Calculation Of Light Propagation Research Articles

Exclusive detection of cerebral hemodynamics in functional near-infrared spectroscopy by reflectance modulation of the scalp surface.

.Significance: Functional near-infrared spectroscopy (fNIRS) is a technique for detecting regional hemodynamic responses associated with neural activation in the cerebral cortex. The absorption changes due to hemodynamic changes in the scalp cause considerable signal contamination in the fNIRS measurement. A method for extracting hemodynamic changes in the cerebral tissue is required for reliable fNIRS measurement.Aim: To exclusively detect cerebral functional hemodynamic changes, we developed an fNIRS technique using reflectance modulation of the scalp surface.Approach: The theoretical feasibility of the proposed method was proven by a simulation calculation of light propagation. Its practical feasibility was evaluated by a phantom experiment and brain activation simulation mimicking human fNIRS experiments.Results: The simulation calculation revealed that the partial path length of the scalp was changed by reflectance modulation of the scalp surface. The influence of absorption change in the superficial layer was successfully reduced by the proposed method, using only measurement data, in the phantom experiment. The proposed method was applicable to human experiments of standard designs, achieving statistical significance within an acceptable experimental time-frame.Conclusions: Removal of the scalp hemodynamic effect by the proposed technique will increase the quality of fNIRS data, particularly in measurements in neonates and infants that typically would require a dense optode arrangement.

A set of basis functions to improve numerical calculation of Mie scattering in the Chandrasekhar-Sekera representation

Numerical calculations of light propagation in random media demand the multiply scattered Stokes intensities to be written in a common fixed reference. In multiple-scattering schemes, a particularly useful way to perform automatically these basis transformations between reference frames is to write the scattered intensities in the Chandrasekhar-Sekera representation. The main drawback with this representation is the necessity of numerical tests to deal with the limiting situations of the small particle (Rayleigh) and forward/backward scattering. Here, a new set of basis functions is presented to describe the scattering of light by spherical particles (Mie scattering) in the Chandrasekhar-Sekera representation. These basis functions can be implemented in a new algorithm to calculate the Mie scattering amplitudes, which leads straightforwardly to all the scattering quantities. In contrast to the traditional implementation, this set of basis functions implies to natural numerical convergence to the above mentioned limiting cases, which are thoroughly discussed.

Light propagation model of titanium dioxide suspensions in water using the radiative transfer equation

Constructions of numerical schemes for solving the radiative transfer equation (RTE) are crucial to evaluate light propagation inside photocatalytic systems. We develop accurate and efficient schemes of the three-dimensional and time-dependent RTE for numerical phantoms modeling aqueous titanium dioxide suspensions, in which the anisotropy of the forward-directed scattering varies and the strength of absorption is comparable to that of scattering. To improve the accuracy and efficiency of the numerical solutions, the forward-directed phase function is renormalized in the zeroth or first order with a small number of discrete angular directions. Then, we investigate the influences of the forward-directed scattering on the numerical solutions by comparing with the analytical solutions. The investigation shows that with the anisotropy factor less than approximately 0.7 corresponding to the moderate forward-directed scattering, the numerical solutions of the RTE using the both of the zeroth and first order renormalization approaches are accurate due to the reductions of the numerical errors of the phase function. With the anisotropy factor more than approximately 0.7 corresponding to the highly forward-directed scattering, the first order renormalization approach still provides the accurate results, while the zeroth order approach does not due to the large errors of the phase function. These results suggest that the developed scheme using the first order renormalization can provide accurate and efficient calculations of light propagation in photocatalytic systems.

Toward real-time diffuse optical tomography: accelerating light propagation modeling employing parallel computing on GPU and CPU.

Parameter recovery in diffuse optical tomography is a computationally expensive algorithm, especially when used for large and complex volumes, as in the case of human brain functional imaging. The modeling of light propagation, also known as the forward problem, is the computational bottleneck of the recovery algorithm, whereby the lack of a real-time solution is impeding practical and clinical applications. The objective of this work is the acceleration of the forward model, within a diffusion approximation-based finite-element modeling framework, employing parallelization to expedite the calculation of light propagation in realistic adult head models. The proposed methodology is applicable for modeling both continuous wave and frequency-domain systems with the results demonstrating a 10-fold speed increase when GPU architectures are available, while maintaining high accuracy. It is shown that, for a very high-resolution finite-element model of the adult human head with ∼600,000 nodes, consisting of heterogeneous layers, light propagation can be calculated at ∼0.25 s/excitation source.

