Analytic algorithms for determining radiative transfer optical properties of ocean waters

A synthetic model for the scattering phase function is used to develop simple algebraic equations, valid for any water type, for evaluating the ratio of the backscattering to absorption coefficients of spatially uniform, very deep waters with data from upward and downward planar irradiances and the remotely sensed reflectance. The phase function is a variable combination of a forward-directed Dirac delta function plus isotropic scattering, which is an elementary model for strongly forward scattering such as that encountered in oceanic optics applications. The incident illumination at the surface is taken to be diffuse plus a collimated beam. The algorithms are compared with other analytic correlations that were previously derived from extensive numerical simulations, and they are also numerically tested with forward problem results computed with a modified FN method.     

Attenuation and impulse response for multiple scattering of light in atmospheric clouds and aerosols

Model phase functions for atmospheric clouds and aerosols typically comprise a narrow forward lobe (corona), a broad diffuse background, and a narrow backscattering peak (glory), which can reach relatively high values, especially for polyhedral scattering particles, such as hexagonal ice columns and plates. The influence of these three major components on the asymptotic and transient attenuation of the scattered light is compared for several analytic phase functions to assess the dependence of radiative transfer in clouds and aerosols on the choice of phase function. The impulse response (temporal evolution of the angular intensity distribution) is sensitive to the higher moments of the phase function and could prove to be a useful technique for inferring the optical scattering parameters of clouds and aerosols.     

Analytic inverse radiative transfer equations for atmospheric and hydrologic optics

Two new sets of analytical equations are derived with which the albedo of single scattering and the coefficients of a Legendre polynomial expansion of the scattering phase function can be determined for a source-free, homogeneous plane-parallel medium uniformly illuminated over the surfaces. The equations, essentially linear in the unknowns, require measurements of the radiance in the interior of the medium, but no iterative forward-problem calculations are needed. Sets of equations for both unpolarized and polarized radiation applications are given, as well as a side-by-side comparison with previously known sets of analytic inversion equations. Applications of the equations are suggested.     

Analytical solution to the optical transfer function of a scattering medium with large particles

A new analytical expression for the optical transfer function of multiple-scattering media such as clouds, mists, and dust aerosols is given in terms of their microphysical characteristics. The geometrical optics approximation is used to find local optical parameters of a scattering medium, including the simple approximation of the phase function, which is the key to the solution of the problem considered here. The optical transfer function is taken within a small-angle approximation of the radiative transfer theory. A comparison with Monte Carlo data shows a fairly satisfactory accuracy of our analytic formulas.     

Effective phase function for light scattered by blood

The scattering process induced in blood by a collimated laser beam is theoretically investigated. An individual red blood cell (RBC) has a scattering phase function strongly peaked in the forward direction. For far-field experiments, the small scattering volumes can be considered as "macroscopic particles" characterized by an effective scattering phase function. Using the single-cell phase function as "input data" the angular distribution of light scattered at small angles by the whole scattering volume, containing RBCs in suspension, is calculated analytically. The angular dispersion of the light scattered by blood can be approximately described by the same formula used to characterize the light scattered by a single cell but with an effective, hematocrit-dependent anisotropy parameter.     

X射线小角散射测定粒度分布的一种数据处理解析程序

本文提出了一种确定材料中微不均匀区大小分布 X 射线小角散射数据处理的解析方法。用 n 个分立的粒度分布解对应的散射强度叠加来逼近实验强度。以尝试法修正结果使误差达到最小。用铁红釉试样作为实例,对液相分离球滴粒度分布作了测定,结果表明该方法简便实用。     

Results of a monte carlo investigation of the diffuse attenuation coefficient

There has been a large effort to relate the apparent optical properties of ocean water to the inherent optical properties, which are the absorption coefficient a, the scattering coefficient b, and the scattering phase function rho(theta). The diffuse attenuation coefficient kdiff' has most often been considered an apparent optical property. However, kdiff' can be considered a quasi-inherent property kdiff' when defined as a steady-state light distribution attenuation coefficient. The Honey-Wilson research empirically relates kdiff' to a and b. The Honey-Wilson relation most likely applies to a limited range of water types because it does not include dependence on rho(theta). A series of Monte Carlo simulations were initiated to calculate kdiff' in an unstratified water column. The calculations, which reflected open ocean water types, used ranges of the single-scattering albedo omega(0) and the mean forward-scattering angle theta(m) for two analytic phase functions with different shapes. It was found that kdiff' is nearly independent of the shape of rho(theta) and can be easily parameterized in terms of a, b, and theta(m) for 0.11 相似文献   

