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NASA NTRS2007

A Support Database System for Integrated System Health Management (ISHM)

The development, deployment, operation and maintenance of Integrated Systems Health Management (ISHM) applications require the storage and processing of tremendous amounts of low-level data. This data must be shared in a secure and cost-effective manner between developers, and processed within several heterogeneous architectures. Modern database technology allows this data to be organized efficiently, while ensuring the integrity and security of the data. The extensibility and interoperability of the current database technologies also allows for the creation of an associated support database system. A support database system provides additional capabilities by building applications on top of the database structure. These applications can then be used to support the various technologies in an ISHM architecture. This presentation and paper propose a detailed structure and application description for a support database system, called the Health Assessment Database System (HADS). The HADS provides a shared context for organizing and distributing data as well as a definition of the applications that provide the required data-driven support to ISHM. This approach provides another powerful tool for ISHM developers, while also enabling novel functionality. This functionality includes: automated firmware updating and deployment, algorithm development assistance and electronic datasheet generation. The architecture for the HADS has been developed as part of the ISHM toolset at Stennis Space Center for rocket engine testing. A detailed implementation has begun for the Methane Thruster Testbed Project (MTTP) in order to assist in developing health assessment and anomaly detection algorithms for ISHM. The structure of this implementation is shown in Figure 1. The database structure consists of three primary components: the system hierarchy model, the historical data archive and the firmware codebase. The system hierarchy model replicates the physical relationships between system elements to provide the logical context for the database. The historical data archive provides a common repository for sensor data that can be shared between developers and applications. The firmware codebase is used by the developer to organize the intelligent element firmware into atomic units which can be assembled into complete firmware for specific elements.

FROM↗
NASA NTRS2003

Computation of Free-Free Transitions in Atomic Physics: Foundations

The amplitude T for "free-free" processes, such as bremsstrahlung or photo- absorption by an electron in the continuum in the presence of an external field, is usually written as the matrix element of the radiation operator taken between two continuum states. However, unlike the case when at least one of the states is bound, as in radiative transitions, electron capture, or the photo-effect, this expression contains an unphysical term, proportional to a delta-function and is not really the physical amplitude Tphys. This continues to be true for both the velocity and length form of the dipole approximation to the amplitude T. We first give an a priori definition of Tphys in terms of the scattering parts of the continuum functions, which has an obvious interpretation in terms of time-ordered diagrams. We then show that when the formal amplitude is modified by a long- distance cutoff, the modified form approaches Tphys as the cutoff is removed. The modified form then serves as a basis for the definition of a physical velocity dipole amplitude and this in turn leads to an equivalent length form of the dipole amplitude. This exercise provides a clear theoretical basis for many extant calculations in which cutoff factors are introduces somewhat ad hoc, as needed.

Bhatia, A. K.↗
NASA NTRS1988

The JPL trapped mercury ion frequency standard

In order to provide frequency standards for the Deep Space Network (DSN) which are more stable than present-day hydrogen masers, a research task was established under the Advanced Systems Program of the TDA to develop a Hg-199(+) trapped ion frequency standard. The first closed-loop operation of this kind is described. Mercury-199 ions are confined in an RF trap and are state-selected through the use of optical pumping with 194 nm UV light from a Hg-202 discharge lamp. Absorption of microwave radiation at the hyperfine frequency (40.5 GHz) is signaled by atomic fluorescence of the UV light. The frequency of a 40.5 GHz oscillator is locked to a 1.6 Hz wide atomic absorption line of the trapped ions. The measured Allan variance of this locked oscillator is currently gamma sub y (pi) = 4.4 x 10 to the minus 12th/square root of pi for 20 is less than pi is less than 320 seconds, which is better stability than the best commercial cesium standards by almost a factor of 2. This initial result was achieved without magnetic shielding and without regulation of ion number.

Prestage, J. D.↗
NASA NTRS2000

It's About Time!

Everything we do in VLBI is connected to time. In this contribution, we review 28 orders of magnitude of the spectrum of time ranging from a few hundred femtoseconds (i.e. one degree of phase at X-band - Pi x 10(exp -13) seconds) upwards to tens of millions of years (i.e. ten million years Pi x 10(exp 14) seconds). In this discussion, we will pay special attention to the relation between the underlying oscillator (the frequency standard that defines a clock's rate) and the time kept by the clock (which counts the oscillations of the frequency standard). We will consider two different types of time - time kept by counting an atomic frequency standard (Hydrogen Maser or Cesium), and time reckoned by the rotation of the Earth underneath the stars and sun.

