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NASA NTRS2012

Assessment of Polarization Effect on Efficiency of Levenberg-Marquardt Algorithm in Case of Thin Atmosphere Over Black Surface

The Levenberg-Marquardt algorithm [1, 2] provides a numerical iterative solution to the problem of minimization of a function over a space of its parameters. In our work, the Levenberg-Marquardt algorithm retrieves optical parameters of a thin (single scattering) plane parallel atmosphere irradiated by collimated infinitely wide monochromatic beam of light. Black ground surface is assumed. Computational accuracy, sensitivity to the initial guess and the presence of noise in the signal, and other properties of the algorithm are investigated in scalar (using intensity only) and vector (including polarization) modes. We consider an atmosphere that contains a mixture of coarse and fine fractions. Following [3], the fractions are simulated using Henyey-Greenstein model. Though not realistic, this assumption is very convenient for tests [4, p.354]. In our case it yields analytical evaluation of Jacobian matrix. Assuming the MISR geometry of observation [5] as an example, the average scattering cosines and the ratio of coarse and fine fractions, the atmosphere optical depth, and the single scattering albedo, are the five parameters to be determined numerically. In our implementation of the algorithm, the system of five linear equations is solved using the fast Cramer s rule [6]. A simple subroutine developed by the authors, makes the algorithm independent from external libraries. All Fortran 90/95 codes discussed in the presentation will be available immediately after the meeting from sergey.v.korkin@nasa.gov by request.

Korkin, S.↗

NASA NTRS2014

CLASS: The Cosmology Large Angular Scale Surveyor

The Cosmology Large Angular Scale Surveyor (CLASS) is an experiment to measure the signature of a gravitational wave background from inflation in the polarization of the cosmic microwave background (CMB). CLASS is a multi-frequency array of four telescopes operating from a high-altitude site in the Atacama Desert in Chile. CLASS will survey 70% of the sky in four frequency bands centered at 38, 93, 148, and 217 GHz, which are chosen to straddle the Galactic-foreground minimum while avoiding strong atmospheric emission lines. This broad frequency coverage ensures that CLASS can distinguish Galactic emission from the CMB. The sky fraction of the CLASS survey will allow the full shape of the primordial B-mode power spectrum to be characterized, including the signal from reionization at low-length. Its unique combination of large sky coverage, control of systematic errors, and high sensitivity will allow CLASS to measure or place upper limits on the tensor-to-scalar ratio at a level of r = 0:01 and make a cosmic-variance-limited measurement of the optical depth to the surface of last scattering, tau. (c) (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

propagation↗

NASA NTRS1993

Development of deterministic transport methods for low energy neutrons for shielding in space

Transport of low energy neutrons associated with the galactic cosmic ray cascade is analyzed in this dissertation. A benchmark quality analytical algorithm is demonstrated for use with BRYNTRN, a computer program written by the High Energy Physics Division of NASA Langley Research Center, which is used to design and analyze shielding against the radiation created by the cascade. BRYNTRN uses numerical methods to solve the integral transport equations for baryons with the straight-ahead approximation, and numerical and empirical methods to generate the interaction probabilities. The straight-ahead approximation is adequate for charged particles, but not for neutrons. As NASA Langley improves BRYNTRN to include low energy neutrons, a benchmark quality solution is needed for comparison. The neutron transport algorithm demonstrated in this dissertation uses the closed-form Green's function solution to the galactic cosmic ray cascade transport equations to generate a source of neutrons. A basis function expansion for finite heterogeneous and semi-infinite homogeneous slabs with multiple energy groups and isotropic scattering is used to generate neutron fluxes resulting from the cascade. This method, called the FN method, is used to solve the neutral particle linear Boltzmann transport equation. As a demonstration of the algorithm coded in the programs MGSLAB and MGSEMI, neutron and ion fluxes are shown for a beam of fluorine ions at 1000 MeV per nucleon incident on semi-infinite and finite aluminum slabs. Also, to demonstrate that the shielding effectiveness against the radiation from the galactic cosmic ray cascade is not directly proportional to shield thickness, a graph of transmitted total neutron scalar flux versus slab thickness is shown. A simple model based on the nuclear liquid drop assumption is used to generate cross sections for the galactic cosmic ray cascade. The ENDF/B V database is used to generate the total and scattering cross sections for neutrons in aluminum. As an external verification, the results from MGSLAB and MGSEMI were compared to ANISN/PC, a routinely used neutron transport code, showing excellent agreement. In an application to an aluminum shield, the FN method seems to generate reasonable results.

