Patterns in Mie scattering: evolution when normalized by the Rayleigh cross section

An alternative to using the traditional scattering angle theta to describe light scattering from a uniform dielectric sphere is the dimensionless parameter qR, where R is the radius of the sphere, q = 2k sin(theta/2), and k is the wavenumber of the incident light. Simple patterns appear in the scattered intensity if qR is used in place of theta. These patterns are characterized by the envelopes approximating the scattered intensity distributions and are quantified by the phase-shift parameter rho = 2kR/m - 1/, where m is the real refractive index of the sphere. Here we find new patterns in these envelopes when the scattered intensity is normalized to the Rayleigh differential cross section. Mie scattering is found to be similar to Rayleigh scattering when p < 1 and follows simple patterns for p > 1, which evolve predictably as a function of p. These patterns allow us to present a unifying picture of the evolution of Mie scattering for changes in kR and m.     

Two-color excitation fluorescence microscopy through highly scattering media

We study the performance of two-color excitation (2CE) fluorescence microscopy [Opt. Lett. 24, 1505 (1999)] in turbid media of different densities and anisotropy. Excitation is achieved with two confocal excitation beams of wavelengths lambda(1) and lambda(2), which are separated by an angular displacement theta, where lambda(1) not equal lambda(2), 1/lambda(e) = 1/lambda(1) + 1/lambda(2), and lambda(e) is the single-photon excitation wavelength of the sample. 2CE fluorescence is generated only in regions of the sample where the two excitation beams overlap. The 2CE fluorescence intensity is proportional to the product of the two excitation intensities and could be detected with a large-area photodetector. The requirement of spatiotemporal simultaneity for the two excitation beams makes 2CE fluorescence imaging a promising tool for observing microscopic objects in a highly scattering medium. Optical scattering asymmetrically broadens the excitation point-spread function and toward the side of the focusing lens that leads to the contrast deterioration of the fluorescence image in single- or two-photon (lambda(1) = lambda(2)) excitation. Image degradation is caused by the decrease in the excitation energy density at the geometrical focus and by the increase in background fluorescence from the out-of-focus planes. In a beam configuration with theta not equal 0, 2CE fluorescence imaging is robust against the deleterious effects of scattering on the excitation-beam distribution. Scattering only decreases the available energy density at the geometrical focus and does not increase the background noise. For both isotropic and anisotropic scattering media the performance of 2CE imaging is studied with a Monte Carlo simulation for theta = 0, pi/2, and pi, and at different h/d(s) values where h is the scattering depth and d(s) is the mean-free path of the scattering medium.     

Results of a monte carlo investigation of the diffuse attenuation coefficient

There has been a large effort to relate the apparent optical properties of ocean water to the inherent optical properties, which are the absorption coefficient a, the scattering coefficient b, and the scattering phase function rho(theta). The diffuse attenuation coefficient kdiff' has most often been considered an apparent optical property. However, kdiff' can be considered a quasi-inherent property kdiff' when defined as a steady-state light distribution attenuation coefficient. The Honey-Wilson research empirically relates kdiff' to a and b. The Honey-Wilson relation most likely applies to a limited range of water types because it does not include dependence on rho(theta). A series of Monte Carlo simulations were initiated to calculate kdiff' in an unstratified water column. The calculations, which reflected open ocean water types, used ranges of the single-scattering albedo omega(0) and the mean forward-scattering angle theta(m) for two analytic phase functions with different shapes. It was found that kdiff' is nearly independent of the shape of rho(theta) and can be easily parameterized in terms of a, b, and theta(m) for 0.11 相似文献   

Primary spherical aberration in two-color (two-photon) excitation fluorescence microscopy with two confocal excitation beams

