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NASA NTRS1993

Pinatubo and pre-Pinatubo optical-depth spectra: Mauna Loa measurements, comparisons, inferred particle size distributions, radiative effects, and relationship to lidar data

The Ames airborne tracking sunphotometer was operated at the National Oceanic and Atmospheric Administration (NOAA) Mauna Loa Observatory (MLO) in 1991 and 1992 along with the NOAA Climate Monitoring and Diagnostics Laboratory (CMDL) automated tracking sunphotometer and lidar. June 1991 measurements provided calibrations, optical-depth spectra, and intercomparisons under relatively clean conditions; later measurements provided spectra and comparisons for the Pinatubo cloud plus calibration checks. June 1991 results are similar to previous MLO springtime measurements, with midvisible particle optical depth at the near-background level of 0.012 +/- 0.006 and no significant wavelength dependence in the measured range (lambda = 0.38 to 1.06 micrometers). The arrival of the Pinatubo cloud in July 1991 increased midvisible particle optical depth by more than an order of magnitude and changed the spectral shape of to an approximate power law with an exponent of about -1.4. By clearly September 1991, the spectrum was broadly peaked near 0.5 micrometers, and by July 1992, it was peaked near 0.8 micrometers. Our optical-depth spectra include corrections for diffuse light. NOAA- and Ames Research Center (ARC)-measured spectra are in good agreement. Columnar size distributions inverted from the spectra show that the initial (July 1991) post-Pinatubo cloud was relatively rich in small particles (r less than 0.25 micrometers), which were progressively depleted in the August-September 1991 and July 1992 periods. Conversely, both of the later periods had more of the optically efficient medium-sized particles (0.25 less than r less than 1 micrometers) than did the fresh July 1991 cloud. These changes are consistent with particle growth by condensation and coagulation. Photometer-inferred column backscatter values agree with those measured by the CMDL lidar on nearby nights. Combining lidar-measured backscatter profiles with photometer-derived backscatter-to-area ratios gives peak particle areas that could cause rapid heterogeneous loss of ozone, given sufficiently low particle acidity and suitable solar zenith angles (achieved at mid- to high latitudes). Top-of-troposphere radiative forcings for the September 1991 and July 1992 optical depths and size distributions over MLO are about -5 and -3 W/sq m, respectively (hence comparable in magnitude but opposite in sign to the radiative forcing caused by the increase in manmade greenhouse gases since the industrial revolution). Heating rates in the Pinatubo layer over MLO are 0.55 +/- 0.13 and 0.41 +/- 0.14 K/d for September 1991 and July 1992, respectively.

Russell, P. B.↗
NASA NTRS1993

An intercomparison of aircraft instrumentation for tropospheric measurements of carbonyl sulfide, hydrogen sulfide, and carbon disulfide

This paper reports results of NASA's Chemical Instrumentation and Test Evaluation (CITE 3) during which airborne measurements for carbonyl sulfide (COS), hydrogen sulfide (H2S), and carbon disulfide (CS2) were intercompared. Instrumentation included a gas chromatograph using flame photometric detection (COS, H2S, and CS2), a gas chromatograph using mass spectrometric detection (COS) and CS2), a gas chromatograph using fluorination and subsequent SF6 detection via electron capture (COS and CS2), and the Natusch technique (H2S). The measurements were made over the Atlantic Ocean east of North and South America during flights from NASA's Wallops Flight Center, Virginia, and Natal, Brazil, in August/September 1989. Most of the intercomparisons for H2S and CS2 were at mixing ratios less than 25 pptv and less than 10 pptv, respectively, with a maximum mixing ratio of about 100 pptv and 50 pptv, respectively. Carbonyl sulfide intercomparisons were at mixing ratios between 400 and 600 pptv. Measurements were intercompared from data bases constructed from time periods of simultaneous or overlapping measurements. Agreement among the COS techniques averaged about 5%, and individual measurements were generally within 10%. For H2S and at mixing ratio greater than 25 pptv, the instruments agreed on average to about 15%. At mixing ratios less than 25 pptv the agreement was about 5 pptv. For CS2 (mixing ratios less than 50 pptv), two techniques agreed on average to about 4 pptv, and the third exhibited a bias (relative to the other two) that varied in the range of 3-7 pptv. CS2 mixing ratios over the ocean east of Natal as measured by the gas chromatograph-mass spectrometer technique were only a few pptv and were below the detection limits of the other two techniques. The CITE 3 data are used to estimate the current uncertainty associated with aircraft measurements of COS, H2S, and CS2 in the remote troposphere.

