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NASA NTRS2014

Mars' Water Vapor Mapping by the SPICAM IR Spectrometer: Five Martian Years of Observations

The SPICAM IR instrument on the Mars Express mission continuously observes the water vapor in the martian atmosphere starting from 2004 in the 1.38-micrometer spectral band. The water vapor column abundance is retrieved from nadir observations to characterize its spatial, seasonal and interannual variations. A reference set of SPICAM water vapor column abundances (zonally averaged) covering the time period from 2004 to 2013 (martian years 27-31) is available for a grid of 2 deg Ls 2 latitude, along with an average reference map of water vapor abundance combining all the martian years of Mars Express observations. Compared to the previous data retrieval by Fedorova et al. (Fedorova, A., Korablev, O., Bertaux, J.L., Rodin, A., Kiselev, A., Perrier, S. [2006]. J. Geophys. Res. 111, E09S08) the new processing algorithm includes many improvements concerning the calibration and assumed parameters. A major improvement is the account for aerosol scattering based on dust and water ice cloud optical depths measured by THEMIS/Mars Odyssey (Smith, M.D. [2009]. Icarus 202, 444-452). The account for multiple scattering by aerosol particles increases the retrieved water vapor amount by approximately 10% in polar areas during summer, and up to 60-70% for large solar zenith angles. The sensitivity of the results to aerosol properties, surface albedo, solar spectrum, and water vapor vertical distribution has also been studied. The retrieved water vapor reveals nominal annual cycle with maximum abundance of about 60-70 pr. lm for the Northern summer and approximately 20 pr. lm for the Southern summer. The annual average amount of water has been estimated to be of 10-20 pr. micrometers, in agreement with other measurements. From year to year the seasonal cycle of water vapor abundance is very stable. An observed decrease during the MY 28 global dust storm cannot be fully attributed to the masking effect of dust, and indicates a real decrease of water amount near or above the surface. No evidence of diurnal variation of column water vapor amount was found, even though the 1.38-micrometer measurements are sensitive to the few lowermost kilometers above the surface.

Mars water vapor↗
NASA NTRS2017

HST WFC3 Observations of Uranus' 2014 Storm Clouds and Comparison with VLT/SINFONI and IRTF/Spex Observations

In November 2014 Uranus was observed with the Wide Field Camera 3 (WFC3) instrument of the Hubble Space Telescope as part of the Hubble 2020: Outer Planet Atmospheres Legacy program, OPAL. OPAL annually maps Jupiter, Uranus and Neptune (and will also map Saturn from 2018) in several visible near- infrared wavelength filters. The Uranus 2014 OPAL observations were made on the 89th November at a time when a huge cloud complex, first observed by de Pater et al. (2015) and subsequently tracked by professional and amateur astronomers (Sayanagi et al., 2016), was present at 30-40deg N. We imaged the entire visible atmosphere, including the storm system, in seven filters spanning 467924 nm, capturing variations in the coloration of Uranus clouds and also vertical distribution due to wavelength dependent changes in Rayleigh scattering and methane absorption optical depth. Here we analyse these new HST observations with the NEMESIS radiative-transfer and retrieval code in multiple-scattering mode to determine the vertical cloud structure in and around the storm cloud system. The same storm system was also observed in the H-band (1.4-1.8 micrometers) with the SINFONI Integral Field Unit Spectrometer on the Very Large Telescope (VLT) on 31st October and 11th November, reported by Irwin et al. (2016, 10.1016j.icarus.2015.09.010). To constrain better the cloud particle sizes and scattering properties over a wide wavelength range we also conducted a limb-darkening analysis of the background cloud structure in the 30-40deg N latitude band by simultaneously fitting: a) these HSTOPAL observations at a range of zenith angles; b) the VLTSINFONI observations at a range of zenith angles; and c) IRTFSpeX observations of this latitude band made in 2009 at a single zenith angle of 23deg, spanning the wavelength range 0.8-1.8 micrometers (Irwin et al., 2015, 10.1016j.icarus.2014.12.020). We find that the HST observations, and the combined HSTVLTIRTF observations at all locations are well modelled with a three-component cloud comprised of: 1) a vertically thin, but optically thick deep tropospheric cloud at a pressure of approximately 2 bars; 2) a methane-ice cloud based at the methane-condensation level of approximately 1.23 bar, with variable vertical extent; and 3) a vertically extended tropospheric haze, also based at the methane-condensation level of 1.23 bar. We find that modelling both haze and tropospheric cloud with particles having an effective radius of approximately 0.1 micron provides a good fit the observations, although for the tropospheric cloud, particles with an effective radius as large as 1.0 micron provide a similarly good fit. We find that the particles in both the tropospheric cloud and haze are more scattering at short wave- lengths, giving them a blue color, but are more absorbing at longer wavelengths, especially for the tropospheric haze. We find that the spectra of the storm clouds are well modelled by localized thickening and vertical extension of the methane-ice cloud. For the particles in the storm clouds, which we assume to be composed of methane ice particles, we find that their mean radii must lie somewhere in the range 0. 1 1. 0 m. We find that the high clouds have low integrated opacity, and that streamers reminiscent of convective thunderstorm anvils are confined to levels deeper than 1 bar. These results argue against vigorous moist convective origins for the cloud features.

