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At least 1,297 records · Page 72
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Compression of thick laminated composite beams with initial impact-like damage

While the study of compression after impact of laminated composites has been under consideration for many years, the complexity of the damage initiated by low velocity impact has not lent itself to simple predictive models for compression strength. The damage modes due to non-penetrating, low velocity impact by large diameter objects can be simulated using quasi-static three-point bending. The resulting damage modes are less coupled and more easily characterized than actual impact damage modes. This study includes the compression testing of specimens with well documented initial damage states obtained from three-point bend testing. Compression strengths and failure modes were obtained for quasi-isotropic stacking sequences from 0.24 to 1.1 inches thick with both grouped and interspersed ply stacking. Initial damage prior to compression testing was divided into four classifications based on the type, extent, and location of the damage. These classifications are multiple through-thickness delaminations, isolated delamination, damage near the surface, and matrix cracks. Specimens from each classification were compared to specimens tested without initial damage in order to determine the effects of the initial damage on the final compression strength and failure modes. A finite element analysis was used to aid in the understanding and explanation of the experimental results.

Breivik, N. L.↗
NASA NTRS1992

Atmospheric correction of remotely sensed image data by a simplified model

The interaction of radiation with the atmosphere is complex and has proved difficult to calculate without reference to measurements made at or close to the time and location of interest. In this paper we describe the use of data from an airborne-tracking sunphotometer mounted on a NASA C-130 aircraft to derive optical properties of the atmospheric aerosols above the aircraft when it is on the ground as well as when the aircraft is at altitude collecting remote sensing data. Furthermore, we describe the use of these optical properties for quantitative atmospheric correction of Landsat Thematic Mapper (TM) and NS001 TM simulator radiances in a simplified radiative transfer model appropriate for each pixel of entire images. Both qualitative and quantitative comparisons of results from use of the model show it provides good to excellent correction for atmospheric effects in TM and NS001 TM simulator data. Quantitative comparisons with measurements of surface radiances measured near the time of the TM overpass showed agreement within a few percent for bands 2, 3, and 4. Band 1 yielded radiances within 15 percent of the surface radiances. We think the simplified atmospheric correction model shows great promise for applying atmospheric corrections to entire images instead of individual points within images to yield surface radiances within a few percent in a computationally efficient manner.

Wrigley, R. C.↗
NASA NTRS2012

Polarimetric Retrievals of Surface and Cirrus Clouds Properties in the Region Affected by the Deepwater Horizon Oil Spill

In 2010, the Goddard Institute for Space Studies (GISS) Research Scanning Polarimeter (RSP) performed several aerial surveys over the region affected by the oil spill caused by the explosion of the Deepwater Horizon offshore platform. The instrument was deployed on the NASA Langley B200 aircraft together with the High Spectral Resolution Lidar (HSRL), which provides information on the distribution of the aerosol layers beneath the aircraft, including an accurate estimate of aerosol optical depth. This work illustrates the merits of polarization measurements in detecting variations of ocean surface properties linked to the presence of an oil slick. In particular, we make use of the degree of linear polarization in the glint region, which is severely affected by variations in the refractive index but insensitive to the waviness of the water surface. Alterations in the surface optical properties are therefore expected to directly affect the polarization response of the RSP channel at 2264 nm, where both molecular and aerosol scattering are negligible and virtually all of the observed signal is generated via Fresnel reflection at the surface. The glint profile at this wavelength is fitted with a model which can optimally estimate refractive index, wind speed and direction, together with aircraft attitude variations affecting the viewing geometry. The retrieved refractive index markedly increases over oil-contaminated waters, while the apparent wind speed is significantly lower than in adjacent uncontaminated areas, suggesting that the slick dampens high-frequency components of the ocean wave spectrum. The constraint on surface reflectance provided by the short-wave infrared channels is a cornerstone of established procedures to retrieve atmospheric aerosol microphysical parameters based on the inversion of the RSP multispectral measurements. This retrieval, which benefits from the ancillary information provided by the HSRL, was in this specific case hampered by prohibitive variability in atmospheric conditions (very inhomogeneous aerosol distribution and cloud cover). Although the results presented for the surface are essentially unaffected, we discuss the results obtained by typing algorithms in sorting the complex mix of aerosol types, and show evidence of oriented ice in cirrus clouds present in the area. In this context, polarization measurements at 1880 nm were used to infer ice habit and cirrus optical depth, which was found in the subvisual/threshold-visible regime, confirming the utility of the aforementioned RSP channel for the remote sensing of even thin cold clouds.