Phase-function normalization for accurate analysis of ultrafast collimated radiative transfer

The scattering of radiation from collimated irradiation is accurately treated via normalization of phase function. This approach is applicable to any numerical method with directional discretization. In this study it is applied to the transient discrete-ordinates method for ultrafast collimated radiative transfer analysis in turbid media. A technique recently developed by the authors, which conserves a phase-function asymmetry factor as well as scattered energy for the Henyey-Greenstein phase function in steady-state diffuse radiative transfer analysis, is applied to the general Legendre scattering phase function in ultrafast collimated radiative transfer. Heat flux profiles in a model tissue cylinder are generated for various phase functions and compared to those generated when normalization of the collimated phase function is neglected. Energy deposition in the medium is also investigated. Lack of conservation of scattered energy and the asymmetry factor for the collimated scattering phase function causes overpredictions in both heat flux and energy deposition for highly anisotropic scattering media. In addition, a discussion is presented to clarify the time-dependent formulation of divergence of radiative heat flux.     

Ensemble-averaged Shack-Hartmann wave-front sensing for imaging through turbid media

A technique is described for ensemble-averaging the light wave emerging from a turbid medium, enabling the recovery of optical information that is otherwise lost in a speckle pattern. The technique recovers both an amplitude and a phase function for a wave that has been corrupted by severe scattering, without the use of holography. With the phase estimated, an ensemble-averaged field is constructed that can be backprojected to form an image of the object obscured by the scattering medium. Experimental results suggest that the technique can resolve two object points whose signals are unresolved on the exit surface of a diffuser.     

Sensitivity studies for imaging a spherical object embedded in a spherically symmetric, two-layer turbid medium with photon-density waves

We present analytic expressions for the amplitude and phase of photon-density waves in strongly scattering, spherically symmetric, two-layer media containing a spherical object. This layered structure is a crude model of multilayered tissues whose absorption and scattering coefficients lie within a range reported in the literature for most tissue types. The embedded object simulates a pathology, such as a tumor. The normal-mode-series method is employed to solve the inhomogeneous Helmholtz equation in spherical coordinates, with suitable boundary conditions. By comparing the total field at points in the outer layer at a fixed distance from the origin when the object is present and when it is absent, we evaluate the potential sensitivity of an optical imaging system to inhomogeneities in absorption and scattering. For four types of background media with different absorption and scattering properties, we determine the modulation frequency that achieves an optimal compromise between signal-detection reliability and sensitivity to the presence of an object, the minimum detectable object radius, and the smallest detectable change in the absorption and scattering coefficients for a fixed object size. Our results indicate that (l) enhanced sensitivity to the object is achieved when the outer layer is more absorbing or scattering than the inner layer; (2) sensitivity to the object increases with the modulation frequency, except when the outer layer is the more absorbing; (3) amplitude measurements are proportionally more sensitive to a change in absorption, phase measurements are proportionally more sensitive to a change in scattering, and phase measurements exhibit a much greater capacity for distinguishing an absorption perturbation from a scattering perturbation.     

Nature of light scattering in dental enamel and dentin at visible and near-infrared wavelengths

The light-scattering properties of dental enamel and dentin were measured at 543, 632, and 1053 nm. Angularly resolved scattering distributions for these materials were measured from 0° to 180° using a rotating goniometer. Surface scattering was minimized by immersing the samples in an index-matching bath. The scattering and absorption coefficients and the scattering phase function were deduced by comparing the measured scattering data with angularly resolved Monte Carlo light-scattering simulations. Enamel and dentin were best represented by a linear combination of a highly forward-peaked Henyey-Greenstein (HG) phase function and an isotropic phase function. Enamel weakly scatters light between 543 nm and 1.06 μm, with the scattering coefficient (μ(s)) ranging from μ(s) = 15 to 105 cm(-1). The phase function is a combination of a HG function with g = 0.96 and a 30-60% isotropic phase function. For enamel, absorption is negligible. Dentin scatters strongly in the visible and near IR (μ(s)?260 cm(-1)) and absorbs weakly (μ(a) ? 4 cm(-1)). The scattering phase function for dentin is described by a HG function with g = 0.93 and a very weak isotropic scattering component (? 2%).     

