Mie theory, airy theory, and the natural rainbow

Compared with Mie scattering theory, Airy rainbow theory clearly miscalculates some monochromatic details of scattering by small water drops. Yet when monodisperse Airy theory is measured by perceptual (rather than purely physical) standards such as chromaticity and luminance contrast, it differs very little from Mie theory. Considering only the angular positions of luminance extrema, Airy theory's errors are largest for small droplets such as those that dominate cloudbows and fogbows. However, integrating over a realistic drop-size distribution for these bows eliminates most perceptible color and luminance differences between the two theories.     

On the mechanics of the arrow: Archer's Paradox

In ancient bows the grip of the bow was in the way of the arrow. The arrow needed to get round the bow while being accelerated; this phenomenon is called the Archer's Paradox. In the forties it was observed experimentally with high-speed cameras that the arrow vibrates in a horizontal plane perpendicular to the vertical median plane of the bow. These movements are started and controlled by the movements of the two points of contact with the bow, viz. the middle of the string in contact with the rear end of the arrow and the grip where the arrow slides along the bow. The latter contact imposes a moving-boundary condition. The numerically obtained results are satisfactorily in agreement with experimental data. The model can be used to estimate the drawing force of ancient bows of which only the contemporary arrows are available and also for the design of new archery equipment.     

Rotating light fields of an azimuthally polarized light beam generated by two-belt spiral phase modulation

The tightly focused light fields of an azimuthally polarized light beam through a two-belt spiral phase plate were investigated. The focused light fields are presented in accordance with vectorial diffraction theory. The results show that a rotating light field with different intensity patterns can be produced by altering the azimuthal polarization state and modulating the two-belt spiral phase. A concurrent change in spiral handedness in the two-belt phase plate causes the rotation to occur along the direction of propagation, and the relative angular offset in the two-belt spiral phase plate can be exploited to rotate the light fields. The proposed method is useful for engineering the intensity distribution near the focal plane and related applications.     

Polarization of 'water-skies' above arctic open waters: how polynyas in the ice-cover can be visually detected from a distance

The foggy sky above a white ice-cover and a dark water surface (permanent polynya or temporary lead) is white and dark gray, phenomena called the 'ice-sky' and the 'water-sky,' respectively. Captains of icebreaker ships used to search for not-directly-visible open waters remotely on the basis of the water sky. Animals depending on open waters in the Arctic region may also detect not-directly-visible waters from a distance by means of the water sky. Since the polarization of ice-skies and water-skies has not, to our knowledge, been studied before, we measured the polarization patterns of water-skies above polynyas in the arctic ice-cover during the Beringia 2005 Swedish polar research expedition to the North Pole region. We show that there are statistically significant differences in the angle of polarization between the water-sky and the ice-sky. This polarization phenomenon could help biological and man-made sensors to detect open waters not directly visible from a distance. However, the threshold of polarization-based detection would be rather low, because the degree of linear polarization of light radiated by water-skies and ice-skies is not higher than 10%.     

Polarization patterns of thick clouds: overcast skies have distribution of the angle of polarization similar to that of clear skies

The distribution of polarization in the overcast sky has been practically unknown. Earlier the polarization of light from heavily overcast skies (when the Sun's disc was invisible) has been measured only sporadically in some celestial points by point-source polarimetry. What kind of patterns of the degree p and angle alpha of linear polarization of light could develop after transmission through a thick layer of ice or water clouds? To answer this question, we measured the p and alpha patterns of numerous totally overcast skies on the Arctic Ocean and in Hungary by full-sky imaging polarimetry. We present here our finding that depending on the optical thickness of the cloud layer, the pattern of alpha of light transmitted through the ice or water clouds of totally overcast skies is qualitatively the same as the alpha pattern of the clear sky. Under overcast conditions the value of alpha is determined predominantly by scattering on cloud particles themselves. Nevertheless, the degrees of linear polarization of light from overcast skies were rather low (p相似文献   

Effect of high temperature aging on ferrite transformation kinetics and tensile properties of type 316L stainless steel weld metal

