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NASA NTRSDate not supplied

Assessing Potential Geophysical and Environmental Impacts from Frequent Rocket Launch Missions at Kennedy Space Center

Kennedy Space Center (KSC) in Florida has been utilized for space missions over many years with a gradually increasing number of rocket launches. There have been multiple studies where air-coupled acoustic waves and infrasound originating from launched rockets were used for operational purposes, such as locating booster trajectories as a function of changing atmospheric conditions. However, no study has utilized the acoustoelastic waves as a signal source for subsurface seismic investigations. We conducted a dispersion analysis using the seismic energy recorded from the Artemis I rocket launch at KSC in November 2022, and from these results we generated depth-sensitivity kernels at different wave frequencies. The kernels were compared with sedimentary core data to verify boundaries of carbonate layers above the Floridan Aquifer System. Accumulative information of bedrock-sediment boundary across the sedimentary platform could especially provide geo-structural evidence that manifests the configuration of coastal features. Continuous dispersion analysis of seismic recordings from consecutive rocket launches also has potential to identify non-stationary environmental effects, such as reorientation of sedimentary structures and fluctuation of the saltwater/groundwater lens from gravitational tides, which may affect erosional susceptibility of coastal features.

Han Byul Woo↗

NASA NTRSDate not supplied

Assessing Potential Geophysical and Environmental Impacts from Frequent Rocket Launch Missions at Kennedy Space Center

Rocket Launch Seismicity↗

NASA NTRS2016

An Optimum Space-to-Ground Communication Concept for CubeSat Platform Utilizing NASA Space Network and Near Earth Network

National Aeronautics and Space Administration (NASA) CubeSat missions are expected to grow rapidly in the next decade. Higher data rate CubeSats are transitioning away from Amateur Radio bands to higher frequency bands. A high-level communication architecture for future space-to-ground CubeSat communication was proposed within NASA Goddard Space Flight Center. This architecture addresses CubeSat direct-to-ground communication, CubeSat to Tracking Data Relay Satellite System (TDRSS) communication, CubeSat constellation with Mothership direct-to-ground communication, and CubeSat Constellation with Mothership communication through K-Band Single Access (KSA). A study has been performed to explore this communication architecture, through simulations, analyses, and identifying technologies, to develop the optimum communication concepts for CubeSat communications. This paper presents details of the simulation and analysis that include CubeSat swarm, daughter ship/mother ship constellation, Near Earth Network (NEN) S and X-band direct to ground link, TDRSS Multiple Access (MA) array vs Single Access mode, notional transceiver/antenna configurations, ground asset configurations and Code Division Multiple Access (CDMA) signal trades for daughter ship/mother ship CubeSat constellation inter-satellite cross link. Results of space science X-band 10 MHz maximum achievable data rate study are summarized. CubeSat NEN Ka-Band end-to-end communication analysis is provided. Current CubeSat communication technologies capabilities are presented. Compatibility test of the CubeSat transceiver through NEN and SN is discussed. Based on the analyses, signal trade studies and technology assessments, the desired CubeSat transceiver features and operation concepts for future CubeSat end-to-end communications are derived.

CubeSat RF Communication↗

NASA NTRS1995

A Data Parallel Multizone Navier-Stokes Code

We have developed a data parallel multizone compressible Navier-Stokes code on the Connection Machine CM-5. The code is set up for implicit time-stepping on single or multiple structured grids. For multiple grids and geometrically complex problems, we follow the "chimera" approach, where flow data on one zone is interpolated onto another in the region of overlap. We will describe our design philosophy and give some timing results for the current code. The design choices can be summarized as: 1. finite differences on structured grids; 2. implicit time-stepping with either distributed solves or data motion and local solves; 3. sequential stepping through multiple zones with interzone data transfer via a distributed data structure. We have implemented these ideas on the CM-5 using CMF (Connection Machine Fortran), a data parallel language which combines elements of Fortran 90 and certain extensions, and which bears a strong similarity to High Performance Fortran (HPF). One interesting feature is the issue of turbulence modeling, where the architecture of a parallel machine makes the use of an algebraic turbulence model awkward, whereas models based on transport equations are more natural. We will present some performance figures for the code on the CM-5, and consider the issues involved in transitioning the code to HPF for portability to other parallel platforms.

