Hollow-beam geometry for dynamic light scattering measurements: a theoretical analysis

Hollow-beam geometry, in conjunction with mode-selective detection, is of importance for the development of high-sensitivity devices for the measurement of dynamic light scattering in living tissues. Its application to scattering methods in the eye makes it possible to increase diagnostic ability for some diseases that alter the scattering parameters in the vitreous as well as in other transparent tissues of the eye. We present a thorough theoretical analysis of the hollow-beam geometry proposed recently for dynamic light scattering measurements in the human eye. The aims of the analysis are the determination of the excitation and the observation beam profiles at the focal plane and the evaluation of the volume under test in the measurement, which allow prediction of the intensity of the measured signal. The above is carried out with comparisons with the classical setup. From the theoretical point of view, the most appealing feature of the hollow-beam geometry is high collection efficiency combined with high stability. In the analysis performed, the concept of the characteristic length of a scattering system is introduced. With simple formalism, this parameter allows the calculation of the collection efficiency for general beam shaping and is extremely useful for the comparison of the performance of different systems.     

Homodyne optical fiber dynamic light scattering

Optical fiber homodyne dynamic light scattering employs both the advantage of a sensitivity improvement over the standard self-beating technique and the inherent self-aligning simplicity of the optics. Ultralow concentrations of approximately nanometer-sized particles become accessible by dynamic light-scattering techniques.     

Phase-space interferences as the source of negative values of the Wigner distribution function

It is shown that the negative values of the Wigner distribution function in classical optics are a consequence of the phase-space interference among the Gaussian beams into which an arbitrary light distribution (or a superposition of light distributions) can be decomposed. These elementary Gaussian beams partition the phase space in wave optics in adjacent, interacting, finite-area cells, in contrast to geometrical optics, where the phase space is continuous and a light beam can be decomposed into a number of perfectly localized, non-interacting rays.     

An Extension of Babinet's Principle

Abstract

It is shown that the diffraction pattern produced by any of two complementary screens and the one produced by a slit having the shape of their boundary, oscillates in opposite phase. This extension of Babinet's principle is illustrated with examples from nuclear scattering and classical optics.     

Photon diffusion coefficient in scattering and absorbing media

We present a unified derivation of the photon diffusion coefficient for both steady-state and time-dependent transport in disordered absorbing media. The derivation is based on a modal analysis of the time-dependent radiative transfer equation. This approach confirms that the dynamic diffusion coefficient is given by the random-walk result D = cl(*)/3, where l(*) is the transport mean free path and c is the energy velocity, independent of the level of absorption. It also shows that the diffusion coefficient for steady-state transport, often used in biomedical optics, depends on absorption, in agreement with recent theoretical and experimental works. These two results resolve a recurrent controversy in light propagation and imaging in scattering media.     

Application of semiclassical and geometrical optics theories to resonant modes of a coated sphere

This work deals with some aspects of the resonant scattering of electromagnetic waves by a metallic sphere covered by a dielectric layer, in the weak-absorption approximation. We carry out a geometrical optics treatment of the scattering and develop semiclassical formulas to determine the positions and widths of the system resonances. In addition, we show that the mean lifetime of broad resonances is strongly dependent on the polarization of the incident light.     

Analysis of the resonant scattering of light by cylinders at oblique incidence

We study the resonant scattering of light at oblique incidence by dielectric uncoated and coated cylinders. We develop a stable algorithm that permits us to calculate the resonances of a single dielectric cylinder as the tilting angle varies. This algorithm is based on semiclassical formulas for the distance between resonances. Results show that the resonances and the resonant electromagnetic energy flux near and internal to the cylindrical surface are highly sensitive to variations in the tilting angle. In addition, the coating effects are studied for scattering of light at oblique incidence by an infinite, perfect cylindrical conductor coated by a dielectric layer. In this case the resonance calculations show a peculiar similarity between this light scattering and atomic-molecular scattering. A physical interpretation for these effects is given, based on an analogy of optics and quantum mechanics.     