Polarization↗
NASA NTRSDate not supplied

Design and Analysis of A Jet Stretcher for High-Altitude Supersonic Free Jet Testing

A jet stretcher can be used to extend the region of clean flow for a test article in a supersonic free jet. The device acts to shield the article from shock waves reflected from the free jet shear layer. It can also allow for overexpanded nozzle operation through blocking shocks emanating from the nozzle lip, enlarging the potential test envelope. The FUN3D computational fluid dynamics solver was used to test a design process for developing jet stretchers. The inner surface of the axisymmetric jet stretcher was obtained from a streamline extracted from a free flight simulation around a notional test article at the intended test condition of Mach 3.2, 53,000 ft. The test article and jet stretcher were then simulated in a free jet nozzle exhaust, and the flowfield within a notional inlet aperture was compared between the installed and free flight calculations. Ambient pressure was increased until separation within the free jet nozzle finally induced disturbances at the inlet. The jet stretcher was shown to provide clean flow to the inlet at cell pressure ratios up to 2.8. A process for trimming the axisymmetric jet stretcher was also tested. This was intended to provide blockage relief for complex test articles, aiding with starting, as well as reducing weight and fabrication cost. The trimmed jet stretcher performed identically to the axisymmetric model at slightly-overexpanded conditions, but at cell pressure ratios above 1.3 allowed disturbances from the trailing edge to reach the inlet.

free jet↗
NASA NTRSDate not supplied

Design and Analysis of A Jet Stretcher for High-Altitude Supersonic Free Jet Testing

A jet stretcher can be used to extend the region of clean flow for a test article in a supersonic free jet. The device acts to shield the article from shock waves reflected from the free jet shear layer. It can also allow for overexpanded nozzle operation through blocking shocks emanating from the nozzle lip, enlarging the potential test envelope. The FUN3D computational fluid dynamics solver was used to test a design process for developing jet stretchers. The inner surface of the axisymmetric jet stretcher was obtained from a streamline extracted from a free flight simulation around a notional test article at the intended test condition of Mach 3.2, 53,000 ft. The test article and jet stretcher were then simulated in a free jet nozzle exhaust, and the flowfield within a notional inlet aperture was compared between the installed and free flight calculations. Ambient pressure was increased until separation within the free jet nozzle finally induced disturbances at the inlet. The jet stretcher was shown to provide clean flow to the inlet at cell pressure ratios up to 2.8. A process for trimming the axisymmetric jet stretcher was also tested. This was intended to provide blockage relief for complex test articles, aiding with starting, as well as reducing weight and fabrication cost. The trimmed jet stretcher performed identically to the axisymmetric model at slightly overexpanded conditions, but at cell pressure ratios above 1.3 allowed disturbances from the trailing edge to reach the inlet.

free jet↗
NASA NTRS1995

Surface modeling and grid generation for aeropropulsion CFD

The efforts in geometry modeling and grid generation at the NASA Lewis Research Center, as applied to the computational fluid dynamic (CFD) analysis of aeropropulsion systems, are presented. The efforts are mainly characterized by a focus on the analysis of components of an aeropropulsion system, which involve turbulent viscous flow with heat transfer and chemistry. Thus, this discussion will follow that characterization and will sequence through the components of typical propulsion systems consisting of inlets, compressors, combustors, turbines, and nozzles. For each component, some applications of CFD analysis will be presented to show how CFD is used to compute the desired performance information, how geometry modeling and grid generation are performed, and what issues have developed related to geometry modeling and grid generation. The discussion will illustrate the following needs related to geometry modeling and grid generation as observed in aeropropulsion analysis: (1) accurate and efficient resolution of turbulent viscous and chemically-reacting flowfields; (2) easy-to-use interfaces with CAD data for automated grid generation about complex geometries; and (3) automated batch grid generation software for use with design and optimization software.