atmospheres↗
NASA NTRS1992

A microwave scattering model for layered vegetation

A microwave scattering model was developed for layered vegetation based on an iterative solution of the radiative transfer equation up to the second order to account for multiple scattering within the canopy and between the ground and the canopy. The model is designed to operate over a wide frequency range for both deciduous and coniferous forest and to account for the branch size distribution, leaf orientation distribution, and branch orientation distribution for each size. The canopy is modeled as a two-layered medium above a rough interface. The upper layer is the crown containing leaves, stems, and branches. The lower layer is the trunk region modeled as randomly positioned cylinders with a preferred orientation distribution above an irregular soil surface. Comparisons of this model with measurements from deciduous and coniferous forests show good agreements at several frequencies for both like and cross polarizations. Major features of the model needed to realize the agreement include allowance for: (1) branch size distribution, (2) second-order effects, and (3) tree component models valid over a wide range of frequencies.

Karam, Mostafa A.↗
NASA NTRS2001

Shape and Structure

The convenient availability and simplicity of the Lorenz-Mie theory has resulted in a widespread practice of treating nonspherical particles (especially those in random orientation) as if they were spheres to which Lorenz-Mie results are applicable. However, the assumption of sphericity is rarely made after first having studied the effects of nonsphericity and having concluded that they are negligible. On the contrary, overwhelming evidence suggests that scattering properties of nonspherical particles, including those in random orientation, can significantly differ from those of volume- or surface-equivalent spheres. Hence, the last few decades have demonstrated major research efforts aimed at a significantly better understanding of the effects of particle shape and morphology on electromagnetic scattering. The goal of this presentation is to provide a concise summary of these efforts. The recent availability of theoretical techniques for computing single and multiple scattering of light by realistic polydispersions of spherical and nonspherical particles and the strong dependence of the Stokes scattering matrix on particle size, shape, and refractive index make polarization and depolarization measurements a powerful particle characterization tool. This presentation will focus on recent applications of photopolarimetric and lidar depolarization measurements to remote sensing characterization of tropospheric aerosols, polar stratospheric clouds (PSCs) and contrails. The talk will include (1) a short theoretical overview of the effects of particle microphysics on particle single-scattering characteristics; (2) the use of multi-angle multi-spectral photopolarimetry to retrieve the optical thickness, size distribution, refractive index, and number concentration of tropospheric aerosols over the ocean surface; and (3) the application of the T-matrix method to constraining the PSC and contrail particle microphysics using multi-spectral measurements of lidar backscatter and depolarization

Mishchenko, Michael↗
NASA NTRS1988

Exact Rayleigh scattering calculations for use with the Nimbus-7 Coastal Zone Color Scanner

The radiance reflected from a plane-parallel atmosphere and flat sea surface in the absence of aerosols has been determined with an exact multiple scattering code to improve the analysis of Nimbus-7 CZCS imagery. It is shown that the single scattering approximation normally used to compute this radiance can result in errors of up to 5 percent for small and moderate solar zenith angles. A scheme to include the effect of variations in the surface pressure in the exact computation of the Rayleigh radiance is discussed. The results of an application of these computations to CZCS imagery suggest that accurate atmospheric corrections can be obtained for solar zenith angles at least as large as 65 deg.