Ganapol, Barry↗

NASA NTRS2019

Testbed Results for Scalar and Vector Radiative Transfer Computations of Light in Atmosphere-Ocean Systems

We generate and tabulate reflectance values of the Stokes parameters I, Q, and U of upwelling radiance just above a rough ocean surface and at the top of the atmosphere (TOA) for 100 scattering geometries, four atmosphere-ocean systems, and four wavelengths. The atmosphere-ocean systems increase in complexity from (a) a molecular atmosphere above a rough ocean surface (AOS-I model); to (b) a pure water body below a rough ocean surface (AOS-II model); to (c) a fully-coupled simple atmosphere-ocean system (AOS-III model) containing a molecular atmosphere, rough ocean surface, and pure water; to (d) a fully-coupled complex atmosphere-ocean system (AOS-IV model) that includes scattering by molecules, rough ocean surface, pure water, and hydrosols. Our wavelengths (350, 450, 550, and 650 nm) capture the ultraviolet-visible range. Our tables provide radiative transfer (RT) testbed results for atmosphere-ocean systems with an accuracy that surpasses the measurement accuracy of state-of-the-art polarimeters. To validate the accuracy of these tables we performed computations using three independent RT codes that provide deterministic numerical solutions for the RT equation. The agreement is 10(exp –5) for AOS-IV model, and 10(exp –6) for the other models. The degree of linear polarization computed by these RT codes differs by ≤0.2% for 15 isolated cases of tabulated reflectance values, and by ≤0.1% for all remaining cases. We also provide comparisons with results obtained by a stochastic RT code for AOS-I model. The agreement between the deterministic and stochastic results for this model is 10(exp –5) at TOA, and 10(exp –6) above the ocean surface.

Polarimeters↗

NASA NTRS2002

Simultaneous Raman-Rayleigh-LIF Measurements and Numerical Modeling Results of a Lifted H2/N2 Turbulent Jet Flame in a Vitiated Coflow

An experimental and numerical investigation is presented of a H2/N2 turbulent jet flame burner that has a novel vitiated coflow. The vitiated coflow emulates the recirculation region of most combustors, such as gas turbines or furnaces. Additionally, since the vitiated gases are coflowing, the burner allows for exploration of recirculation chemistry without the corresponding fluid mechanics of recirculation. Thus the vitiated coflow burner design facilitates the development of chemical kinetic combustion models without the added complexity of recirculation fluid mechanics. Scalar measurements are reported for a turbulent jet flame of H2/N2 in a coflow of combustion products from a lean ((empty set) = 0.25) H2/Air flame. The combination of laser-induced fluorescence, Rayleigh scattering, and Raman scattering is used to obtain simultaneous measurements of the temperature, major species, as well as OH and NO. Laminar flame calculation with equal diffusivity do agree when the premixing and preheating that occurs prior to flame stabilization is accounted for in the boundary conditions. Also presented is an exploratory pdf model that predicts the flame's axial profiles fairly well, but does not accurately predict the lift-off height.