Abstract

Tensile samples of AISI type 316L weld metal, deposited by the gas tungsten arc welding process, were heat treated at 873,973, and 1073 K, before being subjected to tensile loading at an initial strain rate of 5·5 × 10^?5 S^?1 at a temperature of 427 K. The transformation kinetics of δ ferrite was studied in detail. The activation energy for the transformation of δ ferrite was found to be 272 kJ mol^?1. Theferrite transformation kinetics datafor the above three temperatures were thenfitted into a master plot using the Dorn parameter, and its validity in this temperature range was verified by superimposing the ferrite transformation kinetics data at 948 and 1023 K on to the master plot. From examinations by optical microscopy, the weld metal was found to undergo competing transformation reactions during high temperature aging, namely, dissolution of δ ferrite, precipitation of carbidesj carbonitrides and σ phase, changes in σ phase morphology, and spheroidisation of σ phase. The effect of the ferrite transformation kinetics and σ phase precipitation kinetics on the tensile properties of the weld metal were also studied in detail. The yield stresses of all the aged weld metals were lower than that of the as deposited weld metal. The σ phase had no direct influence on changes in the yield stress. The ultimate tensile strength was affected only by the quantity and morphology of σ phase. All the competing processes (except changes in σ phase morphology) significantly influenced ductility. The increase in work hardening exponent n was dependent only on the amount of σ phase and not on its morphology.

MST/1983     

干气密封系统角向摆动的稳定性及其振动响应

干气密封系统角向摆动改变了动静密封环间的微尺度间隙,进而影响了干气密封的密封性能,建立了角向振动下气膜-密封环系统的动力学模型,应用微扰法和龙格-库塔法求解气膜角向刚度、临界转动惯量和角向摆动的二维振动方程,获得了密封系统稳定时的密封结构参数范围,并分析了最佳稳定点和临界点振动响应。研究结果表明:在特例中螺旋角α=75°邻域内,存在着稳定区域α=74°30′06″-75°16′10″,其最佳值为αopt=74°53′48″。最佳稳定点振动响应为准周期运动,而临界点振动响应发生了混沌运动。     

Angular distribution of the forward light scattering from a quartz fiber

Using a new technique based on the fanning of a coherent light beam in a photorefractive BaTiO(3) crystal, we have measured the angular distribution of forward light scattering by quartz fibers of radii from 15 to 30 μm. Data have been obtained over the angular range 0° to 0.3° and are in good agreement with theory.     

Scatter from tilted-columnar birefringent thin films: observation and measurement of anisotropic scatter distributions

We show that the angular distribution of scattered light (haze) from tilted-columnar birefringent thin films is highly anisotropic. When a narrow laser beam is incident normally upon a substrate coated with a tilted-columnar film, such as titania deposited at 60° to a thickness of ≈2 μm, the distribution of light scattered into the surrounding transmission and reflection air spaces has the form of one or more arcs. Scatter of light into the substrate is also highly anisotropic, and secondary scatter from the trapped substrate flux produces characteristic bright patterns that appear superposed on the coating.

When viewed in transmission the bright pattern typically consists of two strong lobes and in reflection four weaker lobes that make a cross. The various anisotropic distributions are shown to be consistent with interference of light from scattering centers that are correlated along the column direction and hence can be described as reflections from the tilted-columnar thin-film microstructure.

     

Supernumerary ice-crystal halos?

Geometric-optics singularities in the intensity profiles of refraction halos formed by randomly oriented ice crystals are softened by diffraction and decorated with fine supernumerary fringes. If the crystals have a fixed symmetry axis (as in parhelia), the geometric singularity is a square-root divergence, as in the rainbow. However, the universal curve that describes diffraction is different from the rainbow's Airy function, with weak maxima (supernumerary fringes) on the geometrically dark region inside the halo (and even fainter fringes outside); these are much smaller than their counterparts on the light side of rainbows. If the crystals have no preferred orientation (as in the 22° halo), the geometric singularity is a step. In this case the universal diffraction function has no maxima, and its supernumeraries are shoulders rather than maxima. The low contrast of the fringes is probably the main reason why supernumerary halos are rarely if ever seen.     