Resonant-state expansion of light propagation in nonuniform waveguides

A new rigorous approach for precise and efficient calculation of light propagation along non-uniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoing-wave boundary conditions, form a natural basis for expansion of the local electromagnetic field. Using such an expansion at fixed frequency, we convert the wave equation for light propagation in a non-uniform waveguide into an ordinary second-order matrix differential equation for the expansion coefficients depending on the coordinate along the waveguide. We illustrate the method on several examples of non-uniform planar waveguides and evaluate its efficiency compared to the aperiodic Fourier modal method and the finite element method, showing improvements of one to four orders of magnitude. A similar improvement can be expected also for applications in other fields of physics showing wave phenomena, such as acoustics and quantum mechanics.

The concentration of energy from Edge Lasers by Diffractive Optical Component

The aim of this paper is to design a diffractive optical element based on the laser junction numerical model. We assumed a ?long? laser junction emitting quasi-monochromatic, spatially incoherent light that corresponds to the high power laser. Diffractive optics approach can be used due to the narrowband illumination. The especially designed numerical junction model was experimentally verified. Then a numerically designed diffractive focusing element was manufactured and tested in the experimental setup. This paper includes theoretical investigations, numerical modeling as well as experimental data. Full Text: PDF ReferencesE. Wolf, "New theory of partial coherence in the space?frequency domain. Part I: spectra and cross spectra of steady-state sources", J. Opt. Soc. Am. 72, 343 (1982). CrossRef E. Wolf, "Coherence theory of laser resonator modes", J. Opt. Soc. Am. A 1, 541 (1984). CrossRef A. Naqwi and F. Durst, "Focusing of diode laser beams: a simple mathematical model", Appl. Opt. 29, 1780 (1990) CrossRef J. Yang, T. Chen, G. Ding and X. Yuan, "Focusing of diode laser beams: a partially coherent Lorentz model", Proc. SPIE 6824, 68240A (2007); CrossRef X. Zeng and A. Naqwi, "Far-field distribution of double-heterostructure diode laser beams", Appl. Opt. 32, 4491 (1993). CrossRef Y. Li and J. Katz, "Nonparaxial analysis of the far-field radiation patterns of double-heterostructure lasers", Appl. Opt. 35, 1442 (1996). CrossRef X. Zeng, Z. Feng, and Y. An, "Far-field expression of a high-power laser diode", Appl. Opt. 43, 5168 (2004) CrossRef J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, "Shifted-elementary-mode representation for partially coherent vectorial fields", J. Opt. Soc. Am. A 27, 2004 (2010). CrossRef J. Turunen, "Elementary-field representations in partially coherent optics", J. Mod. Opt. 58, 509 (2011). CrossRef H. Partanen, J. Tervo, and J. Turunen, "Spatial coherence of broad-area laser diodes", Appl. Opt. 52, 3221 (2013) CrossRef M. Sypek, "Light propagation in the Fresnel region. New numerical approach", Opt. Commun., 116, 43 (1995) CrossRef Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, C. Gomez-Reino, "Non-paraxial analytical solution for the generation of focal curves", J. Mod. Opt., 43, 617 (1996) CrossRef M. Sypek, C. Prokopowicz, M. Gorecki, "Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation", Opt. Eng., 42, 3158 (2003) CrossRef C. Prokopowicz, "Numerical calculation of light propagation in off-axis region", Proc. SPIE, 5484, 482 (2004). CrossRef A. Sobczyk, Z. Jaroszewicz, A. Kolodziejczyk, A. Kowalik, Cz. Prokopowicz, M. Sypek, "Nonparaxial anamorphic diffractive lenses", J. Opt., 15, 025702 (1-5) (2013) CrossRef

Optics of carbon fiber-reinforced plastics – A theoretical and an experimental study

Laser processing of carbon fiber-reinforced plastics (CFRP) as well as their design optimization are strongly emerging fields. As the optics of CFRP is still rather unknown, the optical behavior of CFRP was investigated in this study. Different simulation models were implemented to simulate reflectance from CFRP samples as well as distribution and absorption of light within these samples. The methods include an analytical solution of Maxwell׳s equations and Monte Carlo solutions of the radiative transfer theory. We show that strong inaccurracies occur, if light propagation in CFRP is modeled using the radiative transfer theory. Therefore, the solution of Maxwell׳s equations is the method of choice for calculation of light propagation in CFRP. Furthermore, measurements of the reflectance of light from CFRP were performed and compared to the simulations for investigation of the optical behavior. Information on the refractive index of carbon fibers was obtained via goniometric measurements. The amount of reflected light was determined as 6.05±0.38% for light polarized parallel to the fiber direction, while it was 3.65±0.41% for light polarized perpendicular to the fiber direction in case of laser-processed CFRP.

