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NASA NTRS2016

Using Remotely Sensed Data for Climate Change Mitigation and Adaptation: A Collaborative Effort Between the Climate Change Adaptation Science Investigators Workgroup (CASI), NASA Johnson Space Center, and Jacobs Technology

With ever changing landscapes and environmental conditions due to human induced climate change, adaptability is imperative for the long-term success of facilities and Federal agency missions. To mitigate the effects of climate change, indicators such as above-ground biomass change must be identified to establish a comprehensive monitoring effort. Researching the varying effects of climate change on ecosystems can provide a scientific framework that will help produce informative, strategic and tactical policies for environmental adaptation. As a proactive approach to climate change mitigation, NASA tasked the Climate Change Adaptation Science Investigators Workgroup (CASI) to provide climate change expertise and data to Center facility managers and planners in order to ensure sustainability based on predictive models and current research. Generation of historical datasets that will be used in an agency-wide effort to establish strategies for climate change mitigation and adaptation at NASA facilities is part of the CASI strategy. Using time series of historical remotely sensed data is well-established means of measuring change over time. CASI investigators have acquired multispectral and hyperspectral optical and LiDAR remotely sensed datasets from NASA Earth Observation Satellites (including the International Space Station), airborne sensors, and astronaut photography using hand held digital cameras to create a historical dataset for the Johnson Space Center, as well as the Houston and Galveston area. The raster imagery within each dataset has been georectified, and the multispectral and hyperspectral imagery has been atmospherically corrected. Using ArcGIS for Server, the CASI-Regional Remote Sensing data has been published as an image service, and can be visualized through a basic web mapping application. Future work will include a customized web mapping application created using a JavaScript Application Programming Interface (API), and inclusion of the CASI data for the NASA Johnson Space Center into a NASA-Wide GIS Institutional Portal.

Jagge, Amy↗

NASA NTRS1978

Lidar: A laser technique for remote sensing

Experimental airborne lidar systems proved to be useful for shallow water bathymetric measurements, and detection and identification of oil slicks and algae. Dye fluorescence applications using organic dyes was studied. The possibility of remotely inducing dye flourescence by means of pulsed lasers opens up several hydrospheric applications for measuring water currents, water temperature, and salinity. Aerosol measurements by lidar are also discussed.

Wilkerson, T. D.↗

NASA NTRS1992

Conically scanned lidar telescope using holographic optical elements

Holographic optical elements (HOE) using volume phase holograms make possible a new class of lightweight scanning telescopes having advantages for lidar remote sensing instruments. So far, the only application of HOE's to lidar has been a non-scanning receiver for a laser range finder. We introduce a large aperture, narrow field of view (FOV) telescope used in a conical scanning configuration, having a much smaller rotating mass than in conventional designs. Typically, lidars employ a large aperture collector and require a narrow FOV to limit the amount of skylight background. Focal plane techniques are not good approaches to scanning because they require a large FOV within which to scan a smaller FOV mirror or detector array. Thus, scanning lidar systems have either used a large flat scanning mirror at which the receiver telescope is pointed, or the entire telescope is steered. We present a concept for a conically scanned lidar telescope in which the only moving part is the HOE which serves as the primary collecting optic. We also describe methods by which a multiplexed HOE can be used simultaneously as a dichroic beamsplitter.

