Brian G. Hoover

Coherence and polarization properties of far fields generated by quasi-homogeneous planar electromagnetic sources

In studies of radiation from partially coherent sources the so-called quasi-homogeneous (QH) model sources have been very useful, for instance in elucidating the behavior of fields produced by thermal sources. The analysis of the fields generated by such sources has, however, been largely carried out in the framework of scalar wave theory. In this paper we generalize the concept of the QH source to the domain of the electromagnetic theory, and we derive expressions for the elements of the cross-spectral density matrix, for the spectral density, the spectral degree of coherence, the degree of polarization, and the Stokes parameters of the far field generated by planar QH sources of uniform states of polarization. We then derive reciprocity relations analogous to those familiar in connection with the QH scalar sources. We illustrate the results by determining the properties of the far field produced by transmission of an electromagnetic beam through a system of spatial light modulators.

Design and optimization of partial Mueller matrix polarimeters.

Mueller matrix polarimeters (MMPs) are designed to probe the polarization properties of optical scattering processes. When using a MMP for a detection, discrimination, classification, or identification task, a user considers certain elements of the Mueller matrix. The usual way of performing this task is to measure the full Mueller matrix and discard the unused elements. For polarimeter designs with speed, miniaturization, or other constraints, it may be desirable to have a system with reduced dimensionality that measures only elements of the Mueller matrix that are important in a particular application as efficiently as possible. In this paper, we develop a framework that allows partial MMPs to be analyzed. Quantitative metrics are developed by considering geometrical relationships between the space spanned by a particular MMP and the space occupied by the scene components. The method is generalized to allow the effects of noise to be considered. The results are general and can also be used to optimize complete and overspecified MMPs for performing specific tasks, as well.

Coherence solution for bidirectional reflectance distributions of surfaces with wavelength-scale statistics

The scalar bidirectional reflectance distribution function (BRDF) due to a perfectly conducting surface with roughness and autocorrelation width comparable with the illumination wavelength is derived from coherence theory on the assumption of a random reflective phase screen and an expansion valid for large effective roughness. A general quadratic expansion of the two-dimensional isotropic surface autocorrelation function near the origin yields representative Cauchy and Gaussian BRDF solutions and an intermediate general solution as the sum of an incoherent component and a nonspecular coherent component proportional to an integral of the plasma dispersion function in the complex plane. Plots illustrate agreement of the derived general solution with original bistatic BRDF data due to a machined aluminum surface, and comparisons are drawn with previously published data in the examination of variations with incident angle, roughness, illumination wavelength, and autocorrelation coefficients in the bistatic and monostatic geometries. The general quadratic autocorrelation expansion provides a BRDF solution that smoothly interpolates between the well-known results of the linear and parabolic approximations.

Noise reduction in a laser polarimeter based on discrete waveplate rotations

While several analyses of polarimeter noise-reduction have been published, little data has been presented to support the analytical results, particularly for a laser polarimeter based on measurements taken at discrete, independent rotation angles of two birefringent waveplates. This paper derives and experimentally demonstrates the reduction of both system and speckle noise in this type of laser polarimeter, achieved by optimizing the rotation angles of the waveplates by minimizing the condition numbers of the appropriate matrix equation. Results are demonstrated experimentally in signal-to-noise ratio (SNR) variations for a range of materials and spatial bandwidths. Use of optimal waveplate angles is found to improve the average SNR of the normalized Mueller matrix over speckle by a factor of up to 8 for a non-depolarizing material, but to provide little improvement for a depolarizing material. In the limit of zero spatial bandwidth, the average SNR of the normalized Mueller matrix over speckle is found to be greater than one for a non-depolarizing material and less than one for a depolarizing material.

Polarization components analysis for invariant discrimination

Linear and nonlinear components analysis of data from a monostatic laser polarimeter is developed and applied to the task of remote, nonimaging discrimination among different textures on paint and polymer coupons independent of their spatial orientations. Both principal-components analysis and nonlinear components analysis are applied to multidimensional laser data in measured Mueller matrices, with discrimination via cluster segmentation in derived linear and nonlinear constant channels. Textures on the discriminated coupons are generated by heating and illustrated in optical micrographs.

REALIZATION OF TIME GATING BY USE OF SPATIAL FILTERING

A method for simulating conventional time gating in low-coherence optical imaging processes in highly scattering media is given. The method uses monochromatic instead of broadband light, and spatial filtering is substituted for time gating. The process enables the study of imaging techniques in scattering media to be carried out in an easy and highly controllable way. Experimental results are given.

Ultrafast, cross-correlated harmonic imaging through scattering media

A simple upconversion scheme utilizing 40-fs pulses is shown to permit high-contrast imaging of objects obscured by a highly scattering medium when no ballistic component is evident in the scattered light and imaging is performed with any portion of the scattered light pulse. We present a time-gated, inherently low-pass spatially filtered imaging method that minimizes signal-averaging requirements and greatly facilitates imaging under severe scattering (turbid) conditions.

Classification using active polarimetry

Active (Mueller matrix) remote sensing is an under-utilized technique for material discrimination and classication. A full Mueller matrix instrument returns more information than a passive (Stokes) polarimeter; Mueller polarimeters measure depolarization and other linear transformations that materials impart on incident Stokes vectors, which passive polarimeters cannot measure. This increase in information therefore allows for better classication of materials (in general). Ideally, material classication over the entire polarized BRDF is desired, but sets of Mueller matrices for dierent materials are generally not separable by a linear classier over elevation and azimuthal target angles. We apply non-linear support vector machines (SVM) to classify materials over BRDF (all relevant angles) and show variations in receiver operator characteristic curves with scene composition and number of Mueller matrix channels in the observation.

Designing Partial Mueller Matrix Polarimeters

When using a MMP for a detection or identification task, a user considers certain elements of the Mueller matrix. The usual way of performing this task is to measure the full Mueller matrix and discard the unused elements. For polarimeter designs with speed, miniaturization, or other constraints it may be desirable to have a system with reduced dimensionality that measures only the important elements of the Mueller matrix as efficiently as possible. In this paper, we develop a framework that allows partial MMPs to be analyzed. Quantitative metrics are developed by considering geometrical relationships between the space spanned by a particular MMP and the space occupied by the scene components. The method is generalized to allow the effects of noise to come into the equation when noise performance is important as well.

Investigation of ultrafast time gating by spatial filtering

With a spatial-filtering method of gating, we explore image formation through scattering media using first-arriving light. Gating times of a few femtoseconds and less are produced, and the resolution at these extremely short gating times is investigated.