Clark, Tom↗
NASA NTRS1995

The O IV and S IV intercombination lines in solar and stellar ultraviolet spectra

New calculations of O IV electron density diagnostic emission-line ratios involving the 1399.8, 1401.2, 1404.8, and 14076.4 A transitions are presented. A comparison of these calculations with observational data from a quiet solar region, a sunspot, and an active region obtained with the High Resolution Telescope and Spectrograph (HRTS), two flares observed with the SO82B spectrograph on board Skylab, and Hubble Space Telescope (HST) observations by the Goddard High Resolution Spectrograph (GHRS) of Capella, gives good results using the ratio R(sub 1) = I(1407.4 A)/I(1401.2 A). However, the electron density obtained using the ratio R(sub 2) = I(1407.4 A)/I(1404.8 A) is often an order of magnitude smaller. The O IV 1404.8 A line is blended with the S IV 1404.8 A line, and we investigate whether this ratio may still be used as a density diagnostic if the S IV 1406.1 A line intensity is used to correct for the presence of S IV 1404.8 A, using previous S IV calculations by Dufton et al. We still find systematic differences compared to density determinations from line ratios that do not involve the O IV 1404.8 A line, which we suggest are due to errors in earlier theoretical calculations of the S IV atomic data, and also possibly to previously unconsidered fluorescent pumping of the upper level of the S IV 1404.8 A transition.

Cook, J. W.↗
NASA NTRS1985

A critical analysis of CLO and O3 in the mid-latitude stratosphere

The Caltech one-dimensional photochemical model is used to analyze important questions concerning the upper stratospheric O3 and the key HO(x), NO(x), and ClO(x) free radicals. The model is described and first order effects of the inclusion of diffuse radiation in a spherical rather than plane parallel atmosphere at solar zenith angles close to 90 deg are assessed. A comparison is made between photochemical theory and observations for upper stratospheric O3, where local photochemistry rather than dynamics should control the O3 abundance. The photochemical equilibrium relation for odd oxygen is studied, including the important radicals involves. It is concluded that a significant model ozone deficit exists in the upper stratosphere. Possible causes for such a discrepancy are investigated in light of current model and experimental uncertainties. In particular, the observational ratio of atomic oxygen to zone appears to disagree with the model results.

Froidevaux, L.↗
NASA NTRS1991

Observations of the 2-micron unidentified lines in planetary nebulae

Medium-resolution spectra in the K-window have been obtained for 13 planetary nebulae and one compact H II region in order to study the behavior of the unidentified line at 2.287 microns. The wavelengths of this line and the unidentified 2.199-micron line have been measured in NGC 7027 at high spectral resolution using a Fabry-Perot interferometer. Based on the interferometric measurements and the lack of correlation of the 2.287-micron line with emission in H2 lines, the unidentified lines are not lines of molecular hydrogen. The 2.287-micron line is strongest in medium-high excitation nebulae, and is absent in nebulae of very low and very high excitation, implying that the ionization potential of the parent atom or ion is about 30-40 eV and that the ion itself has an ionization potential of perhaps 40-60 eV.