Cabra, R.↗

NASA NTRS2016

Retrieval of Macro- and Micro-Physical Properties of Oceanic Hydrosols from Polarimetric Observations

Remote sensing has mainly relied on measurements of scalar radiance and its spectral and angular features to retrieve micro- and macro-physical properties of aerosols/hydrosols. However, it is recognized that measurements that include the polarimetric characteristics of light provide more intrinsic information about particulate scattering. To take advantage of this, we used vector radiative transfer (VRT) simulations and developed an analytical relationship to retrieve the macro and micro-physical properties of the oceanic hydrosols. Specifically, we investigated the relationship between the observed degree of linear polarization (DoLP) and the ratio of attenuation-to- absorption coefficients (c/a) in water, from which the scattering coefficient can be readily computed (b equals c minus a), after retrieving a. This relationship was parameterized for various scattering geometries, including sensor zenith/azimuth angles relative to the Sun's principal plane, and for varying Sun zenith angles. An inversion method was also developed for the retrieval of the microphysical properties of hydrosols, such as the bulk refractive index and the particle size distribution. The DoLP vs c/a relationship was tested and validated against in-situ measurements of underwater light polarization obtained by a custom-built polarimeter and measurements of the coefficients a and c, obtained using an in-water WET (Western Environmental Technologies) Labs ac-s (attenuation coefficients In-Situ Spectrophotometer) instrument package. These measurements confirmed the validity of the approach, with retrievals of attenuation coefficients showing a high coefficient of determination depending on the wavelength. We also performed a sensitivity analysis of the DoLP at the Top of Atmosphere (TOA) over coastal waters showing the possibility of polarimetric remote sensing application for ocean color.

PACE↗

NASA NTRS2014

Adjoint Methods for Adjusting Three-Dimensional Atmosphere and Surface Properties to Fit Multi-Angle/Multi-Pixel Polarimetric Measurements

This paper derives an efficient procedure for using the three-dimensional (3D) vector radiative transfer equation (VRTE) to adjust atmosphere and surface properties and improve their fit with multi-angle/multi-pixel radiometric and polarimetric measurements of scattered sunlight. The proposed adjoint method uses the 3D VRTE to compute the measurement misfit function and the adjoint 3D VRTE to compute its gradient with respect to all unknown parameters. In the remote sensing problems of interest, the scalar-valued misfit function quantifies agreement with data as a function of atmosphere and surface properties, and its gradient guides the search through this parameter space. Remote sensing of the atmosphere and surface in a three-dimensional region may require thousands of unknown parameters and millions of data points. Many approaches would require calls to the 3D VRTE solver in proportion to the number of unknown parameters or measurements. To avoid this issue of scale, we focus on computing the gradient of the misfit function as an alternative to the Jacobian of the measurement operator. The resulting adjoint method provides a way to adjust 3D atmosphere and surface properties with only two calls to the 3D VRTE solver for each spectral channel, regardless of the number of retrieval parameters, measurement view angles or pixels. This gives a procedure for adjusting atmosphere and surface parameters that will scale to the large problems of 3D remote sensing. For certain types of multi-angle/multi-pixel polarimetric measurements, this encourages the development of a new class of three-dimensional retrieval algorithms with more flexible parametrizations of spatial heterogeneity, less reliance on data screening procedures, and improved coverage in terms of the resolved physical processes in the Earth's atmosphere.

linearization↗

NASA NTRS2014

Adjoint Methods for Adjusting Three-Dimensional Atmosphere and Surface Properties to Fit Multi-Angle Multi-Pixel Polarimetric Measurements

adjoint methods↗

NASA NTRS1987

A comparison of the Cray-2 performance before and after the installation of memory pseudo-banking

A suite of 13 large Fortran benchmark codes were run on a Cray-2 configured with memory pseudo-banking circuits, and floating point operation rates were measured for each under a variety of system load configurations. These were compared with similar flop measurements taken on the same system before installation of the pseudo-banking. A useful memory access efficiency parameter was defined and calculated for both sets of performance rates, allowing a crude quantitative measure of the improvement in efficiency due to pseudo-banking. Programs were categorized as either highly scalar (S) or highly vectorized (V) and either memory-intensive or register-intensive, giving 4 categories: S-memory, S-register, V-memory, and V-register. Using flop rates as a simple quantifier of these 4 categories, a scatter plot of efficiency gain vs Mflops roughly illustrates the improvement in floating point processing speed due to pseudo-banking. On the Cray-2 system tested this improvement ranged from 1 percent for S-memory codes to about 12 percent for V-memory codes. No significant gains were made for V-register codes, which was to be expected.