Jespersen, Dennis C.↗

NASA NTRS2016

An Optimum Space-to-Ground Communication Concept for CubeSat Platform Utilizing NASA Space Network and Near Earth Network

National Aeronautics and Space Administration (NASA) CubeSat missions are expected to grow rapidly in the next decade. Higher data rate CubeSats are transitioning away from Amateur Radio bands to higher frequency bands. A high-level communication architecture for future space-to-ground CubeSat communication was proposed within NASA Goddard Space Flight Center. This architecture addresses CubeSat direct-to-ground communication, CubeSat to Tracking Data Relay Satellite System (TDRSS) communication, CubeSat constellation with Mothership direct-to-ground communication, and CubeSat Constellation with Mothership communication through K-Band Single Access (KSA).A Study has been performed to explore this communication architecture, through simulations, analyses, and identifying technologies, to develop the optimum communication concepts for CubeSat communications. This paper will present details of the simulation and analysis that include CubeSat swarm, daughter shipmother ship constellation, Near Earth Network (NEN) S and X-band direct to ground link, TDRS Multiple Access (MA) array vs Single Access mode, notional transceiverantenna configurations, ground asset configurations and Code Division Multiple Access (CDMA) signal trades for daughter mother CubeSat constellation inter-satellite crosslink. Results of Space Science X-band 10 MHz maximum achievable data rate study will be summarized. Assessment of Technology Readiness Level (TRL) of current CubeSat communication technologies capabilities will be presented. Compatibility test of the CubeSat transceiver through NEN and Space Network (SN) will be discussed. Based on the analyses, signal trade studies and technology assessments, the functional design and performance requirements as well as operation concepts for future CubeSat end-to-end communications will be derived.

CubeSat RF Communication↗

NASA NTRS2015

Multilateral Research Opportunities in Ground Analogs

The global economy forces many nations to consider their national investments and make difficult decisions regarding their investment in future exploration. International collaboration provides an opportunity to leverage other nations' investments to meet common goals. The Humans In Space Community shares a common goal to enable safe, reliable, and productive human space exploration within and beyond Low Earth Orbit. Meeting this goal requires efficient use of limited resources and International capabilities. The International Space Station (ISS) is our primary platform to conduct microgravity research targeted at reducing human health and performance risks for exploration missions. Access to ISS resources, however, is becoming more and more constrained and will only be available through 2020 or 2024. NASA's Human Research Program (HRP) is actively pursuing methods to effectively utilize the ISS and appropriate ground analogs to understand and mitigate human health and performance risks prior to embarking on human exploration of deep space destinations. HRP developed a plan to use ground analogs of increasing fidelity to address questions related to exploration missions and is inviting International participation in these planned campaigns. Using established working groups and multilateral panels, the HRP is working with multiple Space Agencies to invite International participation in a series of 30- day missions that HRP will conduct in the US owned and operated Human Exploration Research Analog (HERA) during 2016. In addition, the HRP is negotiating access to Antarctic stations (both US and non-US), the German :envihab and Russian NEK facilities. These facilities provide unique capabilities to address critical research questions requiring longer duration simulation or isolation. We are negotiating release of international research opportunities to ensure a multilateral approach to future analog research campaigns, hoping to begin multilateral campaigns in the latter facilities by 2017. Collaborative use of analog facilities and shared investment in the development of spaceflight countermeasures through multilateral campaigns or missions that leverage the global scientific community will focus high quality research and provide sufficient power to accelerate the development of countermeasures and drive sound recommendations for exploration missions. This panel will provide an overview of efforts to encourage and facilitate multilateral collaboration in analog missions or campaigns and describe the facilities currently under consideration to reach the common goal of enabling safe, reliable, and productive human space exploration.