Choo, Yung K.↗
NASA NTRS1983

A coupled ice-ocean model of upwelling in the marginal ice zone

A dynamical coupled ice-ocean numerical model for the marginal ice zone (MIZ) is suggested and used to study upwelling dynamics in the MIZ. The nonlinear sea ice model has a variable ice concentration and includes internal ice stress. The model is forced by stresses on the air/ocean and air/ice surfaces. The main coupling between the ice and the ocean is in the form of an interfacial stress on the ice/ocean interface. The ocean model is a linear reduced gravity model. The wind stress exerted by the atmosphere on the ocean is proportional to the fraction of open water, while the interfacial stress ice/ocean is proportional to the concentration of ice. A new mechanism for ice edge upwelling is suggested based on a geostrophic equilibrium solution for the sea ice medium. The upwelling reported in previous models invoking a stationary ice cover is shown to be replaced by a weak downwelling due to the ice motion. Most of the upwelling dynamics can be understood by analysis of the divergence of the across ice edge upper ocean transport. On the basis of numerical model, an analytical model is suggested that reproduces most of the upwelling dynamics of the more complex numerical model.

Roed, L. P.↗
NASA NTRS1996

Turbulence Modeling and Computation of Turbine Aerodynamics and Heat Transfer

The objective of the present research is to develop improved turbulence models for the computation of complex flows through turbomachinery passages, including the effects of streamline curvature, heat transfer and secondary flows. Advanced turbulence models are crucial for accurate prediction of rocket engine flows, due to existance of very large extra strain rates, such as strong streamline curvature. Numerical simulation of the turbulent flows in strongly curved ducts, including two 180-deg ducts, one 90-deg duct and a strongly concave curved turbulent boundary layer have been carried out with Reynolds stress models (RSM) and algebraic Reynolds stress models (ARSM). An improved near-wall pressure-strain correlation has been developed for capturing the anisotropy of turbulence in the concave region. A comparative study of two modes of transition in gas turbine, the by-pass transition and the separation-induced transition, has been carried out with several representative low-Reynolds number (LRN) k-epsilon models. Effects of blade surface pressure gradient, freestream turbulence and Reynolds number on the blade boundary layer development, and particularly the inception of transition are examined in detail. The present study indicates that the turbine blade transition, in the presence of high freestream turbulence, is predicted well with LRN k-epsilon models employed. The three-dimensional Navier-Stokes procedure developed by the present authors has been used to compute the three-dimensional viscous flow through the turbine nozzle passage of a single stage turbine. A low Reynolds number k-epsilon model and a zonal k-epsilon/ARSM (algebraic Reynolds stress model) are utilized for turbulence closure. An assessment of the performance of the turbulence models has been carried out. The two models are found to provide similar predictions for the mean flow parameters, although slight improvement in the prediction of some secondary flow quantities has been obtained by the ARSM model. It's found that the wake profiles inside the endwall boundary layers are predicted better than those near the mid-span.

Lakshminarayana, B.↗
NASA NTRS1975

Theoretical investigations of plasma processes in the ion bombardment thruster

A physical model for a thruster discharge was developed, consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field. The associated boundary-value problem for the coupled partial differential equations with mixed boundary conditions, which describe the electric potential and the plasma velocity fields, was solved in closed form. By means of quantum-mechanical perturbation theory, a formula for the number S(E) of atoms sputtered on the average by an ion of energy E was derived from first principles. The boundary-value problem describing the diffusion of the sputtered atoms through the surrounding rarefied electron-ion plasma to the system surfaces of ion propulsion systems was formulated and treated analytically. It is shown that outer boundary-value problems of this type lead to a complex integral equation, which requires numerical resolution.