Combined Henyey-Greenstein and Rayleigh phase function

The phase function is an important parameter that affects the distribution of scattered radiation. In Rayleigh scattering, a scatterer is approximated by a dipole, and its phase function is analytically related to the scattering angle. For the Henyey-Greenstein (HG) approximation, the phase function preserves only the correct asymmetry factor (i.e., the first moment), which is essentially important for anisotropic scattering. When the HG function is applied to small particles, it produces a significant error in radiance. In addition, the HG function is applied only for an intensity radiative transfer. We develop a combined HG and Rayleigh (HG-Rayleigh) phase function. The HG phase function plays the role of modulator extending the application of the Rayleigh phase function for small asymmetry scattering. The HG-Rayleigh phase function guarantees the correct asymmetry factor and is valid for a polarization radiative transfer. It approaches the Rayleigh phase function for small particles. Thus the HG-Rayleigh phase function has wider applications for both intensity and polarimetric radiative transfers. For microwave radiative transfer modeling in this study, the largest errors in the brightness temperature calculations for weak asymmetry scattering are generally below 0.02 K by using the HG-Rayleigh phase function. The errors can be much larger, in the 1-3 K range, if the Rayleigh and HG functions are applied separately.     

One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater

A one-parameter two-term Henyey-Greenstein (TTHG) phase function of light scattering in seawater is proposed. The original three-parameter TTHG phase function was reduced to the one-parameter TTHG phase function by use of experimentally derived regression dependencies between integral parameters of the marine phase functions. An approach to calculate a diffuse attenuation coefficient in the depth of seawater is presented.     

Estimation of optical constants from multiple-scattered light using approximations for single particle scattering characteristics

The inversion of multiple-scattered light measurements to extract the optical constant (complex refractive index) is computationally intensive. A significant portion of this time is due to the effort required for computing the single particle characteristics (absorption and scattering cross sections, anisotropy factor, and the phase function). We investigate approximations for computing these characteristics so as to significantly speed up the calculations without introducing large inaccuracies. Two suspensions of spherical particles viz., polystyrene and poly(methyl methacrylate) were used for this investigation. It was found that using the exact Mie theory to compute the absorption and scattering cross sections and the anisotropy factor with the phase function computed using the Henyey-Greenstein approximation yielded the best results. Analysis suggests that errors in the phase functions and thus in the estimated optical constants depend mainly on how closely the approximations match the Mie phase function at small scattering angles.     

Analytic model of ocean color

Ocean color is determined by spectral variations in reflectance at the sea surface. In the analytic model presented here, reflectance at the sea surface is estimated with the quasi-single-scattering approximation that ignores transspectral processes. The analytic solutions we obtained are valid for a vertically homogeneous water column. The solution provides a theoretical expression for the dimensionless, quasi-stable parameter (r), with a value of ~0.33, that appears in many models in which reflectance at the sea surface is expressed as a function of absorption coefficient (a) and backscattering coefficient (b(b)). In the solution this parameter is represented as a function of the mean cosines for downwelling and upwelling irradiances and as the ratio of the upward-scattering coefficient to the backscattering coefficient. Implementation of the model is discussed for two cases: (1) that in which molecular scattering is the main source of upwelling light, and (2) that in which particle scattering is responsible for all the upwelled light. Computations for the two cases are compared with Monte Carlo simulations, which accounts for processes not considered in the analytic model (multiple scattering, and consequent depth-dependent changes in apparent optical properties). The Monte Carlo models show variations in reflectance with the zenith angle of the incident light. The analytic model can be used to reproduce these variations fairly well for the case of molecular scattering. For the particle-scattering case also, the analytic and Monte Carlo models show similar variations in r with zenith angle. However, the analytic model (as implemented here) appears to underestimate r when the value of the backscattering coefficient b(b) increases relative to the absorption coefficient a. The errors also vary with the zenith angle of the incident light field, with the maximum underestimate being approximately 0.06 (equivalent to relative errors from 12 to 17%) for the range of b(b)/a studied here. One implication of this result is that the model could also be used to obtain approximate solutions for the Q factor, defined for a given look angle as the ratio of the upwelling irradiance at the surface to the upwelling radiance at the surface at that angle. This is a quantity that is important in remote-sensing applications of ocean-color models. An advantage of the model discussed here is that its implementation requires inputs that are in principle accessible only in a remote-sensing context.     

