A scattered-light method in photoelasticity

The birefringence and, thereby, the stresses in a photoelastic model are investigated utilizing the light scattered from a beam of light propagating through the model. The retardance from the entry point of the beam into the model to a certain point along the beam is expressed in terms of the intensity of the scattered light. The retardance for a short distance along the light path within the model is determined as a function of the total retardances from the entry point of the model to the two end points of the distance investigated. The effects of retarders and polarizers on the state of polarization of the light beam are treated by Mueller calculus. It is not necessary to make other assumptions than those made in the usual stress-freezing and slicing method.     

Characteristic relations of flow birefringence

The general problems of the flow-induced birefringence in liquids have been presented and discussed in Part 1 of this paper, in which some particular responses of an aqueous solution of NGS 1828 were presented, namely, the pertinent mechanical responses and the birefringence responses in transmitted radiation. This paper presents the optical responses of NGS 1828 observed in the scattered radiation. It is shown that the scattered-light techniques can become a powerful and indispensable tool of flow-birefringence techniques, if the actual patterns of light scattering are taken into account. Proof is given that the light scattering and the related birefringence cannot be described by Rayleigh's mathematical model of scattering (Part 1, Ref. 51). The optical effects of the modulation of the primary beam and the scattered beam, called scattered primary isochromatics and scattered secondary isochromatics, are described in terms of the parameters of the system. A practical example is presented. Samples of typical recordings of light-intensity modulation by typical flow patterns are given in the form of scattered primary and secondary isochromatics and integrated isochromatics. One type of intensity modulation enables the determination of shear-strain rate at an interior point in the flow field. Using the determined shear-strain rates at the interior points, a velocity profile along the axis of symmetry of a rectangular-conduit flow was obtained. The results so obtained were satisfactory when compared with the results of direct volumetric measurement. The other type of intensity modulation reveals the nonuniform distribution of birefringence along the path of the transmitted light in the rectangular-conduit flow. The results presented in Part 1 of this paper, are complementary to the results presented below.     

Application of the maximum entropy technique in tomographic reconstruction from laser diffraction data to determine local spray drop size distribution

This work proposes a new deconvolution technique to obtain local drop size distributions from line-of-sight intensity data measured by laser diffraction technique. The tomographic reconstruction, based on the maximum entropy (ME) technique, is applied to forward scattered light signal from a laser beam scanning horizontally through the spray on each plane from the center to the edge of spray, resulting in the reconstructed scattered light intensities at particular points in the spray. These reconstructed intensities are in turn converted to local drop size distributions. Unlike the classical method of the onion peeling technique or other mathematical transformation techniques that yield unrealistic negative scattered light intensity solutions, the maximum entropy constraints ensure positive light intensity. Experimental validations to the reconstructed results are achieved by using phase Doppler particle analyzer (PDPA). The results from the PDPA measurements agree very well with the proposed ME tomographic reconstruction.     

Study of basic patterns of light scattering in aqueous solution of milling yellow

Basic characteristics of light scattering in an aqueous solution of milling yellow are presented in a form of relations between the scattered radiant power, states of polarization of primary radiation and scattered radiation, observation angle and azimuthal angle.It is found that the state of polarization of the scattered light in milling-yellow solution can be utilized as a foundation of reliable photoelastic scattered-light techniques for flow analysis. However, Rayleight's model of scattering is nnt directly applicable.Paper contains data on major parameters of light scattering, knowledge of which is necessary to correctly design flowbirefringence experiments. In particular, these data can be used to develop a set of conditions and constraints for designing of particular scattered-light flow-birefringence experiments, and of corresponding transfer functions.     

An automatic system for scattered-light photoelasticity

This paper describes the recent development of an automatic data-collecting-and-interpreting system for a dual-observation method in scattered-light photoelasticity. The system incorporates a flexible relay optic, photon counting and computer techniques. Photoelastic parameters are evaluated from the photon counts by means of an electronic digital computer. Evaluation procedures have been improved so that the effect of absorption of scattered light is eliminated.     