Wilhelm, H. E.↗
NASA NTRS2000

Long Term Degradation of Resin for High Temperature Composites

The durability of polymer matrix composites exposed to harsh environments is a major concern. Surface degradation and damage are observed in polyimide composites used in air at 125 to 300 C. It is believed that diffusion of oxygen into the material and oxidative chemical reactions in the matrix are responsible. Previous work has characterized and modeled diffusion behavior, and thermogravimetric analyses (TGAs) have been carried out in nitrogen, air, and oxygen to provide quantitative information on thermal and oxidative reactions. However, the model developed using these data was not able to capture behavior seen in isothermal tests, especially those of long duration. A test program that focuses on lower temperatures and makes use of isothermal tests was undertaken to achieve a better understanding of the degradation reactions under use conditions. A new low-cost technique was developed to collect chemical degradation data for isothermal tests lasting over 200 hr in the temperature range 125 to 300 C. Results indicate complex behavior not captured by the previous TGA tests, including the presence of weight-adding reactions. Weight gain reactions dominated in the 125 to 225 C temperature range, while weight loss reactions dominated beyond 225 C. The data obtained from isothermal tests was used to develop a new model of the material behavior. This model was able to fully capture the behavior seen in the tests up to 275 C. Correlation of the current model with both isothermal data at 300 C and high rate TGA test data is mediocre. At 300 C and above, the reaction mechanisms appear to change. Attempts (which failed) to measure non-oxidative degradation indicate that oxidative reactions dominate the degradation at low temperatures. Based on this work, long term isothermal testing in an oxidative atmosphere is recommended for studying the degradation behavior of this class of materials.

Patekar, Kaustubh A.↗
NASA NTRS2008

Small-Body Extensions for the Satellite Orbit Analysis Program (SOAP)

An extension to the SOAP software allows users to work with tri-axial ellipsoid-based representations of planetary bodies, primarily for working with small, natural satellites, asteroids, and comets. SOAP is a widely used tool for the visualization and analysis of space missions. The small body extension provides the same visualization and analysis constructs for use with small bodies. These constructs allow the user to characterize satellite path and instrument cover information for small bodies in both 3D display and numerical output formats. Tri-axial ellipsoids are geometric shapes the diameters of which are different in each of three principal x, y, and z dimensions. This construct provides a better approximation than using spheres or oblate spheroids (ellipsoids comprising two common equatorial diameters as a distinct polar diameter). However, the tri-axial ellipsoid is considerably more difficult to work with from a modeling perspective. In addition, the SOAP small-body extensions allow the user to actually employ a plate model for highly irregular surfaces. Both tri-axial ellipsoids and plate models can be assigned to coordinate frames, thus allowing for the modeling of arbitrary changes to body orientation. A variety of features have been extended to support tri-axial ellipsoids, including the computation and display of the spacecraft sub-orbital point, ground trace, instrument footprints, and swathes. Displays of 3D instrument volumes can be shown interacting with the ellipsoids. Longitude/latitude grids, contour plots, and texture maps can be displayed on the ellipsoids using a variety of projections. The distance along an arbitrary line of sight can be computed between the spacecraft and the ellipsoid, and the coordinates of that intersection can be plotted as a function of time. The small-body extension supports the same visual and analytical constructs that are supported for spheres and oblate spheroids in SOAP making the implementation of the more complex algorithms largely transparent to the user.