Schmickley, Ronald D.↗

NASA NTRSDate not supplied

Planar Investigation of a CobraMRV Reentry Flowfield Using Pulse-Burst, Cross-Correlation DGV

The flowfield around a Co-Optimization Blunt-body Reentry Analysis Mid-lift/drag-ratio Rigid Vehicle (CobraMRV) vehicle is investigated with a combination of high-speed planar laser Mie scattering (PLMS) and pulse-burst cross-correlation Doppler global velocimetry (PB-CC-DGV). Tests were conducted in the NASA Langley 4-foot Supersonic Unitary Plan Wind Tunnel (UPWT) over a range of different tunnel operating conditions and model configurations. Results indicate a complex shock-boundary layer interaction. Scalar information extracted from the PLMS show the evolution of the bow shock structure, while streamwise velocity measurements indicate the spatial evolution of the shock-boundary layer interaction including the growth of the separation shock foot and eventual reacceleration of the flow at farther downstream locations. Assessment of multiple cases show strong Mach and Reynolds numbers driven effects on the character of the shock-boundary layer interactions. Measurement uncertainties ranged from 50 to 150 m/s throughout the region of interest, driven largely by angular uncertainties and instabilities in the laser pointing. The mean accuracy of the freestream measurements was found to be 5.2-percent of tunnel predicted values.

Laser↗

NASA NTRS1989

Time-domain imaging

The quest for the highest resolution microwave imaging and principle of time-domain imaging has been the primary motivation for recent developments in time-domain techniques. With the present technology, fast time varying signals can now be measured and recorded both in magnitude and in-phase. It has also enhanced our ability to extract relevant details concerning the scattering object. In the past, the interface of object geometry or shape for scattered signals has received substantial attention in radar technology. Various scattering theories were proposed to develop analytical solutions to this problem. Furthermore, the random inversion, frequency swept holography, and the synthetic radar imaging, have two things in common: (1) the physical optic far-field approximation, and (2) the utilization of channels as an extra physical dimension, were also advanced. Despite the inherent vectorial nature of electromagnetic waves, these scalar treatments have brought forth some promising results in practice with notable examples in subsurface and structure sounding. The development of time-domain techniques are studied through the theoretical aspects as well as experimental verification. The use of time-domain imaging for space robotic vision applications has been suggested.

Tolliver, C. L.↗

NASA NTRS1987

Time-domain robotic vision application

The quest for the highest resolution microwaves imaging and the principle of time-domain imaging is the primary motivation for recent developments in time-domain techniques. With the present technology fast time varying signals can now be measured and recorded both in magnitude and in phase. It has also enhanced the ability to extract relevant details concerning the scattering object. In the past, the inference of object geometry or shape from scattered signals has received substantial attention in radar technology. Various inverse scattering theories were proposed to develop analytical solutions to this problem. Furthermore, the random inversion, frequenty swept holography, and the synthetic radar imaging, all of which have two things in common: the physical optic far-field approximation and the utilization of the channels as an extra physical dimension, were also advanced significantly. Despite the inherent vectorial nature of electromagnetic waves, these scalar treatments have brought forth some promising results in practice with notable examples in subsurface and structure sounding. The use of time-domain imaging for space robotic vision applications was proposed. A multisensor approach to vision was shown to have several advantages over the video-only approach.

