating in the visible spectrum. These products are typically made up of materials having different spectral properties and color pigmentation that distorts the perceived shape of the face. The surface of the face emits thermal radiation, due to the living tissue beneath the surface of the skin. The emissivity of skin is approximately 0.99; in comparison, oil- and plastic-based materials, commonly found in cosmetics and face paints, have an emissivity range of 0.9-0.95 in the long-wavelength infrared part of the spectrum. Due to these properties, all three are good thermal emitters and have little impact on the heat transferred from the face. Polarimetric-thermal imaging provides additional details of the face and is also dependent upon the thermal radiation from the face. In this paper, we provide a theoretical analysis on the thermal conductivity of various materials commonly applied to the face using a metallic sphere. Additionally, we observe the impact of environmental conditions on the strength of the polarimetric signature and the ability to recover geometric details. Finally, we show how these materials degrade the performance of traditional face-recognition methods and provide an approach to mitigating this effect using polarimetric-thermal imaging.

Near- and far-field scattering resonance frequency shift in dielectric and perfect electric conducting cylinders.

The ability to infer near-field scattering properties from far-field measurements is of paramount importance in nano-optics. Recently we derived an approximate formula for predicting the frequency shift between near- and far-field intensity peaks in the case of a dielectric sphere. In this work we demonstrate that almost an identical formula can be used to predict the resonance shift of a dielectric cylinder and a perfectly conducting cylinder. We find the redshift of the resonance peak of the perfect electric conducting cylinder to be approximately 2 orders of magnitude greater than for the dielectric cylinder. The errors in our approximate analytic formula for predicting the redshift are approximately only twice as great. Furthermore, we apply the redshift formula to a silicon cylinder and discuss its magneto-dielectric properties, which may be of interest in design of metamaterials.

Frequency shift between near- and far-field scattering resonances in dielectric particles.

The near-field electromagnetic scattering intensity resonances are redshifted in frequency with respect to their far-field counterparts. We derive simple, approximate, analytical formulas for this shift in the case of a plane wave interacting with a dielectric sphere. Numerical results comparing the approximate formulas to the numerically exact solutions show that the two are in good agreement. We also consider the Rayleigh limit of the formulas to gain more insight into the phenomenon.

Enhanced facial recognition for thermal imagery using polarimetric imaging.

We present a series of long-wave-infrared (LWIR) polarimetric-based thermal images of facial profiles in which polarization-state information of the image-forming radiance is retained and displayed. The resultant polarimetric images show enhanced facial features, additional texture, and details that are not present in corresponding conventional thermal imagery. It has been generally thought that conventional thermal imagery (MidIR or LWIR) could not produce the detailed spatial information required for reliable human identification due to the so-called "ghosting" effect often seen in thermal imagery of human subjects. By using polarimetric information, we are able to extract subtle surface features of the human face, thus improving subject identification. Polarimetric image sets considered include the conventional thermal intensity image, S0, the two Stokes images, S1 and S2, and a Stokes image product called the degree-of-linear-polarization image.

Three-dimensional facial recognition using passive long-wavelength infrared polarimetric imaging.

We use a polarimetric camera to record the Stokes parameters and the degree of linear polarization of long-wavelength infrared radiation emitted by human faces. These Stokes images are combined with Fresnel relations to extract the surface normal at each pixel. Integrating over these surface normals yields a three-dimensional facial image. One major difficulty of this technique is that the normal vectors determined from the polarizations are not unique. We overcome this problem by introducing an additional boundary condition on the subject. The major sources of error in producing inversions are noise in the images caused by scattering of the background signal and the ambiguity in determining the surface normals from the Fresnel coefficients.