Anomalous Diffraction Approximation Research Articles

Optical discrimination of pathological red blood cells.

Fast diagnostic methods are crucial to reduce the burden on healthcare systems. Currently, detection of diabetes complications such as neuropathy requires time-consuming approaches to observe the correlated red blood cells (RBCs) morphological changes. To tackle this issue, an optical analysis of RBCs in air was conducted in the 250-2500 nm range. The distinct oscillations present in the scattered and direct transmittance spectra have been analyzed with both Mie theory and anomalous diffraction approximation. The results provide information about the swelling at the ends of RBCs and directly relate the optical data to RBCs morphology and deformability. Both models agree on a reduction in the size and deformability of RBCs in diabetic patients, thus opening the way to diabetes diagnosis and disease progression assessment.

Light diffraction in rotating magnetic emulsions in a magnetic field

The light diffraction in magnetic emulsions with droplets of a kerosene based magnetic fluid in AMG-10 hydraulic oil under the influence of magnetic and hydrodynamic fields has been studied experimentally. Rotation of the emulsion sample in a uniform magnetic field revealed a deflection of the diffraction pattern by a certain angle. An interpretation of the effect based on the anomalous diffraction approximation is proposed. The rotation of the diffraction pattern in the field of hydrodynamic forces is interpreted based on the balance of the torques of magnetic and viscous friction forces acting on an elongated droplet of magnetic fluid.

Probing bio-tissue films by optical internal reflectivity: modeling and measurements.

In this paper, we develop a detailed theoretical model for the optical reflectivity of a bio-tissue film confined between two flat interfaces based on the anomalous-diffraction approximation. We consider bio-tissue films consisting of a few layers of spheroidal cells surrounded by extracellular medium. We explore numerically the predictions of our model and compare them with simple effective medium theories, sometimes used as a first attempt to understand the optical properties of biological media. Then, we fit the model to experimental reflectivity-versus-angle-of-incidence curves of confined whole-blood films measured in an internal reflection configuration. Measurements were performed by confining a drop of fresh blood between a prism and a coverslip. Our experimental results show that it is possible to measure the coherent reflectance with small enough error to infer microstructural parameters with a good precision. The errors in measuring the coherent reflectance depend on the reflectivity magnitude. For instance, for a reflectivity of about 0.3 the error is below 2%, and the refractive indices of cells and surrounding medium can be obtained with a precision better than 1%. These results also indicate that the present model can readily be used to figure out the physical changes experienced at the microscale in bio-tissue films during a physicochemical process.

Small-Angle Scattering and Radiation Polarization by a Stretched Polymer Film with Nematic Liquid Crystal Droplets Having a Single-Domain Structure

The coefficient of directed transmittance of a stretched polymer-dispersed liquid crystal film with a defect-free single-domain liquid crystal droplet structure formed by a stretched surfactant-doped film and the polarization degree of forward-transmitted light in the visible and near-infrared spectrum ranges are studied. Results are presented for the 5CB, E7, and E44 nematic liquid crystals. Dependences of the transmission coefficient and polarizing ability of the film on the photodetector field of view are studied. Relationships allowing one to determine film parameters at which the transmission coefficient and polarizing ability of the films simultaneously reach values close to limit ones (0.5 and ±1.0, respectively) are obtained in the Foldy–Twersky and anomalous diffraction approximations.

Optical model to describe coherent transmittance of polymer dispersed liquid crystal film doped with carbon nanotubes

An optical model has been developed for analyzing the coherent transmittance of a polymer dispersed liquid crystal films doped with carbon nanotubes (CNTs) at uniform normal droplet-polymer interface anchoring. It is based on the Foldy–Twersky and anomalous diffraction approximations, Maxwell-Garnett equations, and the order parameters concept. The model allows one to analyze the electro-optical response of films depending on their thickness, the refractive indices of the liquid crystal (LC) and polymer matrix, size and concentration of the LC droplets, concentration of nanotubes, conductivities of the LC and the polymer. Experimental verification of the model is performed.