Corbin, Barbara J.↗

NASA NTRS2017

Software Defined Radios - Architectures, Systems and Functions

Software Defined Radio is an industry term describing a method of utilizing a minimum amount of Radio Frequency (RF)/analog electronics before digitization takes place. Upon digitization all other functions are performed in software/firmware. There are as many different types of SDRs as there are data systems. Software Defined Radio (SDR) technology has been proven in the commercial sector since the early 90's. Today's rapid advancement in mobile telephone reliability and power management capabilities exemplifies the effectiveness of the SDR technology for the modern communications market. In contrast the foundations of transponder technology presently qualified for satellite applications were developed during the early space program of the 1960's. SDR technology offers potential to revolutionize satellite transponder technology by increasing science data through-put capability by at least an order of magnitude. While the SDR is adaptive in nature and is "One-size-fits-all" by design, conventional transponders are built to a specific platform and must be redesigned for every new bus. The SDR uses a minimum amount of analog/Radio Frequency components to up/down-convert the RF signal to/from a digital format. Once analog data is digitized, all processing is performed using hardware logic. Typical SDR processes include; filtering, modulation, up/down converting and demodulation. This presentation will show how the emerging SDR market has leveraged the existing commercial sector to provide a path to a radiation tolerant SDR transponder. These innovations will reduce the cost of transceivers, a decrease in power requirements and a commensurate reduction in volume. A second pay-off is the increased flexibility of the SDR by allowing the same hardware to implement multiple transponder types by altering hardware logic - no change of analog hardware is required - all of which can be ultimately accomplished in orbit. This in turn would provide high capability and low cost transponder to programs of all sizes.

Sims, William H.↗

NASA NTRS2017

Software Defined Radios - Architectures, Systems and Functions

Sims, Herb↗

NASA NTRS2017

A New Non-Resonant Laser-Induced Fluorescence Instrument for the Airborne in Situ Measurement of Formaldehyde

A new in situ instrument for gas-phase formaldehyde (HCHO), COmpact Formaldehyde FluorescencE Experiment (COFFEE), is presented. COFFEE utilizes nonresonant laser-induced fluorescence (NR-LIF) to measure HCHO, with 300 mW of 40 kHz 355 nm laser output exciting multiple HCHO absorption features. The resulting HCHO fluorescence is collected at 5 ns resolution, and the fluorescence time profile is fit to yield the ambient HCHO mixing ratio. Typical 1 sigma precision at approximately 0 pptv HCHO is 150 pptv for 1 s data. The compact instrument was designed to operate with minimal in-flight operator interaction and infrequent maintenance (1-2 times per year). COFFEE fits in the wing pod of the Alpha Jet stationed at the NASA Ames Research Center and has successfully collected HCHO data on 27 flights through 2017 March. The frequent flights, combined with a potentially long-term data set, makes the Alpha Jet a promising platform for validation of satellite-based column HCHO.

Nonresonant laser-induced fluorescenc↗

NASA NTRS2009

Multiplexed Colorimetric Solid-Phase Extraction

Multiplexed colorimetric solid-phase extraction (MC-SPE) is an extension of colorimetric solid-phase extraction (C-SPE) an analytical platform that combines colorimetric reagents, solid phase extraction, and diffuse reflectance spectroscopy to quantify trace analytes in water. In CSPE, analytes are extracted and complexed on the surface of an extraction membrane impregnated with a colorimetric reagent. The analytes are then quantified directly on the membrane surface using a handheld diffuse reflectance spectrophotometer. Importantly, the use of solid-phase extraction membranes as the matrix for impregnation of the colorimetric reagents creates a concentration factor that enables the detection of low concentrations of analytes in small sample volumes. In extending C-SPE to a multiplexed format, a filter holder that incorporates discrete analysis channels and a jig that facilitates the concurrent operation of multiple sample syringes have been designed, enabling the simultaneous determination of multiple analytes. Separate, single analyte membranes, placed in a readout cartridge create unique, analyte-specific addresses at the exit of each channel. Following sample exposure, the diffuse reflectance spectrum of each address is collected serially and the Kubelka-Munk function is used to quantify each water quality parameter via calibration curves. In a demonstration, MC-SPE was used to measure the pH of a sample and quantitate Ag(I) and Ni(II).

Gazda, Daniel B.↗

NASA NTRS2020

Electric Six Degree of Freedom Installation Timelapse (Six Degree of Freedom Dynamic Test System)

The Six-degree-of-freedom Dynamic Test System (SDTS) is a short-range real-time motion based testing platform. Its primary use at NASA/JSC has been for development and qualification testing of docking systems, robotic assisted berthing mechanisms, and dynamic attachment systems. The SDTS is a closed-loop force feedback system that can simulate on-orbit contact dynamics between two vehicles utilizing the actual mechanical interfaces for testing. The facility is controlled by interconnected computers running real-time simulation software that takes measured contact forces, integrates the equations of motion in real time, and provide those states back into the motion table. This infrastructure can also be used for non-mating applications such as relative position sensor testing/evaluations. The SDTS facility provides a superstructure for mounting test articles, multiple test sensors, an intercom network for voice communications, and a synchronized timing system for data acquisition that includes HD video. This time-lapse video shows the buildup and testing of a modern electric actuation system created by Mikrolar, Inc. at the Johnson Space Center. This motion base will replace the current hydraulic actuator system, which is been in use since the 1970s, for all-future NASA testing. Once the system goes through customization to provide JSC’s unique closed-loop environment, the facility will help certify docking system and attach mechanisms on the ground before we send the first woman and the next man to the lunar surface

