Determination of the particulate extinction-coefficient profile and the column-integrated lidar ratios using the backscatter-coefficient and optical-depth profiles

A new method is considered that can be used for inverting data obtained from a combined elastic-inelastic lidar or a high spectral resolution lidar operating in a one-directional mode, or an elastic lidar operating in a multiangle mode. The particulate extinction coefficient is retrieved from the simultaneously measured profiles of the particulate backscatter coefficient and the particulate optical depth. The stepwise profile of the column-integrated lidar ratio is found that provides best matching of the initial (inverted) profile of the optical depth to that obtained by the inversion of the backscatter-coefficient profile. The retrieval of the extinction coefficient is made without using numerical differentiation. The method reduces the level of random noise in the retrieved extinction coefficient to the level of noise in the inverted backscatter coefficient. Examples of simulated and experimental data are presented.     

Spherical particle size determination by analytical inversion of the UV-visible-NIR extinction spectrum

An analytic inversion method, based on the anomalous diffraction approximation for nonabsorbing spherical particles, was developed to retrieve the size distribution from the optical turbidity or extinction spectrum. This method makes use of a differential Fourier cosine transform approach and provides a simple and fast inversion by means of fast Fourier transform and the Savitzky-Golay filter. The applicability of this algorithm was tested on the extinction data generated by the Mie solution. The effects of noise, modality, band limits, and data set size were analyzed by comparison with simulated data. This method can be used to reconstruct the original monomodal and bimodal distributions from 10% noise-corrupted data. The peak position and ratio of peak heights can be recovered with 10% or less deviation. The experiments with latex spheres showed that the inversion result from this method compares favorably with that from the dynamic light scattering measurement.     

Remote Sensing of the Earth 's Atmosphere by the Spaceborne Occultation Radiometer, ORA: Final Inversion Algorithm

We describe the final inversion algorithm developed to process solar occultation data measured in 1992-1993 by the Occultation Radiometer (ORA) spaceborne experiment. First we develop a new method to improve the ORA total extinction altitude profiles retrieved with the previously described Natural Orthogonal Polynomial Expansion (NOPE) method. Using these improved profiles, we perform spectral inversion and obtain altitude density profiles for O(3) and NO(2) and extinction profiles for the aerosols. Validation of number density profiles between the Stratospheric Aerosol and Gas Experiment II (SAGE II) and the ORA shows satisfactory agreement.     

Application of statistical methods to the determination of slope in lidar data

Assumptions made in the analysis of both Raman lidar measurements of aerosol extinction and differential absorption lidar (DIAL) measurements of an absorbing species are tested. Statistical analysis techniques are used to enhance the estimation of aerosol extinction and aerosol extinction error that is usually handled using a linear model. It is determined that the most probable extinction value can differ from that of the linear assumption by up to 10% and that differences larger than 50% can occur in the calculation of extinction error. Ignoring error in the number density alters the calculated extinction by up to 3% and that of extinction error by up to 10%. The preceding results were obtained using the least-squares technique. The least-squares technique assumes that the data being regressed are normally distributed. However, the quantity that is usually regressed in aerosol extinction and DIAL calculations is not normally distributed. A technique is presented that allows the required numerical derivative to be determined by regressing only normally distributed data. The results from this technique are compared with the usual procedure. The same concerns raised here regarding appropriate choice of a model in the context of aerosol extinction calculations should apply to DIAL calculations of absorbing species such as water vapor or ozone as well because the numerical derivative that is required is identical.     

Validation of the Raman lidar algorithm for quantifying aerosol extinction

To calculate aerosol extinction from Raman lidar data, it is necessary to evaluate the derivative of a molecular Raman signal with respect to range. The typical approach taken in the lidar community is to make an a priori assumption about the functional behavior of the data to calculate the derivative. It has previously been shown that the use of the chi-squared technique to determine the most likely functional behavior of the data prior to actually calculating the derivative eliminates the need for making a priori assumptions. Here that technique is validated through numerical simulation and by application to a significant body of Raman lidar measurements. In general, we show that the chi-squared approach for evaluating extinction yields lower extinction uncertainty than traditional techniques. We also use the technique to study the feasibility of developing a general characterization of the extinction uncertainty that could permit the uncertainty in Raman lidar aerosol extinction measurements to be estimated accurately without the need of the chi-squared technique.     

