Paraxial Approximation of Modern Radiometry for Beamlike Wave Propagation

A new approach to the construction of a system of the generalized radiometric quantities expressed in terms of the cross-spectral density function of the wave field is proposed. The key distinction of this approach lies in the fact that the initial hypothesis of beamlike wave propagation allows to invoke the paraxial approximation when deducing the generalized radiant flux. Within the framework of this approach the new expressions for the generalized radiant emittance, the generalized radiant intensity and the generalized radiance are derived. All the proposed generalized radiometric characteristics represent physically measurable quantities and, hence, may be used in practical radiometry. The results obtained in this paper can be regarded as a particular case of the modern radiometry theory in paraxial approximation for beamlike wave propagation.On leave from Kiev Polytechnic Institute, Ukraine.     

Effect of the reflection of underlying surface on sky radiance distribution

Sky radiance might be influenced by the multiple reflectance between the earth's albedo surface and the atmosphere. Based on the Lambert's law and the radiative transfer equation (RTE), a model is developed to calculate the additional sky radiance at wavelengths of 0.4-3 μm due to the reflectance contribution of the underlying surface. The iterative method is used to calculate sky radiance without the reflectance from underlying surface. The hybrid modified delta-Eddington approximation is used to compute the atmospheric reflection of the radiation from the earth's surface. An interaction factor is introduced to deal with the multiple reflectance between the atmosphere and the underlying surface. The sky radiance increment is evaluated for some different albedos of the earth's surface. The results show that the sky radiance increment rises rapidly while viewing zenith angle is near to 90°, and the larger the albedo of the earth's surface is, the more obvious this effect appears.     

CUDA-accelerated simulation of multiple scattering using decoupling approximation

Abstract  

In this research a CUDA-accelerated simulation method of multiple scattering in dense participating media based on decoupling approximation is proposed. Simulation of multiple scattering is important, in that it visually illustrates how radiance transfers between gaseous particles. The existing radiance transfer equation has poor computational performance because of its complicated integral calculation of in-scattering in each radiance update. However, this computation can be avoided using previous cached results proposed in this paper. To construct the cached results, we first decouple the phase function in radiance transfer equation with singular value decomposition (SVD) approximation. SVD approximates the multivariate phase function as a sum of products of incident light and outgoing light of lower dimensionality. Then the incident light and outgoing light data of current radiance update are cached independently in two textures. The cached two textures are used to replace integral calculation of in-scattering in the next radiance update to improve computation performance. The proposed method is designed in a parallelized way so that the parallel computing power of CUDA can be fully exploited. The simulation results show that our method allows fast rendering of dynamic scenes while high accuracy is maintained.     

Integration of Chandrasekhar's integral equation

We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA “explicitly” in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness.     

地表反射太阳辐射的参数化计算方法

 从能量守恒定律出发，建立了朗伯地表对下行辐射的反射作用引起天空亮度变化的解析计算模型。利用射线追踪原理，提出了地表与大气之间多次反射作用的理论模型。引入了一个多次散射的影响因子，并对附加的天空亮度进行了修正。利用混合修正的d-Eddington近似和互易性原理计算了大气的透射率、反照率以及半球平均反照率。最后计算了地表反照率分别为0.15，0.25和0.35情形下的天空亮度增量，实验测量数据证实了这些结果。结果表明：当地表的反照率不为0时，存在“临边增亮”效应，并且随着地表反照率的增大，这种效应更加明显。     

A single-scattering approximation for infrared radiative transfer in limb geometry in the Martian atmosphere

We present a single-scattering approximation for infrared radiative transfer in limb geometry in the Martian atmosphere. It is based on the assumption that the upwelling internal radiation field is dominated by a surface with a uniform brightness temperature. It allows the calculation of the scattering source function for individual aerosol types, mixtures of aerosol types, and mixtures of gas and aerosol. The approximation can be applied in a Curtis-Godson radiative transfer code and is used for operational retrievals from Mars Climate Sounder measurements. Radiance comparisons with a multiple scattering model show good agreement in the mid- and far-infrared although the approximate model tends to underestimate the radiances in realistic conditions of the Martian atmosphere. Relative radiance differences are found to be about 2% in the lowermost atmosphere, increasing to ∼10% in the middle atmosphere of Mars. The increasing differences with altitude are mostly due to the increasing contribution to limb radiance of scattering relative to emission at the colder, higher atmospheric levels. This effect becomes smaller toward longer wavelengths at typical Martian temperatures. The relative radiance differences are expected to produce systematic errors of similar magnitude in retrieved opacity profiles.     