Backscatter phase-Doppler anemometry for transparent non-absorbing spheres

The application of phase-Doppler anemometer for scattering angles between the main rainbow and direct backscatter, was examined by calculating the spatial intensity distribution and the phase of the light scattered by a particle crossing the measuring volume. Geometrical optics was assumed and contributions to the scattered light due to reflection on the external surface of the particle and first internal reflection were considered. The response curve of the technique was calculated for different particle refractive indices, beam intersection angles, collection angles and spacings between the collection apertures. Linear response curves were obtained after integration of the intensity of the scattered light over sufficiently large rectangular collection apertures, but they became non-monotonic after a critical value of phase shift, which varied with the optical arrangement between around 220° and 360°, did not scale with common scaling parameters used for forward scatter light, and limited the possible size range of the instrument for one optical arrangement. The particle refractive index determined the collection angle and limited sizing to particles with little uncertainty in refractive index, since a 5% change in refractive index led to uncertainties in size of the order of 100%. An alternative sizing technique is suggested for the backscatter region.     

Heterodyne Doppler global velocimetry

Doppler Global Velocimetry (DGV) is an imaging flow measurement technique which allows the measurement of the velocity distribution in a plane. In DGV the frequency shift of scattered light from moving particles within the flow is used to determine the local flow velocity. Heterodyne Doppler Global Velocimetry (HDGV) is a new approach which combines the imaging and geometrical characteristics of DGV with the measurement principles of reference beam laser Doppler anemometry. The frequency shifted scattered light from the flow tracers is heterodyned with a reference beam from the same light source. Due to interference the result of this superposition is a harmonic intensity modulated signal. This signal is detected using a smart pixel detector array to obtain the velocity distribution. Two different experiments are presented. The first experiment compares the measured velocity distribution of a rotating disk with its actual velocity. The second experiment demonstrates the capability of the technique to measure a real flow.     

Photoelastic analysis of a three-dimensional specimen by optical slicing and digital image processing

The authors show a nondestructive method for obtaining the isochromatic and isoclinic fringes in a three-dimensional photoelastic specimen. The basic idea is to delimit a slice between two plane laser beams. The properties of polarization of the scattered light (Rayleigh's law) and the interference possibilities of the diffused beams are used. By introducing speckle pattern properties, the correlation factor of the two scattered beams is similar to the illumination given in a plane polariscope for the investigation of a slice (in a classical frozen-stress technique). The authors use a monochromatic laser beam, a CCD camera and a personal computer. Because they cannot obtain the correlation factor directly, they do a statistical analysis of the speckle patterns. The variance (function of the correlation factor) is computed from the light intensities of three images corresponding to the speckle pattern for plane 1 alone, plane 2 alone, and both planes together.     

Suitability of the photoelastic implementation of polymers with material birefringence

Scattered photoelastic techniques would gain considerable momentum through better understanding of the nature and response of the available photoelastic materials. The influence of the prevailing birefringent effect in the state of load-free polymers on the radiated scattered light energy is investigated. Six different photoelastic materials are considered. The impact of material birefringences on the quality of reading the fringe orders of the scattered radiation in a stressed photoelastic medium is explored. Spectral dependence of the modulation of light vectors in acrylic materials (Plexiglas) is illustrated. The advantage of this characteristic as a convenient means of compensation in scattered photoelasticity is pointed out. Acrylic sheets, a relatively cheap transparent polymer, seem to be suitable for scattered photoelastic analysis. The moiré technique might find application in determining fringe orders in a material such as Homalite-100. Replacing the primary beam by a primary sheet saves the cost and effort consumed in the scanning process. Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

3D stress local nondestructive analysis in the middle plane of a plate

The Isodyne technique based on the scattered light scanning from a thin laser beam can be used to obtain the information inside the loaded object in the room temperature nondestructively, so it is a very powerful technique in 3D stress analysis. The problems are how to interpret the information and how to get sufficient information from the few interference fringe. Birefringence phase shift technique can distinguish the fringe orders automatically and enrich the information in 256 gray levels between maxim and minim light intensity. In the paper the Isodyne birefringence phase shift method with an oblique incidence and equilibrium equation is presented, by which the 3D stresses in the middle plane of a plate with U shape notch are separated successfully. The project supported by the National Natural Science Foundation of China under the Grant No. 1380345     