Tolliver, C. L.↗

NASA NTRS2004

Computational and Experimental Study of Energetic Materials in a Counterflow Microgravity Environment

Counterflow diffusion flames are studied for various fuels flowing against decomposition products from solid ammonium perchlorate (AP) pellets in order to obtain fundamental understanding of composite propellant flame structure and chemistry. We illustrate this approach through a combined experimental and numerical study of a fuel mixture consisting of C2H4 CO + H2, and C2H2 + C2H4 flowing against solid AP. For these particular AP-fuel systems, the resulting flame zone simulates the various flame structures that are ex+ to exist between reaction products from Ap crystals and a hydrocarbon binder. As in all our experimental studies, quantitative species and temperature profiles have been measured between the fuel exit and AP surface. Species measured included CN, NH, NO, OH, N2, CO2, CO, H2, CO, HCl, and H2O. Temperature was measured using a thermocouple at the exit, spontaneous Raman scattering measurements throughout the flame, OH rotational population distributions, and NO vibrational population distributions. The burning rate of AP was also measured as a function of strain rate, given by the separation distance between the AP surface and the gaseous hydrocarbon fuel tube exit plane. This distance was nominally set at 5 mm, although studies have been performed for variations in separation distance. The measured 12 scalars are compared with predictions from a detailed gas-phase kinetics model consisting of 86 species and 531 reactions. Model predictions are found to be in good agreement with experiment and illustrate the type of kinetic features that may be expected to occur in propellants when AP particle size distributions are varied. Furthermore, the results constitute the continued development of a necessary database and validation of a comprehensive model for studying more complex AP-solid fuel systems in microgravity. Exploratory studies have also been performed with liquid and solid fuels at normal gravity. Because of melting (and hence dripping) and deep thermal wave penetration into the liquid, these experiments were found feasible, but not used for obtaining quantitative data. Microgravity experiments are needed to eliminate the dripping and boiling phenomena of these systems at normal gravity. Microgravity tests in the NASA Glenn 2.2 second drop tower were performed (1) to demonstrate the feasibility of performing propellant experiments using the NASA Glenn microgravity facilities, (2) to develop the operational procedures for safe handing of the energetic materials and disposal of their toxic combustion by-products and (3) to obtain initial measurements of the AP burning rate and flame structure under microgravity conditions. Experiments were conducted on the CH4/AP system previously studied at normal gravity using a modified design of the counterflow burner and a NASA Glenn Pig Rig, i.e., one of the existing drop rigs for general-purpose usage. In these experiments, the AP burning rate was measured directly with a linear variable differential transducer (LVDT) and video imaging of the flame structure was recorded ignition was achieved by hot wires stretched across the AP surfaces. Initial drop tower combustion data show that with the same burner separation distance and flow conditions of the normal gravity experiments, the AP burning rate is approximately a factor of two lower. This difference is likely a result of radiation effects, but further tests with longer test times need to be conducted to verify that steady state conditions were achieved under microgravity conditions.

Takahashi, Fumiaki↗

NASA NTRS2015

Secluded WIMPs, Dark QED with Massive Photons, and the Galactic Center Gamma-Ray Excess

We discuss a particular secluded WIMP dark matter model consisting of neutral fermions as the dark matter candidate and a Proca-Wentzel (PW) field as a mediator. In the model that we consider here, dark matter WIMPs interact with standard model (SM) particles only through the PW field of approximately MeV-multi-GeV mass particles. The interactions occur via a U(1)' mediator, V'(sub mu), which couples to the SM by kinetic mixing with U(1) hypercharge bosons, B'(sub mu). One important difference between our model and other such models in the literature is the absence of an extra singlet scalar, so that the parameter with dimension of mass M(sup 2, sub V) is not related to a spontaneous symmetry breaking. This QED based model is also renormalizable. The mass scale of the mediator and the absence of the singlet scalar can lead to interesting astrophysical signatures. The dominant annihilation channels are different from those usually considered in previous work. We show that the GeV energy gamma-ray excess in the galactic center region, as derived from Fermi-LAT Gamma-ray Space Telescope data, can be attributed to such secluded dark matter WIMPs, given parameters of the model that are consistent with both the cosmological dark matter density and the upper limits on WIMP spin-independent elastic scattering. Secluded WIMP models are also consistent with suggested upper limits on a DM contribution to the cosmic-ray antiproton flux.