Gordon, Howard R.↗
NASA NTRS1999

Approximation for Horizontal Photon Transport in Cloud Remote Sensing Problems

The effect of horizontal photon transport within real-world clouds can be of consequence to remote sensing problems based on plane-parallel cloud models. An analytic approximation for the root-mean-square horizontal displacement of reflected and transmitted photons relative to the incident cloud-top location is derived from random walk theory. The resulting formula is a function of the average number of photon scatterings, and particle asymmetry parameter and single scattering albedo. In turn, the average number of scatterings can be determined from efficient adding/doubling radiative transfer procedures. The approximation is applied to liquid water clouds for typical remote sensing solar spectral bands, involving both conservative and non-conservative scattering. Results compare well with Monte Carlo calculations. Though the emphasis is on horizontal photon transport in terrestrial clouds, the derived approximation is applicable to any multiple scattering plane-parallel radiative transfer problem. The complete horizontal transport probability distribution can be described with an analytic distribution specified by the root-mean-square and average displacement values. However, it is shown empirically that the average displacement can be reasonably inferred from the root-mean-square value. An estimate for the horizontal transport distribution can then be made from the root-mean-square photon displacement alone.

Plantnick, Steven↗
NASA NTRS2002

A New Method for Estimating the Single Scattering Phase Functions of Regolith Grains

Hapke's photometric model has been widely used in solar system remote sensing applications for nearly two decades. Recently, Hapke extended his model to describe the coherent-backscatter opposition effect and multiple-scattering by particles with anisotropic single particle phase functions (SPPF's). A practical difficulty for retrieving Hapke's model parameters from typical planet, satellite, and asteroid photometry data sets is that the model employs a large number of adjustable parameters (at least eight) that can be reliably constrained only for a small number of planetary data sets in which both disk-resolved and whole-disk observations are available from opposition to very large phase angles. The present work aims to reduce the number of adjustable parameters and preserve (or even enhance) the model's accuracy and usefulness by expressing Hapke's parameters in terms of more fundamental physical properties on which they mutually depend. The most difficult part of this task, described here, is to develop a simple method for computing the effective SPPF for structurally complex regolith grains from optical constants, grain-size distribution, and average regolith porosity. The development of light-scattering models for irregularly shaped particles is a large, complex subject and many sophisticated methods, such as Discrete Dipole Approximation (DDA) and Monte-Carlo simulations, have been explored elsewhere. Many of these methods are computationally intensive and probably impractical for routine substitution in Hapke's model. Here, progress is reported in developing a practical, semi-empirical method for estimating the directional scattering behavior (i.e. SPPF) of irregular regolith grains. The method employs Optical Transfer Function (OTF) techniques to model how the structural complexity of regolith particles broaden and attenuate the angular distribution of scattered light relative to that expected from ideal spherical particles of equivalent size and composition.

Helfenstein, P.↗
NASA NTRS1991

Isothermal, Compton-heated coronae above accretion disks

The structure of Compton-heated coronae above accretion disks is studied here by using analytic and numerical approaches are used here to determine the direct and scattered radiation reaching the base of the corona for a range of central source luminosities. It is found that the outer region of the corona is unaffected by multiple scattering in the interior, provided that the luminosity of the central source is sufficient below the Eddington limit. How attenuation and scattering by the corona affects the strength of chromospheric emission lines is determined, as is the condition for which the irradiation due to the central source exceeds the locally generated flux from the disk. Finally, it is shown that the stability analysis for irradiated accretion disks of Tuchman et al. is not substantially altered by the corona.

