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At least 109 records · Page 6

A Highly Sensitive Multi-Element HgCdTe E-APD Detector for IPDA Lidar Applications

An HgCdTe electron avalanche photodiode (e-APD) detector has been developed for lidar receivers, one application of which is integrated path differential absorption lidar measurements of such atmospheric trace gases as CO2 and CH4. The HgCdTe APD has a wide, visible to mid-wave-infrared, spectral response, high dynamic range, substantially improved sensitivity, and an expected improvement in operational lifetime. A demonstration sensor-chip assembly consisting of a 4.3 lm cutoff HgCdTe 4 9 4 APD detector array with 80 micrometer pitch pixels and a custom complementary metal-oxide-semiconductor readout integrated circuit was developed. For one typical array the APD gain was 654 at 12 V with corresponding gain normalized dark currents ranging from 1.2 fA to 3.2 fA. The 4 9 4 detector system was characterized at 77 K with a 1.55 micrometer wavelength, 1 microsecond wide, laser pulse. The measured unit gain detector photon conversion efficiency was 91.1%. At 11 V bias the mean measured APD gain at 77 K was 307.8 with sigma/mean uniformity of 1.23%. The average, noise-bandwidth normalized, system noise-equivalent power (NEP) was 1.04 fW/Hz(exp 1/2) with a sigma/mean of 3.8%. The measured, electronics-limited, bandwidth of 6.8 MHz was more than adequate for 1 microsecond pulse detection. The system had an NEP (3 MHz) of 0.4 fW/Hz(exp 1/2) at 12 V APD bias and a linear dynamic range close to 1000. A gain-independent quantum-limited SNR of 80% of full theoretical was indicative of a gain-independent excess noise factor very close to 1.0 and the expected APD mode quantum efficiency.

NEP↗

2-Micron Laser Transmitter for Coherent CO2 DIAL Measurement

Carbon dioxide (CO2) has been recognized as one of the most important greenhouse gases. It is essential for the study of global warming to accurately measure the CO2 concentration in the atmosphere and continuously record its variation. A high repetition rate, highly efficient, Q-switched 2-micron laser system as the transmitter of a coherent differential absorption lidar for CO2 measurement has been developed in NASA Langley Research Center. This laser system is capable of making a vertical profiling of CO2 from ground and column measurement of CO2 from air and space-borne platform. The transmitter is a master-slave laser system. The master laser operates in a single frequency, either on-line or off-line of a selected CO2 absorption line. The slave laser is a Q-switched ring-cavity Ho:YLF laser which is pumped by a Tm:fiber laser. The repetition rate can be adjusted from a few hundred Hz to 10 kHz. The injection seeding success rate is from 99.4% to 99.95%. For 1 kHz operation, the output pulse energy is 5.5mJ with the pulse length of ~50 ns. The optical-to-optical efficiency is 39% when the pump power is 14.5W. A Ho:YLF laser operating in the range of 2.05 micrometers can be tuned over several characteristic lines of CO2 absorption. Experimentally, a diode pumped Ho:Tm:YLF laser has been successfully used as the transmitter of coherent differential absorption lidar for the measurement of CO2 with a repetition rate of 5 Hz and pulse energy of 75 mJ. For coherent detection, high repetition rate is required for speckle averaging to obtain highly precise measurements. However, a diode pumped Ho:Tm:YLF laser can not operate in high repetition rate due to the large heat loading and up-conversion. A Tm:fiber laser pumped Ho:YLF laser with low heat loading can operate in high repetition rate. A theoretical model has been established to simulate the performance of Tm:fiber laser pumped Ho:YLF lasers. For continuous wave (CW) operation, high pump intensity with small beam size is suitable for high efficiency. For Q-switched operation, the optimal energy extraction relies on the pump intensity, pump volume, and pump duration which is inversely proportion to the repetition rate. CW and Q-switched Ho:YLF lasers with different linear cavity configurations have been designed and demonstrated for a 30 W Tm:fiber pump laser. The CW Ho laser slope efficiency and optical-to-optical efficiencies reach 65% and 55%, respectively. The pulsed laser efficiency depends on the repetition rate. For 1 kHz operation, the optical-to-optical efficiency is 39% when the pump power is 14.5W. Currently, the injection seeding success rate is between 99.4% and 99.95%. After a ten thousand pulses, the standard deviation of the laser frequency jitter is about 3 MHz. It meets the requirements of highly precise CO2 concentration measurement. In conclusion, an injection seeded, high repetition rate, Q-switched Ho:YLF laser has been developed for a coherent CO2 differential absorption lidar. This master-slave laser system has high optical-to-optical efficiency and seeding success rate. It can potentially meet the requirements of the coherent detection of CO2 concentration by a differential absorption lidar technique.