Gamma-Rays↗

NASA NTRS2011

Frame-Transfer Gating Raman Spectroscopy for Time-Resolved Multiscalar Combustion Diagnostics

Accurate experimental measurement of spatially and temporally resolved variations in chemical composition (species concentrations) and temperature in turbulent flames is vital for characterizing the complex phenomena occurring in most practical combustion systems. These diagnostic measurements are called multiscalar because they are capable of acquiring multiple scalar quantities simultaneously. Multiscalar diagnostics also play a critical role in the area of computational code validation. In order to improve the design of combustion devices, computational codes for modeling turbulent combustion are often used to speed up and optimize the development process. The experimental validation of these codes is a critical step in accepting their predictions for engine performance in the absence of cost-prohibitive testing. One of the most critical aspects of setting up a time-resolved stimulated Raman scattering (SRS) diagnostic system is the temporal optical gating scheme. A short optical gate is necessary in order for weak SRS signals to be detected with a good signal- to-noise ratio (SNR) in the presence of strong background optical emissions. This time-synchronized optical gating is a classical problem even to other spectroscopic techniques such as laser-induced fluorescence (LIF) or laser-induced breakdown spectroscopy (LIBS). Traditionally, experimenters have had basically two options for gating: (1) an electronic means of gating using an image intensifier before the charge-coupled-device (CCD), or (2) a mechanical optical shutter (a rotary chopper/mechanical shutter combination). A new diagnostic technology has been developed at the NASA Glenn Research Center that utilizes a frame-transfer CCD sensor, in conjunction with a pulsed laser and multiplex optical fiber collection, to realize time-resolved Raman spectroscopy of turbulent flames that is free from optical background noise (interference). The technology permits not only shorter temporal optical gating (down to <1 s, in principle), but also higher optical throughput, thus resulting in a substantial increase in measurement SNR.

Nguyen, Quang-Viet↗

NASA NTRS2020

The AERONET Version 3 Aerosol Retrieval Algorithm, Associated Uncertainties and Comparisons to Version 2