Ostriker, Eve C.↗
NASA NTRS1991

Recent studies of the optical properties of dust and cloud particles in the Mars atmosphere and the interannual frequency of global dust storms

The results of research with two distinctly separate sets of observations yield new information on the optical properties of particulate scatterers in the Mars atmosphere, and on the interannual variability of the abundance of such scatterers in the Mars atmosphere. The first set of observations were taken by the IRTM (Infrared Thermal Mapper) instrument onboard the Viking Orbiters, during the period 1976 to 1980. Several hundred emission phase function (EPF) sequences were obtained over the Viking mission, in which the IRTM visual brightness channel observed the same area of surface/atmosphere as the spacecraft passed overhead. The 1 to 2 percent accuracy of calibration and the phase-angle coverage that characterizes these data make them ideally suited to determining both the optical depths and optical properties of dust and cloud scatterers in the Mars atmosphere versus latitude, longitude, seasons (L sub s), and surface elevation over the extended period of Viking observations. The EPF data were analyzed with a multiple scattering radiative transfer code to determine dust single scattering albedos which are distinctly higher than indicated by the Viking Lander observations. The second set of observations regard ground-based observations of the 1.3 to 2.6 mm rotational transitions of CO in the Martian atmosphere. The low-to-mid latitude average of the atmospheric temperature profile (0 to 70 km altitude) were derived from a number of such observations over the 1980 to 1990 period.

Clancy, R. T.↗
NASA NTRS1974

Scattering and absorption from poly-dispersed aerosols

Results from numerical computations of the diffuse sky radiances and degree of polarization are given. These results were obtained by solving the equation of radiative transfer in the formulation of Eschelbach. In these computations, multiple scattering and absorption by aerosol particles were considered. In addition, results from experimental measurements of the complex refractive index of aerosol samples at different relative humidities are presented. From the radiation flux divergences which were computed based on the determined properties of atmospheric aerosol particles, atmospheric heating rates were derived which were found to be comparable to the heating rates by water vapor.

Bullrich, K.↗
NASA NTRS1994

Asymmetry parameters of the phase function for densely packed scattering grains

Spatial correlation among densely packed particles can substantially change their single-scattering properties, thus making questionable the applicability of the independent scattering approximation in calculations of light scattering by planetary regoliths. The same problem arises in geophysics in light scattering computations for snow, frosts, and bare soil. In this paper, we use a dense-medium light-scattering theory based on the introduction of the static structure factor to calculate asymmetry parameters of the phase function for densely packed particles with real refractive indices 1.31 and 1.66, approximating water ice and soil particles, respectively, and imaginary refractive indices 0, 0.01, and 0.3. For sparsely distributed, independently scattering grains, the calculated asymmetry parameters are always positive and always larger than those for densely packed particles. For densely packed grains, the asymmetry parameters may be negative but only for radius-to-wavelength ratios from about 0.1 to about 0.4. With decreasing particle size, the calculated asymmetry parameters tend to zero independently of the compaction state. In the geometrical optics regime, the asymmetry parameters for densely packed scatterers are positive and very close to those for independently scattering grains. These results may have important implications for remote sensing of the Earth and solid planetary surfaces. In particular, it is demonstrated that negative asymmetry parameters derived with some approximate multiple-scattering theories may be physically irrelevant and can be the result of using an inaccurate bidirectional reflection function combined with the ill-conditionally of the inverse scattering problem.