hexapod↗

NASA NTRS2018

Ka-band High-Rate Downlink System for the NISAR Mission

This paper provides a description and analyses of the high-rate Ka-band telecom system for the upcoming NISAR (NASA-ISRO Synthetic Aperture Radar) mission. NISAR is a collaborative Earth-Science mission between National Aeronautics and Space Administration (NASA) and Indian Space Research Organization (ISRO), which features an L-band SAR instrument and an S-band SAR instrument. The simultaneous dual-frequency radar system at peak rates will produce data at gigabit-per-second speeds, which drives the data-volume requirements. The key driving requirement for the payload communication subsystem is to provide a minimum of 26 Terabits per day of radar science data to the ground. The high-rate transmitter on the flight system is a software-defined radio developed at the Jet Propulsion Laboratory (JPL), based on the Universal Space Transponder platform, providing an offset quadrature phase shift key modulated waveform with Low-Density Parity-Check encoding of the data transfer frames. Two transmitters used in a dual-polarization configuration with each transmitter providing two giga-symbols per second (Gsps) of coded data provides an aggregate rate of four Gsps. In this system, only one watt of signal power is necessary on each polarization to overcome propagation losses and achieve a successful RF link. Several Near Earth Network (NEN) ground station sites (Alaska in the United States, Svalbard in Norway, and Punta Arenas in Chile) are baselined for the space-to-Earth communications link. Each ground station will also feature multiple upgrades to support NISAR’s transmission starting with new Ka-band antennas, wideband downconverters and high-rate receivers. In addition, a baseband data processor called Data Acquisition Processor and Handling Network Environment (DAPHNE), newly developed by the NEN, provides data storage and connectivity to backhaul networks. With NISAR’s large quantities of data (over 3.5 Petabytes over the mission), the processing of science data will be primarily performed on a cloud system to reduce the overall cost to the mission. The system described herein will be the first operational use of Gsps-class downlink rates on an Earth-Science mission.

Dissanayake, Asoka↗

NASA NTRS2020

Integrated Silicon Platform for Co-planar Design of Vertically Stacked 2.06 THz Mixer Module

The process for fabricating and utilizing the threedimensional Si stack receiver front-end is described in this paper. The capability to have exact dimensionality becomes essential as frequency scales due to the complexity arising in assembly and finer tolerances. Total process yields can be improved through Si fabrication by verifying achievement of specified tolerances lithographically and compatibility to rapid process changes and design fine-tuning. The integrated Si platform with the mounted device is shown in Figure 1. Signal I/O and alignment modalities enable lownoise measurements. Silicon micromachining provides the necessary accuracy for integration at the several THz regime. Particularly, processing and etch recipes have demonstrated smooth surfaces of < 1 μm surface roughness. In consideration is pre-compensating for minute offsets, matching mechanical strain on all interfaces, and including passive alignment verification in the design. As compared to metal blocks, computer numerical controlled (CNC) milling can produce slight burrs in the interfaces resulting in misalignment and resultant strain between two pieces of components. Furthermore, Si integration can make possible arrays of pixel transceivers through compact subsystems for the purpose of measuring multiple lines of spectral content simultaneously in space.