Singh, Upendra N.↗

Development of lead salt semiconductor lasers for the 9-17 micron spectral region

Improved diode lasers of Pb sub 1-x Sn sub x Se operating in the 9-17 micrometers spectral region were developed. The performance characteristics of the best lasers exceeded the contract goals of 500 microW/mode at T 30K in the 9-12 micrometers region and 200 microW/mode at T 18K in the 16-17 micrometers region. Increased reliability and device yields resulted from processing improvements which evolved from a series of diagnostic studies. By means of Auger electron spectroscopy, laser shelf storage degradation was shown to be characterized by the presence of In metal on the semiconductor crystal surfaces. Studies of various metal barrier layers between the crystals and the In metal led to the development of an improved metallurgical contacting technology which has resulted in devices with performance stability values exceeding the contract goal of a one year shelf life. Lasers cycled over 500 times between 300K and 77K were also shown to be stable. Studies on improved methods of fabricating striped geometry lasers indicated that good spectral mode characteristics resulted from lasers which stripe widths of 12 and 25 micrometers.

Linden, K. J.↗

Investigating the 3.3 micron infrared fluorescence from naphthalene following ultraviolet excitation

Polycyclic aromatic hydrocarbon (PAH) type molecules are proposed as the carriers of the unidentified infrared (UIR) bands. Detailed studies of the 3.3 micrometer infrared emission features from naphthalene, the simplest PAH, following ultraviolet laser excitation are used in the interpretation of the 3.29 micrometer (3040 cm(sup -1)) UIR band. A time-resolved Fourier transform spectrometer is used to record the infrared emission spectrum of gas-phase naphthalene subsequent to ultraviolet excitation facilitated by an excimer laser operated at either 193 nm or 248 nm. The emission spectra differ significantly from the absorption spectrum in the same spectral region. Following 193 nm excitation the maximum in the emission profile is red-shifted 45 cm(sup -1) relative to the absorption maximum; a 25 cm(sup -1) red-shift is observed after 248 nm excitation. The red-shifting of the emission spectrum is reduced as collisional and radiative relaxation removes energy from the highly vibrationally excited molecules. Coupling between the various vibrational modes is thought to account for the differences between absorption and emission spectra. Strong visible emission is also observed following ultraviolet excitation. Visible emission may play an important role in the rate of radiative relaxation, which according to the interstellar PAH hypothesis occurs only by the slow emission of infrared photons. Studying the visible emission properties of PAH type molecules may be useful in the interpretation of the DIB's observed in absorption.

Williams, Richard M.↗

Microwave Conductivity of Laser Ablated YBa2Cu3O7-delta Superconducting Films and Its Relation to Microstrip Transmission Line Performance

We report on the values of the microwave conductivity in the normal (sigma(subN)) and superconducting (sigma*=sigma(sub1)-j sigma(sub2)) states of two laser ablated YBa2CU3O7(sigma) thin films at 35 GHz, in the temperature range from 20 to 300 K. The films 0.7 and 0.4 micrometers) were deposited on LaA10(sub3) by laser ablation. The conductivity was obtained from the microwave power transmitted through the films and assuming a two-fluid model. Values of sigma(subN) approximately 2.3 X 10(exp5) S/m at room temperature for both films, and of sigma(sub1) approximately 6.3 X 10(exp5) and 4.6 X 10(exp5) S/m at temperatures around 80 K were obtained for the 0.7 and 0.4 micrometer films respectively. For sigma(sub2) values of 4.9 X 10(exp6) and 5.4 X 10(exp6) S/m were obtained for the 0.7 and 0.4 micrometer films at 80 K. The expected conductor losses and Q-factor of a superconducting ring resonator were calculated using these conductivity values. The theoretical values were then compared with the experimental results obtained for a resonator fabricated from one of these films.