We study the effects of primary spherical aberration on the three-dimensional point spread function (PSF) of the two-color (two-photon) excitation (2CE) (2PE) fluorescence microscope with two confocal excitation beams that are separated by an angle theta. The two excitation wavelengths lambda1 and lambda2 are related to the single-photon excitation wavelength lambda(e) by: 1/lambda(e) = 1/lambda1 + 1/lambda2. The general case is considered where both focused beams independently suffer from spherical aberration. For theta = 0, pi/2, and pi, the resulting deterioration of the PSF structure is evaluated for different values of the spherical aberration coefficients via the Linfoot's criteria of fidelity, structural content, and correlation quality. The corresponding degradation of the peak 2CE fluorescence intensity is also determined. Our findings are compared with that of the 2PE fluorescence (lambda1 = lambda2) under the same aberration conditions. We found that the 2CE microscope is more robust against spherical aberration than its 2PE counterpart, with the pi/2 configuration providing the clearest advantage. The prospect of aberration correction in the two-beam 2CE microscope is also discussed.     

Microscopic origin of light scattering in tissue

A newly designed instrument, the static light-scattering (SLS) microscope, which combines light microscopy with SLS, enables us to characterize local light-scattering patterns of thin tissue sections. Each measurement is performed with an illumination beam of 70-microm diameter. On these length scales, tissue is not homogeneous. Both structural ordering and small heterogeneities contribute to the scattering signal. Raw SLS data consist of a two-dimensional intensity distribution map I(theta, phi), showing the dependence of the scattered intensity I on the scattering angle theta and the azimuthal angle phi. In contrast to the majority of experiments and to simulations that consider only the scattering angle, we additionally perform an analysis of the azimuthal dependence I(phi). We estimate different contributions to the azimuthal scattering variation and show that a significant fraction of the azimuthal amplitude is the result of tissue structure. As a demonstration of the importance of the structure-dependent part of the azimuthal signal, we show that this function of the scattered light alone can be used to classify tissue types with surprisingly high specificity and sensitivity.     

Light scattering by ellipsoids in a physical optics approximation

A physical optics approximation based on Presnel's laws is developed to calculate the intensity of light scattered by a three-axis ellipsoid of any orientation and any refractive index. Some results concerning totally reflecting spheres and dielectric spheroids are presented. An approach suitable for large scatterers is particularly good for small scattering angles. The angular intensities, i(1) and i(2), are then plotted versus θ for large axially oriented ellipsoids of various thicknesses. Theoretical small-angle light-scattering patterns are also presented and discussed. The data from one of them correspond to red cells in a shear flow.     

Mueller matrices and information derived from linear polarization lidar measurements: theory

A Mueller matrix M is developed for a single-scattering process such that G(theta, phi) = T (phi(a))M T (phi(p))u, where u is the incident irradiance Stokes vector transmitted through a linear polarizer at azimuthal angle phi(p), with transmission Mueller matrix T (phi(p)), and G(theta, phi) is the polarized irradiance Stokes vector measured by a detector with a field of view F, placed after an analyzer with transmission Mueller matrix T (phi(a)) at angle phi(a). The Mueller matrix M is a function of the Mueller matrix S (theta) of the scattering medium, the scattering angle (theta, phi), and the detector field of view F. The Mueller matrixM is derived for backscattering and forward scattering, along with equations for the detector polarized irradiance measurements (e.g., cross polarization and copolarization) and the depolarization ratio. The information that can be derived from the Mueller matrix M on the scattering Mueller matrixS (theta) is limited because the detector integrates the cone of incoming radiance over a range of azimuths of 2pi for forward scattering and backscattering. However, all nine Mueller matrix elements that affect linearly polarized radiation can be derived if a spatial filter in the form of a pie-slice slit is placed in the focal plane of the detector and azimuthally dependent polarized measurements and azimuthally integrated polarized measurements are combined.     