Geballe, T. R.↗
NASA NTRS2004

Sensor for Monitoring Nanodevice-Fabrication Plasmas

The term plasma process diagnostics (PPD) refers to a spectroscopic technique and sensing hardware that have been proposed for monitoring plasma processes used to fabricate electronic devices that feature sizes as small as several nanometers. Nanometer dimensions are characteristic of the quantum level of miniaturization, where single impurity atoms or molecules can drastically change the local properties of the nanostructures. Such changes may be purposely used in nanoscale design but may also be extremely damaging or cause improper operation of the fabricated devices. Determination of temperature and densities of reactants near the developing features is important, since the structural synthesis is affected by characteristics of the local microenvironment. Consequently, sensors capable of nonintrusive monitoring with high sensitivity and high resolution are essential for real-time atomistic control of reaction kinetics and minimizing trace contamination in plasma processes used to fabricate electronic nanodevices. Such process-monitoring sensors are required to be compact, multiparametric, and immune to the harsh environments of processing plasmas. PPD is intended to satisfy these requirements. The specific technique used to implement plasma diagnostics with a PPD sensor would be an advanced version of continuous-wave cavity-ringdown spectroscopy (CW-CRDS) capable of profiling spectral line broadenings in order to derive both Doppler and Stark components. CRDS is based on measurements of the rate of absorption of laser light in an optical resonator. The ultimate sensitivity results from a very long absorption path length within the cavity and immunity to variations in incident laser intensity. The proposed version of this technique would involve the use of multiplexing tunable laser diodes and an actively modulated high-reflectivity optical resonator, thus offering a synergistic combination of simplicity, compactness, high sensitivity, and high resolution. The multiplexing capabilities of diode lasers could be utilized to make the PPD sensor a single, simple, compact, and inexpensive tool for the acquisition of multiparametric data. A PPD sensor would be capable of continuous measurement of such physical parameters as gas temperature, gas velocity, electron number density, and absolute densities of reacting chemical species. A laser beam can be easily adjusted to analyze the immediate vicinity of the growing nanostructures (or features etched down) in real time. The absorption enhancement in an optical cavity would afford the sensitivity needed for measurement of the temperature and densities of species at concentrations significantly lower than measurable by other nonintrusive techniques. It is anticipated that fully developed PPD sensors would enable simultaneous measurement of local temperature and determination of plasma species responsible for the synthesis and functionalization of nanodevices. These sensors would also enable tracking the pathways and origins of damaging contaminants, thereby providing feedback for adjustment of processes to optimize them and reduce contamination. The PPD sensors should also be useful for optimization of conventional microelectronics manufacturing plasma processes. Going beyond plasma processes for fabrication of electronic devices, PPD sensors could be used for monitoring of atoms, molecules, ions, radicals, clusters, and particles in a variety of other settings, including outer space. Because of their high sensitivity, such sensors could also prove useful for detecting traces of illegal drugs and explosives.

Bolshakov, Alexander↗
NASA NTRS1990

Vibrations in small Mg clusters

The equilibrium geometries, binding energies, and harmonic frequencies of Mg3 and Mg4 have been determined using large atomic natural orbital basis sets in conjunction with high levels of electron correlation. The correlation treatments comprise multireference configuration interaction (MRCI), singles and doubles coupled-cluster (CCSD) theory and the CCSD(T) extension that includes a perturbational estimate of connected triple excitations. As with previous studies of small Be clusters, the CCSD(T) method is found to reproduce the MRCI results with a remarkable degree of accuracy and at a fraction of the computational cost. Using the CCSD(T) method, full quartic force fields for Mg3 and Mg4 have been determined and anharmonic analyses have been performed using second-order perturbation theory. Vibration-rotation interaction constants and centrifugal distortion constants have also been determined.

Lee, Timothy J.↗
NASA NTRS1997

Searching for Biogeochemical Cycles on Mars

The search for life on Mars clearly benefits from a rigorous, yet broad, definition of life that compels us to consider all possible lines of evidence for a martian biosphere. Recent studies in microbial ecology illustrate that the classic definition of life should be expanded beyond the traditional definition of a living cell. The traditional defining characteristics of life are threefold. First, life is capable of metabolism, that is, it performs chemical reactions that utilize energy and also synthesize its cellular constituents. Second, life is capable of self-replication. Third, life can evolve in order to adapt to environmental changes. An expanded, ecological definition of life also recognizes that life is a community of organisms that must interact with their nonliving environment through processes called biogeochemical cycles. This regenerative processing maintains, in an aqueous conditions, a dependable supply of nutrients and energy for growth. In turn, life can significantly affect those processes that control the exchange of materials between the atmosphere, ocean, and upper crust. Because metabolic processes interact directly with the environment, they can alter their surroundings and thus leave behind evidence of life. For example, organic matter is produced from single-carbon-atom precursors for the biosynthesis of cellular constituents. This leads to a reservoir of reduced carbon in sediments that, in turn, can affect the oxidation state of the atmosphere. The harvesting of chemical energy for metabolism often employs oxidation-reduction reactions that can alter the chemistry and oxidation state of the redox-sensitive elements carbon, sulfur, nitrogen, iron, and manganese. Have there ever been biogeochemical cycles on Mars? Certain key planetary processes can offer clues. Active volcanism provides reduced chemical species that biota can use for organic synthesis. Volcanic carbon dioxide and methane can serve as greenhouse gases. Thus the persistence of volcanism on Mars may well have influenced the persistence of a martian biosphere. The geologic processing of the crust can affect the availability of nutrients and also control the deposition of minerals that could have served as a medium for the preservation of fossil information. Finally, the activity of liquid water is crucial to life. Was there ever an Earth-like hydrologic cycle with rainfall? Has aqueous activity instead been restricted principally to hydrothermal activity below the surface? To what extent did the inorganic chemistry driven by sunlight and hydrothermal activity influence organic chemistry (prebiotic chemical evolution)? This paper addresses these and other key questions.