Occlusion culling for computer generated hologram based on ray-wavefront conversion

We propose a new method for occlusion culling in the computation of a hologram based on the mutual conversion between light-rays and wavefront. Since the occlusion culling is performed with light-ray information, conventional rendering techniques such as ray-tracing or image-based rendering can be employed. On the other hand, the wavefront is derived for the calculation of light propagation, the hologram of 3-D objects can be obtained in high accuracy. In the numerical experiment, we demonstrate that our approach can reproduce a high-resolution image for deep 3-D scene with correct occlusion effect between plural objects.

Reference calculation of light propagation between parallel planes of different sizes and sampling rates

The article deals with a method of calculation of off-axis light propagation between parallel planes using discretization of the Rayleigh-Sommerfeld integral and its implementation by fast convolution. It analyses zero-padding in case of different plane sizes. In case of memory restrictions, it suggests splitting the calculation into tiles and shows that splitting leads to a faster calculation when plane sizes are a lot different. Next, it suggests how to calculate propagation in case of different sampling rates by splitting planes into interleaved tiles and shows this to be faster than zero-padding and direct calculation. Neither the speedup nor memory-saving method decreases accuracy; the aim of the proposed method is to provide reference data that can be compared to the results of faster and less precise methods.

Improved method for computing of light-matter interaction in multilayer corrugated structures

An improved method for the calculation of light-matter interaction that appears with the light propagation through multilayer periodically corrugated structures consisting of any dielectric or absorptive media is reported. The method is based on the differential formalism for a system of Maxwell's equations when the boundary conditions are simplified by the introduction of a curvilinear nonorthogonal coordinate system. The solution for electromagnetic fields was written in the form of the superposition of partial plane waves. The obtained method essentially reduces computation time and increases accuracy compared with the Chandezon method. For a numerical demonstration of the proposed method, calculation of long-range surface plasmon polaritons was performed. The presented method can be enhanced for calculations of light propagation through thin absorptive films with various periodic profiles at both film interfaces.

Finite-difference time-domain method calculation of light propagation through H-PDLC

Presented is the study of the diffraction properties of transmission holographic polymer dispersed liquid crystal (H-PDLC) grating. We constructed a two-dimensional model of H-PDLC film with cylindrical LC droplets. Director distribution inside LC droplets was calculated using the Monte-Carlo method. To calculate light propagation through the film we have solved numerically the Maxwell equations using the finite- difference time-domain method (FDTD). The FDTD analysis of diffraction was performed for s- and p-polarized incident light. Externally applied electric field influence on the diffraction efficiency was studied.

Accurate and efficient calculation of light propagation in one-dimensional inhomogeneous anisotropic media through extrapolation

Berreman's 4 x 4 matrix approach has been generally applied to calculating light propagation in one-dimensional (1-D) inhomogeneous anisotropic media. In numerical calculations the propagator (propagation matrix) of whole 1-D inhomogeneous media is approximated by a stack of N homogeneous slab propagators. We analyze the error of the slab propagator in this slab approximation and show it is correct through the order 1/N(2). By using the extrapolation approach, we eliminate the leading error terms of the product (total propagator) of N homogeneous slab propagators successively. Numerical tests for a cholesteric liquid crystal show that the total propagator constructed through extrapolation is of higher accuracy and efficiency than Berreman's and Abdulhalim's or faster 4 x 4 total propagators.

Light propagation in finite and infinite photonic crystals: The recursive Green’s function technique

We report a computational method based on the recursive Green's function technique for calculation of light propagation in photonic crystal structures. The advantage of this method in comparison to the conventional finite-difference time domain (FDTD) technique is that it computes Green's function of the photonic structure recursively by adding slice by slice on the basis of Dyson's equation. This eliminates the need for storage of the wave function in the whole structure, which obviously strongly relaxes the memory requirements and enhances the computational speed. The second advantage of this method is that it can easily account for the infinite extension of the structure both into air and into the space occupied by the photonic crystal by making use of the so-called ``surface Green's functions.'' This eliminates the spurious solutions (often present in the conventional FDTD methods) related to, e.g., waves reflected from the boundaries defining the computational domain. The developed method has been applied to study scattering and propagation of the electromagnetic waves in the photonic band-gap structures including cavities and waveguides. Particular attention has been paid to surface modes residing on a termination of a semi-infinite photonic crystal. We demonstrate that coupling of the surface states with incoming radiation may result in enhanced intensity of an electromagnetic field on the surface and very high $Q$ factor of the surface state. This effect can be employed as an operational principle for surface-mode lasers and sensors.