Aberration reduction by multiple relays of an incoherent image

Consider a generally aberrated one-dimensional (1D) optical pupil P illuminated by quasi-monochromatic light of mean wavelength lambda. In past work it was found that, if the pupil's intensity point-spread function (psf) is multiply convolved with itself, as in an imaging relay system, and then ideally (stigmatically) demagnified, the resulting psf s(x) approaches a fixed Cauchy form s(x) = deltax( pi2x2 + deltax2)(-1), which is independent of the aberrations of the pupil. Here deltax is the Nyquist sampling interval given by deltax = lambdaf/2 with f the f/number of the pupil. This Cauchy form for this intensity psf s(x) also manifestly lacks sidelobes. The overall questions that we examine are how far do these effects carry over to the case of a circular, two-dimensional (2D) pupil, and to what extent do practical imaging considerations compromise the theoretical results? It is found that, in the presence of spherical aberration of all orders, the resulting theoretical psf of a large number of self-convolutions approaches a "circular" Cauchy form, S(r) = 2deltar[pi2r2 + (4deltar/pi)2](-3/2), where deltar is the Nyquist sampling interval lambdaf/2 with f the f/number of the (now) circular pupil. Thus, for these aberrations the 1D effect does carry over to the 2D case: The output psf does not depend on the aberrations and completely lacks sidelobes. However, when all aberrations are generally present, the output psf s(r, theta) does depend on the aberrations, although its azimuthal average over theta still preserves the circular Cauchy form, as a superposition of Cauchy functions. Imaging requirements for achieving these ideal effects are briefly discussed as well as probability laws for photons that are implied by the above-mentioned PSF's s(x) and S(r). Real-time super resolution is not attained, since the stigmatic imaging demanded of the demagnification step requires the use of a larger-apertured lens. Rather, the approach achieves significant aberration suppression.     

Minimal-scan filtered backpropagation algorithms for diffraction tomography

The filtered backpropagation (FBPP) algorithm, originally developed by Devaney [Ultrason. Imaging 4, 336 (1982)], has been widely used for reconstructing images in diffraction tomography. It is generally known that the FBPP algorithm requires scattered data from a full angular range of 2 pi for exact reconstruction of a generally complex-valued object function. However, we reveal that one needs scattered data only over the angular range 0 < or = phi < or = 3 pi/2 for exact reconstruction of a generally complex-valued object function. Using this insight, we develop and analyze a family of minimal-scan filtered backpropagation (MS-FBPP) algorithms, which, unlike the FBPP algorithm, use scattered data acquired from view angles over the range 0 < or = phi < or = 3 pi/2. We show analytically that these MS-FBPP algorithms are mathematically identical to the FBPP algorithm. We also perform computer simulation studies for validation, demonstration, and comparison of these MS-FBPP algorithms. The numerical results in these simulation studies corroborate our theoretical assertions.     

A local-global matching method for the single fiber pullout problem with perfectly bonded interface

This paper presents a local-global matching method to effectively determine the detail spatial structure and magnitude of the locally singular stress field as well as the complete global stress distribution in the single fiber pullout model. The motivation to solve for the local stress field is the belief that these accentuated stresses, strains and energy are likely to induce damage. The local-global matching method consists of three components: a local analysis, a global analysis, and proper matching of the local asymptotic field to the global complete stress field. The method as developed is applicable for various fiber-matrix interfacial conditions: namely perfectly bonded interface, partially debonded interface with interfacial crack, or debonded interface with frictional interfacial sliding. In this paper, results for perfectly bonded fiber-matrix interface are presented to illustrate key features of the local-global matching method. For this problem, the local stress field is asymptotically singular at the location where the fiber protrudes from the matrix. A local analysis at the fiber protrusion point reveals that, when the fiber is stiffer than the matrix, the most dominant singular stresses are of the from: where the exponent is real-valued and <0. The local analysis can solve for the spatial structure of the local field: its radial dependence and angular variations . The actual magnitude of the local stress field is scaled by the amplitude factor K which depends upon externally applied load and global boundary conditions. The global analysis, performed using a finite element model, can be subjected to arbitrary fiber-pulling load and/or thermal load. With solutions from both the local analysis and global analysis, a local-global matching method based on angular variation of stresses is developed to accurately determine K. In local-global matching, a proper region is selected in which the angular variation of stresses of the local field is scaled to match the angular variation of the finite-element computed full-field stresses. Several monitoring parameters are developed to measure the quality of the matching and to determine the region of dominance of the local asymptotic field. The local analysis shows that in many composite material systems, there are two singular terms in the local field: . Hence, local-global matching procedures have been developed for both one-term field and two-term field. The matching method is further generalized to determine complex-valued K for composites having complex-valued . The local-global matching method may also be applied to problems with material nonlinearity.This work was partially supported by a grant from the Air Force Office of Scientific research and by Drexel University. The finite element analyses were performed using ABAQUS made available through an academic license by Hibbitt, Karlsson and Sorensen, Inc. The authors gratefully acknowledge these support     