An Inverse Numerical Simulation for Simultaneous Measurement of Non Spherical Particle Size and Optical Constant by Forward Elastic Light Scattering and Transmittance

This numerical study investigates the feasibility of simultaneous retrieval of particle size distribution (PSD) and optical constants of spheroids by optical spectroscopy. In this simulation the particles are considered as spheroid. The aspect ratio of an oblate and prolate spheroid is set as 0.8 and 1.2, respectively. At this constant aspect ratio, the particle’s orientation has been changed by altering its major semi-axis. Two continuous wavelength lasers are employed to irradiate the particle samples. Multi-angle and multi-wavelengths elastic forward scattering intensity and the spectral collimated transmittance are employed to measure signals. For forward scattering, the spheroid is effectively replaced by a sphere of an approximated radius and the modified Mie theory is employed to calculate the scattering intensity. For the collimated transmittance, the extinction efficiency of non-spherical particle is measured based on the extended anomalous diffraction approximation. The Log-Normal distribution is used to get the volume frequency distribution of the particles and the inverse process is done by using the improved quantum particle swarm optimization. Two different sets of optical constant (e.g., complex refractive index), semi-major axis of non-spherical particle and discrete rate are retrieved by the inverse simulation. The results show that, the proposed spectroscopic technique can retrieve PSD and optical constants of non-spherical particles simultaneously within the tolerable error limit less than 10%.

Inversion algorithm for non-spherical dust particle size distributions

Dust particles are the main aerosol component of the atmosphere, and can influence human, environmental, and ecological health. Particle size distribution is an important aerosol micro-physical parameter that denotes the concentration distribution of particles of different radii and can determine the extinction characteristics of these particles. In traditional inversion algorithms, the aerosol is generally assumed to be spherical according to Mie theory, and the relationship between aerosol optical thickness and particle size distribution is described by the Fredholm integral equation of the first kind. For non-spherical dust particles, this spherical assumption is obviously unreasonable and yields unreliable results. Therefore, we developed an algorithm assuming non-spherical particles for inversion of dust particle size distributions. In the case of non-spherical particles, the extinction efficiency factor kernel functions of the ellipsoid were calculated using the anomalous diffraction approximation method, and the kernel function of Mie scattering theory was substituted with these new kernel functions. Moreover, the Phillips–Twomey method was employed to solve the Fredholm integral equation of the first kind using aerosol optical thickness data from a CE-318 sun photometer. To verify the feasibility of the anomalous diffraction approximation method, experiments were carried out under sunny, dusty, windy and hazy weather conditions. These experiments showed that the extinction kernel function for non-spherical particles obtained using the anomalous diffraction approximation method is suitable for inversion of non-spherical dust particle size distributions under different weather conditions in the Yinchuan area.

Model to describe light scattering by polymer film containing droplets with inhomogeneous anchoring of liquid crystal molecules at the polymer–droplet interface: asymmetry effect in the angular distribution of light

ABSTRACTA model to describe light scattering by polymer film containing of monolayer of liquid crystal droplets with inhomogeneous anchoring of liquid crystal molecules at the polymer-droplet interface is developed. It is based on the interference approximation of the wave scattering theory. The director field distribution in the droplet volume is determined by solving the free energy density minimization problem using the relaxation method. The spatial distribution of droplets in the layer is described by the hard disks model. The amplitude scattering matrices of individual droplets are found in the anomalous diffraction approximation. The algorithm for numerical analysis of the characteristics of light scattered in a polymer film containing droplets at homogeneous and inhomogeneous surface anchoring is described in terms of the partial filling factors of the monolayer film. Electrically controllable symmetry breaking effect of angular distribution of light scattered by films containing droplets with inhomogeneous anchoring at the polymer-droplet interface is described and experimentally confirmed.

Estimation of Optical Properties of “Soft” Radially Inhomogeneous Ellipsoidal Particles

The Rayleigh–Gans–Debye and anomalous diffraction approximations are used to formulate necessary and sufficient conditions of optical equivalence of randomly oriented, radially inhomogeneous, optically “soft” ellipsoidal particles and polydisperse radially inhomogeneous spherical particles. Consequences of optical equivalence are used as a base for the optical classification of isotropic ensembles of soft ellipsoidal particles. The correctness of the classification is illustrated by calculations using the T-matrix method and Mie theory.

