Biogeo-optics: particle optical properties and the partitioning of the spectral scattering coefficient of ocean waters

We propose a direct method of partitioning the particulate spectral scattering coefficient of the marine hydrosol based on the concurrent determination of the concentrations of particulate mineral and organic matter (the total mass of optically active scattering material exclusive of water) with the particulate spectral scattering coefficient. For this we derive a Model II multiple linear regression model. The multiple linear regression of the particulate spectral scattering coefficient against the independent variables, the concentrations of particulate inorganic matter and particulate organic matter, yields their mass-specific spectral scattering cross sections. The mass-specific spectral scattering cross section is simply the particle scattering cross section normalized to the particle mass, a fundamental optical efficiency parameter for the attenuation of electromagnetic radiation [Absorption and Scattering of Light by Small Particles, (Wiley-Interscience, 1983), pp. 80-81, 289]. It is possible to infer the optical properties of the suspended matter from the mass-specific spectral scattering cross sections. From these cross sections we partition the particulate spectral scattering coefficient into its major components.     

A scattering problem by means of the spectral representation of Green's function for a layered acoustic half-space

 The problem in this paper is for scattering waves caused by an object and a plane wave in a layered acoustic half space. The boundary integral equation method as well as the spectral representation of Green's function for a layered acoustic half space are introduced to the present analyses. The spectral form of Green's function developed here is expressed in terms of the eigenfunctions for the point and the continuous spectra, that is the extension form of Green's function expressed by Ewing, Jardetsky and Press (1957). The advantage of the spectral representation of Green's function is that it enables us to decompose the scattering waves into eigenfunctions for the layered medium. Several numerical calculations are carried out to examine the efficiency of the present method as well as the properties of the scattering waves. According to the numerical results, the spectral form of Green's function provides accurate values and is applicable to the boundary element analysis for a layered medium. The spectral structures of the scattering waves are also found to be able to explain their properties. Received 2 November 1999     

Radiative properties of dense nanofluids

The radiative properties of dense nanofluids are investigated. For nanofluids, scattering and absorbing of electromagnetic waves by nanoparticles, as well as light absorption by the matrix/fluid in which the nanoparticles are suspended, should be considered. We compare five models for predicting apparent radiative properties of nanoparticulate media and evaluate their applicability. Using spectral absorption and scattering coefficients predicted by different models, we compute the apparent transmittance of a nanofluid layer, including multiple reflecting interfaces bounding the layer, and compare the model predictions with experimental results from the literature. Finally, we propose a new method to calculate the spectral radiative properties of dense nanofluids that shows quantitatively good agreement with the experimental results.     

Inverse spectral problem for Dirac operator with discontinuous coefficient and polynomials in boundary condition

In this work, the inverse scattering problem for Dirac equations system with discontinuous coefficient and higher order polynomials of spectral parameter in the boundary condition is considered. The scattering function of the problem is defined, and its properties are investigated. The Marchenko-type main equation is obtained and it is shown that the potential is uniquely recovered by the scattering function. A generalization of Marchenko method is given for a class of Dirac operator.     

Radiative properties of snow for clear sky solar radiation

Spectral and integrated radiative properties (reflection, transmission, and the rate of heating) of finegrained wind-packed snow typical of subpolar regions are studied through a model taking into account surface reflection and volumetric multiple scattering. The surface reflection is modeled by a bidirectional reflectance distribution function applicable to powdered dielectric material. For the volumetric multiple scattering, the radiative transfer equation designed for strongly asymmetric scattering is solved. All multiple scattering parameters (single scattering albedo, various moments of the scattering phase function, and optical depth) are related to measurable physical characteristics (density, grain size, and the absorption coefficient of pure ice).Parameterized atmospheric spectral transmission coefficients for scattering and absorption by aerosols and gases are used to obtain the direct and diffuse components of solar flux, incident on the snow-cover. Calculated values of spectral and integrated visible and near infrared reflection and flux attenuation coefficients of snow are compared with observations. The rate of radiative heating at different depths within the snowcover is calculated from the net flux divergence. It is shown that the conventional method of calculating this rate using measured bulk extinction coefficients grossly underestimates the amount of heating within the top few millimeters. This study provides a better overall understanding of the radiative properties of snow under clear sky conditions in terms of the physical characteristics of the snowcover.     