Mass analysis of water-soluble polymers by mobility measurement of charge-reduced ions generated by electrosprays

Aqueous solutions of poly(ethylene glycol) (PEG) in a 10 mM ammonium acetate buffer are electrosprayed, and the maximum charge state on the resulting gas-phase ions is reduced to unity using a radioactive source. The mobility distribution of these charged particles is then measured in air in a differential mobility analyzer of unusually high resolution. The relation Z(m) between the mobility Z of a polymer molecule and its mass m is determined by means of narrowly distributed PEG mass standards. The molecular weight range of available standards is extended by generating clusters containing from one up to six molecules of the primary PEG standard. The mass at the peak of the distribution of the lowest standard (PEG-4k) is determined by MALDI mass spectrometry and agrees with the manufacturer's value and previous MALDI literature data. The masses for the 50K and 120K standards are found to differ by 8.6 and 6.6%, respectively, from the manufacturer's value. Using known relationships, the particle diameter d of the ions is calculated from the measured mobility. Plots of d versus m(1/3) give straight lines over the full mass range studied (4000-700 000 Da, particle diameter from 3 to 12 nm), indicating that these PEG particles are indeed spherical and have a density rho independent of size. The slope of the d versus m(1/3) curve provides a density rho = 1.25 g/cm(3), close to the known bulk density, rho(PEG) = 1.21 g/cm(3).     

Pulse distortion of a scattered chirped pulse

We have studied the time-dependent properties of a chirped short pulse when the pulse is scattered by a spherical particle. We used generalized Lorentz-Mie formulas to study the scattered electrical field and pulse distortion. Plane wave Gaussian pulses of different chirps with a constant pulse-filling coefficient l(0) = 1.98 have been studied. A morphology-dependent resonance causes a prolonged trailing edge (small scattering angle) and oscillations (large scattering angle) in the scattered pulse. When frequency sweeping superimposes on a morphology-dependent resonance, the pulse chirp affects the scattered pattern and distorts the scattered intensity. Multisecondary pulses are generated because of the pulse chirp and even subsecondary pulses occur if the incident pulse is deeply chirped. The pulse widths of secondary and subsecondary pulses are shorter than those of an incident pulse.     

Effect of beam size parameters on internal fields in an infinite cylinder irradiated by an elliptical Gaussian beam

The scattered and internal fields of an infinite, homogeneous cylinder illuminated by a linearly polarized beam depend on the following parameters: the object size parameter of the cylinder (ka, where k=2pi/lambda, lambda is the wavelength of the incident beam in the surrounding medium, and a is the radius of cylinder), the complex relative refractive index of the object, the beam size parameters (komega(1) and komega(2), where omega(1), omega(2) are the representative beam dimensions), the angle between the cylinder axis and the Poynting vector of the incident wave, and the angle between the plane of polarization and the plane of incidence. Only when the dimensions of the beam are much greater than the cylinder diameter, and hence the portion of the beam interacting with the cylinder is essentially uniform, can the plane-wave solution be used in computing the scattered and internal fields. Hence a rigorous electromagnetic approach like the generalized Lorenz-Mie theory for spheres is used to study the effect of beam size parameters on the internal fields in an infinite cylinder irradiated by elliptical Gaussian beams. The significant effects of beam size parameters on the internal fields in an infinite cylinder are presented using specific cases of (1) resonance effects in a glass cylinder (ka=45.726, transverse-electric mode 53,3) and (2) a cylindrical microchannel (ka approximately 760) irradiated by a 632.8 nm laser beam.     

Low-coherence light-scattering calculations for polydisperse size distributions

The calculation of angular light-scattering distributions is considered for low-coherence light incident on a polydisperse particle size distribution of scatterers. As low-coherence light is now commonly used in interferometry schemes when applied to biomedical imaging, the difference between detecting scattered intensity and interferometrically detecting the scattered field is examined. An expression is derived that allows the presence of multiple wavelengths lambda and particle sizes d to be described by a single distribution in the size parameter x = pi d/lambda, which simplifies numerical calculations. The applicability of this expression is examined numerically.     