DesMarais, David J.↗
NASA NTRS1979

Physical processes in directed ion beam sputtering

The general operation of a discharge chamber for the production of ions is described. A model is presented for the magnetic containment of both primary and secondary or Maxwellian electrons in the discharge plasma. Cross sections were calculated for energy and momentum transfer in binary collisions between like pairs of Ar, Kr, and Xe atoms in the energy range from about 1 eV to 1000 eV. These calculations were made from available pair interaction potentials using a classical model. Experimental data from the literature were fit to a theoretical expression for the Ar resonance charge exchange cross section over the same energy range. A model was developed that describes the processes of conical texturing of a surface due to simultaneous directed ion beam etching and sputter deposition of an impurity material. This model accurately predicts both a minimum temperature for texturing to take place and the variation of cone density with temperature. It also provides the correct order of magnitude of cone separation. It was predicted from the model, and subsequently verified experimentally, that a high sputter yield material could serve as a seed for coning of a lower sputter yield substrate. Seeding geometries and seed deposition rates were studied to obtain an important input to the theoretical texturing model.

Robinson, R. S.↗
NASA NTRS2001

CFD Simulation of Liquid Rocket Engine Injectors

Detailed design issues associated with liquid rocket engine injectors and combustion chamber operation require CFD methodology which simulates highly three-dimensional, turbulent, vaporizing, and combusting flows. The primary utility of such simulations involves predicting multi-dimensional effects caused by specific injector configurations. SECA, Inc. and Engineering Sciences, Inc. have been developing appropriate computational methodology for NASA/MSFC for the past decade. CFD tools and computers have improved dramatically during this time period; however, the physical submodels used in these analyses must still remain relatively simple in order to produce useful results. Simulations of clustered coaxial and impinger injector elements for hydrogen and hydrocarbon fuels, which account for real fluid properties, is the immediate goal of this research. The spray combustion codes are based on the FDNS CFD code' and are structured to represent homogeneous and heterogeneous spray combustion. The homogeneous spray model treats the flow as a continuum of multi-phase, multicomponent fluids which move without thermal or velocity lags between the phases. Two heterogeneous models were developed: (1) a volume-of-fluid (VOF) model which represents the liquid core of coaxial or impinger jets and their atomization and vaporization, and (2) a Blob model which represents the injected streams as a cloud of droplets the size of the injector orifice which subsequently exhibit particle interaction, vaporization, and combustion. All of these spray models are computationally intensive, but this is unavoidable to accurately account for the complex physics and combustion which is to be predicted, Work is currently in progress to parallelize these codes to improve their computational efficiency. These spray combustion codes were used to simulate the three test cases which are the subject of the 2nd International Workshop on-Rocket Combustion Modeling. Such test cases are considered by these investigators to be very valuable for code validation because combustion kinetics, turbulence models and atomization models based on low pressure experiments of hydrogen air combustion do not adequately verify analytical or CFD submodels which are necessary to simulate rocket engine combustion. We wish to emphasize that the simulations which we prepared for this meeting are meant to test the accuracy of the approximations used in our general purpose spray combustion models, rather than represent a definitive analysis of each of the experiments which were conducted. Our goal is to accurately predict local temperatures and mixture ratios in rocket engines; hence predicting individual experiments is used only for code validation. To replace the conventional JANNAF standard axisymmetric finite-rate (TDK) computer code 2 for performance prediction with CFD cases, such codes must posses two features. Firstly, they must be as easy to use and of comparable run times for conventional performance predictions. Secondly, they must provide more detailed predictions of the flowfields near the injector face. Specifically, they must accurately predict the convective mixing of injected liquid propellants in terms of the injector element configurations.

