Discrete-dipole approximation for periodic targets: theory and tests

The discrete-dipole approximation (DDA) is a powerful method for calculating absorption and scattering by targets that have sizes smaller than or comparable to the wavelength of the incident radiation. The DDA can be extended to targets that are singly or doubly periodic. We generalize the scattering amplitude matrix and the 4 x 4 Mueller matrix to describe scattering by singly and doubly periodic targets and show how these matrices can be calculated using the DDA. The accuracy of DDA calculations using the open-source code DDSCAT is demonstrated by comparison with exact results for infinite cylinders and infinite slabs. A method for using the DDA solution to obtain fields within and near the target is presented, with results shown for infinite slabs.     

Discrete-dipole-approximation-based light-scattering calculations for particles with a real refractive index smaller than unity

To assess the efficiency and accuracy of light-scattering calculations based on the discrete dipole approximation (DDA) for particles with a real relative refractive index smaller than unity, differential scattering cross sections and scattering efficiency factors were calculated for spherical particles. We performed the calculations for oxide particles and voids embedded in glass and silicon, using the exact scattering theory (Mie scattering) and the DDA. A comparison of the results shows that the DDA is applicable in the above refractive-index regime, and the conditions under which DDA-based calculations can provide scattering data with good accuracy are discussed.     

Evaluation of optical coherence quantitation of analytes in turbid media by use of two wavelengths

We introduce a novel method for determining analyte concentration as a function of depth in a highly scattering media by use of a dual-wavelength optical coherence tomography system. We account for the effect of scattering on the measured attenuation by using a second wavelength that is not absorbed by the sample. We assess the applicability of this technique by measuring the concentration of water in an Intralipid phantom, using a probe wavelength of 1.53 mum and a reference wavelength of 1.31 mum. The results of our study show a strong correlation between the measured absorption and the water content of the sample. The accuracy of the technique, however, was limited by the dominance of scattering over absorption in the turbid media. Thus, although the effects of scattering were minimized, significant errors remained in the calculated absorption values. More-accurate results could be obtained with the use of more powerful superluminescent diodes and a choice of wavelengths at which absorption effects are more significant relative to scattering.     

Light scattering and absorption caused by bacterial activity in water

There is a growing class of elementary particle detectors, large-water ?erenkov detectors, that have a body of water (thousands of tons) as a sensitive medium. Particles are detected when they interact with the water and produce ?erenkov light, so detection efficiency relies on the transparency of the water. These detectors are active typically for many years, so biological activity (primarily bacterial growth) is one of the means by which the transparency of the water may be reduced. We present the results of a measurement of light scattering and absorption from a population of Escherichia coli in water, which is used as a model for bacteria in general. One can separate the scattering and absorption by varying the refractive index of the medium by using a solute of high molecular weight. We show that the results can be understood simply in terms of light scattering from small spheres (radius ≈ wavelength) with an effective refractive index, n(b), plus a small amount of absorption in the ultraviolet. We compare his scattering with Rayleigh scattering in pure water.     

Irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: Raman-scattering effects

We modify an algorithm for retrieving the absorption (a) and backscattering (b(b)) coefficient profiles in natural waters by inverting profiles of downwelling and upwelling irradiance so as to include the presence of Raman scattering. For a given wavelength of interest, lambda, the light field at the appropriate Raman excitation wavelength lambda(e) is first inverted to obtain the Raman source function at lambda. Starting from estimates of the inherent optical properties at lambda, the contribution to the irradiances at lambda from Raman scattering is then estimated and subtracted from the total irradiances to obtain the elastically scattered irradiances. We then inverted the elastically scattered irradiances to find new estimates of a and b(b) using our original method [Appl. Opt. 37, 3886 (1998)]. The algorithm then operates iteratively: The new estimates are used with the Raman source function to derive a new estimate of the Raman contribution, etc. Sample results are provided that demonstrate the working of the algorithm and show that the absorption and scattering coefficients can be retrieved with accuracies similar to those in the absence of Raman scattering down to depths at which the light field is significantly perturbed by it, e.g., with ~90% of the upwelling light field originating from Raman scattering.     

Experimental and theoretical study of light scattering by individual mature red blood cells by use of scanning flow cytometry and a discrete dipole approximation

Elastic light scattering by mature red blood cells (RBCs) was theoretically and experimentally analyzed by use of the discrete dipole approximation (DDA) and scanning flow cytometry (SFC), respectively. SFC permits measurement of the angular dependence of the light-scattering intensity (indicatrix) of single particles. A mature RBC is modeled as a biconcave disk in DDA simulations of light scattering. We have studied the effect of RBC orientation related to the direction of the light incident upon the indicatrix. Numerical calculations of indicatrices for several axis ratios and volumes of RBC have been carried out. Comparison of the simulated indicatrices and indicatrices measured by SFC showed good agreement, validating the biconcave disk model for a mature RBC. We simulated the light-scattering output signals from the SFC with the DDA for RBCs modeled as a disk-sphere and as an oblate spheroid. The biconcave disk, the disk-sphere, and the oblate spheroid models have been compared for two orientations, i.e., face-on and rim-on incidence, relative to the direction of the incident beam. Only the oblate spheroid model for rim-on incidence gives results similar to those of the rigorous biconcave disk model.     

