Showing papers on "Light scattering published in 1972"

Analysis of Macromolecular Polydispersity in Intensity Correlation Spectroscopy: The Method of Cumulants

Abstract: The first order electric field correlation function of laser light scattered by polydisperse solutions of macromolecules can be written as a sum or distribution of exponentials, with decay rates proportional to the diffusion coefficients of the solute molecules. It is shown that the logarithm of this correlation function is formally equivalent to a cumulant generating function. A method is described by which the distribution function of the decay rates (and thus the extent of polydispersity) can be characterized, in a light scattering experiment, by calculation of the moments or cumulants. The systematic and random statistical errors in the calculated cumulants are discussed.

Light Scattering by a Spheroidal Particle

Abstract: The solution of electromagnetic scattering by a homogeneous prolate (or oblate) spheroidal particle with an arbitrary size and refractive index is obtained for any angle of incidence by solving Maxwell's equations under given boundary conditions. The method used is that of separating the vector wave equations in the spheroidal coordinates and expanding them in terms of the spheroidal wavefunctions. The unknown coefficients for the expansion are determined by a system of equations derived from the boundary conditions regarding the continuity of tangential components of the electric and magnetic vectors across the surface of the spheroid. The solutions both in the prolate and oblate spheroidal coordinate systems result in a same form, and the equations for the oblate spheroidal system can be obtained from those for the prolate one by replacing the prolate spheroidal wavefunctions with the oblate ones and vice versa. For an oblique incidence, the polarized incident wave is resolved into two components, the TM mode for which the magnetic vector vibrates perpendicularly to the incident plane and the TE mode for which the electric vector vibrates perpendicularly to this plane. For the incidence along the rotation axis the resultant equations are given in the form similar to the one for a sphere given by the Mie theory. The physical parameters involved are the following five quantities: the size parameter defined by the product of the semifocal distance of the spheroid and the propagation constant of the incident wave, the eccentricity, the refractive index of the spheroid relative to the surrounding medium, the incident angle between the direction of the incident wave and the rotation axis, and the angles that specify the direction of the scattered wave.

A Study of the Relationship of Chemical Composition and Humidity to Light Scattering by Aerosols

Abstract: A chemically pure aerosol of defined size distribution exhibits a unique growth pattern due to adsorption of water vapor, and to hygroscopic and/or deliquescence effects which are dependent upon relative humidity and which can be followed by measuring light scattering by the aerosol. A number of pure aerosols were produced artificially in the laboratory, subjected to a controlled humidity environment, and the magnitude of their light scattering coefficient measured continuously over a wide range of relative humidity (20–90%) with an integrating nephelometer. The results obtained can be applied to similar measurements on ambient air to yield qualitative chemical information and to determine the amount of visibility degradation which may be attributed to the association of water vapor with atmospheric aerosols. Examples of light scattering-relative humidity relationships for atmospheric aerosols are given.

Response Functions in the Theory of Raman Scattering by Vibrational and Polariton Modes in Dielectric Crystals

Abstract: The paper begins with a tutorial introduction to the theory of inelastic light scattering by polaritons in dielectric crystals. The treatment is based on a simple two-oscillator model which represents the ionic and electronic motions of a crystal. The model contains a third-order anharmonicity which allows an incident laser beam to mix with the oscillator fluctuations and produce scattered light of frequency different from the incident frequency. The magnitude of the oscillator fluctuations is determined by an application of the Nyquist of fluctuation-dissipation theorem, using the response functions of the oscillators for externally applied forces. The simple model gives results for light scattering cross sections which agree with more rigorous derivations in the existing literature. The response function approach is generalized to apply to crystals having many ionic resonances and of uniaxial or orthorhombic structure. The general formulas reduce in appropriate special cases to results already published. Experimental and theoretical work on light scattering by polaritons and by pure phonons is reviewed in the context of both the two-oscillator model and the general theory. Particular attention is given to resonance scattering in an attempt to achieve consistency between the differing theoretical treatments in the literature. The subject matter of the review overlaps some topics in nonlinear optics, and contact is made with the theories of the electrooptic effect and stimulated Raman scattering.