光敏液晶高弹体梁光致弯曲的特性研究

光敏液晶高弹体是一类新型智能材料,它兼有液晶和橡胶的特性,可以同时由光、热实现驱动,具有广阔的应用前景.本文着重研究了光敏液晶高弹体梁的光致弯曲特性,根据该材料的一维线性化本构关系,在小变形假设下,用简单梁理论得到了光致弯曲模型.将光照的效应等价为一等效力矩,分析了各种参数对其的影响规律,得到了自由梁弯曲曲率和超静定梁约束反力的解析表达式,并计算了梁内应力分布及中性面的个数.结果表明,各种参量对弯曲的影响相互耦合,显现出非线性性;液晶高弹体光致弯曲存在两个或三个中性面,应力分布与通常的梁弯曲有很大不同.     

Displacement measurements in the interior of 3-D bodies using scattered-light speckle patterns

Two new techniques making use of the scattered-light speckle pattern have been developed which yield the displacements on an arbitrary interior plane of a 3-D body. When a sheet of coherent light passes through a transparent 3-D body, a small fraction is scattered. This scattered light produces a speckle pattern in an imaging system. By recording two superimposed images of this speckle pattern, one before and one after body deformation, the displacements on the interior illuminated plane can be found. The technique of scattered-light photography uses a single illuminating beam and is sensitive to displacements greater than one speckle diameter, approximately 3 μm. Scattered-light speckle interferometry uses two illuminating beams and is sensitive to displacements greater than one half the wavelength of light being used, approximately 0.2 μm. With both techniques, the double-exposed speckle photograph is optically processed to yield displacement information. With both techniques, the maximum displacement measurable is limited by correlation requirements between the two speckle patterns. Experimental results are presented demonstrating the two new techniques.     

光检测器参数对相位—多普勒粒子分析系统特性的影响

应用几何光学近似理论模型计算了激光相位多普勒系统中微粒的光散射特性,得到了散射光强与粒径关系、检测器表现的散射光强分布、相位差与粒径特性中的非线性跃变以及检测器形状对特性的影响。     

Application of digital speckle pattern interferometry for fluid velocimetry in wind tunnel flows

This paper shows the feasibility of using digital speckle pattern interferometry (DSPI) as a fluid velocimetry technique in high speed gaseous flows. The light scattered from an illuminated plane was recorded with a CCD camera at the same time as a uniform reference beam. A fibre optic was used to bring this reference beam from the laser cavity to the CCD camera. The comparison of two subsequent frames gives information about the velocity field. DSPI was applied to a Von Karman street flow set up in a wind tunnel. Particle image velocimetry (PIV) measurements were also obtained for comparison with the information provided by DSPI. A system for increasing the measurement region when using short coherence length lasers is proposed. Received: 15 June 2000/Accepted: 8 September 2000     

The scattering of a scalar beam from isotropic and anisotropic two-dimensional randomly rough Dirichlet or Neumann surfaces: The full angular intensity distributions

By the use of Green’s second integral identity we determine the field scattered from a two-dimensional randomly rough isotropic or anisotropic Dirichlet or Neumann surface when it is illuminated by a scalar Gaussian beam. The integral equations for the scattering amplitudes are solved nonperturbatively by a rigorous computer simulation approach. The results of these calculations are used to calculate the full angular distribution of the mean differential reflection coefficient. For isotropic surfaces, the results of the present calculations for in-plane scattering are compared with those of earlier studies of this problem. The reflectivities of Dirichlet and Neumann surfaces are calculated as functions of the polar angle of incidence, and the reflectivities for the two kinds of surfaces of similar roughness parameters are found to be different. For an increasing level of surface anisotropy, we study how the angular intensity distributions of the scattered waves are affected by this level. We find that even small to moderate levels of surface anisotropy can significantly alter the symmetry, shape, and amplitude of the scattered intensity distributions when Gaussian beams are incident on the anisotropic surfaces from different azimuthal angles of incidence.     