Evaluation of nonisothermal band models for H2O

Comparisons of predicted and measured radiance spectra for nonuniform hot H₂O gas samples are reported. The predicted spectra are generated with band models formulated in a companion paper, and band model parameters constructed to handle optical path temperature variations from 200 to 3000°K. The model identified in the companion paper as the intuitive derivative approximation is shown to be superior to the traditional Curtis-Godson approximation in treating general optical paths along which high degrees of nonuniformity occur.     

Radiometry and Radiation Efficiency of Twisted Gaussian Schell-Model Sources

Wavefields endowed with the coherence-induced property of optical twist have recently attracted a good deal of theoretical and experimental attention. We present the generalized radiometric theory of fields generated by twisted Gaussian Schell-model sources. The effects introduced by the novel, rotationally symmetric, twist phenomenon in the radiant intensity, generalized radiance, radiant emittance (irradiance), and the radiation efficiency are assessed. The radiance becomes directionally skewed as a result of the twist, whereas the radiant intensity remains axially symmetric. The twist reduces the radiation efficiency and broadens the radiation distribution, in agreement with the notion that the twist decreases the effective coherence. Several special cases, such as quasihomogeneous sources, are analyzed in detail. The radiometric results, which are physically consistent with the superposition models of twisted sources, are demonstrated by illustrative examples.     

基于P3近似的空间分辨漫反射研究

光源附近组织的空间分辨漫反射是近年来生物医学光子学领域的一个研究热点,其目的是发展一种能够测定活体生物组织光学参量的新技术。漫射近似理论研究光源附近组织的空间分辨漫反射具有很大局限性。P3近似理论考虑了相函数的三阶矩,能较准确地描述光源附近组织的光辐射分布。研究了基于P3近似的空间分辨漫反射,从输运理论的PN方程组出发,导出了P3近似方程组和P3近似的格林函数解;阐述了漫射近似与P1近似的关系,给出了外推边界条件下,准直光束近似后的P3近似漫反射率的完整表示,讨论了相函数二阶参量对P3近似漫反射的影响,并与漫射近似和蒙特卡罗模拟结果进行了比较,指出了P3近似的应用范围。     

Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method

In this paper, we analyze the generalized Camassa and Holm （CH） equation by the improved element-free Galerkin （IEFG） method. By employing the improved moving least-square （IMLS） approximation, we derive the formulas for the generalized CH equation with the IEFG method. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Because there are fewer coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method, fewer nodes are selected in the entire domain than in the conventional EFG method, the IEFG method should result in a higher computing speed. The effectiveness of the IEFG method for the generalized CH equation is investigated by numerical examples in this paper.     

Generalization of the Curtis-Godson approximation to inhomogeneous scattering atmospheres

The Curtis-Godson approximation, which was initially derived to compute the transmission through clear inhomogeneous atmospheres, has been generalized to any cloudy atmosphere by means of the scaled amount distribition. For most of the realistic atmospheres, the accuracy of this generalized approximation is comparable to or even better than for the clear case.     

自治广义Birkhoff系统的平衡稳定性

研究广义Birkhoff系统的平衡稳定性问题.建立了自治广义Birkhoff系统的平衡方程;给出了自治广义Birkhoff系统的一次近似方程,利用Lyapunov一次近似理论,建立了系统平衡状态稳定性的判据;构建了Lyapunov函数,利用Lyapunov直接法,建立了自治广义Birkhoff系统平衡状态稳定性的判据.给出了若干算例以说明结果的应用.     

Improving the description of sunglint for accurate prediction of remotely sensed radiances

The bidirectional reflection distribution function (BRDF) of the ocean is a critical boundary condition for radiative transfer calculations in the coupled atmosphere-ocean system. Existing models express the extent of the glint-contaminated region and its contribution to the radiance essentially as a function of the wind speed. An accurate treatment of the glint contribution and its propagation in the atmosphere would improve current correction schemes and hence rescue a significant portion of data presently discarded as “glint contaminated”. In current satellite imagery, a correction to the sensor-measured radiances is limited to the region at the edge of the glint, where the contribution is below a certain threshold. This correction assumes the sunglint radiance to be directly transmitted through the atmosphere. To quantify the error introduced by this approximation we employ a radiative transfer code that allows for a user-specified BRDF at the atmosphere-ocean interface and rigorously accounts for multiple scattering. We show that the errors incurred by ignoring multiple scattering are very significant and typically lie in the range 10-90%. Multiple reflections and shadowing at the surface can also be accounted for, and we illustrate the importance of such processes at grazing geometries.     