Reflectivity and transmissivity of a surface covered by a disordered monolayer of large and tenuous particles: theory versus experiment.

The main objective of this paper is to endorse a recently derived theoretical model for the coherent reflectance and transmittance from a surface supporting a disordered monolayer of large and tenuous particles by comparison with experimental measurements. The model is based on the so-called anomalous-diffraction approximation and is assumed to be valid for small and moderate angles of incidence. We prepared disordered monolayers of spherical polystyrene particles of 1.8μm diameter and of human red blood cells on glass microscope slides. In both cases, particles were immersed in a liquid of refractive index close to that of the particle. We measured the relative reflectivity and transmissivity of the samples versus the wavelength of light at normal incidence and the reflectivity and transmissivity versus the angle of incidence at a fixed wavelength, and compared with predictions of the anomalous-diffraction approximation model. For the polystyrene particle samples, we also compare the results with another available theoretical model developed some years ago to deal with disordered monolayers of highly scattering particles. In the case of red blood cell monolayers, we also present measurements with a hemolyzed sample and a disordered multilayer film for comparison. We find that the anomalous diffraction model can be fitted very well to the experimental curves, in some cases, even for high angles of incidence.

Role of carboxyl ester lipase (CEL) in pancreatic disease: Functional characterization of CEL protein variants differing in C-terminal sequence

An improved quantum-behaved particle swarm optimization (IQPSO) algorithm is employed to determine aerosol size distribution (ASD). The direct problem is solved using the anomalous diffraction approximation and Lambert–Beer's Law. Compared with the standard particle swarm optimization algorithm, the stochastic particle size optimization algorithm and the original QPSO, our IQPSO has faster convergence speed and higher accuracy within a smaller number of generations. Optimization parameters for the IQPSO were also evaluated; we recommend using four measurement wavelengths and 50 particles. Size distributions of various aerosol types were estimated using the IQPSO under dependent and independent models. Finally, experimental ASDs at different locations in Harbin were recovered using the IQPSO. All our results confirm that the IQPSO algorithm is an effective and reliable technique for estimating ASD.

Polarization of light by a polymer film containing elongated drops of liquid crystal with inhomogeneous interfacial anchoring

An optico-mechanical model describing the coherent (directed) transmittance and the degree of polarization of forward-transmitted light by a polymer film with elongated liquid-crystal (LC) drops has been developed. This model, based on the Foldy–Twersky and anomalous-diffraction approximations, makes it possible to analyze the optical response of a film under extension as a function of the film thickness, refractive index of the polymer, the sizes and anisometry parameters of liquid-crystal drops, their concentration, internal structure, polydispersity, and orientation of optical axes. The model is verified based on the comparison of numerical and experimental data for the inverse modification of interfacial anchoring by an ion-forming surfactant. The internal drop structure is determined by solving the problem of minimizing the volume free energy density. A comparative analysis of the calculated transmittance and degree of polarization for films with uniform homeotropic and modified inhomogeneous interfacial anchoring is performed. The spectral polarization characteristics of a film with elongated LC drops and single-domain internal structure, formed under mechanical extension with the aid of surfactants, are investigated.

Small-angle light scattering symmetry breaking in polymer-dispersed liquid crystal films with inhomogeneous electrically controlled interface anchoring

