No abstract

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.

The sizes and shapes of voids in a galaxy survey depend not only on the physics of structure formation, but also on the sampling density of the survey and on the algorithm used to deÐne voids. Using an N-body simulation with a qCDM power spectrum, we study the properties of voids in samples with di †erent number densities of galaxies, in both redshift space and real space. When voids are deÐned as totally empty regions of space, their characteristic volume is strongly dependent on sampling density ; when they are deÐned as regions whose density is 0.2 times the mean galaxy density, the dependence is less strong. We compare two void-Ðnding algorithms, one in which voids are nonoverlapping spheres, and one, based on the algorithm of Aikio & that does not predeÐne the shape of a void. Mahonen, Regardless of the algorithm chosen, the characteristic void size is larger in redshift space than in real space, and is larger for low sampling densities than for high sampling densities. We deÐne an elongation statistic Q that measures the tendency of voids to be stretched or squashed along the line of sight. Using this statistic, we Ðnd that at sufficiently high sampling densities (comparable to the number density of galaxies), large voids tend to be slightly elongated along the line of sight in redshift space.

Numerical simulation of optical wave propagation with examples in MATLAB / Jason D. Schmidt. p. cm.-(Press monograph ; 199) Includes bibliographical references and index.

Strong turbulence causes phase discontinuities known as branch points in an optical field. These discontinuities complicate the phase unwrapping necessary to apply phase corrections onto a deformable mirror in an adaptive optics (AO) system. This paper proposes a non-optimal but effective and implementable phase unwrapping method for optical fields containing branch points. This method first applies a least-squares (LS) unwrapper to the field which isolates and unwraps the LS component of the field. Four modulo-2pi-equivalent non-LS components are created by subtracting the LS component from the original field and then restricting the result to differing ranges. 2pi phase jumps known as branch cuts are isolated to the non-LS components and the different non-LS realizations have different branch cut placements. The best placement of branch cuts is determined by finding the non-LS realization with the lowest normalized cut length and adding it to the LS component. The result is an unwrapped field which is modulo-2pi -equivalent to the original field while minimizing the effect of phase cuts on system performance. This variable-range 'phi LS +phi non phi LS' unwrapper, is found to outperform other unwrappers designed to work in the presence of branch points at a reasonable computational burden. The effect of improved unwrapping is demonstrated by comparing the performance of a system using a fixed-range phi 'LS + phi non--LS' realization unwrapper against the variable-range 'phi LS +phi non--LS' unwrapper in a closed-loop simulation. For the 0.5 log-amplitude variance turbulence tested, the system Strehl performance is improved by as much as 41.6 percent at points where fixed-range 'phi LS + phi non phi LS' unwrappers result in particularly poor branch cut placement. This significant improvement in previously poorly performing regions is particularly important for systems such as laser communications which require minimum Strehl ratios to operate successfully.