Association of evaluation methods of the effective permittivity of heterogeneous media on the basis of a generalized singular approximation

Various methods for evaluation of the effective permittivity of heterogeneous media, namely, the effective medium approximation (Bruggeman’s approximation), the Maxwell-Garnett approximation, Wiener’s bounds, and the Hashin-Shtrikman variational bounds (for effective static characteristics) are combined on the basis of a generalized singular approximation.     

Structure of interfaces from uniformity of the chemical potential

It is shown that a generalized chemical potential suggested by the potential-distribution theory is uniform even in a nonuniform fluid. Leng, Rowlinson, and Thompson had already observed its uniformity through the liquid-vapor interface in the penetrable-sphere model, in mean-field approximation. Following those authors, we exploit the uniformity of that generalized chemical potential to obtain unified and transparent derivations of the results of Ono and Kondo and of van der Waals on the liquid-vapor interfaces in the lattice-gas model and in the model of attracting hard spheres, respectively, both in mean-field approximation.Work supported by the National Science Foundation and the Cornell University Materials Science Center.     

雪的热辐射多角度偏振特性研究

针对现今遥感对地面目标自身热辐射偏振特性研究的需要,对雪的热辐射多角度偏振特性进行测量,分析探测天顶角、探测方位角、波段、偏振角四个因子对雪的热辐射特性的影响。结果表明：雪的辐射亮度和亮度温度均随探测天顶角的增大而增大,当探测天顶角＞30°时,增长速度加快,且探测天顶角对雪的亮度温度的影响较辐射亮度更为显著;探测方位角的变化对雪的辐射亮度和亮度温度有一定的影响,且对雪的亮度温度的影响较辐射亮度更为显著;波段的变化对雪的辐射亮度和亮度温度均有显著影响,相比而言,其对辐射亮度的影响更为显著;偏振角的变化对雪的辐射亮度和亮度温度有一定的影响,且对亮度温度的影响较辐射亮度较为显著。该研究成果为应用遥感技术开展雪的热红外定量研究提供了新的思路与方法,具有重要的理论意义和广阔的应用前景。     

A theory of vibrations of solid solutions with inclusion of the cluster effects: Non-self-consistent and self-consistent approximations

A theory of vibrational spectra of solid solutions proposed by the author has been developed, in which a cluster of n cells statistically filled with impurity atoms is used as a phonon scattering unit. The calculation of vibrational spectra of a disordered linear chain in the generalized non-self-consistent approximation has demonstrated a strong dependence of the spectrum on the number n. For n = 6, the calculated spectrum is in an excellent agreement with the result of the computer experiment performed by Dean for a chain of 8000 atoms. The maximum number of impurities in the cluster to be considered depends on the magnitude of the initial damping (in real crystals, it is damping due to anharmonicity). The spectrum has also been calculated in the generalized self-consistent approximation. This calculation gives a smeared structureless curve, which absolutely does not agree either with the theoretical calculation in the non-self-consistent approximation or with the results obtained by Dean. This means that the generalized self-consistent approximation overestimates the weight of the incoherent scattering processes, which leads to averaging of the phases. The spectrum of a three-dimensional solid solution is calculated using a simple model of the crystal.     

Conversion issues between microwave radiance and brightness temperature

Microwave radiances are usually converted into brightness temperatures for data assimilation and retrievals. The Rayleigh-Jeans approximation has been believed to be a good approximation for the conversion at low frequencies, but inaccurate at high frequencies. However, the simplified radiative transfer models under the Rayleigh-Jeans approximation (hereafter referred as BT-RTE) have been successfully applied in radiance simulations for frequencies below 183 GHz, which has somewhat puzzled the radiative transfer community. This paper clarifies the confusion. In addition, the conversion formula for the third and the fourth Stokes components are derived.Simulations for a polarized sensor, the Special Sensor Microwave Imager and Sounder, show that the BT-RTE is generally accurate. Results for a polarimetric sensor, WINDSAT, show that the third and the fourth Stokes radiances should be converted using the exact conversion formula given in this study rather than using a direct Planck function conversion.