Mishchenko, Michael I.↗
NASA NTRS1997

Re-Analysis of the Solar Phase Curves of the Icy Galilean Satellites

Re-analysis of the solar phase curves of the icy Galilean satellites demonstrates that the quantitative results are dependent on the single particle scattering function incorporated into the photometric model; however, the qualitative properties are independent. The results presented here show that the general physical characteristics predicted by a Hapke model (B. Hapke, 1986, Icarus 67, 264-280) incorporating a two parameter double Henyey-Greenstein scattering function are similar to the predictions given by the same model incorporating a three parameter double Henyey-Greenstein scattering function as long as the data set being modeled has adequate coverage in phase angle. Conflicting results occur when the large phase angle coverage is inadequate. Analysis of the role of isotropic versus anisotropic multiple scattering shows that for surfaces as bright as Europa the two models predict very similar results over phase angles covered by the data. Differences arise only at those phase angles for which there are no data. The single particle scattering behavior between the leading and trailing hemispheres of Europa and Ganymede is commensurate with magnetospheric alterations of their surfaces. Ion bombardment will produce more forward scattering single scattering functions due to annealing of potential scattering centers within regolith particles (N. J. Sack et al., 1992, Icarus 100, 534-540). Both leading and trailing hemispheres of Europa are consistent with a high porosity model and commensurate with a frost surface. There are no strong differences in predicted porosity between the two hemispheres of Callisto, both are consistent with model porosities midway between that deduced for Europa and the Moon. Surface roughness model estimates predict that surface roughness increases with satellite distance from Jupiter, with lunar surface roughness values falling midway between those measured for Ganymede and Callisto. There is no obvious variation in predicted surface roughness with hemisphere for any of the Galilean satellites.

Domingue, Deborah↗
NASA NTRS1992

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

Tsang, Leung↗
NASA NTRS2015

An Innovative Concept for Spacebased Lidar Measurement of Ocean Carbon Biomass

Beam attenuation coefficient, c, provides an important optical index of plankton standing stocks, such as phytoplankton biomass and total particulate carbon concentration. Unfortunately, c has proven difficult to quantify through remote sensing. Here, we introduce an innovative approach for estimating c using lidar depolarization measurements and diffuse attenuation coefficients from ocean color products or lidar measurements of Brillouin scattering. The new approach is based on a theoretical formula established from Monte Carlo simulations that links the depolarization ratio of sea water to the ratio of diffuse attenuation Kd and beam attenuation C (i.e., a multiple scattering factor). On July 17, 2014, the CALIPSO satellite was tilted 30Âdeg off-nadir for one nighttime orbit in order to minimize ocean surface backscatter and demonstrate the lidar ocean subsurface measurement concept from space. Depolarization ratios of ocean subsurface backscatter are measured accurately. Beam attenuation coefficients computed from the depolarization ratio measurements compare well with empirical estimates from ocean color measurements. We further verify the beam attenuation coefficient retrievals using aircraft-based high spectral resolution lidar (HSRL) data that are collocated with in-water optical measurements.

Hu, Yongxiang↗
NASA NTRS2013

Evaluating Light Rain Drop Size Estimates from Multiwavelength Micropulse Lidar Network Profiling

This paper investigates multiwavelength retrievals of median equivolumetric drop diameter D(sub 0) suitable for drizzle and light rain, through collocated 355-/527-nm Micropulse Lidar Network (MPLNET) observations collected during precipitation occurring 9 May 2012 at the Goddard Space Flight Center (GSFC) project site. By applying a previously developed retrieval technique for infrared bands, the method exploits the differential backscatter by liquid water at 355 and 527 nm for water drops larger than approximately 50 micrometers. In the absence of molecular and aerosol scattering and neglecting any transmission losses, the ratio of the backscattering profiles at the two wavelengths (355 and 527 nm), measured from light rain below the cloud melting layer, can be described as a color ratio, which is directly related to D(sub 0). The uncertainty associated with this method is related to the unknown shape of the drop size spectrum and to the measurement error. Molecular and aerosol scattering contributions and relative transmission losses due to the various atmospheric constituents should be evaluated to derive D(sub 0) from the observed color ratio profiles. This process is responsible for increasing the uncertainty in the retrieval. Multiple scattering, especially for UV lidar, is another source of error, but it exhibits lower overall uncertainty with respect to other identified error sources. It is found that the total error upper limit on D(sub 0) approaches 50%. The impact of this retrieval for long-term MPLNET monitoring and its global data archive is discussed.