Effective medium theories for irregular fluffy structures: aggregation of small particles

The extinction efficiencies as well as the scattering properties of particles of different porosity are studied. Calculations are performed for porous pseudospheres with small size (Rayleigh) inclusions using the discrete dipole approximation. Five refractive indices of materials covering the range from 1.20+0.00i to 1.75+0.58i were selected. They correspond to biological particles, dirty ice, silicate, and amorphous carbon and soot in the visual part of the spectrum. We attempt to describe the optical properties of such particles using Lorenz-Mie theory and a refractive index found from some effective medium theory (EMT) assuming the particle is homogeneous. We refer to this as the effective model. It is found that the deviations are minimal when utilizing the EMT based on the Bruggeman mixing rule. Usually the deviations in the extinction factor do not exceed approximately 5% for particle porosity P = 0 - 0.9 and size parameters x(porous) = 2 pi r(s,porous)/lambda < or approximately = 25. The deviations are larger for scattering and absorption efficiencies and smaller for particle albedo and the asymmetry parameter. Our calculations made for spheroids confirm these conclusions. Preliminary consideration shows that the effective model represents the intensity and polarization of radiation scattered by fluffy aggregates quite well. Thus the effective models of spherical and nonspherical particles can be used to significantly simplify the computations of the optical properties of aggregates containing only Rayleigh inclusions.     

Energy barrier for electron penetration into helium

The Galitskii approach to the calculation of self-energies is used to find the energy barrierΔE opposing the penetration of electrons into He, Ne, and Ar. To second order in thes-wave scattering lengtha, it is found that $$\Delta {\text{E = (2}}\pi \hbar ^2 {\text{na/m)}}\left\{ {{\text{1 + 2a}}\pi ^{{\text{ - 1}}} \int_0^\infty {{\text{dk[1 - S(k)]}}} } \right\}$$ wheren is the fluid number density,m is the electron mass, andS(k) is the fluid static structure factor. Typical barrier energies for⁴He and³He are 0.97 and 0.67 eV.     

Alignment of Gaussian beams

The design of a coupling between a semiconductor laser and a single-mode fiber, or between any two optical or acoustical elements that support Gaussian modes, is presented as a trade-off among coupling efficiency T(a), offset misalignment tolerance d(e), and angular misalignment tolerance theta(e). We show that these three parameters are subject to a trade-off limitation which takes the form 0 < T(a)(1/2)theta(e)d(e) < or = lambda/pi, and we show how to design a coupling so that the upper bound on the alignment product T(a)(1/2)theta(e)d(e) is achieved.     

Law of normal scattering--a comprehensive law for wave propagation at an interface

The fundamental laws of wave propagation at an interface, the laws of reflection, refraction, and diffraction are arrived at from a consideration of wave scattering from an array of scattering centers. It is shown that the number, spacing, and dimension of the scattering centers decide whether the laws of reflection and refraction or the more comprehensive law of normal scattering is obeyed. An exact equation for the summation of the phases and amplitudes of scattered waves arriving at a point is developed. Scattered ray directions are arrived at from the analytical behavior of this equation, and the region of validity of the solutions is discussed. It is shown that the length of the array plays as important a role as the spacing of the scattering centers. The modulation of diffracted ray intensity with an increase in scattering center size is identified and investigated. An expression for far-field distance is arrived at based on numerical simulation and is valid for all scattered angles.     

Mie scattering in the time domain. Part 1. The role of surface waves

We computed the Debye series p=1 and p=2 terms of the Mie scattered intensity as a function of scattering angle and delay time for a linearly polarized plane wave pulse incident on a spherical dielectric particle and physically interpreted the resulting numerical data. Radiation shed by electromagnetic surface waves plays a prominent role in the scattered intensity. We determined the surface wave phase and damping rate and studied the structure of the p=1,2 surface wave glory in the time domain.