We have described the method of analyzing and reporting on the results of calculation of the small-angle structure of radiation scattered by a polymer-dispersed liquid crystal film with electrically controlled interfacial anchoring. The method is based on the interference approximation of the wave scattering theory and the hard disk model. Scattering from an individual liquid crystal droplet has been described using the anomalous diffraction approximation extended to the case of droplets with uniform and nonuniform interface anchoring at the droplet–polymer boundary. The director field structure in an individual droplet is determined from the solution of the problem of minimizing the volume density of the free energy. The electrooptical effect of symmetry breaking in the angular distribution of scattered radiation has been analyzed. This effect means that the intensities of radiation scattered within angles +θ s and–θ s relative to the direction of illumination in the scattering plane can be different. The effect is of the interference origin and is associated with asymmetry of the phase shift of the wavefront of an incident wave from individual parts of the droplet, which appears due to asymmetry of the director field structure in the droplet, caused by nonuniform anchoring of liquid crystal molecules with the polymer on its surface. This effect is analyzed in the case of normal illumination of the film depending on the interfacial anchoring at the liquid crystal–polymer interface, the orientation of the optical axes of droplets, their concentration, sizes, anisometry, and polydispersity.

Approximative derivation of the extinction efficiency for a two and threefold stratified cylinder

This paper discusses the applicability of the anomalous diffraction approximation to describe scattering at stratified, tilted and randomly oriented infinite cylinders. The results of the approximation are compared with the established exact scattering formulas based on Maxwell-Equations. We show that in many cases the simplified theory delivers good agreement in a broad size parameter range. Within the applicability limits discussed in the paper, the anomalous diffraction theory delivers a fast and useful tool for rapidly scanning a broad wavelength spectrum to investigate the effects of parameter variations in layered cylindrical media.

Light transmission of polymer-dispersed liquid crystal layer composed of droplets with inhomogeneous surface anchoring

We have developed a model and realized an algorithm for the calculation of the coefficient of coherent (direct) transmission of light through a layer of liquid crystal (LC) droplets in a polymer matrix. The model is based on the Hulst anomalous diffraction approximation for describing the scattering by an individual particle and the Foldy-Twersky approximation for a coherent field. It allows one to investigate polymer dispersed LC (PDLC) materials with homogeneous and inhomogeneous interphase surface anchoring on the droplet surface. In order to calculate the configuration of the field of the local director in the droplet, the relaxation method of solving the problem of minimization of the free energy volume density has been used. We have verified the model by comparison with experiment under the inverse regime of the ionic modification of the LC-polymer interphase boundary. The model makes it possible to solve problems of optimization of the optical response of PDLC films in relation to their thickness and optical characteristics of the polymer matrix, sizes, polydispersity, concentration, and anisometry parameters of droplets. Based on this model, we have proposed a technique for estimating the size of LC droplets from the data on the dependence of the transmission coefficient on the applied voltage.

Application of the LSQR algorithm in non-parametric estimation of aerosol size distribution

Based on the Least Squares QR decomposition (LSQR) algorithm, the aerosol size distribution (ASD) is retrieved in non-parametric approach. The direct problem is solved by the Anomalous Diffraction Approximation (ADA) and the Lambert–Beer Law. An optimal wavelength selection method is developed to improve the retrieval accuracy of the ASD. The proposed optimal wavelength set is selected by the method which can make the measurement signals sensitive to wavelength and decrease the degree of the ill-condition of coefficient matrix of linear systems effectively to enhance the anti-interference ability of retrieval results. Two common kinds of monomodal and bimodal ASDs, log-normal (L-N) and Gamma distributions, are estimated, respectively. Numerical tests show that the LSQR algorithm can be successfully applied to retrieve the ASD with high stability in the presence of random noise and low susceptibility to the shape of distributions. Finally, the experimental measurement ASD over Harbin in China is recovered reasonably. All the results confirm that the LSQR algorithm combined with the optimal wavelength selection method is an effective and reliable technique in non-parametric estimation of ASD.