Numerical computation and measurement of infrared extinction of the powder of brass 70Cu/30Zn

Abstract

The FDTD method is used to calculate the specific extinction cross section of the powder of brass 70Cu/30Zn with 1.35×10⁴ to 2.56×10⁵ particles in the infrared frequency range. A digitized model of body‐center‐like structures is used for the calculations of specific extinction cross‐section. From theoretical calculations, the value of a specific extinction cross section of the powder of brass 70Cu/30Zn is between 0.14 to 4.0 m²/g. While the experimental measurement shows the value of specific extinction cross section to be between 0.58 to 3.78 m²/g. The theoretical results concur with those obtained from the experimental measurement for the cell sizes of particles in the range of 0.05 to 0.4 p.m. There are some differences between the theoretical value and measurement data of specific extinction cross section for other particle sizes outside the range of 0.05 to 0.4μm.     

基于主成分分析的消光法波长选择算法

在消光法颗粒粒径测量中,被测颗粒系的消光光谱包含有颗粒粒径、折射率等信息.在可见及可见-红外波段内,对单峰R-R分布的消光光谱,一阶微分以及二阶微分消光光谱进行主成分变换.通过分析比较,提出一种基于主成分分析的特征波长的选择算法.该算法首先对一阶微分消光光谱进行主成分变换,然后将每个波长下的一阶微分消光谱对主成分贡献率的大小作为特征波长选择的主要依据,同时将光谱范围的边界波长也作为特征波长,这样的波长选择方法保证了选出的光谱消光值具有较高的信息量.文中分别对单峰及双峰R-R分布的颗粒系采用独立模式反演算法进行仿真实验验证,仿真实验证实了所提方法的有效性和实用性.     

Optimal eigenanalysis for the treatment of aerosols in the retrieval of atmospheric composition from transmission measurements

The separation of the individual contributions of aerosol and gases to the total attenuation of radiation through the atmosphere has been the subject of much scientific investigation since remote sensing experiments first began. We describe a new scheme to account for the spectral variation of the aerosol extinction in the inversion of transmission data from occultation measurements. Because the spectral variation of the aerosol extinction is generally unknown,the inversion problem is underdetermined and cannot be solved without a reduction in the number of unknowns in the set of equations used to describe the attenuation at each wavelength. This reduction can be accomplished by a variety of methods, including use of a priori information, the parameterization of the aerosol spectral attenuation, and the specification of the form of the aerosol size distribution. We have developed and implemented a parameterization scheme based on existing empirical and modeled information about the microphysical properties of aerosols. This scheme employs the eigenvectors from an extensive set of simulations to parameterize the aerosol extinction coefficient for incorporation into the inversion algorithm. We examine the accuracy of our method using data sets containing over 24,000 extinction spectra and compare it with that of another scheme that is currently implemented in the Polar Ozone and Aerosol Measurement (POAM) satellite experiment. In simulations using 80 wavelengths in the UV-visible-near-IR spectral range of the Stratospheric Aerosol and Gas Experiment III (SAGE) instrument, we show that, for our optimal parameterization, errors below 1% are observed in 80% of cases, whereas only approximately 20% of all cases are as accurate as this in a quadratic parameterization employing the logarithm of the wavelength.     

Aerosol properties from spectral extinction and backscatter estimated by an inverse Monte Carlo method

The feasibility of using a generalized stochastic inversion methodology to estimate aerosol size distributions accurately by use of spectral extinction, backscatter data, or both is examined. The stochastic method used, inverse Monte Carlo (IMC), is verified with both simulated and experimental data from aerosols composed of spherical dielectrics with a known refractive index. Various levels of noise are superimposed on the data such that the effect of noise on the stability and results of inversion can be determined. Computational results show that the application of the IMC technique to inversion of spectral extinction or backscatter data or both can produce good estimates of aerosol size distributions. Specifically, for inversions for which both spectral extinction and backscatter data are used, the IMC technique was extremely accurate in determining particle size distributions well outside the wavelength range. Also, the IMC inversion results proved to be stable and accurate even when the data had significant noise, with a signal-to-noise ratio of 3.     

Repetitive genetic inversion of optical extinction data

We describe a genetic method of deriving aerosol size distributions from multiwavelength extinction measurements. The genetic inversion searches for log-normal size distribution parameters whose calculated extinctions best fit the data. By repetitively applying the genetic inversion using different random number seeds, we are able to generate multiple solutions that fit the data equally well. When these solutions are similar, they lend confidence to an interpretation, whereas when they vary widely, they demonstrate nonuniqueness. In this way we show that, even in the case of a single log-normal distribution, many different distributions can fit the same set of extinction data unless the misfit is reduced below typical measurement error levels. In the case of a bimodal distribution, we find many dissimilar size distributions that fit the data to within 1% at six wavelengths. To recover the original bimodal distribution satisfactorily, we found that extinctions at ten wavelengths must be fitted to within 0.5%. Our results imply that many size distributions recovered from existing extinction measurements can be highly nonunique and should be treated with caution.     