Bhasin, K. B.↗

Backscatter and extinction measurements in cloud and drizzle at CO2 laser wavelengths

The backscatter and extinction of laboratory generated cloud and drizzle sized water drops were measured at carbon dioxide laser wavelengths (predominately at lambda = 10.591 micrometers). Two distinctly different drop size regimes were studied: one which covers the range normally encompassed by natural cloud droplets and the other representative of mist or drizzle sized drops. The derivation and verification of the relation between extinction and backscatter at carbon dioxide laser wavelengths should allow the determination of large cloud drop and drizzle extinction coefficient solely from a lidar return signal without requiring knowledge of the drop size distribution. This result will also apply to precipitation sized drops so long as they are spherical.

Jennings, S. G.↗

C-O-H ratios of silicate melt inclusions in basalts from the Galapagos Spreading Center near 95 degrees W: a laser decrepitation mass spectrometry study

Volatile ratios (primarily of H2O and CO2) in individual silicate melt (glass) inclusions in minerals have been analyzed using laser volatilization and mass spectrometry. A Nd-glass laser was used to produce 50-micrometer diameter pits in silicate melt inclusions. Released volatiles were analyzed directly with a computer-controlled quadrupole mass spectrometer. The detection limits for CO2 and H2O were on the order of 3 x 10(-14) and 3 x 10(-13) moles, respectively. The reproducibility for CO2/H2O was better than +/- 9%. The total range of volatile ratios from vitreous silicate glass inclusions contained in a suite of Galapagos lavas were: 0.018 to 1.193 for CO2/H2O; 0.002 to 0.758 for CO/H2O; 0 to 0.454 for CH4/H2O; and 0 to 0.432 for Ar/H2O. The mean CO2/H2O from the propagating rift (0.245 +/- 0.068) silicate glass inclusions is significantly lower than that of the actively failing rift (0.641 +/- 0.241); this difference probably reflects different degrees of degassing during magmatic histories for the two regions. Relatively undifferentiated failing rift magmas must have relatively short crustal residence times prior to eruption and, therefore, have not undergone significant degassing of CO2, as would appear to be the case for the more highly fractionated propagating rift magmas. The laser-mass spectrometric system described herein has the ability to act as a point-source probing device that can differentiate between the various volatile sites in minerals and rocks (as well as synthetic materials) on a micrometer scale.

NASA Discipline Exobiology↗

long wavelength Pb(1-x)Sn(X)Se and Pb(1-x)Sn(x)Te diode lasers as local oscillators

A breadboard heterodyne receiver is described which was used to establish the characteristics of lead salt diode lasers pertinent to their use as local oscillators using laser devices operating in the 15-25 micrometer spectral region. Heterodyne detection efficiency is directly correlated with the transverse mode structure and emphasizes the necessity of stable lowest order mode operation for lasers when used as local oscillators. The results obtained indicate that the continued development of these lasers provide suitable local oscillators for a variety of applications.

Washwell, E. R.↗

Laser system for natural gas detection. Phase 1: Laboratory feasibility studies

This project demonstrated the feasibility of using laser remote sensing technology as a tool for leak survey work in natural gas distribution systems. A laboratory device was assembled using a pair of helium neon (HeNe) lasers to measure methane. One HeNe laser emits radiation at a wavelength of 3.3922 micrometers, which corresponds to a strong absorption feature of methane, while the other emits radiation at a wavelength of 3.3911 micrometers, which corresponds to a weak absorption by methane. As a particular area is scanned for leaks, the laser is pointed at convenient topographic targets within its operating range, about 25 m. A portion of the backscattered radiation is collected by a receiver and focused onto an indium antimonide (InSb) photodetector, cooled to 77K. Methane concentrations were determined from the differential absorption at the two wavelengths for the backscattered radiation.

Grant, W. B.↗

Exposure damage mechanisms for KCl windows in high power laser systems

An experimental study of the 10.6 micrometer and 0.6328 micrometer optical properties of single crystal and europium doped polycrystal is described. Significant variations in the optical properties are observed over periods of exposure up to 100 hours. Models are proposed to predict the 10.6 micrometer absorptivity for long exposure periods. Mechanical creep has been detected in both materials at high temperature.

Blaszuk, P. R.↗

10-micrometer band communication terminals in space.

Ten-micrometer band communication systems using CO2 lasers for space to space links are discussed. Particular emphasis is on low earth orbiting earth observation satellites to geosynchronous satellites at high data rate. Four key technology areas are discussed: wideband mixers for Doppler tracking; tunable laser local oscillators; high data rate modulators; and laser transmitters.