Depolarized Light Scattering: Theory of the Sharp and Broad Rayleigh Lines

Abstract: A statistical theory of depolarized laser light scattering is developed, based upon the projection operator transport theory of Mori. It is assumed that the autocorrelation function of the dielectric tensor is proportional to the autocorrelation function of a ``primary'' variable, and the time evolution of this autocorrelation function is calculated by means of a pair of coupled linear transport equations in which the primary variable is coupled to a ``secondary'' variable. The theory ignores some of the k−dependent fine structure of the spectra and concentrates upon explaining the sharp and broad depolarized Rayleigh lines which dominate the spectra. It is concluded, in contradiction to numerous existing theories, that the observed spectra cannot be explained in terms of a single primary variable. It is believed that the sharp line arises from molecular reorientations in the role of primary variable and that a separate mechanism, dependent upon a distinct primary variable such as the one describing local...

A noncoherent model for microwave emissions and backscattering from the sea surface

Abstract: The two-scale (small irregularities superimposed upon large undulations) scattering theory proposed by Semyonov was extended and used to compute microwave apparent temperature and the backscattering cross section from ocean surfaces. The effect of the small irregularities upon the scattering characteristics of the large undulations is included by modifying the Fresnel reflection coefficients; whereas the effect of the large undulations upon those of the small irregularities is taken into account by averaging over the surface normals of the large undulations. The same set of surface parameters is employed for a given wind speed to predict both the scattering and the emission characteristics at both polarizations.

Introduction to Classical and Modern Optics

Abstract: Preface. 1. Reflection and Refraction. 2. Thin Lenses. 3. Thick Lenses and Combinations of Lenses. 4. Mirrors. 5. Aberrations. 6. Stops and Pupils. 7. Gradient-Index, Fiber, and Integrated Optics. 8. Lens Design. 9. Optical Systems. 10. Systems Evaluation. 11. Interference. 12. Thin Films. 13. Coherence. 14. Diffraction. 15. Diffraction Gratings. 16. Light Scattering. 17. Polarization of Light. 18. Optical Data Processing. 19. Holography. 20. Light Sources and Detectors. 21. Radiometry/Photometry. 22. Absorption. 23. Lasers. 24. Relativistic Optics. Answers to Odd-Numbered Problems. Index.

Raman and Infrared Spectral Investigations of Water Structure

Abstract: The models that have been proposed to represent the structure of liquid water are too numerous to be described here, but they are discussed in Chapter 14. Two general classes of models of interest for present purposes are usually designated by the terms continuum(1132) and mixture.(356) Continuum models treat water in terms of a continuous distribution of interactions that are presumed to be spectroscopically indistinguishable, whereas mixture models generally relate distinct spectral features to structures differing in the extent of hydrogen bonding. Some of the earlier spectroscopic investigations(1132) appeared to favor continuum models, but recent laser- Raman investigations(1138) as well as results from nonlinear optical techniques such as stimulated Raman scattering and hyper-Raman or inelastic harmonic light scattering strongly favor mixture models, e.g., the consecutive hydrogen-bond disruption model.

Light Scattering from Non-Gaussian Concentration Fluctuations

Abstract: Quasielastic light-scattering studies from a solution of 1-\ensuremath{\mu}m-diam polystyrene spheres indicate that at sufficient dilution the homodyne autocorrelation function is not consistent with the common assumption that the concentration fluctuations are Gaussian stochastic processes. In this note we show that the non-Gaussian behavior at low concentrations arises because the particles in the scattering volume are Poisson distributed.

Light scattering from coated spheres: model for biological cells.

Abstract: Efficient methods for the calculation of light scattering intensity functions for concentrically coated spheres (~10-μ diam) are discussed. This model represents many types of biological cells whose nuclei have a low refractive index (~1.1) and cytoplasms with a slightly lower refractive index. Studies are made on the relationships between the scattering coefficients for nonabsorbing, spherically symmetric scatterers. The physical origin of these coefficients is examined for absorbingscatterers. A comparison of the angular half-width of the scattered intensity functions for the coated sphere and an equivalent homogeneous sphere shows that diffraction dominates the small angle scattering in both cases. At larger angles, the coated sphere scattering pattern is more structured and quite sensitive to core sphere size, suggesting a possible method of distinguishing types of biological cells that are similar in gross size but different in internal detail.