Stable near-end solution of the lidar equation for clear atmospheres

A stable variant of the near-end solution has been developed for inversion of lidar signals measured in clear atmospheres. The inversion is based on the use of reference values of the extinction coefficient obtained with a nephelometer at the lidar measurement site. The inversion method, based on a combination of the optical depth and boundary point solutions, is illustrated by simulated and experimental data.     

Extension of the graphical technique for estimation of particle size distribution parameters for the consistent intercomparison of diverse sets of multiwavelength lidar derived optical coefficients

In applying the graphical technique to the estimation of the particle size distribution (PSD) parameters, determination of proper bounds surrounding the solution space for a particular confidence level is essential to the consistent intercomparison of diverse multiwavelength lidar optical data sets. The graphical technique utilizes ratios of backscatter and/or extinction coefficients, and it is shown that if the correlation between ratios is not taken into account in calculating the error bounds, the solution space will be overestimated, resulting in relatively larger discrepancies for a larger number of optical coefficients. A method for correcting the bounds, to account for the correlation is developed for various numbers of wavelengths. These improved bounds are then applied, for the case of a monomodal lognormal PSD, with an assumed refractive index, to assess the role additional Raman extinction channels play in improving retrieval capability of a typical three-channel backscatter lidar (1064, 532, and 355 nm) under varying noise levels. Applying the same formalism to underlying bimodal distributions of coarse and fine particles can result in false monomodal solutions. However, when both Raman optical extinction channels are available, no solution is obtained. This can potentially serve as a quick and simple method, prior to a more complex regularization analysis, to differentiate between cases in which the fine mode is dominant versus the cases in which the contribution from the coarse mode is significant.     

Generalized eikonal approximation for fast retrieval of particle size distribution in spectral extinction technique

In retrieving particle size distribution from spectral extinction data, a critical issue is the calculation of extinction efficiency, which affects the accuracy and rapidity of the whole retrieval. The generalized eikonal approximation (GEA) method, used as an alternative to the rigorous Mie theory, is introduced for retrieval of the unparameterized shape-independent particle size distribution (PSD). To compute the extinction efficiency more efficiently, the combination of GEA method and Mie theory is adopted in this paper, which not only extends the applicable range of the approximation method but also improves the speed of the whole retrieval. Within the framework of the combined approximation method, the accuracy and limitations of the retrieval are investigated. Moreover, the retrieval time and memory requirement are also discussed. Both simulations and experimental results show that the combined approximation method can be successfully applied to retrieval of PSD when the refractive index is within the validity range. The retrieval results we present demonstrate the high reliability and stability of the method. By using this method, we find the complexity and computation time of the retrieval are significantly reduced and the memory resources can also be saved effectively, thus making this method more suitable for online particle sizing.     

General method for calibrating Sun photometers

A general method for calibrating Sun photometers that relaxes the constraints on atmospheric conditions is described. Instead of requiring constant extinction conditions the method requires only that the relative aerosol size distribution remains constant during observations over a range of air masses during a morning or afternoon. Provided that the relative aerosol extinction component [m(a)(t)δ(t, λ(0))] can be obtained at wavelength λ(0), the calibration at wavelength channel λ can be calculated with simple least-squares techniques. A variant of the method in which a Sun photometer is used to provide [m(a)(t)δ(t, λ(0))] is detailed and is verified with both model atmospheres and Sun-photometer data for 1988-1991 from Cape Grim, Tasmania (41°S). The method produces calibration data having sample variances more than 5 times smaller than Langley method calibration results.     

Sensitivity of the lidar solution to errors of the aerosol backscatter-to-extinction ratio: influence of a monotonic change in the aerosol extinction coefficient

Unlike other errors in the lidar equation solution for the two-component atmosphere, the error of the measured aerosol extinction coefficient caused by inaccuracies in the assumed aerosol backscatter-to-extinction ratios significantly depends on the aerosol spatial inhomogeneity. In a slightly nonhomogeneous atmosphere, an incorrect value in the assumed aerosol backscatter-to-extinction ratio does not significantly corrupt the measurement result, whereas in an atmosphere with a large monotonic change of the aerosol extinction [e.g., in the lower troposphere], the incorrect value yields a large distortion of the retrieved extinction-coefficient profile. In the latter case, even the far-end solution can produce a large error in the retrieved extinction coefficient. The analytical formulas for the determination of the range errors, obtained for the Klett and the optical-depth solutions, show that these errors significantly depend on the method of the boundary-condition determination. Distortions of the retrieved aerosol extinction profiles are, in general, larger if the assumed aerosol backscatter-to-extinction ratio is underestimated in relation to the real value.     