Mcavoy, N.↗

Infrared spectra of van de Waals complexes of importance in planetary atmospheres

It has been suggested that (CO2)2 and Ar-CO2 are important constituents of the planetary atmospheres of Venus and Mars. Recent results on the laboratory spectroscopy of CO2 containing van der Waals complexes which may be of use in the modeling of the spectra of planetary atmospheres are presented. Sub-Doppler infrared spectra were obtained for (CO2)2, (CO2)3, and rare-gas-CO2 complexes in the vicinity of the CO2 Fermi diad at 2.7 micrometers using a color-center-laser optothermal spectrometer. From the spectroscopic constants the geometries of the complexes have been determined and van der Waals vibrational frequencies have been estimated. The equilibrium configurations are C2h, C3h, and C2v, for (CO2)2, (CO2)3, and the rare-gas-CO2 complexes, respectively. Most of the homogeneous linewidths for the revibrational transitions range from 0.5 to 22 MHz, indicating that predissociation is as much as four orders of magnitude faster than radiative processes for vibrational relaxation in these complexes.

Fraser, G. T.↗

Stimulated Raman-scattering threshold behavior of binary mixture micrometer-sized droplets

Stimulated Raman scattering (SRS) from binary liquid mixture micrometer-sized droplets irradiated by nanosecond laser pulses exhibits previously unreported features. SRS emission at wavelength shifts corresponding to combination frequencies of the individual component Stokes shifts are observed in droplets but not in bulk mixtures. Furthermore, droplet SRS thresholds are determined by component refractive indices and concentrations, in contrast to bulk thresholds, for which self-focusing likely plays a dominant role.

Biswas, Abhijit↗

Investigation of Magmatic Activities on Early Mars Using Igneous Mineral Chemistry in Gale Crater, Mars