Diffuse optical tomography with spectral constraints and wavelength optimization

We present an algorithm that explicitly utilizes the wavelength dependence of tissue optical properties for diffuse optical tomography. We have previously shown that the method gives superior separation of absorption and scattering. Here the technique is described and tested in detail, and optimum wavelength sets for a broad range of chromophore combinations are discovered and analyzed.     

Variability of light absorption by aquatic particles in the near-infrared spectral region

We have measured the light absorption of a set of particle suspensions of varying nature (pure minerals, particulate standards, aquatic particles) using a double-beam spectrophotometer with a 15-cm-diameter integrating sphere. The sample was located inside the sphere so as to minimize the effect of light scattering by the particles. The results obtained showed highly variable absorption in the near-IR region of the wavelength spectrum. The same particle samples were deposited on glass-fiber filters, and their absorption was measured by the transmittance-reflectance method, based on a theoretical model that corrects for the effect of light scattering. The good agreement found between the results of the measurements carried out inside the sphere and by the transmittance-reflectance method confirms the validity of the scattering correction included in the above method.     

Estimation of scattering error in spectrophotometric measurements of light absorption by aquatic particles from three-dimensional radiative transfer simulations

We present an approach based on three-dimensional Monte Carlo radiative transfer simulations for estimating scattering error in measurements of light absorption by aquatic particles with a typical laboratory double-beam spectrophotometer. The scattering error is calculated by combining the weighting function describing the angular distribution of photon losses that are due to scattering on suspended particles with the volume scattering function of particles. We applied this method to absorption measurements made on marine phytoplankton, a diatom Thalassiosira pseudonana and a cyanobacterium Synechococcus. Assuming that the scattering phase function is described by the Henyey-Greenstein formula, we determined the backscatter probability of phytoplankton, which yields the best correction for scattering error at a light wavelength of 750 nm, where true absorption is null. The backscattering ratio estimated for both phytoplankton species is significantly higher than previously reported data based on Mie-scattering calculations for homogeneous spheres. Depending on the type of particles, the corrected absorption spectra obtained with our method may be similar or significantly different from spectra obtained with the null-point correction based on wavelength-independent scattering error.     

Simultaneous reconstruction of absorption and scattering maps with ultrasound localization: feasibility study using transmission geometry

We report the experimental results of the simultaneous reconstruction of absorption and scattering coefficient maps with ultrasound localization. Near-infrared (NIR) data were obtained from frequency domain and dc systems with source and detector fibers configured in transmission geometry. High- or low-contrast targets located close to either the boundary or the center of the turbid medium were reconstructed by using NIR data only and NIR data with ultrasound localization. Results show that the mean reconstructed absorption coefficient and the spatial distribution of the absorption map have been improved significantly with ultrasound localization. The improvements in the mean scattering coefficient and the spatial distribution of the scattering coefficient are moderate. When both the absorption and the scattering coefficients are reconstructed the performance of the frequency-domain systemis much better than that of the dc system.     

Simultaneous measurement of changes in light absorption due to the reduction of cytochrome c oxidase and light scattering in rat brains during loss of tissue viability

We performed the simultaneous measurement of intrinsic optical signals (IOSs) related to metabolic activity and cellular and subcellular morphological characteristics, i.e., light scattering for a rat global ischemic brain model made by rapidly removing blood by saline infusion. The signals were measured on the basis of multiwavelength diffuse reflectances in which 605 and 830 nm were used to detect the IOSs that are thought to be dominantly affected by redox changes of heme aa(3) and CuA in cytochrome c oxidase (CcO), respectively. For measuring the scattering signal, the wavelength that was found to be most insensitive to the absorption changes, e.g., approximately 620 nm, was used. The measurements suggested that an increase in the absorption due to reduction of heme aa(3) occurred soon after blood clearance, and this was followed by a large triphasic change in light scattering, during which time a decrease in the absorption due to reduction of CuA occurred. Through the triphasic scattering change, scattering signals increased by 5.2 +/- 1.5% (n = 5), and the increase in light scattering showed significant correlation with both the reflectance intensity changes at 605 and 830 nm. This suggests that morphological changes in cells correlate with reductions of heme aa(3) and CuA. Histological analysis of tissue after the triphasic scattering change showed no alteration in either the nuclei or the cytoskeleton, but electron microscopic observation revealed deformed, enlarged mitochondria and expanded dendrites. These findings suggest that the simultaneous measurement of absorption signals related to the redox changes in the CcO and the scattering signal is useful for monitoring tissue viability in the brain.     