Changes in light scattering that accompany the action potential in squid giant axons: potential‐dependent components

Abstract: 1. To obtain information about structural events that occur in axons, changes in light scattering from squid giant axons were measured during action potentials and voltage-clamp steps.2. The scattering changes were measured at several scattering angles. Because the changes in scattering divided by the resting scattering were between 10(-6) and 10(-5), signal-averaging techniques were used to increase the signal-to-noise ratio.3. The scattering changes during the action potential were different at different angles. Two types were found, one at 10-30 degrees (forward angles) and the other at 60-120 degrees (right angles).4. At forward angles, there was a transient scattering decrease during the action potential. The time course of the change was similar to that of the action potential; this change was thought to be potential-dependent.5. At right angles, there was a transient scattering increase during the action potential followed later by a second, longer-lasting increase. Indirect evidence indicated that neither component could be totally potential-dependent.6. To further analyse these effects, scattering was measured during voltage-clamp steps. The changes seen during hyperpolarizing steps were presumed to be potential-dependent; again two different changes were found, one at forward angles and one at right angles.7. The potential-dependent change at right angles occurred with a time course that could be approximated by a single exponential with a time constant tau = 24 musec. The change at forward angles required two exponentials, tau(1) = 23 musec, tau(2) = 900 musec, to represent its time course.8. The size of both potential-dependent changes was proportional to the square of potential. The change at right angles, but not that at forward angles, was increased in size by the addition of butanol or octanol to the bathing solution.

Light scattering from fused polycrystalline aluminum oxide surfaces

Abstract: The results of a study of the topography of fused polycrystalline aluminum oxide surfaces using reflected coherent light of 6328-A wavelength are reported. It is shown that the wavelength and angular dependences of the specular intensity can be understood in terms of optical scattering theory in the Kirchhoff approximation for a surface with a Gaussian roughness distribution. The values of the rms roughness obtained optically by fitting the experimental observations to the theory agree well with those obtained from Talysurf measurements. Estimates of the rms slope and correlation distance of the surface structure are obtained from a treatment of the specular and diffuse components of the reflected light intensity using the Beckmann model. An empirical relationship is shown to exist between the mean surface grain size as determined by microscopic observation using the line intercept method and the rms surface roughness. These results have formed the basis of an optical technique for rapidly estimating the mean surface grain size on high alumina substrates used in the microelectronics industry.

Quasi-elastic light scattering from macromolecules.

Abstract: Light-scattering spectroscopy has recently undergone a revival because of the development of lasers and their associated detection techniques. Raman and Brillouin scattering studies (which have frequency changes ;::: 107 Hz) could be done only with great difficulty using prelaser sources (usually mercury). These studies can now be performed easily with laser sources combined with much improved versions of classical predetection filters (interferometers and diffraction gratings). On the other hand, the Rayleigh scattered light from dilute macromo­ lecular solutions exhibits frequency broadening of only about 10-108 Hz, an impossible region for experiments using prelaser sources or even for those using laser sources combined with filter methods (except at frequencies greater than about 107 Hz). However, a newly developed nonlinear detection technique known as optical mixing has made measurement of these small frequency changes a relatively routine matter over most of the range between 10-106 Hz. Thus, while studies of the Rayleigh scattered light from macromolecular solutions were formerly con­ fined to the measurement of frequency-integrated intensities, optical-mixing spectroscopy allows measurements of the frequency distribution of the scattered intensity to be made. The frequency-integrated scattering intensity provides information only on "equilibrium" properties of dilute macromolecular solutions (molecular weights, radii of gyration, optical anisotropies, etc), while the fre­ quency distribution of this scattered intensity provides, in addition, information about dynamic properties (translationaland rotational-diffusion coefficients, intramolecular relaxation times, etc). Optical mixing (or beating) methods, usually subdivided into homodyning and heterodyning techniques, are essentially ex­ tensions into the optical region of nonlinear detection methods long used in the radio region of the spectrum. This article reviews the theory and applications of these low-frequency change (or quasi-elastic) light-scattering experiments to the study of macromolecules in solution, with emphasis on biological molecules. Raman and Brillouin scattering