Gregory, Gerald L.↗
NASA NTRS1995

Robust Quantitative Measurement of Flows and Transparent or Highly Reflective Objects

The liquid crystal point diffraction interferometer (LCPDI) is a new instrument that has been developed for the measurement of phase objects. The LCPDI uses the compact, robust design of Linnik's point diffraction interferometer and adds to it phase stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wave-fronts. A solid state camera provides very high data density and automated data reduction. The instrument can measure either transparent objects like fluids and lenses, or highly reflective opaque objects like mirrors. In the former case, the refractive index distribution is measured and then related to various properties like temperature, density, chemical composition, or thickness. In the latter case, the measured phase distribution is related to the object shape. The objects measured must be stationary or quasisteady state because the measurement requires the acquisition of several frames of image data during which time the object's properties must not have changed. The data acquisition time depends on the speed of the frame grabber and the required number of data frames. Typically, three to five frames taking 1 to 2 seconds are required. The potential for faster data acquisition exists.

Mercer, Carolyn R.↗
NASA NTRS1995

PULSAUR 2: Rocket and groundbased measurements in a pulsating aurora

The second pulsating aurora rocket (PULSAUR 2) rocket was launched into a pulsating aurora on 9 February 1994 and carried a broad range of instruments in order to perform a study of this type of aurora. The rocket measurements were complemented with a set of ground-based measurements. The particle measurements performed in the rocket are related to the ground-based optical measurements performed along the rocket trajectory. It is found that the high energy electrons are largely in phase with the measured luminosity. The EISCAT measurements carried out during the flight are reviewed. The PULSAUR 2 campaign is described. Results concerning the auroral conditions and the particle measurements are presented.

Soeraas, Finn↗
NASA NTRS1996

Apparatus Measures Thicknesses Of Ice On Bars

Semiautomated apparatus measures diameters, at selected lengthwise positions, of nine vertical ice-coated bars in icing-research wind tunnel. Includes measuring head that travels on rails parallel to bar, driven by ball screw actuated by stepping motor. Position of measuring head along bar measured by string potentiometer, providing position feedback for closed-loop control circuit. Circuit provides for smooth motion of measuring head, and used to select various programmed sequences of motions and measurements. Measurements needed to determine degree of uniformity of icing conditions for experiments on aircraft models.

Gibson, Theresa L.↗
NASA NTRS1995

Morphology of solar wind fluctuations and structure in the vicinity of the Sun from radio propagation measurements

Radio propagation measurements represent a powerful means for remote probing of electron density and solar wind speed in the acceleration region of the solar wind not yet explored by in situ measurements. Recent investigations based on radio propagation measurements have led to considerable progress in our knowledge of the general morphology of solar wind fluctuations and structure, especially in terms of their relationship to solar wind properties that have been observed directly by fields and particles measurements, and to coronal features observed in white-light measurements. The purpose of this paper is to present an overview of the latest results on quasi-stationary structure covering the large scale variation of solar wind speed over the streamer belt and coronal hole regions, coronal streamers (source of slow solar wind) and their associated small-scale electron density structure, plumes, density and fractional or relative density fluctuations, and the spectral characteristics of the electron density fluctuations. The radio propagation measurements not only reveal new information on the structure near the Sun, but also show that the structure appears to undergo substantial evolution on its way to 0.3 AU, the closest radial distance for which direct in situ spacecraft measurements are available.