Mehdi, Imran↗

NASA NTRS2009

Ares V: Shifting the Payload Design Paradigm

NASA's Ares V heavy-lift cargo launch vehicle is being designed send more crew and cargo to more places on the lunar surface than the 1960s-era Apollo program and provide ongoing support to a permanent lunar outpost. In addition to that role, however, its unmatched mass and volume capability represent a global asset for exploration, science, and commerce. The Ares V also is an enabler of a large class of space missions not thought possible by scientists and engineers since the Saturn V program ended over 30 years ago. Compared to current systems, it will offer approximately 5 times the mass and volume to most orbits and locations. This should allow prospective mission planners to build robust payloads with margins that are 3 to 5 times the industry norm. The space inside the planned payload shroud has enough usable volume to launch the volumetric equivalent of approximately 10 Apollo Lunar Excursion Modules or approximately 5 equivalent Hubble Space Telescopes. This mass and volume capability to Low Earth Orbit enables a host of new scientific and observation platforms, such as telescopes, satellites, planetary and solar missions, as well as being able to provide the lift for future large in-space infrastructure missions, such as space based power and mining, Earth asteroid defense, propellant depots, etc. The Ares V team is engaging the potential payload community now, 2-3 years before System Requirements Review, in order to better understand the potential limitations and or additional requirements that could be added to the Ares V from the mission planning community. If a viable mission is determined and added to the Ares V as a design case, tradeoffs will be conducted to determine if other mission design requirements can be included in the system. Multiple shroud options for the Ares V have been analyzed to identify their impact on performance. Ares V is in a conceptual design stage prior to a formal design phase. The initial concept for the cargo launch vehicle (CaLV) that would later be dubbed "Ares V" was produced by the Exploration Systems Architecture Study in 2005. Since then, it has evolved through hundreds of concepts. The current point-of-departure (POD) concept was approved during the Lunar Capabilities Concept Review/Ares V Mission Concept Review in June 2008. This reference concept serves as a starting point for a renewed set of design trades and detailed analysis into its interaction with the other components of the Constellation architecture and existing launch infrastructure. This paper will discuss the Ares V design evolution, the most recent point-of-departure concept, and its capabilities to support future science missions.

Summrall, Phil↗

NASA NTRS2022

Virtual Assistant for First Responders Using Natural Language Understanding and Optical Character Recognition

Commercial deep learning capabilities are available for many applications such as computer vision processing and intelligent chat bots. The Google Cloud Platform product Google Dialogflow provides lifelike conversational artificial intelligence (AI) using machine learning (ML) to generate natural conversations between computers and humans. This ML utilizes natural language understanding (NLU) to recognize a user’s intent and extracts key information into a form of entities. We have developed a user-friendly application through understanding the hazardous material database, first aid safety guidelines and observing the process of first responders who access this information in the field. We created the Trusted and Explainable Artificial Intelligence for Saving Lives (TruePAL) virtual assistant using Dialogflow1 and TensorFlow2 paired with EasyOCR.3 The chatbot supports first responders by providing voice interaction which helps limit additional steps such as browsing through multiple categories when searching for information. Using feedback from our field interviews, the voice interface has been developed to enable the first responder to focus on the immediate emergency. With less distractions, the first responder is able to engage the incident more effectively. The partial hands-free TruePAL chatbot assistant improves the accessibility to the correct guidance by an average of 1.9 seconds compared to the widely used application, NIH WISER, which requires full attention to operate. We combined this intelligent chatbot with a separate visual processing capability to produce hazardous signage analysis and generate the proper guidance for first responders. With the evolving functionality of AI tools, the use of virtual assistants in first responder technology will be an advancement, benefiting the safety of both first responders and civilians.

Chow, Edward↗

NASA NTRS2000

Use of a GCM to Explore Sampling Issues in Connection with Satellite Remote Sensing of the Earth Radiation Budget