On the effective refractive index of blood

We calculated the real and imaginary parts of the effective refractive index of blood as functions of wavelength from 400 to 800 nm; we employed van de Hulst’s theory, together with the anomalous diffraction approximation, for the calculation. We modelled blood as a mixture of plasma and erythrocytes. Our results indicate that erythrocyte orientation has a strong effect on , making blood an optically anisotropic medium except when the erythrocytes are randomly oriented. In the case in which their symmetry axis is perpendicular to the wave vector, equals the refractive index of plasma at certain wavelengths. Furthermore, the erythrocytes’ shape affects their contribution to in an important way, implying that studies on the effective refractive index of blood should avoid approximating them as spheres or spheroids. Finally, the effective refractive index of blood predicted by van de Hulst’s theory is different from what would be obtained by averaging the refractive indices of its constituents weighted by volume; such a volume-weighted average is appropriate only for haemolysed blood. We then measured the real part of the refractive index of various blood solutions using two different experimental setups. One of the most important results of our expriment is that is measurable to a good degree of precision even for undiluted blood, although not all measuring apparatuses are appropriate. The experimental data is self-consistent and in reasonable agreement with our theoretical calculations.

Monte Carlo implementation of Schiff׳s approximation for estimating radiative properties of homogeneous, simple-shaped and optically soft particles: Application to photosynthetic micro-organisms

In the present paper, Schiff׳s approximation is applied to the study of light scattering by large and optically-soft axisymmetric particles, with special attention to cylindrical and spheroidal photosynthetic micro-organisms. This approximation is similar to the anomalous diffraction approximation but includes a description of phase functions. Resulting formulations for the radiative properties are multidimensional integrals, the numerical resolution of which requires close attention. It is here argued that strong benefits can be expected from a statistical resolution by the Monte Carlo method. But designing such efficient Monte Carlo algorithms requires the development of non-standard algorithmic tricks using careful mathematical analysis of the integral formulations: the codes that we develop (and make available) include an original treatment of the nonlinearity in the differential scattering cross-section (squared modulus of the scattering amplitude) thanks to a double sampling procedure. This approach makes it possible to take advantage of recent methodological advances in the field of Monte Carlo methods, illustrated here by the estimation of sensitivities to parameters. Comparison with reference solutions provided by the T-Matrix method is presented whenever possible. Required geometric calculations are closely similar to those used in standard Monte Carlo codes for geometric optics by the computer-graphics community, i.e. calculation of intersections between rays and surfaces, which opens interesting perspectives for the treatment of particles with complex shapes.

Retrieval of aerosol size distribution using improved quantum-behaved particle swarm optimization on spectral extinction measurements

An improved quantum-behaved particle swarm optimization (IQPSO) algorithm is employed to determine aerosol size distribution (ASD). The direct problem is solved using the anomalous diffraction approximation and Lambert–Beer's Law. Compared with the standard particle swarm optimization algorithm, the stochastic particle size optimization algorithm and the original QPSO, our IQPSO has faster convergence speed and higher accuracy within a smaller number of generations. Optimization parameters for the IQPSO were also evaluated; we recommend using four measurement wavelengths and 50 particles. Size distributions of various aerosol types were estimated using the IQPSO under dependent and independent models. Finally, experimental ASDs at different locations in Harbin were recovered using the IQPSO. All our results confirm that the IQPSO algorithm is an effective and reliable technique for estimating ASD.

Inversion of particle size distribution by spectral extinction technique using the attractive and repulsive particle swarm optimization algorithm

The particle size distribution (PSD) plays an important role in environmental pollution detection and human health protection, such as fog, haze and soot. In this study, the Attractive and Repulsive Particle Swarm Optimization (ARPSO) algorithm and the basic PSO were applied to retrieve the PSD. The spectral extinction technique coupled with the Anomalous Diffraction Approximation (ADA) and the Lambert-Beer Law were employed to investigate the retrieval of the PSD. Three commonly used monomodal PSDs, i.e. the Rosin-Rammer (R-R) distribution, the normal (N-N) distribution, the logarithmic normal (L-N) distribution were studied in the dependent model. Then, an optimal wavelengths selection algorithm was proposed. To study the accuracy and robustness of the inverse results, some characteristic parameters were employed. The research revealed that the ARPSO showed more accurate and faster convergence rate than the basic PSO, even with random measurement error. Moreover, the investigation also demonstrated that the inverse results of four incident laser wavelengths showed more accurate and robust than those of two wavelengths. The research also found that if increasing the interval of the selected incident laser wavelengths, inverse results would show more accurate, even in the presence of random error.