Woo, R.↗
NASA NTRS1995

Modal Correction Method For Dynamically Induced Errors In Wind-Tunnel Model Attitude Measurements

This paper describes a method for correcting the dynamically induced bias errors in wind tunnel model attitude measurements using measured modal properties of the model system. At NASA Langley Research Center, the predominant instrumentation used to measure model attitude is a servo-accelerometer device that senses the model attitude with respect to the local vertical. Under smooth wind tunnel operating conditions, this inertial device can measure the model attitude with an accuracy of 0.01 degree. During wind tunnel tests when the model is responding at high dynamic amplitudes, the inertial device also senses the centrifugal acceleration associated with model vibration. This centrifugal acceleration results in a bias error in the model attitude measurement. A study of the response of a cantilevered model system to a simulated dynamic environment shows significant bias error in the model attitude measurement can occur and is vibration mode and amplitude dependent. For each vibration mode contributing to the bias error, the error is estimated from the measured modal properties and tangential accelerations at the model attitude device. Linear superposition is used to combine the bias estimates for individual modes to determine the overall bias error as a function of time. The modal correction model predicts the bias error to a high degree of accuracy for the vibration modes characterized in the simulated dynamic environment.

Buehrle, R. D.↗
NASA NTRS1996

Correction of WindScat Scatterometric Measurements by Combining with AMSR Radiometric Data

The Seawinds scatterometer on the advanced Earth observing satellite-2 (ADEOS-2) will determine surface wind vectors by measuring the radar cross section. Multiple measurements will be made at different points in a wind-vector cell. When dense clouds and rain are present, the signal will be attenuated, thereby giving erroneous results for the wind. This report describes algorithms to use with the advanced mechanically scanned radiometer (AMSR) scanning radiometer on ADEOS-2 to correct for the attenuation. One can determine attenuation from a radiometer measurement based on the excess brightness temperature measured. This is the difference between the total measured brightness temperature and the contribution from surface emission. A major problem that the algorithm must address is determining the surface contribution. Two basic approaches were developed for this, one using the scattering coefficient measured along with the brightness temperature, and the other using the brightness temperature alone. For both methods, best results will occur if the wind from the preceding wind-vector cell can be used as an input to the algorithm. In the method based on the scattering coefficient, we need the wind direction from the preceding cell. In the method using brightness temperature alone, we need the wind speed from the preceding cell. If neither is available, the algorithm can work, but the corrections will be less accurate. Both correction methods require iterative solutions. Simulations show that the algorithms make significant improvements in the measured scattering coefficient and thus is the retrieved wind vector. For stratiform rains, the errors without correction can be quite large, so the correction makes a major improvement. For systems of separated convective cells, the initial error is smaller and the correction, although about the same percentage, has a smaller effect.

Song, S.↗
NASA NTRS1995

Fluid flow volume measurements using a capacitance/conductance probe system

A probe system has been developed to measure the flow volume of a single fluid passing through an orifice or flow line. The system employs both capacitance and a conductance probe at the orifice, together with phase detection and data acquisition circuitry to measure flow volume and salinity under low or zero gravity conditions. A wide variety of frequencies can be used for the radio frequency (RF) signal source which is chosen primarily by the capacitance of the orifice probe and the fluid passing through the orifice. Rapid measurements are made using the reflected signal from the orifice probe to determine the 'instantaneous' permittivity of the fluid/gas mixture passing through. The 'instantaneous' measurements are integrated over time to determine flow volume. Analysis reveals that a narrow orifice helps to reduce non-linearities caused by differing flow rates. The geometry of 'deflectors' and 'directors' for the flowing fluid are important in obtaining linearity. Measured data shows that a volume measurement accuracy of approximately four percent can be consistently achieved. The prototype hardware system and associated software have been optimized and are available for further applications. The system has immediate application in low or zero gravity environments for measurements of urine or other liquid volumes.