One objective of rover missions is exploring the geological context of the surroundings. Over the years, igneous petrology and sedimentology have been disconnected, the first investigating magmatic processes and volcanic activities, and the second seeking environmental conditions in the past and assessing the habitability of the planet. Although different, one is related to the other: igneous rocks are altered and broken down, leading to the formation of sedimentary rocks, which can in turn be used to back out the nature of their magmatic source. The Curiosity rover that landed in the 3.7 Gyr old impact crater Gale is traveling through sedimentary rocks. About fifty float rocks have been observed, and several of them with ambiguous texture and composition have been classified as igneous or sedimentary depending on studies such as Jake_M. The composition of several unambiguous igneous rocks has been analyzed [4- 6] but their heterogeneity at a larger instrumental (measurement size < 2 cm) scale prevents the measurement of a bulk composition as performed on Earth. An original approach avoiding these two last issues is to consider igneous mineral chemistry analyzed within igneous and sedimentary rocks to assess magmatic processes that could have formed them. Most Curiosity data are used to explore ancient environmental conditions, and a significant number of compositional analyses are under-explored for constraining magmatic activities. We will present how we can make use of sedimentary data for investigating igneous processes in the vicinity of Gale crater. Geological Context: We focus on the first 750 martian days, corresponding to measurements in a coherent lacustrine sedimentary unit called Bradbury, because all sedimentary rocks were sourced from the same watershed and appear to have a consistent source with minimal alteration [2-3]. Igneous detrital minerals including feldspar and pyroxene, are observed in sedimentary rocks. Monte Carlo models showed that minimal cation loss is observed based on the composition of all Bradbury rocks, implying negligible weathering [3]. Although clay minerals are detected in few rocks [7], chemical compositions of rocks can be explained by a mixture of primary igneous minerals [3]. Variation of composition within Bradbury rocks can be explained by mineral sorting and one distinct source component. While a common magmatic source is suggested, Bradbury sediments likely come from several volcanic eruptions from a single magmatic chamber [9- 10]. The occurrence of alkali minerals like sanidine and K-rich rocks throughout Bradbury supports the presence of a potassic component, likely trachytic, while plagioclase and a mafic composition suggest a basaltic component [8-9]. Instruments: Mineral chemistry can be estimated by three instruments onboard Curiosity. The CheMin instrument enables detection of mineral assemblages using X-ray diffraction (XRD). Using Rietveld refinement, each mineral is identified according to their 1D XRD pattern [11]. Note that distinction between pyroxene minerals is challenging with the CheMin instrument due to overlapping peaks on XRD patterns and low angular resolution of the instrument [12]. Then, using least square regression and optimization algorithms based on unit-cell parameters, mineral chemistry has been estimated by [11]. Plagioclase composition has been estimated using the NaAlSi3O8- CaAl2Si2O8 system and alkali feldspar is based on the NaAlSi3O8-KAlSi3O8 system (stars in Fig.1). Two mudstone samples (John Klein and Cumberland) and one sandstone sample (Windjana) were analyzed by CheMin at Yellowknife Bay and Kimberley, respectively. Figure 1. Ternary diagrams of feldspars (top) and pyroxene (bottom) quadrilateral. Stars correspond to CheMin composition and the gray patches to ChemCam composition. The colored dots are the composition of feldspar and pyroxene that crystallized during fractional crystallization at FMQ+1 of a melt extracted at distinct melting degree during the adiabatic ascent of a primitive mantle composition, without any water (left panels) and with 0.5 wt.% of water (right panels) at distinct pressure. The ChemCam instrument enables the analysis of the chemical compositions of rocks at hundreds of micrometer scale (350-550 μm) using laser induced breakdown spectroscopy (LIBS), which may provide the composition of minerals when they are larger than the beam spot (>550 μm) [13]. Within >5000 LIBS points, we performed a typical stoichiometric filtering allowing us to distinguish 56 feldspar and 10 pyroxene mineral compositions (grey patches in Fig. 1). Finally, the Alpha Particle X-ray Spectrometer (APXS) analyzes the composition of rocks with a 1.6 cm diameter spot size. Monte Carlo mass balance modeling allowed [3] to decipher a feldspar range varying between An30 and An40 (Fig. 1). Discussion: Although there could be a more complex history and other ways to form the whole compositional range of igneous minerals analyzed within the Bradbury formation, we are presenting here simple magmatic pathways commonly occurring on Earth using the thermodynamical softwares pMELTS and rhyoliteMELTS [14]. The objective is to find reasonable igneous processes that produce minerals that parallel the compositions of feldspar and pyroxene analyzed by the Curiosity rover. As commonly observed for mid-ocean ridge basalts, the adiabatic ascent of a primitive mantle composition [15] partially melting at 2 GPa has been modeled, followed by the extraction of a liquid at distinct degrees of partial melting, which undergoes fractional crystallization at an oxygen fugacity +1 log unit above the fayalite-magnetite-quartz (FMQ) buffer within the crust (0.02-0.4 GPa) with H2O = 0- 0.5 wt. %. These latter conditions correspond to those recorded within igneous clasts from the Noachian martian breccia NWA 7034 and paired and within Gale igneous rocks (colored dots in Fig. 1) [16-17]. To check the reliability of these 2-step models, we also tested fractional crystallization at similar conditions (FMQ+1; P=0.02-0.4 GPa; H2O = 0-0.5 wt. %) of starting compositions corresponding to that of magmas with distinct melting degrees obtained from isobaric experiments at 2 GPa [18]. Mineral compositions obtained from both models are similar. As shown on Fig. 1, the whole range of observed feldspar compositions cannot be reproduced by fractionation of one magma only. Indeed, while alkali feldspar and Na-plagioclase likely crystallized from fractional crystallization of a low-degree melt (here <15%), plagioclase and pyroxene can only be formed by fractional crystallization of a higher degree melt (here >19%). The corresponding liquid descent lines are broadly in agreement with compositions estimated by ChemCam corresponding to float igneous rocks (Fig. 2) [4-6]. Figure 2. Silica versus alkali content. Lines show the liquid lines of descent from magmas with distinct degrees of melting. Gray patches represents the composition of Gale igneous rocks [4-6]. Trachytic to rhyolitic magmas crystallize alkali feldspar, and andesite to dacite magmas likely form plagioclase. Therefore, at least two starting magmas at distinct melting degrees, which could easily come from a single mantle source, are necessary to explain the whole compositional range of feldspar and pyroxene analyzed within Bradbury rocks. Conclusion: Because rocks from the Bradbury formation are likely originating from the same magmatic source with minimal weathering as supported by several studies using different approaches, igneous mineral chemistry analyzed by CheMin and ChemCam allows us to back out reasonable magmatic pathways that could have crystallized them. Fractional crystallization of at least two starting magmas originating from distinct melting degrees of a single mantle source can explain the whole range of feldspar and pyroxene composition. Both alkaline and sub-alkaline liquids can be produced, with compositions corresponding to those of the igneous rocks analyzed by ChemCam within the Bradbury formation, highlighting the complexity of Mars magmatism.

