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## Full-Text Articles in Physics

Further Thoughts On Newton's Zero-Order Rainbow, James A. Lock, Timothy A. Mccollum

#### Further Thoughts On Newton's Zero-Order Rainbow, James A. Lock, Timothy A. Mccollum

*Physics Faculty Publications*

A zero-order rainbow angle may be defined as the relative minimum angle of deviation of geometrical light rays transmitted without internal reflections through a transparent particle. If the incident rays are parallel and the particle is a sphere, such a minimum does not exist. But if the incident rays ale not parallel or if the particle has an elliptical rather than circular cross section, an angle of minimum deviation, hence a zero-order rainbow, can occur. For a spherical water droplet, the zero-order rainbow will occur when a point source is placed less than a droplet radius away from its surface ...

Rigorous Justification Of The Localized Approximation To The Beam Shape Coefficients In Generalized Lorenz-Mie Theory .1. On-Axis Beams, James A. Lock, Gérard Gouesbet

#### Rigorous Justification Of The Localized Approximation To The Beam Shape Coefficients In Generalized Lorenz-Mie Theory .1. On-Axis Beams, James A. Lock, Gérard Gouesbet

*Physics Faculty Publications*

Generalized Lorenz-Mie theory describes electromagnetic scattering of an arbitrary light beam by a spherical particle. The computationally most expensive feature of the theory is the evaluation of the beam-shape coefficients, which give the decomposition of the incident light beam into partial waves. The so-called localized approximation to these coefficients for a focused Gaussian beam is an analytical function whose use greatly simplifies Gaussian-beam scattering calculations. A mathematical justification and physical interpretation of the localized approximation is presented for on-axis beams.

Light And Color In The Open Air: Introduction By The Feature Editors, James A. Lock

#### Light And Color In The Open Air: Introduction By The Feature Editors, James A. Lock

*Physics Faculty Publications*

The natural environment is still rich in new observable phenomena despite centuries of scientific observation. Reflecting this fact, the papers in this feature issue of Applied Optics report the observation and analysis of both new and well-known naked-eye optical phenomena.

Rainbow Scattering By A Coated Sphere, James A. Lock, J. Michael Jamison, Chih-Yang Lin

#### Rainbow Scattering By A Coated Sphere, James A. Lock, J. Michael Jamison, Chih-Yang Lin

*Physics Faculty Publications*

We examine the behavior of the first-order rainbow for a coated sphere by using both ray theory and Aden-Kerker wave theory as the radius of the core alpha12 and the thickness of the coating delta are varied. As the ratio delta/alpha12 increases from 10(-4) to 0.33, we find three classes of rainbow phenomena that cannot occur for a homogeneous-sphere rainbow. For delta/alpha12 less than or similar to 10(-3), the rainbow intensity is an oscillatory function of the coating thickness, for delta/alpha12 almost-equal-to 10(-2), the first-order rainbow breaks into a pair of twin rainbows ...

Correlated Light Scattering By A Dense Distribution Of Condensation Droplets On A Window Pane, James A. Lock, Chin-Lien Chiu

#### Correlated Light Scattering By A Dense Distribution Of Condensation Droplets On A Window Pane, James A. Lock, Chin-Lien Chiu

*Physics Faculty Publications*

An analytical model of the scattering structure factor for an assembly of noninteracting hard disks has recently appeared in the literature [Phys. Rev. A 42, 5978-5989 (1990)]. We employ this model to calculate correlated light scattering by monodispersions and binary mixtures of condensation droplets on a window pane. We find that an area fraction of f greater-than-or-equal-to 0.6 is required for producing the near-forward direction scattering suppression and that a moderately wide polydispersion of droplet sizes is capable of producing the experimentally observed bright ring of colored light.

Scaling Behavior Of Fluctuations In Systems With Continuous Symmetry, Ulrich Zürcher

#### Scaling Behavior Of Fluctuations In Systems With Continuous Symmetry, Ulrich Zürcher

*Physics Faculty Publications*

In nematic liquid crystals, director fluctuations correpond to the dynamical mode that is critical for all temperatures in zero external fields. The Hurst exponent characterizes the temporal behavior of the mean square displacement of director fluctuations, 〈[δn(r,t)-δn(r,0)]2〉∼t2H. We find H=1/2 in finite fields and H=3/4 in zero field. This result differs from that of Zhang et al. [Phys. Rev. Lett. 70, 1834 (1993)] who find a Hurst exponent that varies continuously from H≃1 in zero field to H≃1/2 in moderate fields.

Phase Diagram Of The Ising Model On Percolation Clusters, Miron Kaufman, T. Berger, P. D. Gujrati, D. Bowman

#### Phase Diagram Of The Ising Model On Percolation Clusters, Miron Kaufman, T. Berger, P. D. Gujrati, D. Bowman

*Physics Faculty Publications*

The annealed Ising magnet on percolation clusters is studied by means of a mapping into a Potts-Ising model and with the Migdal-Kadanoff renormalization-group method. The phase diagram is determined in the three-dimensional parameter space of the Ising coupling K, the bond-occupation probability p, and the fugacity q, which controls the number of clusters. Three phases are identified: percolating ferromagnetic, percolating paramagnetic, and nonpercolating paramagnetic. For large q the phase diagram includes a multicritical point at the intersection of the Ising critical line and the percolation critical line. In the case of random bond percolation (q = 1) the Ising critical line ...

A Fringe Center Detection Technique Based On A Sub-Pixel Resolution, And Its Applications Using Sinusoidal Gratings, Ming Chang, Paul P. Lin, Wen Chih Tai

#### A Fringe Center Detection Technique Based On A Sub-Pixel Resolution, And Its Applications Using Sinusoidal Gratings, Ming Chang, Paul P. Lin, Wen Chih Tai

*Mechanical Engineering Faculty Publications*

A common problem in optical profilometry is the accuracy in locating *fringe* centers. This paper presents an accurate *fringe* *center* *detection* *technique* *based* on *sub*-*pixel* *resolution* *using* the *fringe* projection method. An optimum reconstruction filter is developed which has low sensitivity to noise. In *fringe* *center* *detection*, computer simulation results of *using* one-*pixel* and *sub*-*pixel* resolutions are compared. The *detection* *technique* is then applied to radius measurement of cylindrical objects and surface profile measurement of diffuse objects. The experimental results thus obtained through the proposed optimum reconstruction filter show significant improvement in measurement accuracy.