Schwemmer, Geary K.↗

NASA NTRSDate not supplied

Polarimeter + Lidar Derived Aerosol Particle Number Concentration

In this study, we propose a simple method to derive vertically resolved aerosol particle number concentration (Na) using combined polarimetric and lidar remote sensing observations. This method relies on accurate polarimeter retrievals of the fine-mode column-averaged aerosol particle extinction cross section and accurate lidar measurements of vertically resolved aerosol particle extinction coefficient such as those provided by multiwavelength high spectral resolution lidar. We compare the resulting lidar + polarimeter vertically resolved Na product to in situ Na data collected by airborne instruments during the NASA aerosol cloud meteorology interactions over the western Atlantic experiment (ACTIVATE). Based on all 35 joint ACTIVATE flights in 2020, we find a total of 32 collocated in situ and remote sensing profiles that occur on 11 separate days, which contain a total of 322 cloud-free vertically resolved altitude bins of 150 m resolution. We demonstrate that the lidar + polarimeter Na agrees to within 106% for 90% of the 322 vertically resolved points. We also demonstrate similar agreement to within 121% for the polarimeter-derived column-averaged Na. We find that the range-normalized mean absolute deviation (NMAD) for the polarimeter-derived column-averaged Na is 21%, and the NMAD for the lidar + polarimeter-derived vertically resolved Na is 16%. Taken together, these findings suggest that the error in the polarimeter-only column-averaged Na and the lidar + polarimeter vertically resolved Na are of similar magnitude and represent a significant improvement upon current remote sensing estimates of Na.

Aerosol number concentration↗

NASA NTRS2008

Processing LiDAR Data to Predict Natural Hazards

ELF-Base and ELF-Hazards (wherein 'ELF' signifies 'Extract LiDAR Features' and 'LiDAR' signifies 'light detection and ranging') are developmental software modules for processing remote-sensing LiDAR data to identify past natural hazards (principally, landslides) and predict future ones. ELF-Base processes raw LiDAR data, including LiDAR intensity data that are often ignored in other software, to create digital terrain models (DTMs) and digital feature models (DFMs) with sub-meter accuracy. ELF-Hazards fuses raw LiDAR data, data from multispectral and hyperspectral optical images, and DTMs and DFMs generated by ELF-Base to generate hazard risk maps. Advanced algorithms in these software modules include line-enhancement and edge-detection algorithms, surface-characterization algorithms, and algorithms that implement innovative data-fusion techniques. The line-extraction and edge-detection algorithms enable users to locate such features as faults and landslide headwall scarps. Also implemented in this software are improved methodologies for identification and mapping of past landslide events by use of (1) accurate, ELF-derived surface characterizations and (2) three LiDAR/optical-data-fusion techniques: post-classification data fusion, maximum-likelihood estimation modeling, and hierarchical within-class discrimination. This software is expected to enable faster, more accurate forecasting of natural hazards than has previously been possible.

Fairweather, Ian↗

NASA NTRSDate not supplied

TPSAS-NF1676L-34528-DND

Since 2006, the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP), aboard the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite, has provided a unique vertical perspective of Earth's atmosphere. These measurements have furthered our understanding of the role aerosols and clouds play in the climate system and have been leveraged for atmospheric modeling and air quality studies. In this seminar, the basics of LIDAR remote sensing will first be presented, including its operating principles, setup and geometry, the LIDAR equation, and different LIDAR types and techniques. Next, an overview of the LIDAR systems at NASA Langley Research Center will be provided, with an emphasis on the CALIPSO satellite mission, including available data products and examples of browse images. Lastly, several CALIPSO-based science applications and research projects will be discussed, including cloud contamination in passive satellite aerosol retrievals, aerosol detection limits, trends in aerosol vertical distribution, and air quality (PM2.5 concentrations).

Travis Toth↗

NASA NTRS2022

Polarimeter + Lidar–Derived Aerosol Particle Number Concentration

In this study, we propose a simple method to derive vertically resolved aerosol particle number concentration (Na) using combined polarimetric and lidar remote sensing observations. This method relies on accurate polarimeter retrievals of the fine-mode column-averaged aerosol particle extinction cross section and accurate lidar measurements of vertically resolved aerosol particle extinction coefficient such as those provided by multiwavelength high spectral resolution lidar. We compare the resulting lidar + polarimeter vertically resolved N(a) product to in situ N(a) data collected by airborne instruments during the NASA aerosol cloud meteorology interactions over the western Atlantic experiment (ACTIVATE). Based on all 35 joint ACTIVATE flights in 2020, we find a total of 32 collocated in situ and remote sensing profiles that occur on 11separate days, which contain a total of 322 cloud-free vertically resolved altitude bins of 150 m resolution. We demonstrate that the lidar + polarimeter N(a) agrees to within 106% for 90% of the 322 vertically resolved points. We also demonstrate similar agreement to within 121% for the polarimeter-derived column-averaged N(a). We find that the range-normalized mean absolute deviation (NMAD) for the polarimeter-derived column-averaged Na is 21%, and the NMAD for the lidar + polarimeter-derived vertically resolved Na is 16%. Taken together, these findings suggest that the error in the polarimeter-only column-averaged N(a) and the lidar + polarimeter vertically resolved N(a) are of similar magnitude and represent a significant improvement upon current remote sensing estimates of N(a).