Payre, V.↗

Qualification of a Multi-Channel Infrared Laser Absorption Spectrometer for Monitoring CO, HCl, HCN, HF, and CO2 Aboard Manned Spacecraft

Monitoring of specific combustion products can provide early-warning detection of accidental fires aboard manned spacecraft and also identify the source and severity of combustion events. Furthermore, quantitative in situ measurements are important for gauging levels of exposure to hazardous gases, particularly on long-duration missions where analysis of returned samples becomes impractical. Absorption spectroscopy using tunable laser sources in the 2 to 5 micrometer wavelength range enables accurate, unambiguous detection of CO, HCl, HCN, HF, and CO2, which are produced in varying amounts through the heating of electrical components and packaging materials commonly used aboard spacecraft. Here, we report on calibration and testing of a five-channel laser absorption spectrometer designed to accurately monitor ambient gas-phase concentrations of these five compounds, with low-level detection limits based on the Spacecraft Maximum Allowable Concentrations. The instrument employs a two-pass absorption cell with a total optical pathlength of 50 cm and a dedicated infrared semiconductor laser source for each target gas. We present results from testing the five-channel sensor in the presence of trace concentrations of the target compounds that were introduced using both gas sources and oxidative pyrolysis (non-flaming combustion) of solid material mixtures.

environmental monitoring↗

A directed search for extraterrestrial laser signals

This paper analyzes the technical feasibility of interstellar communication at infrared frequencies, both in its own right and in comparison with communication at radio frequencies. The analysis considers both the practical and fundamental limits affecting communication over interstellar distances and concludes that for specified transmitter and receiver locations communications at infrared and radio frequencies can be equally effective. On this basis a search for extraterrestrial signals at infrared wavelengths is equally as valid as any planned microwave effort. Work is now in progress to adapt a 10 micrometers heterodyne spectrometer to search for CO2 laser signals from 200 nearby stars.

NASA Discipline Exobiology↗

Laser Surface Preparation of Epoxy Composites for Secondary Bonding: Optimization of Ablation Depth

Surface preparation has been identified as one of the most critical aspects of attaining predictable and reliable adhesive bonds. Energetic processes such as laser ablation or plasma treatment are amenable to automation and are easily monitored and adjusted for controlled surface preparation. A laser ablation process was developed to accurately remove a targeted depth of resin, approximately 0.1 to 20 micrometers, from a carbon fiber reinforced epoxy composite surface while simultaneously changing surface chemistry and creating micro-roughness. This work demonstrates the application of this process to prepare composite surfaces for bonding without exposing or damaging fibers on the surface. Composite panels were prepared in an autoclave and had a resin layer approximately 10 micrometers thick above the fiber reinforcement. These composite panels were laser surface treated using several conditions, fabricated into bonded panels and hygrothermally aged. Bond performance of aged, experimental specimens was compared with grit blast surface treated specimens using a modified double cantilever beam test that enabled accelerated saturation of the specimen with water. Comparison of bonded specimens will be used to determine how ablation depth may affect average fracture energies and failure modes.

Palmieri, Frank L.↗

Investigation of multiple scattering effects in aerosols

The results are presented of investigations on the various aspects of multiple scattering effects on visible and infrared laser beams transversing dense fog oil aerosols contained in a chamber (4' x 4' x 9'). The report briefly describes: (1) the experimental details and measurements; (2) analytical representation of the aerosol size distribution data by two analytical models (the regularized power law distribution and the inverse modified gamma distribution); (3) retrieval of aerosol size distributions from multispectral optical depth measurements by two methods (the two and three parameter fast table search methods and the nonlinear least squares method); (4) modeling of the effects of aerosol microphysical (coagulation and evaporation) and dynamical processes (gravitational settling) on the temporal behavior of aerosol size distribution, and hence on the extinction of four laser beams with wavelengths 0.44, 0.6328, 1.15, and 3.39 micrometers; and (5) the exact and approximate formulations for four methods for computing the effects of multiple scattering on the transmittance of laser beams in dense aerosols, all of which are based on the solution of the radiative transfer equation under the small angle approximation.

Deepak, A.↗