Nguyen, T. X.↗
NASA NTRS1997

Summary Report of Mission Acceleration Measurements for STS-78. Launched June 20, 1996

The microgravity environment of the Space Shuttle Columbia was measured during the STS-78 mission using accelerometers from three different instruments: the Orbital Acceleration Research Experiment, the Space Acceleration Measurement System and the Microgravity Measurement Assembly. The quasi-steady environment was also calculated in near real-time during the mission by the Microgravity Analysis Workstation. The Orbital Acceleration Research Experiment provided investigators with real-time quasi-steady acceleration measurements. The Space Acceleration Measurement System recorded higher frequency data on-board for post-mission analysis. The Microgravity Measurement Assembly provided investigators with real-time quasi-steady and higher frequency acceleration measurements. The Microgravity Analysis Workstation provided calculation of the quasi-steady environment. This calculation was presented to the science teams in real-time during the mission. The microgravity environment related to several different Orbiter, crew and experiment operations is presented and interpreted in this report. A radiator deploy, the Flight Control System checkout, and a vernier reaction control system reboost demonstration had minimal effects on the acceleration environment, with excitation of frequencies in the 0.01 to 10 Hz range. Flash Evaporator System venting had no noticeable effect on the environment while supply and waste water dumps caused excursions of 2 x lO(exp -6) to 4 x 10(exp -6) g in the Y(sub b) and Z(sub b) directions. Crew sleep and ergometer exercise periods can be clearly seen in the acceleration data, as expected. Accelerations related to the two Life Science Laboratory Equipment Refrigerator/Freezers were apparent in the data as are accelerations caused by the Johnson Space Center Projects Centrifuge. As on previous microgravity missions, several signals are present in the acceleration data for which a source has not been identified. The causes of these accelerations are under investigation.

Hakimzadeh, Roshanak↗
NASA NTRS1993

Pinatubo and Pre-Pinatubo Optical-Depth Spectra: Mauna Loa Measurements, Comparisons, Inferred Particle Size Distributions, Radiative Effects, and Relationship to Lidar Data

The Ames airborne tracking sunphotometer was operated at the National Oceanic and Atmospheric Administration (NOAA) Mauna Loa Observatory (MLO) in 1991 and 1992 along with the NOAA Climate Monitoring and Diagnostics Laboratory (CMDL) automated tracking sunphotometer and lidar. June 1991 measurements provided calibrations, optical-depth spectra, and intercomparisons under relatively clean conditions; later measurements provided spectra and comparisons for the Pinatubo cloud plus calibration checks. June 1991 results are similar to previous MLO springtime measurements, with midvisible particle optical depth tau(sub p)(lambda = 0.526 microns) at the near-background level of 0.012 +/- 0.006 and no significant wavelength dependence in the measured range (lambda = 0.38 to 1.06 microns). The arrival of the Pinatubo cloud in July 1991 increased midvisible particle optical depth by more than an order of magnitude and changed the spectral shape of tau(sub p)(lambda) to an approximate power law with an exponent of about -1.4. By early September 1991, the spectrum was broadly peaked near 0.5 microns, and by July 1992, it was peaked near 0.8 microns. Our optical-depth spectra include corrections for diffuse light which increase postvolcanic midvisible tau(sub p) values by 1 to 3% (i.e., 0.0015 to 0.0023). NOAA- and Ames Research Center (ARC)-measured spectra are in good agreement. Columnar size distributions inverted from the spectra show that the initial (July 1991) post-Pinatubo cloud was relatively rich in small particles (r less than 0.25 microns), which were progressively depleted in the August-September 1991 and July 1992 periods. Conversely, both of the later periods had more of the optically efficient medium-sized particles (0.25 less than r less than 1 micron) than did the fresh July 1991 cloud. These changes are consistent with particle growth by condensation and coagulation. The effective, or area-weighted, radius increased from 0.22 +/- 0.06 micron in July 1991 to 0.56 +/- 0.12 micron in August-September 1991 and to 0.86 +/- 0.29 micron in July 1992. Corresponding column mass values were 4.8 +/- 0.7, 9.1 +/- 2.7, and 5.5 +/- 2 micro g/sq cm, and corresponding column surface areas were 4.4 +/- 0.5, 2.9 +/- 0.2, and 1.1 +/- 0.1 sq micron/sq cm,. Photometer-inferred column backscatter values agree with those measured by the CMDL lidar on nearby nights. Combining lidar-measured backscatter profiles with photometer-derived backscatter-to-area ratios gives peak particle areas that could cause rapid heterogeneous loss of ozone, given sufficiently low particle acidity and suitable solar zenith angles (achieved at mid- to high latitudes). Top-of-troposphere radiative forcings for the September 1991 and July 1992 optical depths and size distributions over MLO are about -5 and -3 W 1/sq m, respectively (hence comparable in magnitude but opposite in sign to the radiative forcing caused by the increase in manmade greenhouse gases since the industrial revolution). Heating rates in Pinatubo layer over MLO are 0.55 +/- 0.13 and 0.41 +/- 0.14 K/d for September 1991 and July 1992, respectively.