Carnright, Robert↗
NASA NTRS2014

Evaluating LSM-Based Water Budgets Over a West African Basin Assisted with a River Routing Scheme

Within the framework of the African Monsoon Multidisciplinary Analysis (AMMA) Land Surface Model Intercomparison Project phase 2 (ALMIP-2), this study evaluates the water balance simulated by the Interactions between Soil, Biosphere, and Atmosphere (ISBA) over the upper Oum River basin, in Benin, using a mesoscale river routing scheme (RRS). The RRS is based on the nonlinear Muskingum Cunge method coupled with two linear reservoirs that simulate the time delay of both surface runoff and base flow that are produced by land surface models. On the basis of the evidence of a deep water-table recharge in that region,a reservoir representing the deep-water infiltration (DWI) is introduced. The hydrological processes of the basin are simulated for the 2005-08 AMMA field campaign period during which rainfall and stream flow data were intensively collected over the study area. Optimal RRS parameter sets were determined for three optimization experiments that were performed using daily stream flow at five gauges within the basin. Results demonstrate that the RRS simulates stream flow at all gauges with relative errors varying from -22% to 3% and Nash-Sutcliffe coefficients varying from 0.62 to 0.90. DWI varies from 24% to 67% of the base flow as a function of the sub-basin. The relatively simple reservoir DWI approach is quite robust, and further improvements would likely necessitate more complex solutions (e.g., considering seasonality and soil type in ISBA); thus, such modifications are recommended for future studies. Although the evaluation shows that the simulated stream flows are generally satisfactory, further field investigations are necessary to confirm some of the model assumptions.

Multidisciplinary↗
NASA NTRS1989

Integrated approach for active coupling of structures and fluids

Strong coupling of structure and fluids is common in many engineering environments, particularly when the flow is nonlinear and very sensitive to structural motions. Such coupling can give rise to physically important phenomena, such as a dip in the transonic flutter boundary of a wing. The coupled phenomenon can be analyzed in closed form for simple cases that are defined by linear structural and fluid equations of motion. However, complex cases defined by nonlinear equations pose a more difficult task for solution. It is important to understand these nonlinear coupled problems, since they may lead to physically important new phenomena. Flow discontinuities, such as a shock wave, and structural discontinuities, such as a hinge line of a control surface of a wing, can magnify the coupled effects and give rise to new phenomena. To study such a strongly coupled phenomenon, an integrated approach is presented in this paper. The aerodynamic and structural equations of motion are simultaneously integrated by a time-accurate numerical scheme. The theoretical simulation is done using the time-accurate unsteady transonic aerodynamic equations coupled with modal structural equations of motion. As an example, the coupled effect of shock waves and hinge-line discontinuities are studied for aeroelastically flexible wings with active control surfaces. The simulation in this study is modeled in the time domain and can be extended to simulate accurately other systems where fluids and structures are strongly coupled.

Guruswamy, Guru P.↗
NASA NTRS1995

Viscous-flow analysis of a subsonic transport aircraft high-lift system and correlation with flight data

High-lift system aerodynamics has been gaining attention in recent years. In an effort to improve aircraft performance, comprehensive studies of multi-element airfoil systems are being undertaken in wind-tunnel and flight experiments. Recent developments in Computational Fluid Dynamics (CFD) offer a relatively inexpensive alternative for studying complex viscous flows by numerically solving the Navier-Stokes (N-S) equations. Current limitations in computer resources restrict practical high-lift N-S computations to two dimensions, but CFD predictions can yield tremendous insight into flow structure, interactions between airfoil elements, and effects of changes in airfoil geometry or free-stream conditions. These codes are very accurate when compared to strictly 2D data provided by wind-tunnel testing, as will be shown here. Yet, additional challenges must be faced in the analysis of a production aircraft wing section, such as that of the NASA Langley Transport Systems Research Vehicle (TSRV). A primary issue is the sweep theory used to correlate 2D predictions with 3D flight results, accounting for sweep, taper, and finite wing effects. Other computational issues addressed here include the effects of surface roughness of the geometry, cove shape modeling, grid topology, and transition specification. The sensitivity of the flow to changing free-stream conditions is investigated. In addition, the effects of Gurney flaps on the aerodynamic characteristics of the airfoil system are predicted.

