Multiple-scattering effects on differential absorption for the transmission of a plane-parallel beam in a homogeneous medium

The transmission, including all scattering orders, of a plane-parallel beam in a homogeneous scattering medium containing aerosols (e.g., water cloud) mixed with an absorbing gas (e.g., ozone) is computed with a two-stream radiative transfer model. From differential transmission the concentration of the gas is deduced. The effect of multiple-scattering on the deduced concentration is shown for conservative scattering aerosols for which the multiple scattering by the aerosols is differentially absorbed by the gas and for nonconservative scattering aerosols for which the multiple scattering is differentially absorbed by the aerosols as well as differentially absorbed by the gas. The two-stream analytical model (with no dependence on the field of view) shows good qualitative agreement (especially for a small field of view) with a numerical radiative transfer model in which the trace gas concentration is computed for the different detector's field of view.     

Optical path difference in a plane-parallel uniaxial plate

The flux of energy given by the Poynting vector Se and the kt-wave vector normal to the geometrical wavefront for the extraordinary ray propagating through uniaxial crystals can be evaluated by using the theory developed by Avenda?o-Alejo et al. [J. Opt. Soc. Am. A 19, 1668 (2002)] and Avenda?o-Alejo and Stavroudis [J. Opt. Soc. Am. A 19, 1674 (2002)]. We give here the equations necessary to evaluate the general dispersion angle Se x kt. Additionally we define two new dispersion angles, Se x A and kt x A, where A is the crystal axis vector. With these new dispersion angles we evaluate the optical path length traversed by the extraordinary ray in a plane-parallel uniaxial plate when the crystal axis lies in the plane of incidence.     

Monte Carlo study of coherent diffuse photon transport in a homogeneous turbid medium: a degree-of-coherence based approach

We employ a Monte Carlo (MC) algorithm to investigate the decoherence of diffuse photons in turbid media. For the MC simulation of coherent photons, the degree of coherence, defined as a random variable for a photon packet, is associated with a decoherence function that depends on the scattering angle and is updated as a photon interacts with a medium via scattering. Using a slab model, the effects of medium scattering properties were studied, which reveals that a linear random variable model for the degree of coherence is in better agreement with experimental results than a sinusoidal model and that decoherence is quick for the initial few scattering events followed by a slow and gradual decrease of coherence.     

Optical radiation flux illuminating a circular disk from an off-axis point source separated by a homogeneous plane-parallel plate

In a number of techniques that measure weak fluxes of optical radiation, it is frequently necessary to keep a detector in a medium different from that of the radiating source by separating it from the source with a planar transparent window. However, sources such as systems of light-emitting diodes, large-fiber illuminators, and microscopic living objects that emit biological luminescence may sometimes be regarded as multiple-point sources. To estimate the fluxes of optical radiation illuminating a surface from a nonuniformly distributed multiple-point source, a method for calculating fluxes from a single off-axis point source is needed. A formula is derived to estimate a flux of temporally incoherent optical radiation incident on a circular disk from a single off-axis point source separated by a plane-parallel plate (PPP). This formula is expressed by a series of single integrals of some superposed elementary functions. These functions depend on the variables that characterize the point-source-plane-parallel-plate-circular-disk geometry and on the optical properties of the media that separate the source from the PPP and the PPP from the disk. The solution was obtained for isotropic media. For illustrative purposes some examples of the use of the formula are presented. The selected results are illustrated by three-dimensional surface plots and compared with the values of the fluxes calculated for radiation incident on the disk from a point source not separated by a PPP.     

Geometric propagation of an axially symmetric optical wavefront in a homogeneous medium

We obtain a Taylor series neighbor expansion that allows the geometric propagation of an axially symmetric wavefront in such a way that the change in shape of the wavefront is determined as an explicit function of coordinates. We then apply the expansion to the propagation of conicoids in particular. The theory is applied to the propagation of a general conicoidal, a spherical, and a paraboloidal wavefront. Application of the theory to the general conicoid leads to a proof of the invariance of the product of radius of curvature and conic constant for short propagation distances in homogeneous media. For the case of the spherical wavefront, the intuitive result is obtained (i.e. the wavefront remains spherical).     

Unified analysis of the sensitivities of reflectance and path length to scattering variations in a diffusive medium

A unified analysis is presented for the sensitivities of reflectance and path length to scattering variations in a diffusive medium, using an improved solution of the steady-state diffusion equation. This approach enables one to (1) explain theoretically two kinds of dependency of near-infrared reflectance on source-detector separations and (2) obtain an analytical expression for optical path lengths. The results shown here are consistent with those of Kumar and Schmitt [Appl. Opt. 36, 2286 (1997)] and Mourant et al. [Appl. Opt. 36, 5655 (1997)]. Also, discussions are given on (1) possible reasons for some inconsistency between the conclusion drawn by Mourant et al. and results given here and (2) the usefulness of making reflectance measurements while minimizing the sensitivity of reflectance and path length to scattering variations.     