Russell, P. B.↗
NASA NTRS1997

HO(x) Measurements in SONEX with the Airborne Tropospheric Hydrogen Oxides Sensor (ATHOS)

SONEX, which was delayed by aircraft inspection problems, began the second week of October and concluded in mid-November with 16 flights. These flights covered the Pacific Ocean off the western United States, transits across the United States, the western coast of Europe, and the North and Central Atlantic Ocean. Particular attention was paid to the North Atlantic Flight Corridor. ATHOS collected high-quality HO(x) data on 15 flights. Observations taken at 5 Hz were typically averaged into 20-second measurements. Each 20-second measurement has precision 1(sigma) of less than 0.01 pptv. OH measurements were generally made from the surface to flight altitudes. HO2 measurements, which require reagent NO flow, were made from flight altitudes to near the top of the planetary boundary layer. Measured OH and HO2 during SONEX was generally lower than the measured OH and HO2 during SUCCESS (April-May, 1996, central United States). Whereas during SUCCESS midday OH was 0.1-0.5 pptv and HO2 was 3-15 pptv, during SONEX midday OH was 0.02-0.2 pptv and HO2 was 0.5-8 pptv. Part of this difference results from the midday solar zenith angles, which were larger during SONEX than during SUCCESS due to both the season and the generally higher latitudes sampled during SONEX. However, some of the difference may be due to differences in HOx sources, since less air influenced by convection was sampled during SONEX. These possibilities await post-flight calibrations of ATHOS and analysis of observations of HO(x) and simultaneously measured meteorology and trace species.

Brune, William M.↗
NASA NTRS1997

Improvement in Suppression of Pulsed Nd:YAG Laser Light With Iodine Absorption Cells for Filtered Rayleigh Scattering Measurements