Transmission as an input boundary value for an analytical solution of a single-scatter lidar equation

Single-scatter lidar signals carry information on the spatial atmospheric backscatter coefficient, attenuated by the path-integrated extinction. Assuming that the relationship between the backscatter and the extinction is known, the inverted extinction profile and the path-integrated extinction are uniquely related to the input boundary value. The integrated extinction over a certain range interval is a measure of the optical transmission along that path. In reverse, for a given transmission over the path of interest, the input boundary value is uniquely defined. An analytical expression is derived that describes the input boundary condition for the inversion of the single-scatter lidar equation in terms of the transmission losses over the path of interest. The proposed method is useful in situations in which independent transmission measurements are carried out or in situations in which targets such as multiple cloud layers or beam stops are available in the lidar path. Equations for both the forward and the backward integration method are presented. Compared with the widely accepted inversion schemes that are based on single-point reference extinction values, the proposed method is less sensitive to noise.     

Determination of Optical Constants of Solgel-Derived Inhomogeneous TiO(2) Thin Films by Spectroscopic Ellipsometry and Transmission Spectroscopy

Amorphous and nanocrystalline TiO(2) thin films coated on a vitreous silica substrate by a solgel dip coating method are investigated for optical properties by spectroscopic ellipsometry (SE) together with transmission spectroscopy. A method of analysis of SE data to determine the degree of inhomogeneity of TiO(2) films has also been presented. Instead of the refractive index, the volume fraction of void has been assumed to vary along the thickness of the films and an excellent agreement between the experimental and calculated data of SE below the fundamental band gap has been obtained. The transmission spectrum of these samples is inverted to obtain the extinction coefficient k spectrum in the wavelength range of 300-1600 nm by using the refractive indices and parameters of structure determined by SE. The nonzero extinction coefficient below the fundamental band-gap energy (3.2 eV) has been obtained for the nanocrystalline TiO(2) and shows the presence of optical scattering in the film.     

Measurement of the extinction of sputtered TiO2 films

In this paper a method for separate measurement of the extinction of optical thin films is presented. The method combines a laser calorimetric technique and a light-scattering goniophotometer. As an example, the spectral extinction properties of r.f. reactively sputtered TiO₂ films were measured. Under certain conditions absorption indices of 10^-5 or less can be achieved. Thus light scattering, rather than absorption, is the dominant optical loss mechanism in sputtered TiO₂ films.     

III-posed retrieval of aerosol extinction coefficient profiles from Raman lidar data by regularization

In the analysis of Raman lidar measurements of aerosol extinction, it is necessary to calculate the derivative of the logarithm of the ratio between the atmospheric number density and the range-corrected lidar-received power. The statistical fluctuations of the Raman signal can produce large fluctuations in the derivative and thus in the aerosol extinction profile. To overcome this difficult situation we discuss three methods: Tikhonov regularization, variational, and the sliding best-fit (SBF). Three methods are performed on the profiles taken from the European Aerosol Research Lidar Network lidar database simulated at the Raman shifted wavelengths of 387 and 607 nm associated with the emitted signals at 355 and 532 nm. Our results show that the SBF method does not deliver good results for low fluctuation in the profile. However, Tikhonov regularization and the variational method yield very good aerosol extinction coefficient profiles for our examples. With regard to, e.g., the 532 nm wavelength, the L2 errors of the aerosol extinction coefficient profile by using the SBF, Tikhonov, and variational methods with respect to synthetic noisy data are 0.0015(0.0024), 0.00049(0.00086), and 0.00048(0.00082), respectively. Moreover, the L2 errors by using the Tikhonov and variational methods with respect to a more realistic noisy profile are 0.0014(0.0016) and 0.0012(0.0016), respectively. In both cases the L2 error given in parentheses concerns the second example.     

Bridging technique for calculating the extinction efficiency of arbitrary shaped particles

A general bridging technique is developed to calculate the extinction efficiency of particles by combining the extended Rayleigh-Debye approximation and the modified anomalous diffraction theory. Comparisons with the exact methods are performed for spheres, spheroids, infinite cylinders, and finite cylinders. The overall features of the extinction efficiencies calculated from the new, to our knowledge, bridging method are in agreement with those calculated from the exact methods. Also discussed are accuracy of the new method and its domain of applicability. The new technique can be potentially applied to particles of virtually any shapes and sizes.