The Aerosol Robotic Network (AERONET) Version 3 (V3) aerosol retrieval algorithm is described, which is based on the Version 2 (V2) algorithm with numerous updates. Comparisons of V3 aerosol retrievals to those of V2 are presented, along with a new approach to estimate uncertainties in many of the retrieved aerosol parameters. Changes in the V3 aerosol retrieval algorithm include (1) a new polarized radiative transfer code (RTC), which replaced the scalar RTC of V2, (2) detailed characterization of gas absorption by adding NO2 and H2O to specify total gas absorption in the atmospheric column, specification of vertical profiles of all the atmospheric species, (3) new bidirectional reflectance distribution function (BRDF) parameters for land sites adopted from the MODIS BRDF/Albedo product, (4) a new version of the extraterrestrial solar flux spectrum, and (5) a new temperature correction procedure of both direct Sun and sky radiance measurements. The potential effect of each change in V3 on single scattering albedo (SSA) retrievals was analyzed. The operational almucantar retrievals of V2 versus V3 were compared for four AERONET sites: GSFC, Mezaira, Mongu, and Kanpur. Analysis showed very good agreement in retrieved parameters of the size distributions. Comparisons of SSA retrievals for dust aerosols (Mezaira) showed a good agreement in 440 nm SSA, while for longer wavelengths V3 SSAs are systematically higher than those of V2, with the largest mean difference at 675 nm due to cumulative effects of both extraterrestrial solar flux and BRDF changes. For non-dust aerosols, the largest SSA deviation is at 675 nm due to differences in extraterrestrial solar flux spectrums used in each version. Further, the SSA 675 nm mean differences are very different for weakly (GSFC) and strongly (Mongu) absorbing aerosols, which is explained by the lower sensitivity to a bias in aerosol scattering optical depth by less absorbing aerosols. A new hybrid (HYB) sky radiance measurement scan is introduced and discussed. The HYB combines features of scans in two different planes to maximize the range of scattering angles and achieve scan symmetry, thereby allowing for cloud screening and spatial averaging, which is an advantage over the principal plane scan that lacks robust symmetry. We show that due to an extended range of scattering angles, HYB SSA retrievals for dust aerosols exhibit smaller variability with solar zenith angles (SZAs) than those of almucantar (ALM), which allows extension of HYB SSA retrievals to SZAs less than 50∘ to as small as 25∘. The comparison of SSA retrievals from closely time-matched HYB and ALM scans in the 50 to 75∘ SZA range showed good agreement with the differences below ∼0.005. We also present an approach to estimate retrieval uncertainties which utilizes the variability in retrieved parameters generated by perturbing both measurements and auxiliary input parameters as a proxy for retrieval uncertainty. The perturbations in measurements and auxiliary inputs are assumed as estimated biases in aerosol optical depth (AOD), radiometric calibration of sky radiances combined with solar spectral irradiance, and surface reflectance. For each set of Level 2 Sun/sky radiometer observations, 27 inputs corresponding to 27 combinations of biases were produced and separately inverted to generate the following statistics of the inversion results: average, standard deviation, minimum and maximum values. From these statistics, standard deviation (labeled U27) is used as a proxy for estimated uncertainty, and a lookup table (LUT) approach was implemented to reduce the computational time. The U27 climatological LUT was generated from the entire AERONET almucantar (1993–2018) and hybrid (2014–2018) scan databases by binning U27s in AOD (440 nm), Angström exponent (AE, 440–870 nm), and SSA (440, 675, 870, 1020 nm). Using this LUT approach, the uncertainty estimates U27 for each individual V3 Level 2 retrieval can be obtained by interpolation using the corresponding measured and inverted combination of AOD, AE, and SSA.

Aliaksandr Siniuk↗

NASA NTRS1995

A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties

An expression for the ratio of the upwelling nadir radiance L(pi, z) and the downwelling scalar irradiance E(sub od)(Z) is derived from the following equation of radiative transfer. This expression is given by RSR(z) = (L(pi, z))/E(sub od) = (f(sub b)(z)b(sub b)(z))/2 pi(k(pi, z) + c(z) - F(sub L)(z)b(sub f)(z)), where b(sub b)(z) is the backscattering coefficient, k(pi, z) is the vertical attenuation coefficient of the nadir radiance, c(z) is the beam attenuation coefficient, and f(sub b)(z) and f(sub L)(z) are shape parameters that depend on the shape of the volume scattering function and the radiance distribution. Successive approximations are subsequently applied to the above exact equation. These are f(sub b)(z) = (2 pi beta(pi - theta(sub m), z)/(b(sub b)(z))), where beta(pi - theta(sub m), z) is the volume scattering function at 180 deg minus the zenith angle of the maximum radiance, and k(pi, z) = am = c(1 - 0.52 b/c - 0.44 (b/c)(exp 2)), where m is a parameter that is numerically equal to the inverse of the average cosine of the asymptotic light field for a medium with the same inherent optical properties, a is the absorption coefficient, and b/c is the single scattering albedo. Together with f(sub L)(z) = 1.05 and application of Gershun's equation, it is shown that for nearly all oceanic cases RSR(z) identical to L(pi, z)/E(sub od)(z) = (Beta(pi - theta(sub m), z))/(a(z)(1 + m(z))).

Zaneveld, J. Ronald V.↗

NASA NTRS1994

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

Goorjian, Peter M.↗