RSP↗

NASA NTRS1993

Multi-center Airborne Coherent Atmospheric Wind Sensor (MACAWS)

This effort involves development of a calibrated, pulsed coherent CO2 Doppler lidar, followed by a carefully-planned and -executed program of multi-dimensional wind velocity and aerosol backscatter measurements from the NASA DC-8 research aircraft. The lidar, designated as the Multi-center Airborne Coherent Atmospheric Wind Sensor (MACAWS), will be applicable to two research areas. First, MACAWS will enable specialized measurements of atmospheric dynamical processes in the planetary boundary layer and free troposphere in geographic locations and over scales of motion not routinely or easily accessible to conventional sensors. The proposed observations will contribute fundamentally to a greater understanding of the role of the mesoscale, helping to improve predictive capabilities for mesoscale phenomena and to provide insights into improving model parameterizations of sub-grid scale processes within large-scale circulation models. As such, it has the potential to contribute uniquely to major, multi-institutional field programs planned for the mid 1990's. Second, MACAWS measurements can be used to reduce the degree of uncertainty in performance assessments and algorithm development for NASA's prospective Laser Atmospheric Wind Sounder (LAWS), which has no space-based instrument heritage. Ground-based lidar measurements alone are insufficient to address all of the key issues. To minimize costs, MACAWS is being developed cooperatively by the lidar remote sensing groups of the Jet Propulsion Laboratory, NOAA Wave Propagation Laboratory, and MSFC using existing lidar hardware and manpower resources. Several lidar components have already been exercised in previous airborne lidar programs (for example, MSFC Airborne Doppler Lidar System (ADLS) used in 1981,4 Severe Storms Wind Measurement Program; JPL Airborne Backscatter Lidar Experiment (ABLE) used in 1989,90 Global Backscatter Experiment Survey Missions). MSFC has been given responsibility for directing the overall program of instrument development and scientific measurement. The focus of current research and plans for next year are presented.

Rhothermel, Jeffry↗

NASA NTRS1997

The Multi-Center Airborne Coherent Atmospheric Wind Sensor, MACAWS

In 1992 the atmospheric lidar remote sensing groups of the NASA Marshall Space Flight Center, NOAA Environmental Technology Laboratory, and Jet Propulsion Laboratory began a joint collaboration to develop an airborne high-energy Doppler laser radar (lidar) system for atmospheric research and satellite validation and simulation studies. The result is the Multi-center Airborne Coherent Atmospheric Wind Sensor, MACAWS, which has the capability to remotely sense the distribution of wind and absolute aerosol backscatter in the troposphere and lower stratosphere. A factor critical to the programmatic feasibility and technical success of this collaboration has been the utilization of existing components and expertise which were developed for previous atmospheric research by the respective institutions. The motivation for the MACAWS program Is three-fold: to obtain fundamental measurements of sub-synoptic scale processes and features which may be used as a basis to improve sub-grid scale parameterizations in large-scale models; to obtain similar datasets in order to improve the understanding and predictive capabilities on the mesoscale; and to validate (simulate) the performance of existing (planned) satellite-borne sensors. Examples of the latter include participation in the validation of the NASA Scatterometer and the assessment of prospective satellite Doppler lidar for global tropospheric wind measurement. Initial flight tests were made in September 1995; subsequent flights were made in June 1996 following improvements. This paper describes the MACAWS instrument, principles of operation, examples of measurements over the eastern Pacific Ocean and western United States, and future applications.