Farmer, Richard↗
NASA NTRS1987

The local interstellar medium

The structure of the local interstellar medium is reviewed with emphasis on the new observations of the cold neutral component. The properties of the high latitude molecular clouds are discussed as well as their relationship to the 'infrared cirrus' and atomic gas. The molecular clouds are shown to lie preferentially along the loops and filaments of local H I gas, but a detailed examination shows the CO and H I peaks are offset from one another. An expansion velocity of 7 km/s is derived for one of the shells, suggesting an expansion energy of about 8 x 10 to the 47th ergs, which is somewhat smaller than that expected for a supernova explosion. If the pressure in the clumps of the high latitude clouds is in equilibrium with the surrounding gas, the pressure in the shells is 10,000-100,000/cu cm K, an order of magnitude higher than what is generally argued to exist in the interstellar medium.

Blitz, Leo↗
NASA NTRS2004

Thermal and Nonthermal Contributions to the Solar Flare X-Ray Flux

The relative thermal and nonthermal contributions to the total energy budget of a solar flare are being determined through analysis of RHESSI X-ray imaging and spectral observations in the energy range from approx. 5 to approx. 50 keV. The classic ways of differentiating between the thermal and nonthermal components - exponential vs. sources - can now be combined for individual flares. In addition, RHESSI's sensitivity down to approx. 4 keV and energy resolution of approx. 1 keV FWHM allow the intensities and equivalent widths of the complex of highly ionized iron lines at approx. 6.7 keV and the complex of highly ionized iron and nickel lines at approx. 8 keV to be measured as a function of time. Using the spectral line and continuum intensities from the Chianti (version 4.2) atomic code, the thermal component of the total flare emission can be more reliably separated from the nonthermal component in the measured X-ray spectrum. The abundance of iron can also be determined from RHESSI line-to-continuum measurements as a function of time during larger flares. Results will be shown of the intensity and equivalent widths of these line complexes for several flares and the temperatures, emission measures, and iron abundances derived from them. Comparisons will be made with 6.7-keV Fe-line fluxes measured with the RESIK bent crystal spectrometer on the Coronas-F spacecraft operating in third order during the peak times of three flares (2002 May 31 at 00:12 UT, 2002 December 2 at 19:26 UT, and 2003 April 26 at 03:OO UT). During the rise and decay of these flares, RESIK was operating in first order allowing the continuum flux to be measured between 2.9 and 3.7 keV for comparison with RHESSI fluxes at its low-energy end.

Dennis, Brian R.↗
NASA NTRS1996

Transparent, Conductive Coatings Developed for Arc-Proof Solar Arrays

Transparent, conductive thin-film coatings have many potential applications where a surface must be able to dissipate electrical charges without sacrificing its optical properties. Such applications include automotive and aircraft windows, heat mirrors, optoelectronic devices, gas sensors, and solar cell array surfaces for space applications. Many spacecraft missions require that solar cell array surfaces dissipate charges in order to avoid damage such as electronic upsets, formation of pinholes in the protective coatings on solar array blankets, and contamination due to deposition of sputtered products. In tests at the NASA Lewis Research Center, mixed thin-films of sputter-deposited indium tin oxide (ITO) and magnesium fluoride (MgF2) that could be tailored to the desired sheet resistivity, showed transmittance values of greater than 90 percent. The samples evaluated were composed of mixed, thin-film ITO/MgF2 coatings, with a nominal thickness of 650 angstroms, deposited onto glass substrates. Preliminary results indicated that these coatings were durable to vacuum ultraviolet radiation and atomic oxygen. These coatings show promise for use on solar array surfaces in polar low-Earth-orbit environments, where a sheet resistivity of less than 10(exp 8)/square is required, and in geosynchronous orbit environments, where a resistivity of less than 10(exp 9)/square is required.

Source record↗
NASA NTRS1983

Solar concentrator degradation in Low Earth Orbit (LEO)

The use of parabolically or spherically-shaped mirrors is being considered in order to increase the solar energy intensity on solar cells. Their use will significantly decrease the size and number of the cells needed for a particular application, hence the total array cost. Questions arise, however, regarding the long-term (five to ten years) efficiency of these devices. Performance degradation of the mirror surfaces might result from known hostile elements in the low earth orbit (LEO) environment (150-350 nautical miles). The degradation issue is addressed in light of present knowledge of this environment. The following characteristics of the LEO environment are identified for study: (1) the vacuum of space; (2) sputtering by the residual atoms and particles in space; (3) solar electromagnetic radiation; (4) contamination of the mirror surface; (5) atomic oxygen interactions with the surface; (6) bombardment of the surface by meteoroids; and (7) irradiation of the surface by ionizing particles (protons). Using the best available information for the magnitudes of the necessary quantities, a mathematical analysis was carried out, where possible, to determine the degradation in reflectance or other loss caused by each characteristic. Otherwise, reasonable estimates are made of corresponding losses, based on already published data.

