Jeremy Ellis

Complex degree of mutual polarization.

Starting from the concepts of coherence and polarization, we generalize the conventional degree of polarization, introducing a two-point parameter, the complex degree of mutual polarization V, which is defined in terms of measurable quantities. We demonstrate the physical significance of this new quantity for the case of fully correlated, pure states of polarization at the two points, showing that the magnitude of V is a measure of the similarity between the states of polarization at two different points in space.

Correlation matrix of a completely polarized, statistically stationary electromagnetic field.

It is shown that, for a 3 x 3 correlation matrix Wij(r, r, omega), (i, j = x, y, z) of the electric vector of a random, stationary electromagnetic field to represent a field that is completely polarized at a point r and frequency omega, each element of the matrix must factorize. More precisely, a necessary and sufficient condition for the correlation matrix to represent a fully polarized field at a point r is that the matrix has the form Wij(r, r, omega) = epsilon(i)*(r, omega)epsilon(j)(r, omega), where epsilon(i)(r, omega) (i = x, y, z) are deterministic functions, i.e., that all pairs of the Cartesian components of the electric field at a point r and frequency omega are completely correlated.

Differentiation of globally unpolarized complex random fields

Different types of random vector fields can be depolarized in a global sense. They can be physically discriminated by probing the statistical invariance when they are subject to operations such as a change of the reference frame or the introduction of an arbitrary retardance. With use of the observable polarization sphere as a visualization tool, a set of measurements is capable of discriminating between certain types of globally depolarized light, and we discuss the geometric interpretation of the physical invariances.

Discrimination of globally unpolarized fields through Stokes vector element correlations.

In a previous publication [J. Opt. Soc. Am. A 21, 988 (2004)], we examined theoretically joint probability distributions of Stokes vector elements and suggested the existence of various types of globally unpolarized light that could be discriminated through measurement of the Stokes vector element correlations. We now study the joint distribution of the degree of polarization and the three Stokes parameters as it relates to material properties in highly scattering, depolarizing random media. We describe numerical and experimental results of second-order Stokes vector element correlations, demonstrating the existence of various types of nonclassical, globally unpolarized light, and we suggest experimental means for discriminating between such field distributions. We also discuss the usefulness of the Stokes vector element correlations as an experimental tool for discriminating between different globally unpolarized fields and for verifying the assumption of Gaussian statistics usually invoked in the context of multiple light scattering.

Off-diagonal Mueller matrix elements in backscattering from highly diffusive media

Measurements of a reduced Mueller matrix in backscattering from highly diffusive, dielectric samples are reported as a function of the angle of incidence. It was found that the off-diagonal terms depend greatly on the angle of incidence, increasing to a maximum near grazing incidence. We show that, despite a significant scattering originating in the bulk of such diffusive media, the nontrivial behavior of the off-diagonal Muller matrix is primarily due to surface scattering phenomena. The experimental data can be simply explained by assuming a random orientation of small particles and considering only double scattering in the plane of the surface.

Identifying non-stationarities in random EM fields: are speckles really disturbing?

In dealing with random EM fields, ensemble averaging is an ubiquitous procedure. However, we demonstrate that spatial non-stationarities such as enhanced backscattering can be identified even from one single realization (snapshot) of the wave interaction with a random medium. Fourth-order correlations between field components at two different spatial points are shown to provide the necessary information.

Fluctuations of scattered waves: going beyond the ensemble average

The interaction between coherent waves and random media is a complicated, deterministic process that is usually examined upon ensemble averaging. The result of one realization of the interaction process depends on the specific disorder present in an experimentally controllable interaction volume. We show that this randomness can be quantified and structural information not apparent in the ensemble average can be obtained. We use the information entropy as a viable measure of randomness and we demonstrate that its rate of change provides means for discriminating between media with identical mean characteristics.

Resampling considerations for registering remotely sensed images

Satellite imagery data typically requires the use of interpolation techniques during the orthorectification and registration stages of processing. Given that satellite imagery is typically undersampled, interpolation cannot perfectly recover the original signal and therefore consideration must be given to the concept of the optimal interpolation technique for a given application. We address these issues and suggest a metric to define interpolation quality. We also propose a new interpolation scheme which performs well for certain classes of image features, most importantly sub-pixel image features and features of low pixel count.

Expanded Field of View Using Polarization Multiplexing

We introduce and demonstrate experimentally a method for expanding the field of view of an imaging system by multiplexing polarimetrically encoded images and decoding them with a limited a number of measurements.

Stokes vector correlations and material discrimination from speckle fields

We examine the joint probability distribution of polarization information; specifically the joint distribution of the degree of polarization and the three Stokes parameters, as it relates to material properties in a highly scattering, highly depolarizing transmission geometry, making use of the Observable Polarization Sphere (OPS) for visualization of this distribution. We comment on the role of the source’s coherence in terms of the polarization properties of the resulting speckle field, and describe numerical and experimental results of second order Stokes vector element correlations and their applicability to material discrimination.