Rothermel, Jeffry↗

NASA NTRS2015

Lidar Observations of Atmospheric CO2 Column During 2014 Summer Flight Campaigns

Advanced knowledge in atmospheric CO2 is critical in reducing large uncertainties in predictions of the Earth' future climate. Thus, Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) from space was recommended by the U.S. National Research Council to NASA. As part of the preparation for the ASCENDS mission, NASA Langley Research Center (LaRC) and Exelis, Inc. have been collaborating in development and demonstration of the Intensity-Modulated Continuous-Wave (IM-CW) lidar approach for measuring atmospheric CO2 column from space. Airborne laser absorption lidars such as the Multi-Functional Fiber Laser Lidar (MFLL) and ASCENDS CarbonHawk Experiment Simulator (ACES) operating in the 1.57 micron CO2 absorption band have been developed and tested to obtain precise atmospheric CO2 column measurements using integrated path differential absorption technique and to evaluate the potential of the space ASCENDS mission. This presentation reports the results of our lidar atmospheric CO2 column measurements from 2014 summer flight campaign. Analysis shows that for the 27 Aug OCO-2 under flight over northern California forest regions, significant variations of CO2 column approximately 2 ppm) in the lower troposphere have been observed, which may be a challenge for space measurements owing to complicated topographic condition, heterogeneity of surface reflection and difference in vegetation evapotranspiration. Compared to the observed 2011 summer CO2 drawdown (about 8 ppm) over mid-west, 2014 summer drawdown in the same region measured was much weak (approximately 3 ppm). The observed drawdown difference could be the results of the changes in both meteorological states and the phases of growing seasons. Individual lidar CO2 column measurements of 0.1-s integration were within 1-2 ppm of the CO2 estimates obtained from on-board in-situ sensors. For weak surface reflection conditions such as ocean surfaces, the 1- s integrated signal-to-noise ratio (SNR) of lidar measurements at 11 km altitude reached 376, which was equivalent to a 10-s CO2 error 0.33 ppm. For the entire processed 2014 summer flight campaign data, the mean differences between lidar remote sensed and in-situ estimated CO2 values were about -0.013 ppm. These results indicate that current laser absorption lidar approach could meet space measurement requirements for CO2 science goals.

Lin, Bing↗

NASA NTRS2016

Beyond 3-D: The New Spectrum of Lidar Applications for Earth and Ecological Sciences

Capturing and quantifying the world in three dimensions (x,y,z) using light detection and ranging (lidar) technology drives fundamental advances in the Earth and Ecological Sciences (EES). However, additional lidar dimensions offer the possibility to transcend basic 3-D mapping capabilities, including i) the physical time (t) dimension from repeat lidar acquisition and ii) laser return intensity (LRIλ) data dimension based on the brightness of single- or multi-wavelength (λ) laser returns. The additional dimensions thus add to the x,y, and z dimensions to constitute the five dimensions of lidar (x,y,z, t, LRIλ1... λn). This broader spectrum of lidar dimensionality has already revealed new insights across multiple EES topics, and will enable a wide range of new research and applications. Here, we review recent advances based on repeat lidar collections and analysis of LRI data to highlight novel applications of lidar remote sensing beyond 3-D. Our review outlines the potential and current challenges of time and LRI information from lidar sensors to expand the scope of research applications and insights across the full range of EES applications.