Changes in optical properties of rat cerebral cortical slices during oxygen glucose deprivation

We simultaneously measured the diffuse reflectance spectra and transmittance spectra of in vitro rat cerebral cortical tissue slices perfused with artificial cerebrospinal fluid (aCSF) in the wavelength range from 500 to 900 nm. An ischemia-like condition in the cortical tissue was induced by oxygen/glucose deprivation (OGD) of the aCSF. Diffuse reflectance and transmittance of the cortical slices were decreased and increased, respectively, during OGD. Spectral data of reduced scattering coefficients and absorption coefficients were estimated by the inverse Monte Carlo simulation for light transport in tissue. As with OGD, significant decrease of the reduced scattering coefficients and alteration of the absorption coefficient spectrum were observed over the measured wavelength range. The mean maximum amplitudes of change in the absorption coefficient at 520, 550, 605, and 830 nm were 0.33 ± 0.14, 0.30 ± 0.12, 0.30 ± 0.14, and -0.04 ± 0.16, respectively, whereas those in the reduced scattering coefficient at 520, 550, 605, and 830 nm were -0.37 ± 0.08, -0.38 ± 0.08, -0.38 ± 0.08, and -0.39 ± 0.08. Variations in the reduced scattering coefficients implied cell deformation mainly due to cell swelling, whereas those in the absorption spectra indicated reductions in heme aa(3) and CuA in cytochrome c oxidase and cytochrome c.     

Design and testing of a white-light, steady-state diffuse reflectance spectrometer for determination of optical properties of highly scattering systems

We present a steady-state radially resolved diffuse reflectance spectrometer capable of measuring the absorption and transport scattering spectra of tissue-simulating phantoms over an adjustable 170-nm wavelength interval in the visible and near infrared. Measurements in a variety of phantoms are demonstrated over the relevant range of tissue optical properties, and the accuracy of the instrument is found to be approximately 10% in both scattering and absorption. Monte Carlo simulations designed to test the accuracy of the instrument are presented that support the experimental findings.     

Blood oxygenation measurements by multichannel reflectometry on the venous and arterial structures of the retina

The aim of the present study was to propose a model and a method to derive the oxyhemoglobin blood content in the retinal veins and arteries by full spectrum reflectometry measurements in the spectral zone from 430 to 680?nm. We proposed a mathematical equation expressed as a linear combination of two terms S(OHb)(λ) and S(Hb)(λ) representing the normalized spectral absorption functions of the hemoglobin and the oxyhemoglobin, one term λ(-n) representing the ocular media absorption with scattering, and a family of multi-Gaussian functions, which usefully compensate for the noncompatibility of the model and the experimental data in the red spectral zone. The present paper suggests that the spectral reflection function in the area from 520 to 580?nm is optimal in calculating the oxyhemoglobin concentration of the blood contained in the endothelial structures of retinal vessels. The model calculation needs a function (1/λ)(-n) that corrects for the ocular media absorption and light scattering on the vessels' structures. For the spectral area of lights with wavelength larger than 580?nm, the reflected light represents mainly the light scattering on the red blood cells.     

Evidence for wavelength dependence of the scattering phase function and its implication for modeling radiance transfer in shelf seas

More than 90% of stations from the Irish and Celtic Seas are found to have significantly higher back-scattering ratios in the blue (470 nm) than in the red (676 nm) wave band. Attempts to obtain optical closure by use of radiance transfer modeling were least successful for stations at which backscattering ratios are most strongly wavelength dependent. Significantly improved radiance transfer simulation results were obtained with a modified scattering correction algorithm for AC-9 absorption measurements that took wavelength dependency in the scattering phase function into account.     

Semi-empirical correction algorithm for AC-9 measurements in a coccolithophore bloom

Values for the coefficients of absorption (a) and attenuation (c) obtained from AC-9 measurements in coccolithophore blooms do not provide satisfactory inputs for radiance transfer models. We have therefore modified the standard AC-9 scattering correction algorithm by including an extra term, F(lambda, lambda(r)), which allows for possible wavelength dependence in the scattering phase function. We estimated the magnitude of F(lambda, lambda(r)), which is unity in the standard algorithm, by adjusting the absorption and scattering values in Hydrolight radiance transfer calculations until the depth profiles of downward irradiance (E(d)) and upward radiance (L(u)) matched those measured in situ. The modified algorithm was tested with data from a phytoplankton bloom dominated by the coccolithophore Emiliania huxleyi, which occurred in the western English Channel in May 2001. In this paper, we only have sufficient data to adequately constrain the radiance transfer model in one wave band centered on 488 ma. A single value of F(lambda, lambda(r)) = 1.4 was found to produce satisfactory agreement between modeled and observed profiles at four widely spaced stations within the bloom. Measurements of the ratio of backscattering (b(b)) to total scattering (b) showed significant wavelength dependence at these stations.     