用激光散射法测量大颗粒时使用衍射理论的误差

从实验数据，物理和几何光学的定性分析及Ｍｉｅ理论的严格计算等三个方面证明了即便是远远大于光波长的颗粒的散射光场，其实际光能分布与衍射理论给出的结果之间也有不可忽略的误差：表现为较大散射角上实际的散射光能远大于衍射理论光能。按照衍射理论的计算结果，这一误差等效于１μｍ左右的颗粒产生的光能分布。如果颗粒对光具有吸收性，则误差将显著减少。     

Stochastic modeling of paper structure and Monte Carlo simulation of light scattering

A simplified stochastic model for the fiber structure of paper is introduced. The packing density and optical thickness of the fiber network are derived analytically, and their dependence on fiber characteristics can be seen. We undertake a Monte Carlo simulation of light scattering that is based on geometrical optics, using a realization of the model, which gives packing densities and optical thicknesses well in accordance with those given by the stochastic model and the scattering quantities as functions of three angles.     

Rainbows, water droplets, and seeing--slow motion analysis of experiments in atmospheric optics

Many physics processes underlying phenomena in atmospheric optics happen on a rather short time scale such that neither the human eye nor video cameras are able to analyze the details. We report applications of high-speed imaging of laboratory experiments in atmospheric optics with subsequent slow motion analysis. The potential to study respective transient effects is investigated in general and for a few phenomena in detail, in particular for rainbow scattering due to single oscillating droplets during free fall, and for light propagation effects through atmospheric paths with turbulences, leading, e.g., to scintillation of stars or shimmering of mirage images.     

Novel small-angle collective Thomson scattering system

A Thomson scattering opticals system is described with the following characteristics: (1) it allows scattering angles down to 1 mrad before collection optics interfere with beam dumping; (2) it gives excellent k resolution for angles of > or approximately 1.5 mrad; (3) it collects light from a scattering volume which can be variably positioned without optical realignment; and (4) it is compact in size. The design, test data, and an application to ruby-laser scattering from 100-microm wavelength plasma waves are presented.     

Scattering from a cylindrical reflector: modified theory of physical optics solution

The problem of scattering from a perfectly conducting cylindrical reflector is examined with the method of the modified theory of physical optics. In this technique the physical optics currents are modified by using a variable unit vector on the scatterer's surface. These current components are obtained for the reflector, which is fed by an offset electric line source. The scattering integral is expressed by using these currents and evaluated asymptotically with the stationary phase method. The results are compared numerically by using physical optics theory, geometrical optics diffraction theory, and the exact solution of the Helmholtz equation. It is found that the modified theory of physical optics scattering field equations agrees with the geometrical optics diffraction theory and the exact solution of the Helmholtz equation.     

Re-examination of analytical models for microwave scattering from deciduous leaves

This paper presents an examination of classical scattering models for radar cross sections of deciduous leaves, such as the generalised Rayleigh-Gans (GRG) model and the physical optics (PO) model. The PO model employs the resistive sheet approximation in this study. The validity regions of the analytical models for microwave scattering from deciduous leaves are investigated by comparison with the precise numerical results of the method of moment. It was found that the GRG and PO models extend their validity regions for estimating the scattering amplitudes as the thickness of a lossy dielectric disk decreases. The GRG and PO models can be used alternatively for computing the scattering matrices of natural deciduous leaves at microwave frequencies regardless of the size of the leaves, because of the very small thickness of the leaves (0.2-0.4 mm)     

Multiple scattering in optical coherence tomography. I. Investigation and modeling

We present a new model of optical coherence tomography (OCT) taking into account multiple scattering. A theoretical analysis and experimental investigation reveals that in OCT, despite multiple scattering, the field backscattered from the sample is generally spatially coherent and that the resulting interference signal with the reference field is stationary relative to measurement time. On the basis of this result, we model an OCT signal as a sum of spatially coherent fields with random-phase arguments--constant during measurement time--caused by multiple scattering. We calculate the mean of such a random signal from classical results of statistical optics and a Monte Carlo simulation. OCT signals predicted by our model are in very good agreement with a depth scan measurement of a sample consisting of a mirror covered with an aqueous suspension of microspheres. We discuss other comprehensive OCT models based on the extended Huygens-Fresnel principle, which rest on the assumption of partially coherent interfering fields.     