Potter, R. C.↗
NASA NTRS2022

NASA GEOS Composition Forecast Modeling System GEOS-CF v1.0: Stratospheric Composition

The NASA Goddard Earth Observing System (GEOS) Composition Forecast (GEOS-29CF) provides recent estimates and five-day forecasts of atmospheric composition to the public in near-real time. To do this, the GEOS Earth system model is coupled with the GEOS-Chem tropospheric-stratospheric unified chemistry extension (UCX) to represent composition from the surface to the top of the GEOS atmosphere (0.01 hPa). The GEOS-CF system is described, including updates made to the GEOS-Chem UCX mechanism within GEOS-CF for improved representation of stratospheric chemistry. Comparisons are made against balloon, lidar and satellite observations for stratospheric composition, including measurements of ozone (O3) and important nitrogen and chlorine species related to stratospheric O3recovery. The GEOS-CF nudges the stratospheric O3towards the GEOS Forward Processing (GEOS FP) assimilated O3product; as a result the stratospheric O3in the GEOS-CF historical estimate agrees well with observations. During abnormal dynamical and chemical environments such as the 2020 polar vortexes, the GEOS-CF O3forecasts are more realistic than GEOS FP O3forecasts because of the inclusion of the complex GEOS-Chem UCX stratospheric chemistry. Overall, the spatial patterns of the GEOS-CF simulated concentrations of stratospheric composition agree well with satellite observations. However, there are notable biases – such as low NOx and HNO3 in the polar regions and generally low HCl throughout the stratosphere – and future improvements to the chemistry mechanism and emissions are discussed. GEOS-CF is a new tool for the research community and instrument teams observing trace gases in the stratosphere and troposphere, providing near-real-time three-dimensional gridded information on atmospheric composition.

GEOS-CF↗
NASA NTRS2000

A New Neural Network Approach Including First-Guess for Retrieval of Atmospheric Water Vapor, Cloud Liquid Water Path, Surface Temperature and Emissivities Over Land From Satellite Microwave Observations

The analysis of microwave observations over land to determine atmospheric and surface parameters is still limited due to the complexity of the inverse problem. Neural network techniques have already proved successful as the basis of efficient retrieval methods for non-linear cases, however, first-guess estimates, which are used in variational methods to avoid problems of solution non-uniqueness or other forms of solution irregularity, have up to now not been used with neural network methods. In this study, a neural network approach is developed that uses a first-guess. Conceptual bridges are established between the neural network and variational methods. The new neural method retrieves the surface skin temperature, the integrated water vapor content, the cloud liquid water path and the microwave surface emissivities between 19 and 85 GHz over land from SSM/I observations. The retrieval, in parallel, of all these quantities improves the results for consistency reasons. A data base to train the neural network is calculated with a radiative transfer model and a a global collection of coincident surface and atmospheric parameters extracted from the National Center for Environmental Prediction reanalysis, from the International Satellite Cloud Climatology Project data and from microwave emissivity atlases previously calculated. The results of the neural network inversion are very encouraging. The r.m.s. error of the surface temperature retrieval over the globe is 1.3 K in clear sky conditions and 1.6 K in cloudy scenes. Water vapor is retrieved with a r.m.s. error of 3.8 kg/sq m in clear conditions and 4.9 kg/sq m in cloudy situations. The r.m.s. error in cloud liquid water path is 0.08 kg/sq m . The surface emissivities are retrieved with an accuracy of better than 0.008 in clear conditions and 0.010 in cloudy conditions. Microwave land surface temperature retrieval presents a very attractive complement to the infrared estimates in cloudy areas: time record of land surface temperature will be produced.