Mechanism and symmetry properties of depolarization in weak scattering of light

The mechanism and some symmetry properties of depolarization upon weak scattering of light from a class of random media were studied theoretically. Departing from the angular distribution of the degree of polarization, our derivations showed the mechanism that induces the change of polarization can be split into two parts of different nature. One is the vectorial effect that redistributes the original light components, and the other is the interaction effect of the medium that modulates the correlation properties of the incident field. We also showed that there is dependence of the angular distribution on the incident polarization state; i.e., the angular pattern and its symmetry depend on both the orientation and ellipticity of the incident polarization. Random light was analyzed in the space-frequency domain.     

Backscattered polarization patterns determined by conservation of angular momentum

It is demonstrated that the occurence of backscattered polarization patterns relates to the conservation of angular momentum of light. Using the geometrical phase formalism in the spin space, we develop a model where the helicity-maintaining and the helicity-flipping multiple-scattering processes can be accounted for. The model explains practically all the symmetries present in the spatially resolved Mueller matrices.     

Some physical properties of Mg-Zn ferrites

Abstract

Electric, dielectric, and structural studies were carried out at room temperature for a series of Mg_xZn_l-xFe₂0₄ ferrite samples prepared by the usual ceramic technique. The experimental results showed that the real dielectric constant ε and dielectric loss factor tan δ decrease whereas the ac electrical conductivity σ₂ (ω, T) increases on increasing the angular frequency ω. The dc and ac electrical conductivities, real dielectric constant, and dielectric loss factor were found to decrease with increasing Mg ion substitution. The parameters nand B in the power law σ₂ (ω, T) = Bωⁿ for the electrical conductivity σ (ω, T) were found to be composition dependent, with both nand B decreasing as the Mg ion addition increased. According to the experimental results, empirical formulae are suggested for the composition dependences of the electrical conductivity σ and the parameters nand B. The analysis of X-ray diffraction patterns showed that the samples investigated have a single phase cubic spinel structure. The bulk and theoretical density, lattice constant, and radius of the tetrahedral ion decrease whereas porosity increases as Mg ion substitution increases. The infrared absorption spectra showed three of the characteristic bands for ferrites with intensities and positions (wavenumbers) that are composition dependent. The fourth band of the infrared spectra V4, related to the lattice vibrations, was too weak to be observed at room temperature.     

Investigation of the polarization optics of the living human cornea and lens with purkinje images

We present what to our knowledge is a new method for assessing the polarization optics of the cornea and lens, by examining the state of polarization of the first, second, and fourth Purkinje images. When linearly polarized light is incident on the cornea at 70 degrees to the line of gaze along the horizontal meridian, and then traverses the cornea, or the cornea and the lens, the emergent light is elliptically polarized. The degree of ellipticity varies widely between subjects. The results indicate that both the cornea and the lens may be optically active and to our knowledge are the first to suggest that the cornea may exhibit circular birefringence.     

Imaging polarimetry of the rainbow

Using imaging polarimetry, we measured the polarization patterns of a rainbow on the shore of the Finnish town of Oulu in July 2001. We present here high-resolution color-coded maps of the spatial distributions of the degree and angle of linear polarization of the rainbow in the red (650 +/- 30 nm), green (550 +/- 30 nm), and blue (450 +/- 30 nm) ranges of the spectrum. The measured polarization characteristics of the investigated rainbow support earlier theoretical and computational results and are in accordance with previous qualitative observations. To our knowledge, this is the first imaging polarimetric study of rainbow polarization.     

Angular-scattering characteristics of ferroelectric liquid-crystal electro-optical devices operating in the transient-scattering and the extended-scattering modes

The angular distribution of forward-scattered light in transient-scattering-mode (TSM) and extended-scattering-mode (ESM) ferroelectric liquid-crystal (FLC) devices was evaluated by use of circularly polarized incident light. For both modes the intensity and the distribution of forward-scattered light depended primarily on the FLC birefringence, spontaneous polarization, and the cell path length. In the FLC materials examined, the forward-scattering intensity under ESM drive conditions increased with longer FLC pitch lengths, whereas under TSM conditions stronger forward scattering was observed with increasing FLC spontaneous polarization. Although both TSM and ESM drive conditions displayed a similar angular distribution for forward-scattered light, the intensity of ESM scattering over a 0 degrees -6 degrees range was considerably smaller than that observed in earlier experiments with linearly polarized incident light.     