MADSTRESS: a linear approach for evaluating scattering and absorption coefficients of samples measured using time-resolved spectroscopy in reflection

Time-resolved spectroscopy is a powerful technique permitting the separation of the scattering properties from the chemical absorption properties of a sample. The reduced scattering coefficient and the absorption coefficient are usually obtained by fitting diffusion or Monte Carlo models to the measured data using numerical optimization techniques. However, these methods do not take the spectral dimension of the data into account during the evaluation procedure, but evaluate each wavelength separately. A procedure involving multivariate methods may seem more appealing for people used to handling conventional near-infrared data. In this study we present a new method for processing TRS spectra in order to compute the absorption and reduced scattering coefficients. This approach, MADSTRESS, is based on linear regression and a two-dimensional (2D) interpolation procedure. The method has allowed us to calculate absorption and scattering coefficients of apples and fructose powder. The accuracy of the method was good enough to provide the identification of fructose absorption peaks in apple absorption spectra and the construction of a calibration model predicting the sugar content of apples.     

Scattering of light from quasi-homogeneous sources by quasi-homogeneous media

The field generated by scattering of light from a quasi-homogeneous source on a quasi-homogeneous, random medium is investigated. It is found that, within the accuracy of the first-order Born approximation, the far field satisfies two reciprocity relations (sometimes called uncertainty relations). One of them implies that the spectral density (or spectral intensity) is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential. The other implies that the spectral degree of coherence of the far field is proportional to the convolution of the correlation coefficient of the source and the spatial Fourier transform of the strength of the scattering potential. While the case we consider might seem restrictive, it is actually quite general. For instance, the quasi-homogeneous source model can be used to describe the generation of beams with different coherence properties and different angular spreads. In addition, the quasi-homogeneous scattering model adequately describes a wide class of turbulent media, including a stratified, turbulent atmosphere and confined plasmas.     

Attenuation estimation using spectral cross-correlation

Estimation of the local attenuation coefficient in soft tissue is important both for clinical diagnosis and for further analysis of ultrasound B-mode images. However, it is difficult to extract spectral properties in a small region of interest from noisy backscattered ultrasound radio frequency (RF) signals. Diffraction effects due to transducer beam focal properties also have to be corrected for accurate estimation of the attenuation coefficient. In this paper, we propose a new attenuation estimation method using spectral cross-correlation between consecutive power spectra obtained from the backscattered RF signals at different depths. Since the spectral cross-correlation method estimates the spectral shift by comparing the entire power spectra, it is more robust and stable to the spectral noise artifacts in the backscattered RF signals. A diffraction compensation technique using a reference phantom with a known attenuation coefficient value is also presented. Local attenuation coefficient estimates obtained using spectral cross-correlation are within 2.3% of the actual value with small estimation variances, as demonstrated in the simulation results.     

Variability in atmospheric light-scattering properties with altitude

The altitudinal variability in angular scattering properties of the troposphere and stratosphere was measured with a balloonborne polar nephelometer. An analysis of interdependent experimental parameters provides information on the scattering phase function and inferred size distribution of aerosol particles as a function of altitude. These aerosol characteristics are extractable from the scattering dissymmetry index and its relationship to spectral dispersion in turbidity and the aerosol phase function. The problem of the correlation between backscatter and extinction is addressed from the perspectives of in situ observations.     

Application of dynamic light scattering to the study of small marine particles

Small particles ranging from approximately 0.1 μm to several micrometers in size, which include detrital material, bacteria, and other planktonic microorganisms, make a significant contribution to light scattering in the upper ocean. The scattering properties of these particles are strongly dependent on their size, which is difficult to measure in the submicrometer range with commonly used electronic resistive counters and microscopic techniques. We examined the size of small marine particles by application of the dynamic light scattering (DLS) method. In this method the time-dependent autocorrelation function of scattered intensity by particles undergoing Brownian motion provides information about the size of particles. The samples were collected in clear oceanic waters off the coast of Southern California. The mean hydrodynamic diameter of particles, determined from the DLS measurements at a scattering angle of 45°, was 0.54μ m. This indicates that the major contribution to scattering at this angle comes rom submicrometer particles. We also described an inverse method for estimating the general slope of the size distribution of small marine particles from the mean hydrodynamic diameter. This method is based on calculations of the size distribution weighted by distribution from Mie theory and assumes that a power-law approximation represents the actual particle scattered intensity. These calculations suggested that particulate assemblage in our seawater samples was best characterized by a differential size distribution with a slope of -4.35. This estimation was supported by independent measurements of particle size distribution and the spectral beam attenuation coefficient taken from the same samples as those used for the DLS measurements. We also demonstrated that multiangle DLS measurements may be used to determine the representative value of the refractive index of particles.     