Filtered Rayleigh scattering using iodine absorption cells is an effective technique for obtaining density, temperature, and velocity measurements in high speed confined flows. By tuning a single frequency laser to a strong iodine absorption line, stray scattered laser light can be greatly suppressed. For example, the minimum transmission predicted by an iodine absorption model calculation is less than 10(exp -5) at the 18788.44/cm line using a 200 mm absorption cell containing iodine vapor at 0.46 T. Measurements obtained by other researches using a CW Nd:YAG laser agree with the model calculations. However, measurements made by us and by others using Q-switched, injection-seeded, frequency doubled Nd:YAG lasers only show minimum transmission of about 3 x 10(exp -3). This greatly reduces the applicability of the filtered Rayleigh scattering technique using these lasers in experiments having large amounts of stray scattered laser light. The purposes of the present study are to characterize the spectrum of the excess light transmitted by the iodine cell and to make changes to the laser to reduce the transmitted laser light. Transmission data as a function of laser frequency for the iodine absorption line at 18788.44/cm are presented. A planar mirror Fabry-Perot interferometer was used to characterize the frequency spectrum of the light passed through the cell. Measurements taken with the laser tuned to the center of the iodine absorption line show the light transmitted through the iodine cell to have a component with a bandwidth of about 40 GHz. This is probably caused by other modes in the laser that exist in spite of the single frequency injection beam. A second broadband component was also observed, possibly caused by the laser flash lamps or by fluorescence. An intracavity etalon was installed in the laser oscillator cavity to suppress the 40 GHz component. Measurements taken with the etalon tuned to the injection frequency showed a reduction in the transmitted laser light. This improvement allows the iodine cell to block significantly more of the stray laser light in filtered Rayleigh scattering experiments. Examples are given of filtered Rayleigh scattering measurements showing the effect of the etalon on measurements taken in a Mach 3 flow in the NASA Lewis 4 inch by 10 inch supersonic wind tunnel.

Seasholtz, Richard G.↗
NASA NTRS1997

Interchange for Joint Research Entitled: Measurement of Stable Nitrogen and Sulfur Isotopes

Viking measurements of the Martian atmosphere indicate a value of N-15/N-14 which is markedly greater than that found in Earth's atmosphere. These isotopic measurements provide a powerful diagnostic tool which may be used to derive valuable information regarding the past history of Mars and they have been used to place important constraints on the evolution of Mars' atmosphere. Initial partial pressures of nitrogen, outgassing rates, and integrated deposition of nitrogen into minerals have been calculated from this important atmospheric data (McElroy et al., 1976 and 1977; Fox and Dalgarno, 1983). The greater precision obtained in laser spectrometer isotopic measurements compared to the Viking data will greatly improve these calculated values. It has also been proposed that the N-15/N-14 value in Mars' atmosphere has increased monotonically over time (McElroy et al., 1977; Fox and Dalgarno, 1983; Wallis, 1989) owing to preferential escape of atmospheric 14N to space. Nitrogen isotopic ratios might be used to identify relatively ancient crustal rocks (R. Mancinelli, personal communication), and perhaps determine relative aces of surface samples. As a first step in successfully measuring nitrogen isotopes optically we have demonstrated the measurement of 15NI14N to a precision of 0.1% (See Figures 1-4) using a tunable diode laser and an available gas (N-,O) with spectral lines in the 2188 cm-1 region. The sample and reference gas cells contained gases of identical isotopic composition so that the 15NI14N absorption ratio determined from the sample cell, when divided by the 15NI14N absorption ratio determined from the reference cell, should yield an ideal value of unity. The average measured value of this "ratio of ratios" was 0.9983 with a standard deviation (20 values) of 0.0010. This corresponds to a precision of 0.1% (1 per mil) for nitrogen isotopes, a value sufficiently precise to provide important isotopic data of interest to exobiologists. The precision presently attainable in gases is sufficient to permit the instrument to be used in the measurement of isotopic ratios of interest to exobiologists as well as geologists and planetary scientists.

Becker, Joseph F.↗
NASA NTRS1981

Skin Friction Measurements by a Dual-Laser-Beam Interferometer Technique

A portable dual-laser-beam interferometer that nonintrusively measures skin friction by monitoring the thickness change of an oil film subject to shear stress is described. The method is an advance over past versions in that the troublesome and error-introducing need to measure the distance to the oil leading edge and the starting time for the oil flow has been eliminated. The validity of the method was verified by measuring oil viscosity in the laboratory, and then using those results to measure skin friction beneath the turbulent boundary layer in a low speed wind tunnel. The dual-laser-beam skin friction measurements are compared with Preston tube measurements, with mean velocity profile data in a "law-of-the-well" coordinate system, and with computations based on turbulent boundary-layer theory. Excellent agreement is found in all cases. (This validation and the aforementioned improvements appear to make the present form of the instrument usable to measure skin friction reliably and nonintrusively in a wide range of flow situations in which previous methods are not practical.)