Light scattering on oceanic turbulence

Turbulent inhomogeneities of fluid flow have the effect of scattering light in near-forward angles, thus providing an opportunity to use optics to quantify turbulence. Here we report measurements of the volume-scattering function in the range of 10(-7) to 10(-3) rad using a wave-front sensing technique. The total scattering coefficient b, due to scattering on turbulent inhomogeneities, is between 1 and 10 m(-1) under typical oceanographic conditions. The numerical calculations of turbulent volume-scattering functions compare well with the laboratory measurement. These results suggest that optical measurements at small angles are affected by turbulence-related scattering, and their effects can be well modeled with numerical calculations.     

Light Scattering by Composite Rough Surfaces

Abstract

Light scattering from a dielectric surface with composite roughness is considered, where the surface irregularities are modelled as a superposition of two roughness types of different length scales. Geometrical optics and the Rayleigh-Rice expansion, respectively, are employed in describing the scattering from the two roughness structures. Contrary to previous work, we concentrate on bistatic cross-sections, which are calculated analytically for scattering in the plane of incidence, and resulting plots for various parameter values are shown, especially for small-scale correlation lengths of the order of the wavelength of the incident light. The main effects of the small-scale roughness are an overall decrease of the coherent reflectance and a depolarization of the scattered light, which in the plane of incidence is not present for scattering from a surface with a single scale of roughness. It is, however, concluded that scattering at the surface and volume scattering have to be taken into account in order to explain the experimentally found degrees of depolarization.     

Optical detection of small changes in refractive indices in water by single-beam scattering

We studied forward-scattered laser light that is produced when the light strikes an abrupt interface (air bubble in water) and when it passes unimpeded through diffused water layers caused by temperature gradients. Measured intensities of the scattered light indicated patterns that are due to both geometrical and physical optics. Distribution of intensities within the scattered beam changed with the average vertical temperature gradient. Shifts in locations of intensities indicated small changes in the index of refraction in the diffused scattering case.     

Role of the tunneling ray in near-critical-angle scattering by a dielectric sphere

The scattering far zone for light transmitted through a sphere following p - 1 internal reflections by a family of near-grazing incident rays is subdivided into a lit region and a shadow region. The sharpness of the ray theory transition between the lit and the shadow regions is smoothed in wave theory by radiation shed by electromagnetic surface waves. It is shown that when higher-order terms in the physical optics approximation to the phase of the partial-wave scattering amplitudes are included, the transition between the lit and the shadow regions becomes a two-ray-to-zero-ray transition, called a superweak caustic in analogy to the more familiar scattering caustics and weak scattering caustics. One of the merged rays is a tunneling ray.     

Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles

We ascertain the usefulness of simple ice particle geometries for modeling the intensity distribution of light scattering by atmospheric ice particles. To this end, similarities and differences in light scattering by axis-equivalent, regular and distorted hexagonal cylindric, ellipsoidal, and circular cylindric ice particles are reported. All the results pertain to particles with sizes much larger than a wavelength and are based on a geometrical optics approximation. At a nonabsorbing wavelength of 0.55 μm, ellipsoids (circular cylinders) have a much (slightly) larger asymmetry parameter g than regular hexagonal cylinders. However, our computations show that only random distortion of the crystal shape leads to a closer agreement with g values as small as 0.7 as derived from some remote-sensing data analysis. This may suggest that scattering by regular particle shapes is not necessarily representative of real atmospheric ice crystals at nonabsorbing wavelengths. On the other hand, if real ice particles happen to be hexagonal, they may be approximated by circular cylinders at absorbing wavelengths.     

Second-harmonic specular and scattered generated light: application to the experimental study of zinc-sulfide thin films

We present measurements of second-harmonic generation with zinc-sulfide thin films. Both scattered light and specular light are investigated in linear optics as well as in second-harmonic generation. We show that second-harmonic generation is a powerful tool for understanding the nonlinear properties of thin films; it allows the study of the anisotropy found in the scattered and specular second harmonic. Using the symmetry of susceptibility tensors, we show that the films cannot be considered homogeneous when the crystallites are large. Finally, we outline nonlinear scattering measurements, which bring out the usefulness of second-harmonic light in probing the structure of thin films.