Changes in spectral shape of tissue optical properties in conjunction with laser-induced thermotherapy

We measured the optical properties on samples of rat liver tissue before and after laser-induced thermotherapy performed in vivo with Nd:YAG laser irradiation. This made it possible to monitor not only the influence of coagulation on the scattering properties but also the influence of damages to vessels and heat-induced damage to blood on the absorption properties. An experimental integrating-sphere arrangement was modified to allow the determination of the g factor and the absorption and scattering coefficients versus the wavelength in the 600-1050-nm spectral region, with the use of a spectrometer and a CCD camera. The results show a relative decrease in the g factor of on average 21 ? 7% over the entire spectral range following thermotherapy, and a corresponding relative increase in the scattering and absorption coefficients of 23 ? 8% and 200 ? 100%, respectively. An increase of on average 200 ? 80% was consequently found for the reduced scattering coefficient. The cause of these changes in terms of the Mie-equivalent average radius of tissue scatterers as well as of the distribution and biochemistry of tissue absorbers was analyzed, utilizing the information yielded by the g factor and the spectral shapes of the reduced scattering and absorption coefficients. These results were correlated with the alterations in the ultrastructure found in the histological evaluation. The average radius of tissue scattering centers, determined by using either the g factors calculated on the basis of Mie theory or the spectral shape of reduced scattering coefficients calculated on the Mie theory, was estimated to be 21-32% lower in treated than in untreated liver samples. The Mie-equivalent average radii of scattering centers in untreated liver tissue deduced by the two methods corresponded well and were found to be 0.31 and 0.29 mum, respectively, yielding particle sizes in the same range as the size of a mitochondrion.     

High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1: theory and instrumentation

A high spectral resolution lidar technique to measure optical scattering properties of atmospheric aerosols is described. Light backscattered by the atmosphere from a narrowband optically pumped oscillator-amplifier dye laser is separated into its Doppler broadened molecular and elastically scattered aerosol components by a two-channel Fabry-Perot polyetalon interferometer. Aerosol optical properties, such as the backscatter ratio, optical depth, extinction cross section, scattering cross section, and the backscatter phase function, are derived from the two-channel measurements.     

Measurement of the optical properties of a two-layer model of the human head using broadband near-infrared spectroscopy

We present the development of a continuous-wave method of quantifying the optical properties of a two-layered model of the human head using a broadband spectral approach. Absolute absorption and scattering properties of the upper and lower layers of phantoms with known optical properties were reconstructed from steady-state multi-distance measurements by performing differential fit analysis of the near-infrared reflectance spectrum between 700 and 1000 nm. From spectra acquired at 10, 20, and 30 mm, the concentration of a chromophore in the bottom layer was determined within an error of 10% in the presence of a 15 mm thick top layer. These results demonstrate that our method was able to determine the optical properties of the lower layer, which represents brain, with acceptable error at specific source-detector distances.     

Optical properties of GeO2 glass and optical fibers

The optical properties of GeO(2) glass were investigated to clarify its potentiality as an optical fiber material. Glass samples were prepared by the flame hydrolysis and the melting techniques, and their Rayleigh scattering and infrared absorption properties were examined. Optical fibers composed of a pure GeO(2) core and an F-doped GeO(2) cladding were drawn to clarify the scattering loss characteristics. The Rayleigh-scattering intensity obtained from spectral loss measurements on the fibers agreed with that measured in bulk samples, and the intensity relative to that of SiO(2) glass was found to be approximately 3. These results suggest that a minimum loss of 0.15 dB/km is expected at a wavelength of 2 mum.     

Photomodulated rayleigh scattering of single semiconductor nanowires: probing electronic band structure

The internal electronic structures of single semiconductor nanowires can be resolved using photomodulated Rayleigh scattering spectroscopy. The Rayleigh scattering from semiconductor nanowires is strongly polarization sensitive which allows a nearly background-free method for detecting only the light that is scattered from a single nanowire. While the Rayleigh scattering efficiency from a semiconductor nanowire depends on the dielectric contrast, it is relatively featureless as a function of energy. However, if the nanowire is photomodulated using a second pump laser beam, the internal electronic structure can be resolved with extremely high signal-to-noise and spectral resolution. The photomodulated Rayleigh scattering spectra can be understood theoretically as a first derivative of the scattering efficiency that results from a modulation of the band gap and depends sensitively on the nanowire diameter. Fits to spectral lineshapes provide both the band structure and the diameter of individual GaAs and InP nanowires under investigation.     