Aires, F.↗
NASA NTRS2014

Comparison of Forced ENSO-Like Hydrological Expressions in Simulations of the Preindustrial and Mid-Holocene

Using the water isotope- and vapor source distribution (VSD) tracer-enabled Goddard Institute for Space Studies ModelE-R, we examine changing El Nino-Southern Oscillation (ENSO)-like expressions in the hydrological cycle in a suite of model experiments. We apply strong surface temperature anomalies associated with composite observed El Nino and La Nina events as surface boundary conditions to preindustrial and mid-Holocene model experiments in order to investigate ENSO-like expressions in the hydrological cycle under varying boundary conditions. We find distinct simulated hydrological anomalies associated with El Nino-like ("ENSOWARM") and La Nina-like ("ENSOCOOL") conditions, and the region-specific VSD tracers show hydrological differences across the Pacific basin between El Nino-like and La Nina-like events. The application of ENSOCOOL forcings does not produce climatological anomalies that represent the equal but opposite impacts of the ENSOWARM experiment, as the isotopic anomalies associated with ENSOWARM conditions are generally stronger than with ENSOCOOL and the spatial patterns of change distinct. Also, when the same ENSO-like surface temperature anomalies are imposed on the mid-Holocene, the hydrological response is muted, relative to the preindustrial. Mid-Holocene changes in moisture sources to the analyzed regions across the Pacific reveal potentially complex relationships between ENSO-like conditions and boundary conditions. Given the complex impacts of ENSO-like conditions on various aspects of the hydrological cycle, we suggest that proxy record insights into paleo-ENSO variability are most likely to be robust when synthesized from a network of many spatially diverse archives, which can account for the potential nonstationarity of ENSO teleconnections under different boundary conditions.

boundary conditions↗
NASA NTRS2008

Determining Concentration of Nanoparticles from Ellipsometry

A method of using ellipsometry or polarization analysis of light in total internal reflection of a surface to determine the number density of gold nanoparticles on a smooth substrate has been developed. The method can be modified to enable determination of densities of sparse distributions of nanoparticles in general, and is expected to be especially useful for measuring gold-nanoparticle-labeled biomolecules on microarrays. The method is based on theoretical calculations of the ellipsometric responses of gold nanoparticles. Elements of the calculations include the following: For simplicity, the gold nanoparticles are assumed to be spherical and to have the same radius. The distribution of gold nanoparticles is assumed to be a sub-monolayer (that is, sparser than a monolayer). The optical response of the sub-monolayer is modeled by use of a thin-island-film theory, according to which the polarizabilities parallel and perpendicular to the substrate are functions of the wavelength of light, the dielectric functions (permittivities expressed as complex functions of frequency or wavelength) of the gold and the suspending medium (in this case, the suspending medium is air), the fraction of the substrate area covered by the nanoparticles, and the radius of the nanoparticles. For the purpose of the thin-island-film theory, the dielectric function of the gold nanoparticles is modeled as the known dielectric function of bulk gold plus a correction term that is necessitated by the fact that the mean free path length for electrons in gold decreases with decreasing radius, in such a manner as to cause the imaginary part of the dielectric function to increase with decreasing radius (see figure). The correction term is a function of the nanoparticle radius, the wavelength of light, the mean free path and the Fermi speed of electrons in bulk gold, the plasma frequency of gold, and the speed of light in a vacuum. These models are used to calculate ellipsometric responses for various concentrations of gold nanoparticles having an assumed radius. The modeled data indicates distinct spectral features for both the real and the imaginary part of the dielectric function. An ellipsometric measurement would determine this distinct feature and thus can be used to measure nanoparticle concentration. By "ellipsometric responses" is meant the intensities of light measured in various polarization states as functions of the angle of incidence and the polarization states of the incident light. These calculated ellipsometric responses are used as calibration curves: Data from subsequent ellipsometric measurements on real specimens are compared with the calibration curves. The concentration of the nanoparticles on a specimen is assumed to be that of the calibration curve that most closely matches the data pertaining to that specimen.

Venkatasubbarao, Srivatsa↗