Thomas, R. G.↗
NASA NTRS1997

Kinetics and Mechanism of the Reaction of Hydoxyl Radicals with Acetonitrile under Atmospheric Conditions

The pulsed laser photolysis-pulsed laser induced fluorescence technique has been employed to determine absolute rate coefficients for the reaction OH + CH3CN (1) and its isotopic variants, OH + CD3CN (2), OD + CH3CN (3), and OD + CD3CN (4). Reactions 1 and 2 were studied as a function of pressure and temperature in N2, N2/O2, and He buffer gases. In the absence of O2 all four reactions displayed well-behaved kinetics with exponential OH decays and pseudo-first rate constants which were proportional to substrate concentration. Data obtained in N2 over the range 50-700 Torr at 298 K are consistent with k(sub 1), showing a small pressure dependence. The Arrhenius expression obtained by averaging data at all pressures in k(sub 1)(T) = (1.1(sup +0.5)/(sub -0.3)) x 10(exp -12) exp[(-1130 +/- 90)/T] cu cm /(molecule s). The kinetics of reaction 2 are found to be pressure dependent with k(sub 2) (298 K) increasing from (1.21 +/- 0.12) x 10(exp -14) to (2.16 +/- 0.11) x 10(exp -14) cm(exp 3)/ (molecule s) over the pressure range 50-700 Torr of N2 at 298 K. Data at pressures greater than 600 Torr give k(sub 2)(T) = (9.4((sup +13.4)(sub -5.0))) x 10(exp -13) exp[(-1180 +/- 250)/T] cu cm/(molecule s). The rates of reactions 3 and 4 are found to be independent of pressure over the range 50-700 Torr of N2 with 298 K rate coefficient given by k(sub 3) =(3.18 +/- 0.40) x 10(exp -14) cu cm/(molecule s) and k(sub 4) = (2.25 +/-0.28) x 10(exp -14) cu cm/(molecule s). In the presence of O2 each reaction shows complex (non-pseudo-first-order) kinetic behavior and/or an apparent decrease in the observed rate constant with increasing [O2], indicating the presence of significant OH or OD regeneration. Observation of regeneration of OH in (2) and OD in (3) is indicative of a reaction channel which proceeds via addition followed by reaction of the adduct, or one of its decomposition products, with O2. The observed OH and OD decay profiles have been modeled by using a simple mechanistic scheme to extract kinetic information about the adduct reations with O2 and branching ratios for OH regeneration. A plausible mechanism for OH regeneration in (2) involves OH addition to the nitrogen atom followed by O2 addition to the cyano carbon atom, isomeriazation and decomposition to D2CO + DOCN + OH. Our results suggest that the OH + CH3CN reaction occurs via a complex mechanism involving both bimolecular and termolecular pathways, analogous to the mechanisms for the the important atmospheric reactions of OH with CO and HNO3.

Hynes, A. J.↗
NASA NTRS2005

Measuring Two Key Parameters of H3 Color Centers in Diamond

A method of measuring two key parameters of H3 color centers in diamond has been created as part of a continuing effort to develop tunable, continuous-wave, visible lasers that would utilize diamond as the lasing medium. (An H3 color center in a diamond crystal lattice comprises two nitrogen atoms substituted for two carbon atoms bonded to a third carbon atom. H3 color centers can be induced artificially; they also occur naturally. If present in sufficient density, they impart a yellow hue.) The method may also be applicable to the corresponding parameters of other candidate lasing media. One of the parameters is the number density of color centers, which is needed for designing an efficient laser. The other parameter is an optical-absorption cross section, which, as explained below, is needed for determining the number density. The present method represents an improvement over prior methods in which optical-absorption measurements have been used to determine absorption cross sections or number densities. Heretofore, in order to determine a number density from such measurements, it has been necessary to know the applicable absorption cross section; alternatively, to determine the absorption cross section from such measurements, it has been necessary to know the number density. If, as in this case, both the number density and the absorption cross section are initially unknown, then it is impossible to determine either parameter in the absence of additional information.

Roberts, W. Thomas↗