Weak value amplification of an optical Faraday differential refraction effect

In the presence of a longitudinal magnetic field B, a beam of linearly polarized light incident from a Faraday medium of Verdet constant V refracts at its interface with a medium of negligible Verdet constant and emerges as two opposite circularly polarized beams that are separated by a small divergence angle δ that is proportional to the product BV. Judicious postselection of the polarization state of the emergent light can be used to amplify the measured value of δ by several orders of magnitude. This technique makes it possible to optically measure either very small V values when B is known or small magnetic fields when V is known.     

Exact theory of fibre fragmentation in a single-filament composite

An exact theory is developed to describe the evolution of fibre fragmentation in a single-filament composite test as a function of the underlying fibre statistical strength and fibre/matrix interfacial shear stress, τ. The fragment distribution is a complicated function of fibre strength and τ because the stress around breaks which do occur recovers to the applied value, σ, over a length δ(σ) determined by τ. Therefore, no other breaks can occur within δ (σ) of an existing break. To account for this effect, the fibre fragment distribution is decomposed into two parts; fragments formed by breaks separated by more than δ (σ) at stress σ, and fragments smaller than δ (σ) which were formed at some prior stress σ′ < σ when a smaller δ(σ′) < δ(σ) prevailed. The distribution of fragments larger than δ (σ) is identical to that of a fibre with a unique non-statistical strength σ and is known exactly. The distribution of fragments smaller than δ(σ) can then be determined from the distribution of the longer fragments. Predictions of the theory are compared to simulations of fibre fragmentation for several common models of stress recovery around fibre breaks with excellent agreement obtained. The present theory can be utilized to thus derive both thein situ fibre strength at short gauge lengths ? δ and the τ from experimentally obtained fragment distributions, and an unambiguous inversion procedure is briefly discussed. The application of the theory to other multiple-cracking phenomena in composites is also discussed.     

Simulating glories and cloudbows in color

Glories and cloudbows are simulated in color by use of the Mie scattering theory of light upwelling from small-droplet clouds of finite optical thickness embedded in a Rayleigh scattering atmosphere. Glories are generally more distinct for clouds of droplets of as much as approximately 10 microm in radius. As droplet radius increases, the glory shrinks and becomes less prominent, whereas the cloudbow becomes more distinct and eventually colorful. Cloudbows typically consist of a broad, almost white band with a slightly orange outer edge and a dark inner band. Multiple light and dark bands that are related to supernumerary rainbows first appear inside the cloudbow as droplet radius increases above approximately 10 microm and gradually become more prominent when all droplets are the same size. Bright glories with multiple rings and high color purity are simulated when all droplets are the same size and every light beam is scattered just once. Color purity decreases and outer rings fade as the range of droplet sizes widens and when skylight, reflected light from the ground or background, and multiply scattered light from the cloud are included. Consequently, the brightest and most colorful glories and bows are seen when the observer is near a cloud or a rain swath with optical thickness of approximately 0.25 that consists of uniform-sized drops and when a dark or shaded background lies a short distance behind the cloud.     

Special configuration of a very large Schmidt telescope for extensive astronomical spectroscopic observation

A special reflecting Schmidt telescope is used to observe celestial objects. The telescope has an aperture of 4m, f ratio of 5, and a 5° field of view. Its optical axis is fixed and tilted 25° to the horizontal that runs from south to north. The celestial objects were observed for 1.5 h as they passed through the meridian. The shape of the reflecting Schmidt plate has to be changed with each different declination δ and in the tracking process. This is achieved with active optics. The sky area to be observed is -10° ≤ δ ≤ +90°. There are plans to place ~4000 optical fibers on the telescope focal surface that will lead to a dozen spectrographs.