A fast computational method for computer‐generated Fourier hologram using patch model

AbstractComputer‐generated holography is a technique for displaying a three‐dimensional image from a virtual object inside the computer. It has drawn attention as a display format to satisfy three‐dimensional visual characteristics. However, one problem of the method is the enormous amount of time for calculation of light propagation needed in the generation of holograms. In this paper, as a method of modeling objects, a patch model that defines an object in terms of basic drawings is used. A method is proposed to calculate holograms at high speed from these models. Further, the algorithm is verified by computer simulation. The results of an optical experiment with the hologram fabricated by this proposed method are also reported. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 85(11): 16–24, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.10051

Forward Modelling of Light Propagation in a Brain.

Near infrared spectroscopy and imaging have been applied to measure brain activities. The light scattering in the tissue causes ambiguity in the volume of tissue sampled with a source-detector pair of near infrared instruments and hence theoretical modelling to obtain light propagation in the head is very important for the brain activity measurements. In this paper two theoretical methods, Monte Carlo simulation and hybrid Monte Carlo-diffusion method, for calculation of light propagation in the brain are reviewed. The light propagation in the brain is strongly affected by the heterogeneity of tissue, especially the presence of low scattering cerebrospinal fluid (CSF). The results indicate that the presence of the CSF layer improves the sensitivity of the optical signal to brain activities.

Optical Properties of Hybrid Aligned Short Pitch Cholesterics

Diffractive optical properties of selective reflection in short pitch cholesterics are considered in the confined geometry with different boundary conditions at upper and lower substrates. The main difference in the intensities of back selective reflection at the opposite interfaces has been detected. Additionally new stable cholesteric textures were found and explored. The asymmetric structure obtained may be used as non-reciprocal dichroic element. A new method for calculation of light propagation in stratified inhomogeneous anisotropic media, where optical properties may vary along three major axis is proposed and applied for continuous distribution function calculation of helical axes within hybrid aligned cholesteric layer.

Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues

We analyse the limits of the diffusion approximation to the time-independent equation of radiative transfer for homogeneous and heterogeneous biological media. Analytical calculations and finite-difference simulations based on diffusion theory are compared with discrete-ordinate, finite-difference transport calculations. The influence of the ratio of absorption and transport scattering coefficient on the accuracy of the diffusion approximation are quantified and different definitions for the diffusion coefficient, D, are discussed. We also address effects caused by void-like heterogeneities in which absorption and scattering are very small compared with the surrounding medium. Based on results for simple homogeneous and heterogeneous systems, we analyse diffusion and transport calculation of light propagation in the human brain. For these simulations we convert density maps obtained from magnetic resonance imaging (MRI) to optical-parameter maps ( and ) of the brain. We show that diffusion theory fails to describe accurately light propagation in highly absorbing regions, such as haematoma, and void-like spaces, such as the ventricles and the subarachnoid space.

Simulation of light propagation in optical linear and nonlinear resist layers by finite difference beam propagation and other methods

This article presents a new method for the calculation of light propagation in resist layers and compares it with scaled defocus and transfer matrix algorithms. Our method is not restricted to homogeneous resist and substrate layers. For the first time, a simulation of focus drilling is presented.

Rigorous Calculation of Light Propagation in Proton-Exchanged LiNbO3 Waveguides

Rigorous Calculation of Light Propagation in Proton-Exchanged LiNbO3 Waveguides

Multiple Scattering Calculations of Light Propagation in Ocean Water

Monte Carlo techniques have been used to simulate the propagation of light from sources with a variety of beam patterns. Basic scattering and absorption properties of ocean water are used to determine the probability distributions required for the calculations. The results of the computer simulation have been summarized as sets of effective attenuation coefficients. The use of these coefficients permits simple engineering equations to be formulated that describe the performance of underwater imaging systems under conditions where multiple scattering is an important factor. Comparisons with published experimental measurements and internal consistency checks indicate the validity of the simulation model.