Radiation forces in the discrete-dipole approximation

The theory of the discrete-dipole approximation (DDA) for light scattering is extended to allow for the calculation of radiation forces on each dipole in the DDA model. Starting with the theory of Draine and Weingartner [Astrophys. J. 470, 551 (1996)] we derive an expression for the radiation force on each dipole. These expressions are reformulated into discrete convolutions, allowing for an efficient, O(N logN) evaluation of the forces. The total radiation pressure on the particle is obtained by summation of the individual forces. The theory is tested on spherical particles. The resulting accumulated radiation forces are compared with Mie theory. The accuracy is within the order of a few percent, i.e., comparable with that obtained for extinction cross sections calculated with the DDA.     

Discrete dipole moment method for calculation of the T matrix for nonspherical particles

A computational method, based on a moment solution to the discrete dipole approximation (DDA) interaction equations, is proposed for calculation of the T matrix of arbitrary-shaped particles. It is shown that the method will automatically provide the conservation-of-energy and origin-invariance properties required of the T matrix. Furthermore, the method is significantly faster than a T-matrix calculation by direct inversion of the DDA equations. Because the method retains the dipole lattice representation of the particle, it can be applied with relative ease to particles with irregular shapes-although in the same respect it will not automatically simplify for axisymmetric particles. Calculations of scattering matrix distributions, in fixed and random orientations, are made for tetrahedron, cylindrical, and prolate spheroid particle shapes and compared with DDA and extended boundary condition method results.     

Measurement of the lidar ratio for atmospheric aerosols with a 180 degrees backscatter nephelometer

Laser radar (lidar) can be used to estimate atmospheric extinction coefficients that are due to aerosols if the ratio between optical extinction and 180 degrees backscatter (the lidar ratio) at the laser wavelength is known or if Raman or high spectral resolution data are available. Most lidar instruments, however, do not have Raman or high spectral resolution capability, which makes knowledge of the lidar ratio essential. We have modified an integrating nephelometer, which measures the scattering component of light extinction, by addition of a backward-pointing laser light source such that the detected light corresponds to integrated scattering over 176-178 degrees at a common lidar wavelength of 532 nm. Mie calculations indicate that the detected quantity is an excellent proxy for 180 degrees backscatter. When combined with existing techniques for measuring total scattering and absorption by particles, the new device permits a direct determination of the lidar ratio. A four-point calibration, run by filling the enclosed sample volume with particle-free gases of a known scattering coefficient, indicates a linear response and calibration reproducibility to within 4%. The instrument has a detection limit of 1.5 x 10(-7) m(-1) sr(-1) (~10% of Rayleigh scattering by air at STP) for a 5-min average and is suitable for ground and mobile/airborne surveys. Initial field measurements yielded a lidar ratio of ~20 for marine aerosols and ~60-70 for continental aerosols, with an uncertainty of ~20%.     

Broadband Light Absorption and Efficient Charge Separation Using a Light Scattering Layer with Mixed Cavities for High‐Performance Perovskite Photovoltaic Cells with Stability

CH₃NH₃PbI₃ is one of the promising light sensitizers for perovskite photovoltaic cells, but a thick layer is required to enhance light absorption in the long‐wavelength regime ranging from PbI₂ absorption edge (500 nm) to its optical band‐gap edge (780 nm) in visible light. Meanwhile, the thick perovskite layer suppresses visible‐light absorption in the short wavelengths below 500 nm and charge extraction capability of electron–hole pairs produced upon light absorption. Herein, we find that a new light scattering layer with the mixed cavities of sizes in 100 and 200 nm between transparent fluorine‐doped tin oxide and mesoporous titanium dioxide electron transport layer enables full absorption of short‐wavelength photons (λ < 500 nm) to the perovskite along with enhanced absorption of long‐wavelength photons (500 nm < λ < 780 nm). Moreover, the light‐driven electric field is proven to allow efficient charge extraction upon light absorption, thereby leading to the increased photocurrent density as well as the fill factor prompted by the slow recombination rate. Additionally, the photocurrent density of the cell with a light scattering layer of mixed cavities is stabilized due to suppressed charge accumulation. Consequently, this work provides a new route to realize broadband light harvesting of visible light for high‐performance perovskite photovoltaic cells.