Xiaoshu Cai

Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by a homogeneous spheroid

The theory of an arbitrarily oriented, shaped, and located beam scattered by a homogeneous spheroid is developed within the framework of the generalized Lorenz-Mie theory (GLMT). The incident beam is expanded in terms of the spheroidal vector wave functions and described by a set of beam shape coefficients (G(m)(n),(TM),G(m)(n),(TE)). Analytical expressions of the far-field scattering and extinction cross sections are derived. As two special cases, plane wave scattering by a spheroid and shaped beam scattered by a sphere can be recovered from the present theory, which is verified both theoretically and numerically. Calculations of the far-field scattering and cross sections are performed to study the shaped beam scattered by a spheroid, which can be prolate or oblate, transparent or absorbing.

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence

On the basis of our previous work on the extension of the geometrical-optics approximation to Gaussian beam scattering by a spherical particle, we present a further extension of the method to the scattering of a transparent or absorbing spheroidal particle with the same symmetric axis as the incident beam. As was done for the spherical particle, the phase shifts of the emerging rays due to focal lines, optical path, and total reflection are carefully considered. The angular position of the geometric rainbow of primary order is theoretically predicted. Compared with our results, the Möbius prediction of the rainbow angle has a discrepancy of less than 0.5 degrees for a spheroidal droplet of aspect radio kappa within 0.95 and 1.05 and less than 2 degrees for kappa within 0.89 and 1.11. The flux ratio index F, which qualitatively indicates the effect of a surface wave, is also studied and found to be dependent on the size, refractive index, and surface curvature of the particle.

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle

The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.

Expansion of an arbitrarily oriented, located, and shaped beam in spheroidal coordinates

Within the framework of the generalized Lorenz-Mie theory (GLMT), the incident shaped beam of an arbitrary orientation and location is expanded in terms of the spheroidal vector wave functions in given spheroidal coordinates. The beam shape coefficients (BSCs) in spheroidal coordinates are computed by the quadrature method. The classical localization approximation method for BSC evaluation is found to be inapplicable when the Cartesian coordinates of the beam and the particle are not parallel to each other. Once they are parallel, all the symmetry relationships existing for the BSCs in spherical coordinates (spherical BSCs) [J. Opt. Soc. Am. A11, 1812 (1994)] still pertain to the BSCs in spheroidal coordinates (spheroidal BSCs). In addition, the spheroidal BSCs computed by our method are verified by comparing them with those evaluated by Asano and Yamamoto for plane wave incidence [Appl. Opt.14, 29 (1975)]. Furthermore, formulas are given for field reconstruction from the spheroidal BSCs, and consistency is found between the original incident fields and the reconstructed ones.

Geometrical-optics approximation of forward scattering by coated particles

By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0 degrees-60 degrees) for coated particles illuminated by a collimated incident beam. Phases of emerging rays are exactly calculated to improve the approximation precision. This method proves effective for transparent and tiny absorbent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. When the absorption coefficient of a particle is greater than 0.01, the geometrical optics approximation is effective only for forward small angles, typically less than 10 degrees or so.

DEVELOPMENT OF A PRECISE AND IN SITU TURBIDITY MEASUREMENT SYSTEM

Turbidimetry is a technique based on the transmittance spectra of the light passing through the media containing small particles. It permits measuring the size distribution of particles for size in the range of sub-micrometer or micrometer. But the inversion problem is one of the most important obstacles for its applications. Based on the nonnegative least square method, we have developed a stable and rapid algorithm and a measurement system permitting temporal acquisition (in milliseconds) and realizing in-line measurement. To ensure its performance, the sensitivity and the stability of the system have been examined in different stages: the light source, the spectrometer, and the variation of the media concentration according to the optics configuration. By the measurements in the laboratory and that of the wet steam in a turbine we show that such a system permits measuring very precisely the variation of the volume fraction of the particle or the wetness of wet steam.

AN INVESTIGATION ON CHARACTERIZING DENSE COAL-WATER SLURRY WITH ULTRASOUND: THEORETICAL AND EXPERIMENTAL METHOD

Particle size distribution and concentration in particulate two-phase flow are important parameters in a wide variety of industrial areas. For the purpose of online characterization in dense coal-water slurries, ultrasonic methods have many advantages such as avoiding dilution, the capability for being used in real time, and noninvasive testing, while light-based techniques are not capable of providing information because optical methods often require the slurry to be diluted. In this article, the modified Urick equation including temperature modification, which can be used to determine the concentration by means of the measurement of ultrasonic velocity in a coal-water slurry, is evaluated on the basis of theoretical analysis and experimental study. A combination of the coupled-phase model and the Bouguer-Lambert-Beer law is employed in this work, and the attenuation spectrum is measured within the frequency region from 3 to 12 MHz. Particle size distributions of the coal-water slurry at different volume fractions are obtained with the optimum regularization technique. Therefore, the ultrasonic technique presented in this work brings the possibility of using ultrasound for online measurements of dense slurries.

Application of genetic algorithm in particle size analysis by multispectral extinction measurements

Abstract Both dependent and independent model algorithms are designed with genetic algorithm (GA) to retrieve aerosol size data from multispectral extinction measurements. Compared with the traditional dependent model algorithm, e.g., simplex, GA can locate the global optimized solution instead of local ones. As an independent model algorithm, when combined with B-splines, GA gives consistent results with Chahine and Phillip-Twomey-NNLS algorithms. Numerical simulations also show that GA has high stability and good resistance to relatively higher error levels. For a population size of 50 in the present paper, the feasible ranges for genetic operators p c and p m are found to be [0.01, 0.5] and [0.01, 0.15], respectively, and the generation number Gen_Max should be larger than 250.

In-line measurement of particle size and concentration with light fluctuation method

Abstract This paper presents a new method for in-line and in-situ particle sizing based on the Light Fluctuation Method, including the development of a novel optical probe capable of measuring particle size and concentration in the broad range of 10∼1000 microns.

Simultaneous measurement of film thickness, temperature, and mass fraction of urea-water-solutions by multi-wavelength laser absorption spectroscopy

Quantitative analysis for thickness, temperature, and mass fraction of liquid film is extremely crucial to the relevant industrial processes, but these parameters cannot be determined simultaneously by conventional measurement techniques. In the present work, a novel measurement method based on laser absorption spectroscopy was developed to measure the film temperature, thickness, and mass fraction of urea-water-solutions simultaneously by combining three wavelengths, 1420 nm, 1488 nm, and 1531 nm. Moreover, measurement accuracy of this method was validated by a calibration tool which provided liquid film with known film thickness, temperature, and mass fraction, respectively. It revealed that the deviation between the measured and known parameters with the developed method was 0.86%, 4.58%, and 3.85%, respectively.