Multiple scattering calculations for technology II

Abstract: Equations are developed for calculating the reflectance and transmittance of media which scatter and absorb light and are bounded by parallel planes. A comparison between the differential equations of the many-flux and the two-flux (Kubelka-Munk) calculation methods shows that the two-flux scattering and absorption coefficients are usually different for the forward and reverse flux, and gives values for these coefficients which make the two-flux equations give the same results as the many-flux equations. This comparison can be made in the limit of an infinite number of manyflux channels, and it provides a straightforward theoretical derivation of the two-flux scattering and absorption coefficients. The comparison is extended to obtain accurate coefficients for the four-flux, six-flux, etc., calculation methods. It is shown that the six-flux calculation is particularly useful when the internal reflection at the boundaries of the scattering medium depends strongly on the angular distribution of the radiation.

Spatial Dispersion Effects in Resonant Polariton Scattering. II. Resonant Brillouin Scattering

Abstract: Inelastic scattering of light near an exciton resonance is considered, using a polariton description of the scattering process. We obtain the following results: for incident frequency approaching the resonance from below, the Brillouin shift increases; very near and above resonance, extra lines are predicted with intensities comparable to the usual lines. They form an octet instead of the familiar Brillouin doublet. Numerical calculations of the Brillouin scattering for CdS are given: The shifts and extra lines seem to be observable.

Light Scattering by Ice Clouds in the Visible and Infrared: A Theoretical Study.

Abstract: Computations of the intensity and linear polarization for single scattering by ice clouds have been made based on the assumption that the particles in ice clouds can be approximated by long circular cylinders which are allowed to be polydispersive as well as arbitrarily oriented in space. The results of two models of optically thin ice clouds are presented and compared with those for polydisperse ice spheres. The two models for ice cylinders are assumed to be either uniformly or randomly oriented in a horizontal plane. Four different wavelengths, 0.7, 3, 3.5 and 6.05 microns, are employed in the light scattering computations. It is found that, compared to ice spheres, long ice cylinders scatter more light in the region with scattering angles near 90 deg, at the expense of scattering in both the forward and backward directions. The glory and cloudbows, which occur in light scattered by spherical particles, are either lost (the glory) or largely reduced and distorted (the cloudbows in the case of cylinders). It is probable that for more irregular particles the cloudbows would also disappear. These differences in scattering by spherical and non-spherical scatterers therefore provide useful information for the differentiation between the ice and liquid phase of cloud particles.

Propagation Mode and Scattering Loss of a Two-Dimensional Dielectric Waveguide with Gradual Distribution of Refractive Index

Abstract: An analytical discussion of the mode property and the scattering loss of a two-dimensional dielectric waveguide with gradual refractive-index distribution in the transverse direction is presented. To describe scattering loss, a transverse correlation as well as an axial correlation of the irregular variation of the refractive index have been used. The field distribution, the group delay, and the maximum film thickness of a single-mode waveguide scarcely depends on the shape of the distribution. The maximum value of the film thickness in the single-mode transmission region optimizes the scattering loss and the energy confinement. The scattering loss of a waveguide with a gradual index distribution is smaller than that of a three-layer waveguide when the transverse correlation is small, but it is not much altered when the transverse correlation is large.

Angular Dependence of Scattering from Escherichia coli Cells

Abstract: The scattering of visible light from randomly oriented systems of heterogeneous E. coli cells in water was measured as a function of angle for 10–90°. The cells are assumed to be prolate ellipsoids of revolution whose dimensions are independently measured. For these cultures the average cell volume and axial ratio is 0.6 μ3 and 2.81, respectively. Using the measured dimensions, the Rayleigh-Debye approximation for the homogeneous ellipsoid was used to calculate theoretical scattering. A newly developed Rayleigh-Debye equation for a coated ellipsoid was also used. Both cell models lead to good theory–experiment agreement, especially the coated ellipsoid model. The absolute position of the two observed scattering minima and the wavelength dependence of these positions is in excellent agreement with the theoretical predictions. The existence of the scattering minima in randomly oriented heterogeneous cultures of E. coli is attributed to the uniformity of their minor axes.