On the calculation of effective path lengths through beam scattering chambers

Relationship for the effective scattering path lengths through chambers with identical beam entrance and exit apertures are calculated for the special case for which the chamber walls are assumed to be in equilibrium with the scattering gas.     

Temperature effects on the optical path length of infrared liquid transmission cells

Infrared (IR) spectroscopy is widely used for studies of temperature-dependent properties of liquids and solutions, such as thermal denaturation of proteins and other molecules of biological interest. The variation of the spectroscopic signals with temperature can be affected by the changes in the optical path length due to the thermal expansion of the components of the sample cell. In this report we investigate the temperature dependence of the optical path length for a liquid IR sample cell of a design typical for aqueous solution experiments. The path lengths were measured from the interference fringes, both in dry cells and with cells partially filled with water. We found that the optical path length variations are significant, on the order of several percent within the temperature range used (0-87 °C). Several commercially available spacers (Teflon, mylar, and lead) and gaskets (Teflon, lead, silicone rubber, Viton, and neoprene) were tested to find materials with either the smallest or most reproducible effect. Teflon, due to its phase transition (known as the "knee point") near room temperature, leads to abrupt changes in path length when used as either spacer or gasket component. On the other hand, Teflon is preferred for its inertness, while several of the other tested materials, most notably lead, are not practically usable due to adhesion to the cell windows upon heating and contact with the aqueous sample. The combination that yielded the most reproducible results, with minimal complications due to adhesion, was Teflon spacer with neoprene gaskets. The implications of the optical path length changes for the temperature-dependent IR experiments and their possible corrections are discussed.     

Weight function for an elliptical planar crack embedded in a homogeneous elastic medium

The method of simultaneous dual integral equations is used for obtaining the exact analytical solution for the weight function for an elliptical crack embedded in an infinite elastic solid. We show that the solution is unique and can be reduced to the known solutions for a number of particular cases.     

Determination of bond dissociation energies using electrospray tandem mass spectrometry and a derived effective reaction path length approach

A new approach for calculating bond dissociation energies (BDEs) from ES-MS/MS measurements has been developed. The new method features a "derived effective reaction path length" that has been applied to measure BDEs of alkali metal (Li+) adducts and halide (Cl-) adducts of monoacylglycerol, 1,2-diacylglycerol, and 1,3-diacylglycerol lipids. Also studied were lithium-bound dimers of monoacylglycerols, 1,2-diacylglycerols, and 1,3-diacylglycerols. BDEs for the adducts and dimers of the lipids were derived from collision-induced dissociation experiments using a triple quadrupole mass spectrometer with electrospray as the ionization source. Mass spectral data were used to empirically derive a single-exponential growth equation that relates product cross section to collision energy. From these single-exponential equations, a general second-order polynomial was derived using a multivariate growth curve model that enables prediction of BDEs of unknown complexes. Mass spectral results were compared to computer-generated bond dissociation energies using Becke-style three-parameter density functional theory (B3LYP, employing the Lee-Yang-Parr correlation functional), with excellent agreement between experimental and theoretical energy values. The newly developed method is general in nature and can be used for the measurement of metal or halide ionic adduct bond dissociation energies and for the measurement of bond energies of noncovalent interactions such as dimer dissociation energies. The validity of the method has been rigorously established using a triple quadrupole, but it may also be applied to other mass spectrometers that allow user control of the collision cell potential.     

Absorption distribution of an optical beam focused into a turbid medium

The focusing of light into a turbid medium was studied with Monte Carlo simulations. Focusing was found to have a significant effect on the absorption distribution in turbid media when the depth of the focal point (the distance between the focal point and the surface of the turbid media) was less than or comparable with the transport mean free path. Focusing could significantly increase the peak absorption and narrow the absorption distribution. As the depth of the focal point increased, the peak absorption decreased, and the depth of peak absorption increased initially but quickly reached a plateau that was less than the transport mean free path. A refractive-index-mismatched boundary between the ambient medium and the turbid medium deteriorated the focusing effect, increased the absorption near the boundary, lowered the peak absorption, and broadened the absorption distribution.     

Determination of attenuation-velocity products in a layered homogeneous medium

Attenuation imaging has the promise to become a measurement technique for ultrasound imaging systems more sophisticated than those we currently possess; however, the difficulties in using the presently available methods tend to limit this potential for the non-specialist. In our recent work, we have investigated the attenuation imaging problem, and have had some success with an alternative technique, namely, attenuation-velocity product imaging. In certain cases this can be an acceptable substitute for purely attenuation imaging, particularly for the soft tissues encountered in some diagnostic medical situations where the acoustic velocities of the various layers are all of approximately the same value. This article discusses our technique in detail, beginning with fundamental considerations. We make no unreasonable assumptions about the object under study, and yet are able to show the uniqueness of the solution and also deal effectively with the problem of multiple reflections. The data encountered in this experimental configuration have several intriguing properties, which allow us to draw some conclusions about acoustic imaging in general.     