Eitel, Jan U. H.↗

NASA NTRS1995

Analysis of measurements for solid state laser remote lidar system

The merits of using lidar systems for remote measurements of various atmospheric processes such as wind, turbulence, moisture, and aerosol concentration are widely recognized. Although the lidar technology has progressed considerably over the past two decades, significant research particularly in the area of solid state lidars remains to be conducted in order to fully exploit this technology. The work performed by the UAH (University of Alabama in Huntsville) personnel under this Delivery Order concentrated on analyses of measurements required in support of solid state laser remote sensing lidar systems which are to be designed, deployed, and used to measure atmospheric processes and constituents. UAH personnel has studied and recommended to NASA/MSFC the requirements of the optical systems needed to characterize the detection devices suitable for solid state wavelengths and to evaluate various heterodyne detection schemes. The 2-micron solid state laser technology was investigated and several preliminary laser designs were developed and their performance for remote sensing of atmospheric winds and clouds from a spaceborne platform were specified. In addition to the laser source and the detector, the other critical technologies necessary for global wind measurements by a spaceborne solid state coherent lidar systems were identified to be developed and demonstrated. As part of this work, an analysis was performed to determine the atmospheric wind velocity estimation accuracy using the line-of-sight measurements of a scanning coherent lidar. Under this delivery order, a computer database of materials related to the theory, development, testing, and operation of lidar systems was developed to serve as a source of information for lidar research and development.

Amzajerdian, Farzin↗

NASA NTRS1975

A theoretical/experimental program to develop active optical pollution sensors, part 2

Progress is reported on experimental investigations of Lidar and the application of Lidar to environmental and atmospheric science. Specifically the following programs are considered: calibration and application of the LaRC 48-inch Lidar; efficient and certain detection of SO2 and other gases in the calibration tank using the Raman Stack Monitor Lidar; the potential of Lidar remote sensing from the space shuttle; and the planning and mounting of efforts to realize the promise of backscatter differential absorption Lidar.

Poultney, S. K.↗

NASA NTRS1999

The Multi-Center Airborne Coherent Atmospheric Wind Sensor: Recent Measurements and Future Applications

The atmospheric lidar remote sensing groups of NOAA Environmental Technology Laboratory, Jet Propulsion Laboratory and NASA Marshall Space Flight Center jointly developed an airborne scanning coherent Doppler Lidar. We describe the system, present recent measurement (including the first wind fields measured within a hurricane using Doppler lidar), and describe prospective instrument improvements and research applications.

Rothermel, Jeffry↗

NASA NTRS1981

Investigation of potential of differential absorption Lidar techniques for remote sensing of atmospheric pollutants

The NASA multipurpose differential absorption lidar (DIAL) system uses two high conversion efficiency dye lasers which are optically pumped by two frequency-doubled Nd:YAG lasers mounted rigidly on a supporting structure that also contains the transmitter, receiver, and data system. The DIAL system hardware design and data acquisition system are described. Timing diagrams, logic diagrams, and schematics, and the theory of operation of the control electronics are presented. Success in obtaining remote measurements of ozone profiles with an airborne systems is reported and results are analyzed.

Butler, C. F.↗

NASA NTRS2018

Toward a Satellite-Derived Climatology of Blowing Snow Over Antarctica

Satellite lidar remote sensing of the atmosphere has been ongoing for more than a decade providing the opportunity to study atmospheric processes in great detail. Here we use 12 years of Cloud‐Aerosol Lidar with Orthogonal Polarization measurements to derive a climatology of blowing snow layer height, optical depth, and frequency over Antarctica for the period 2006–2017. Limited to the vertical resolution of the Cloud‐Aerosol Lidar with Orthogonal Polarization data, our climatology includes all blowing snow layers greater than about 30 m in thickness for clear or optically thin cloud regions. Our results show that blowing snow occurs over 50% of the time over large regions with frequencies often exceeding 70%. The overall pattern of blowing snow frequency is fairly consistent from year to year, but there are regional differences. We examined the data for temporal trends in blowing snow properties and found significant trends only in blowing snow frequency. A small area of East Antarctica with generally low blowing snow frequency shows a statistically significant increase in blowing snow frequency ranging from 10% to 100% per decade. No significant trends in frequency were found in regions of high (>50%) blowing snow frequency, and only isolated small areas exhibited a decrease in frequency through the study period.