Collocated in time and space, top-of-the-atmosphere measurements of the Earth radiation budget (ERB) and cloudiness from passive scanning radiometers, and lidar- and radar-in-space measurements of multilayered cloud systems, are the required combination to improve our understanding of the role of clouds and radiation in climate. Experiments to fly multiple satellites "in formation" to measure simultaneously the radiative and optical properties of overlapping cloud systems are being designed. Because satellites carrying ERB experiments and satellites carrying lidars- or radars-in space have different orbital characteristics, the number of simultaneous measurements of radiation and clouds is reduced relative to the number of measurements made by each satellite independently. Monthly averaged coincident observations of radiation and cloudiness are biased when compared against more frequently sampled observations due, in particular, to the undersampling of their diurnal cycle, Using the Colorado State University General Circulation Model (CSU GCM), the goal of this study is to measure the impact of using simultaneous observations from the Earth Observing System (EOS) platform and companion satellites flying lidars or radars on monthly averaged diagnostics of longwave radiation, cloudiness, and its cloud optical properties. To do so, the hourly varying geographical distributions of coincident locations between the afternoon EOS (EOS-PM) orbit and the orbit of the ICESAT satellite set to fly at the altitude of 600 km, and between the EOS PM orbit and the orbits of the PICASSO satellite proposed to fly at the altitudes of 485 km (PICA485) or 705 km (PICA705), are simulated in the CSU GCM for a 60-month time period starting at the idealistic July 1, 2001, launch date. Monthly averaged diagnostics of the top-of-the-atmosphere, atmospheric, and surface longwave radiation budgets and clouds accumulated over grid boxes corresponding to satellite overpasses are compared against monthly averaged diagnostics obtained from hourly samplings over the entire globe. Results show that differences between irregularly (satellite) and regularly (true) sampled diagnostics of the longwave net radiative budgets are the greatest at the surface and the smallest in the atmosphere and at the top-of-the-atmosphere, under both cloud-free and cloudy conditions. In contrast, differences between the satellite and the true diagnostics of the longwave cloud radiative forcings are the largest in the atmosphere and at the top-of-the-atmosphere, and the smallest at the surface. A poorer diurnal sampling of the surface temperature in the satellite simulations relative to the true simulation contributes a major part to sampling biases in the longwave net radiative budgets, while a poorer diurnal sampling of cloudiness and its optical properties directly affects diagnostics of the longwave cloud radiative forcings. A factor of 8 difference in the number of satellite overpasses between PICA705 and PICA485 and ICESAT leads to a systematic factor of 3 difference in the spatial standard deviations of all radiative and cloudiness diagnostics.

Fowler, Laura D.↗

NASA NTRS2011

MW-Class Electric Propulsion System Designs

Electric propulsion systems are well developed and have been in commercial use for several years. Ion and Hall thrusters have propelled robotic spacecraft to encounters with asteroids, the Moon, and minor planetary bodies within the solar system, while higher power systems are being considered to support even more demanding future space science and exploration missions. Such missions may include orbit raising and station-keeping for large platforms, robotic and human missions to near earth asteroids, cargo transport for sustained lunar or Mars exploration, and at very high-power, fast piloted missions to Mars and the outer planets. The Advanced In-Space Propulsion Project, High Efficiency Space Power Systems Project, and High Power Electric Propulsion Demonstration Project were established within the NASA Exploration Technology Development and Demonstration Program to develop and advance the fundamental technologies required for these long-range, future exploration missions. Under the auspices of the High Efficiency Space Power Systems Project, and supported by the Advanced In-Space Propulsion and High Power Electric Propulsion Projects, the COMPASS design team at the NASA Glenn Research Center performed multiple parametric design analyses to determine solar and nuclear electric power technology requirements for representative 300-kW class and pulsed and steady-state MW-class electric propulsion systems. This paper describes the results of the MW-class electric power and propulsion design analysis. Starting with the representative MW-class vehicle configurations, and using design reference missions bounded by launch dates, several power system technology improvements were introduced into the parametric COMPASS simulations to determine the potential system level benefits such technologies might provide. Those technologies providing quantitative system level benefits were then assessed for technical feasibility, cost, and time to develop. Key assumptions and primary results of the COMPASS MW-class electric propulsion power system study are reported, and discussion is provided on how the analysis might be used to guide future technology investments as NASA moves to more capable high power in-space propulsion systems.

LaPointe, Michael R.↗

NASA NTRS1989

Report on the multicolor pyrometry session at the Second NASA Non-Contact Temperature-Measurement Workshop

The session met jointly with the other special sessions. Due to time constraints, the concerns of multicolor pyrometry were not addressed in depth. Multicolor pyrometry attempts to determine an object's temperature and emittance as a function of wavelength from simultaneous measurement of the spectral radiance of the object at multiple wavelengths. The main issues are those of the most appropriate model for the wavelength dependence of the emittance, the number of undetermined parameters, and the error in the measured temperature. It has long been known that it is inappropriate to attempt to model the emittance with a functional form that contains as many unknowns as wavelengths. Such attempts will lead to gross errors in the measured temperature. However, more recent work by Hunter and Khan has indicated that emittance can be modeled by a function with many fewer degrees of freedom than sampled wavelengths (e.g., it may be appropriate to use a second order polynomial to fit data from a forty-color pyrometer). In a platform lecture, Khan described algorithms for determination of the parameters by minimization of the errors between the model and the data in a least-squares sense. The first was a linear method and the second was a non-linear method where the emittance could assume any functional form. Both methods were shown to be very sensitive to random noise and non-linearity in the measurement system.

Spjut, R. Erik↗