Short-term average intensity of a cosh-Gaussian beam in Kolmogorov turbulence

With the help of the extended Huygens–Fresnel principle and the spherical-wave short-term mutual coherence function, an analytical expression was derived for the short-term average intensity of a cosh-Gaussian beam through Kolmogorov turbulence. As special cases, the properties of the short-term average intensity with different propagation distances and parameters are studied. In addition, a comparison is presented of average intensity between short exposure and long exposure. The results show that the effect of turbulence on long- and short-term average intensity is different for different factors of the cosh part.     

Multiple-scattering model for the coherent reflection and transmission of light from a disordered monolayer of particles

Using a multiple-scattering formalism, we derive closed-form expressions for the coherent reflection and transmission coefficients of monochromatic electromagnetic plane waves incident upon a two-dimensional array of randomly located spherical particles. The calculation is performed within the quasi-crystalline approximation, and the statistical correlation among the particles is assumed to be given simply by a correlation hole. In the resulting model, the size of the spheres and the angle of incidence are both unrestricted. The final formulas are relatively simple, making the model suitable for a straightforward interpretation of optical-sensing measurements.     

The effective crack length of an edge slot in a semi-infinite sheet under tension

The rate of change of the elastic strain energy with respect to notch depth is considered for edge notches or slots with a finite constant radius, , at the tip. Numerical results are obtained for an edge slot in a semi-infinite sheet under tension. It is found that the slot can be considered as a crack of length L + 1.18 for this purpose. In finite sheet, this result is valid for small L/ ratios.

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Zusammenfassung Das Wechselverhältnis der elastischen Dehnungsenergie zur Kerbentiefe wird fuer Randkerben oder Schlitze mit endlichem konstanten Radius, , an der Spitze betrachtet. Numerische Ergebnisse werden für einen Randschlitz in einer halb-unendlichen Platte unter Zugspannung gefunden. Es wird gefunden, dass zu diesem Zwecke der Schlitz als Riss mit Länge L + 1.18 betrachtet werden kann. Für eine endliche Platte ist dieses Resultat für kleine L/ Verhältnisse gültig.

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Résumé L'evolution de l'énergie de deformation elastique en fonction de la profondear d'entaille est etudiée dans le cas d'entailles lateriales ou de saignées .....dont le rayen de courbure d'extrémité a une valeur finie et constante.Des données numeriques oat été oblénues dans le cas d'une saignée effectivée sur les bord d'un feuillard semi infini soumis à tension. On trouve que la saignee peut-être dans ce cas assimilee a une fissure qui aurait une longueur L + 1.18 . En ce qui concerne le cas de la tole finie, ce resultat n'est applicable que pout de faibles valeurs du rapport L/.

     

Determination of a neutron source position in an unknown homogeneous medium; the 2D case

The localisation of an unknown neutron source in various bulky homogeneous media was studied. For the planar case two (3)He detectors on the opposite faces of a box were used. It is shown that the location of a single small neutron emitting source in a large box can be found to a better than 7% by using two neutron detectors positioned on parallel faces of the box, coplanar with the source. The localisation requires measurement of the count rate of both the unknown source (ratio of the count rates of the two detectors is R(x)) and an extra source positioned on one of the faces of the box (ratio of the count rates of the two detectors R(0)). The location of the neutron source is found according to the equation. (Formula see text). The localisation is based on the finding that the ratio of the count rates of the two detectors is an exponential function of the distance of the source from one of the detectors.     

Fourier description of the propagation and focusing of an extraordinary beam in a planar uniaxial medium

The scalar-angular-spectrum approach is used to examine a focused extraordinary wave propagating along an arbitrary direction in a homogeneous uniaxial planar medium, and the Fraunhofer diffraction formula is generalized for this case. The size of the focal spot is found to be inversely proportional to an effective index, depending on the refractive indices and the propagation direction. The validity of the paraxial model is checked by nonparaxial (but scalar) numerical calculations. They show that the paraxial formulas predict the spot size correctly, but if the beam propagates neither parallel with nor perpendicular to the optic axis, they do not reproduce the symmetries of the amplitude distribution in the focal line.     

The determination of a neutron source position in an unknown homogeneous medium; the 3D case

The possibility of localisation of an unknown neutron source in various bulky homogeneous media (box) was studied. Previous study showed that for the planar case, neutron source could be localised with accuracy better than 7%, by using the count rates ratio of two (3)He detectors, positioned on the opposite faces of the box. The influence of the deviation of the source from the virtual plane connecting the two (3)He detectors was studied. It was found that for detectors placed on the centres of the sample faces, larger distance of the source from the central line leads to larger error, up to 15%. It was found that while using the measurement of the ratio R(0) of external source placed on the box face coplanar with unknown source, accuracy does not depend on the distance from central line. Different ways to determine the plane of the unknown source were investigated. It was found that it is impossible to determine it by looking for maximum count rate of one detector or geometric mean of a pair of detectors. The experimental results were confirmed with Monte-Carlo N-particle (MCNP) simulations.