light-rain drop size estimates↗
NASA NTRS1994

Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres

Although neglecting polarization and replacing the rigorous vector radiative transfer equation by its approximate scalar counterpart has no physical background, it is a widely used simplification when the incident light is unpolarized and only the intensity of the reflected light is to be computed. We employ accurate vector and scalar multiple-scattering calculations to perform a systematic study of the errors induced by the neglect of polarization in radiance calculations for a homogeneous, plane-parallel Rayleigh-scattering atmosphere (with and without depolarization) above a Lambertian surface. Specifically, we calculate percent errors in the reflected intensity for various directions of light incidence and reflection, optical thicknesses of the atmosphere, single-scattering albedos, depolarization factors, and surface albedos. The numerical data displayed can be used to decide whether or not the scalar approximation may be employed depending on the parameters of the problem. We show that the errors decrease with increasing depolarization factor and/or increasing surface albedo. For conservative or nearly conservative scattering and small surface albedos, the errors are maximum at optical thicknesses of about 1. The calculated errors may be too large for some practical applications, and, therefore, rigorous vector calculations should be employed whenever possible. However, if approximate scalar calculations are used, we recommend to avoid geometries involving phase angles equal or close to 0 deg and 90 deg, where the errors are especially significant. We propose a theoretical explanation of the large vector/scalar differences in the case of Rayleigh scattering. According to this explanation, the differences are caused by the particular structure of the Rayleigh scattering matrix and come from lower-order (except first-order) light scattering paths involving right scattering angles and right-angle rotations of the scattering plane.

Mishchenko, M. I.↗
NASA NTRS1989

Analytical optical scattering in clouds

An analytical optical model for scattering of light due to lightning by clouds of different geometry is being developed. The self-consistent approach and the equivalent medium concept of Twersky was used to treat the case corresponding to outside illumination. Thus, the resulting multiple scattering problem is transformed with the knowledge of the bulk parameters, into scattering by a single obstacle in isolation. Based on the size parameter of a typical water droplet as compared to the incident wave length, the problem for the single scatterer equivalent to the distribution of cloud particles can be solved either by Mie or Rayleigh scattering theory. The super computing code of Wiscombe can be used immediately to produce results that can be compared to the Monte Carlo computer simulation for outside incidence. A fairly reasonable inverse approach using the solution of the outside illumination case was proposed to model analytically the situation for point sources located inside the thick optical cloud. Its mathematical details are still being investigated. When finished, it will provide scientists an enhanced capability to study more realistic clouds. For testing purposes, the direct approach to the inside illumination of clouds by lightning is under consideration. Presently, an analytical solution for the cubic cloud will soon be obtained. For cylindrical or spherical clouds, preliminary results are needed for scattering by bounded obstacles above or below a penetrable surface interface.

Phanord, Dieudonne D.↗
NASA NTRS2016

A FDTD Solution of Scattering of Laser Beam with Orbital Angular Momentum by Dielectric Particles: Far-Field Characteristics

Electromagnetic (EM) beams with orbital angular momentum (OAM) may have great potential applications in communication technology and in remote sensing of the Earth-atmosphere system and outer planets. Study of their interaction with optical lenses and dielectric or metallic objects, or scattering of them by particles in the Earth-atmosphere system, is a necessary step to explore the advantage of the OAM EM beams. In this study, the 3-dimensional (3D) scattered-field (SF) finite-difference time domain (FDTD) technique with the convolutional perfectly matched layer (CPML) absorbing boundary conditions (ABC) is applied to calculate the scattering of the purely azimuthal (the radial mode number is assumed to be zero) Laguerre–Gaussian (LG) beams with the OAM by dielectric particles. We found that for OAM beam׳s interaction with dielectric particles, the forward-scattering peak in the conventional phase function (P11) disappears, and light scattering peak occurs at a scattering angle of ~15° to 45°. The disappearance of forward-scattering peak means that, in laser communications most of the particle-scattered noise cannot enter the receiver, thus the received light is optimally the original OAM-encoded signal. This feature of the OAM beam also implies that in lidar remote sensing of the atmospheric particulates, most of the multiple-scattering energy will be off lidar sensors, and this may result in an accurate profiling of particle layers in the atmosphere or in the oceans by lidar, or even in the ground when a ground penetration radar (GPR) with the OAM is applied. This far-field characteristics of the scattered OAM light also imply that the optical theorem, which is derived from plane-parallel wave scattering case and relates the forward scattering amplitude to the total cross section of the scatterer, is invalid for the scattering of OAM beams by dielectric particles.

Electromagnetic beams↗