Monson, D. J.↗
NASA NTRS1998

Double-Edge Molecular Technique for Doppler Lidar Wind Measurement

The double-edge lidar technique for measuring the wind using molecular backscatter is described. Two high spectral resolution edge filters are located in the wings of the Rayleigh-Brillouin profile. This doubles the signal change per unit Doppler shift, the sensitivity, and gives nearly a factor of two improvement in measurement accuracy. The use of a crossover region is described where the sensitivity of a molecular and aerosol-based measurement are equal. This desensitizes the molecular measurement to the effects of aerosol scattering over a frequency range of +/- 100 m/s. We give methods for correcting for short-term frequency jitter and drift using a laser reference frequency measurement and methods for long-term frequency correction using a servo control system. The effects of Rayleigh-Brillouin scattering on the measurement are shown to be significant and are included in the analysis. Simulations for a conical scanning satellite-based lidar at 355 nm show an accuracy of 2-3 m/s for altitudes of 2 to 15 km for a 1 km vertical resolution, a satellite altitude of 400 km and a 200 km x 200 km spatial resolution. Results of ground based wind measurements are presented.

Flesia, Cristina↗
NASA NTRS1998

Apparatus and Method for Measuring Strain in Bragg Gratings

An apparatus and method for measuring strain of gratings written into an optical fiber is disclosed. Optical radiation is transmitted over a plurality of contiguous predetermined wavelength ranges into a reference optical fiber network and an optical fiber network under test to produce a plurality of reference interference fringes and measurement interference fringes. respectively. The reference and measurement fringes are detected and sampled such that each sampled value of the reference and measurement fringes is associated with a corresponding sample number. The wavelength change of the reference optical fiber, for each sample number, due to the wavelength of the optical radiation is determined. Each determined wavelength change is matched with a corresponding sampled value of each measurement fringe. Each sampled measurement fringe of each wavelength sweep is transformed into a spatial domain waveform. The spatial domain waveforms are summed to form a summation spatial domain waveform that is used to determine location of each grating with respect to a reference reflector. A portion of each spatial domain waveform that corresponds to a particular grating is determined and transformed into a corresponding frequency spectrum representation. The strain on the grating at each wavelength of optical radiation is determined by determining the difference between the current wavelength and an earlier, zero-strain wavelength measurement.

Froggatt, Mark E.↗
NASA NTRS1995

Property-Based Software Engineering Measurement

Little theory exists in the field of software system measurement. Concepts such as complexity, coupling, cohesion or even size are very often subject to interpretation and appear to have inconsistent definitions in the literature. As a consequence, there is little guidance provided to the analyst attempting to define proper measures for specific problems. Many controversies in the literature are simply misunderstandings and stem from the fact that some people talk about different measurement concepts under the same label (complexity is the most common case). There is a need to define unambiguously the most important measurement concepts used in the measurement of software products. One way of doing so is to define precisely what mathematical properties characterize these concepts regardless of the specific software artifacts to which these concepts are applied. Such a mathematical framework could generate a consensus in the software engineering community and provide a means for better communication among researchers, better guidelines for analysis, and better evaluation methods for commercial static analyzers for practitioners. In this paper, we propose a mathematical framework which is generic, because it is not specific to any particular software artifact, and rigorous, because it is based on precise mathematical concepts. This framework defines several important measurement concepts (size, length, complexity, cohesion, coupling). It is not intended to be complete or fully objective; other frameworks could have been proposed and different choices could have been made. However, we believe that the formalism and properties we introduce are convenient and intuitive. In addition, we have reviewed the literature on this subject and compared it with our work. This framework contributes constructively to a firmer theoretical ground of software measurement.

Briand, Lionel↗