偏振状态下球形粒子的散射相位函数研究

本文根据散射相位函数的定义,得到了偏振状态下单个粒子散射相位函数的表达式,并且通过研究发现以下规律:1)粒子半径越小,极值差随散射角越趋向于对称分布;2)散射角在0～0.025π以及O.997π～π之间,散射相位函数随极化角基本不变;3)散射角在O.025π～0.997π之间,散射相位函数随极化角变化明显.同时比较了偏振状态下多粒子和单粒子散射相位函数随散射角和极化角的分布.最后从大气中光传输理论出发,建立了非偏振状态与偏振状态下散射相位函数的关系,为大气散射回波功率测量以及近似散射相位函数的研究提供参考.     

Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle scattering in a random medium

Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens-Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s > 1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens-Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.     

Statistical estimation of ultrasonic propagation path parameters for aberration correction

Parameters in a linear filter model for ultrasonic propagation are found using statistical estimation. The model uses an inhomogeneous-medium Green's function that is decomposed into a homogeneous-transmission term and a path-dependent aberration term. Power and cross-power spectra of random-medium scattering are estimated over the frequency band of the transmit-receive system by using closely situated scattering volumes. The frequency-domain magnitude of the aberration is obtained from a normalization of the power spectrum. The corresponding phase is reconstructed from cross-power spectra of subaperture signals at adjacent receive positions by a recursion. The subapertures constrain the receive sensitivity pattern to eliminate measurement system phase contributions. The recursion uses a Laplacian-based algorithm to obtain phase from phase differences. Pulse-echo waveforms were acquired from a point reflector and a tissue-like scattering phantom through a tissue-mimicking aberration path from neighboring volumes having essentially the same aberration path. Propagation path aberration parameters calculated from the measurements of random scattering through the aberration phantom agree with corresponding parameters calculated for the same aberrator and array position by using echoes from the point reflector. The results indicate the approach describes, in addition to time shifts, waveform amplitude and shape changes produced by propagation through distributed aberration under realistic conditions.     

Cloud-droplet-size distribution from lidar multiple-scattering measurements

A method for calculating droplet-size distribution in atmospheric clouds is presented, based on measurement of laser backscattering and multiple scattering from water clouds. The lidar uses a Nd:YAG laser that emits short pulses at a moderate repetition rate. The backscattering, which is composed mainly of single scattering, is measured with a detector pointing along the laser beam. The multiple scattering, which is mainly double scattering, is measured with a second detector, pointing at a specified angle to the laser beam. The domain of scattering angles that contribute to the doublescattering signal increases monotonically as the pulse penetrates the cloud. The water droplets within the probed volume are assumed to have a constant size distribution. Hence, from the double-scatteringmeasured signal as a function of penetration depth within the cloud, the double-scattering phase function of the scattering volume is derived. Inverting the phase function results in a cloud-droplet-size distribution in the form of a log-normal function.     

Modeling ultrasound imaging as a linear, shift-variant system

Wo solve the equation that governs acoustic wave propagation in an inhomogeneous medium to show that the radio-frequency (RF) ultrasound signal can he expressed as the result of filtering the scatterer field with a point-spread function. We extend the analysis to make the link between the RF ultrasound signal and the representation of ultrasound scatterers as vectors with small magnitude and random phase in the complex plane. Others have previously performed parts of this analysis. The contribution of the present paper is to provide a single, coherent treatment emphasizing the assumptions that have to be made and the physical consequences of the models derived. This leads to insights into the interaction of monopole and dipole scattering, useful techniques for simulating and analyzing speckle statistics in the complex plane and a new expression for the normalized covariance of the analytic RF ultrasound signal in terms of the complex envelope of the point-spread function.