Palm, Stephen P.↗

NASA NTRS2001

Large Aperture Scanning Lidar Based on Holographic Optical Elements

Lidar remote sensing instruments can make a significant contribution to satisfying many of the required measurements of atmospheric and surface parameters for future spaceborne platforms, including topographic altimeters, atmospheric profiles of, wind, humidity, temperature, trace molecules, aerosols, and clouds. It is highly desirable to have wide measurement swaths for rapid coverage rather than just the narrow ribbon of data that is obtained with a nadir only observation. For most applications global coverage is required, and for wind measurements scanning or pointing is required in order to retrieve the full 3-D wind vector from multiple line-of-sight Doppler measurements. Conventional lidar receivers make up a substantial portion of the instrument's size and weight. Wide angle scanning typically requires a large scanning mirror in front of the receiver telescope, or pointing the entire telescope and aft optics assembly, Either of these methods entails the use of large bearings, motors, gearing and their associated electronics. Spaceborne instruments also need reaction wheels to counter the torque applied to the spacecraft by these motions. NASA has developed simplified conical scanning telescopes using Holographic Optical Elements (HOEs) to reduce the size, mass, angular momentum, and cost of scanning lidar systems. NASA has developed two operating lidar systems based on 40 cm diameter HOEs. The first such system, named Prototype Holographic Atmospheric Scanner for Environmental Remote Sensing (PHASERS) was a joint development between NASA Goddard Space Flight Center (GSFC) and the University of Maryland College Park. PHASERS is based on a reflection HOE for use at the doubled Nd:YAG laser wavelength of 532 nm and has recently undergone a number of design changes in a collaborative effort between GSFC and Saint Anselm College in New Hampshire. The next step was to develop IR transmission HOEs for use with the Nd:YAG fundamental in the Holographic Airborne Rotating Lidar Instrument Experiment (HARLIE). The HOE spins like a compact disk in a large ring ball bearing. In an aircraft the HOE faces down, looking out through a window at an angle of 45 degrees off-nadir. The HOE diffracts 85% of the incident 532 nm light into a 160 micron spot at a focal length of 1 meter. HARLIE is a field deployable lidar measuring aerosol, cloud, and boundary layer backscatter for atmospheric research. It has flown several times and is also used from a ground-based trailer in an upward-looking mode. The HOE generates a 45 degree conical scan pattern by rotating at speeds up to 30 rpm. Like PHASERS, the HOE in HARLIE serves both as the laser collimating lens as well as the receiver telescope primary optic. The telescope is coupled to the receiver package via fiber optic. The transmitter is a diode pumped Nd:YAG laser operating at 1064 nm, delivering 1 mJ pulses at a 5 KHz rep-rate. The receiver has a 200 microradian field-of-view and a 0.5 nm optical bandpass. The photon counting data system utilizes a single Geiger-mode silicon avalanche photodiode detector, This new technology has also presented us with new data visualization challenges as well as new measurement techniques. The backscatter data obtained from a stationary (i.e. ground-based) scanning HOE lidar is on the surface of a cone, which when viewed over many consecutive scans can reveal atmospheric motions on this surface over time as the atmosphere advects over the site. In a moving platform such as an airplane or satellite, the data from consecutive scans cover different areas under the flight path, revealing atmospheric structure in 3-dimensions. An example of a visualization of HARLIE ground-based data is presented, showing aerosol backscatter on a 90 degree conical surface generated from one 360 degree scan of the lidar during the HOLO-1 field campaign on the afternoon of 10 March 1999. Higher backscatter levels are rendered as lighter signal against a dark background. Breaking Kelvin-Helmholtz waves are evident on the north side of the scan at an altitude of 10-11 km. Time series of successive scans made at regular intervals render unique views of atmospheric motions, from which vertical profiles of atmospheric wind vectors can be obtained using a unique data analysis approach. Wind vectors obtained from the lidar were compared with co-located radiosonde wind profiles during an intensive operating period in September-October 2000 at the Atmospheric Radiation Measurement Program's Southern Great Plains Central Facility.

Schwemmer, Geary K.↗

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↗