Rectilinear and circular analysis of a plane slice optically isolated in a three-dimensional photoelastic model

Because of the coherence of scattered light, it is possible to produce a speckle image from a plane beam of light passing through a transparent model. When two plane parallel beams of light are transmitted through the model the slice between the beams is then optically isolated. The two speckle patterns corresponding to the two beams are superposed and provide optical data relative to the slice (principal stress directions, birefrengence), the data being collected on high contrast photographic plates or by optical filtering to obtain the square of the contrast. The isoclinic and isochromatic fringes are shown to exist. The concepts of rectilinear or circular analysis are extended to the observation of a plane slice in a three-dimensional model without freezing or cutting the model.     

Simplifications for scattered-light photoelasticity when using the unpolarized incident beam

A method is presented for obtaining scettered-light photoelastic data in three-dimensional problems using an unpolarized incident light beam. Using simplifying optical assumptions, the scattered-light observation path is considered tobe a series of half-wave retarders. Data are obtained through rotation of the optical analyzer and translation of the incident light beam with respect to the model. The method is applied to obtain data in problems where the secondary principal directions are: (1) fixed and (2) rotate. Results compare favorably with those obatained using a polarized incident beam.     

Time-average measurement of velocity, density, temperature, and turbulence velocity fluctuations using Rayleigh and Mie scattering

Measurement of time-averaged velocity, density, temperature, and turbulence velocity fluctuations in sparsely seeded gas flows using a non-intrusive, point-wise technique based on Rayleigh and Mie scattering is discussed. A Fabry-Perot interferometer (FPI) is used to spectrally resolve laser light scattered by molecules and particulates in gas flows. The spectral content of the scattered light provides information about velocity, density, and temperature of the gas. A CCD camera is used to record images of the fringes formed by scattered light passing through the interferometer. Models of the spectral components are used in a least squares fitting routine to estimate the parameters from fringe images. Flow measurements are presented for subsonic and supersonic jet flows. The application range for this technique is mostly for high velocity situations (>25 m/s). Velocity, density, temperature, and turbulence velocity fluctuations were determined with accuracies within 5 m/s, 4%, 2%, and 5 m/s, respectively.     

预应力混凝土T形梁桥动力特性分析模型

本文对预应力混凝土Ｔ形梁桥动力分析建方法进行了详细研究。将桥梁划分为梁段单元,考虑Ｔ形梁的弯曲、自由扭转、约束扭转变形以及桥梁局部构件（如横隔板等）的作用,由能量原理建立结构的单元特性矩阵。实践应用表明,本文提出了方法使用方便,适合于计算机求解,是装配式预应力混凝土Ｔ形梁桥结构动力分析的一种实用可靠的方法。     

多个椭圆柱波浪力的一种解析解

波浪在大尺寸结构表面产生不可忽略的散射波, 该散射波在多柱体体系中继续传播, 并在同体系中的其他柱体上产生高次散射波. 本文基于椭圆坐标系和绕射波理论首先推导了波浪作用下椭圆单柱体产生的散射波压力公式, 随后考虑该散射波在多柱体系中的传播, 将其视为第二次入射波, 推导出柱体上第二次散射波压力公式, 同理可以推导出高次散射波压力公式, 最后得到椭圆多柱体波浪力解析解, 并用数值解验证了本文解析方法的正确性. 本文以双柱体和四柱体体系为例, 分析了不同参数(波数、净距、波浪入射角度等)下, 高次散射波对柱体上波浪作用的影响. 结果表明: 波数较大的情况下, 高次散射波引起柱体上的波浪力不能忽略; 结构间距较大的情况下, 虽然高次波的作用有减小的趋势但仍然明显; 高次散射波来自多个柱体对入射波的散射, 柱体数目的增加后, 高次波的影响会增加, 结构所受的高次波作用因参数变化而起的波动会变剧烈; 高次波对上游柱体波浪力的贡献较对下游柱体的贡献大.