Scattering from topological insulator circular cylinder buried in a semi-infinite medium

The problem of electromagnetic scattering of a plane wave from a topological insulator (TI) cylinder buried beneath a flat interface is undertaken with the method of analysis based on spectral plane wave representation of fields. Saddle point method is employed to evaluate the involved spectral integrals serving as basis functions in the representations of scattered-reflected and scattered-transmitted fields. The distinctions between the scattering pattern for time reversal symmetry TI cylinder and that of time reversal symmetry broken TI cylinder are pronounced. Results are validated through the comparison with the previously available results.     

Application of the pseudospectral time-domain method to the scattering of light by nonspherical particles

The pseudospectral time-domain (PSTD) method is a powerful approach for computing the single-scattering properties of arbitrarily shaped particles with small-to-moderate-sized parameters. In the PSTD method, the spatial derivative approximation based on the spectral method is more accurate than its counterpart based on the finite-difference technique. Additionally, the PSTD method can substantially diminish accumulated errors that increase with the spatial scale and temporal duration of simulation. We report on the application of the PSTD method to the scattering of light by nonspherical ice particles. The applicability of the PSTD method is validated against the Lorenz-Mie theory and the T-matrix method. The phase functions computed from the PSTD method and the Lorenz-Mie theory agree well for size parameters as large as 80. Furthermore, the PSTD code is also applied to the scattering of light by nonspherical ice crystals, namely, hollow hexagonal columns and aggregates, which are frequently observed in cirrus clouds. The phase functions computed from the PSTD method are compared with the counterparts computed from the finite-difference time-domain (FDTD) method for a size parameter of 20 and an incident wavelength of 3.7 microm. The comparisons show good agreement between the two methods.     

Removal of analyte-irrelevant variations in near-infrared tissue spectra

This paper describes mathematical techniques to correct for analyte-irrelevant optical variability in tissue spectra by combining multiple preprocessing techniques to address variability in spectral properties of tissue overlying and within the muscle. A mathematical preprocessing method called principal component analysis (PCA) loading correction is discussed for removal of inter-subject, analyte-irrelevant variations in muscle scattering from continuous-wave diffuse reflectance near-infrared (NIR) spectra. The correction is completed by orthogonalizing spectra to a set of loading vectors of the principal components obtained from principal component analysis of spectra with the same analyte value, across different subjects in the calibration set. Once the loading vectors are obtained, no knowledge of analyte values is required for future spectral correction. The method was tested on tissue-like, three-layer phantoms using partial least squares (PLS) regression to predict the absorber concentration in the phantom muscle layer from the NIR spectra. Two other mathematical methods, short-distance correction to remove spectral interference from skin and fat layers and standard normal variate scaling, were also applied and/or combined with the proposed method prior to the PLS analysis. Each of the preprocessing methods improved model prediction and/or reduced model complexity. The combination of the three preprocessing methods provided the most accurate prediction results. We also performed a preliminary validation on in vivo human tissue spectra.     

Modeling the optical properties of mineral particles suspended in seawater and their influence on ocean reflectance and chlorophyll estimation from remote sensing algorithms

The optical properties of mineral particles suspended in seawater were calculated from the Mie scattering theory for different size distributions and complex refractive indices of the particles. The ratio of the spectral backscattering coefficient to the sum of the spectral absorption and backscattering coefficients of seawater, b(b)(lambda)/[a(lambda) + b(b)(lambda)], was analyzed as a proxy for ocean reflectance for varying properties and concentrations of mineral particles. Given the plausible range of variability in the particle size distribution and the refractive index, the general parameterizations of the absorption and scattering properties of mineral particles and their effects on ocean reflectance in terms of particle mass concentration alone are inadequate. The variations in the particle size distribution and the refractive index must be taken into account. The errors in chlorophyll estimation obtained from the remote sensing algorithms that are due to the presence of mineral particles can be very large. For example, when the mineral concentration is 1 g m(-3) and the chlorophyll a concentration is low (0.05 mg m(-3)), current global algorithms based on a blue-to-green reflectance ratio can produce a chlorophyll overestimation ranging from approximately 50% to as much as 20-fold.     

大粗糙度起伏下一维海面声散射建模与分析

针对起伏海面高频声散射计算问题,提出了一种改进的基尔霍夫(Kirchhoff)近似方法。该方法考虑了海面的阴影区和亮区之间的多次散射声场,可对小入射角下大粗糙度起伏海面的散射声场进行计算。以一维余弦和高斯谱海面散射声场的有限元计算结果为标准解验证了所提方法的准确性和适用性。利用该方法计算了一维余弦海面的散射强度,分析了不同入射声波频率和角度下海面散射强度的分布情况,并解释了Bragg散射的产生机理,同时讨论了不同海面均方根高度和相关长度情况下高斯谱海面散射强度的变化规律。