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NASA NTRS2005

Isogrid Membranes for Precise, Singly Curved Reflectors

A new type of composite material has been proposed for membranes that would constitute the reflective surfaces of planned lightweight, single-curvature (e.g., parabolic cylindrical) reflectors for some radar and radio-communication systems. The proposed composite materials would consist of polyimide membranes containing embedded grids of highstrength (e.g., carbon) fibers. The purpose of the fiber reinforcements, as explained in more detail below, is to prevent wrinkling or rippling of the membrane.

Fang, Houfei↗

NASA NTRS2005

Centralized Planning for Multiple Exploratory Robots

A computer program automatically generates plans for a group of robotic vehicles (rovers) engaged in geological exploration of terrain. The program rapidly generates multiple command sequences that can be executed simultaneously by the rovers. Starting from a set of high-level goals, the program creates a sequence of commands for each rover while respecting hardware constraints and limitations on resources of each rover and of hardware (e.g., a radio communication terminal) shared by all the rovers. First, a separate model of each rover is loaded into a centralized planning subprogram. The centralized planning software uses the models of the rovers plus an iterative repair algorithm to resolve conflicts posed by demands for resources and by constraints associated with the all the rovers and the shared hardware. During repair, heuristics are used to make planning decisions that will result in solutions that will be better and will be found faster than would otherwise be possible. In particular, techniques from prior solutions of the multiple-traveling- salesmen problem are used as heuristics to generate plans in which the paths taken by the rovers to assigned scientific targets are shorter than they would otherwise be.

Estlin, Tara↗

NASA NTRS2004

Electrically Small Microstrip Quarter-Wave Monopole Antennas

Microstrip-patch-style antennas that generate monopole radiation patterns similar to those of quarter-wave whip antennas can be designed to have dimensions smaller than those needed heretofore for this purpose, by taking advantage of a feed configuration different from the conventional one. The large sizes necessitated by the conventional feed configuration have, until now, made such antennas impractical for frequencies below about 800 MHz: for example, at 200 MHz, the conventional feed configuration necessitates a patch diameter of about 8 ft (.2.4 m) . too large, for example, for mounting on the roof of an automobile or on a small or medium-size aircraft. By making it possible to reduce diameters to between a tenth and a third of that necessitated by the conventional feed configuration, the modified configuration makes it possible to install such antennas in places where they could not previously be installed and thereby helps to realize the potential advantages (concealment and/or reduction of aerodynamic drag) of microstrip versus whip antennas. In both the conventional approach and the innovative approach, a microstrip-patch (or microstrip-patch-style) antenna for generating a monopole radiation pattern includes an electrically conductive patch or plate separated from an electrically conductive ground plane by a layer of electrically insulating material. In the conventional approach, the electrically insulating layer is typically a printed-circuit board about 1/16 in. (.1.6 mm) thick. Ordinarily, a coaxial cable from a transmitter, receiver, or transceiver is attached at the center on the ground-plane side, the shield of the cable being electrically connected to the ground plane. In the conventional approach, the coaxial cable is mated with a connector mounted on the ground plane. The center pin of this connector connects to the center of the coaxial cable and passes through a hole in the ground plane and a small hole in the insulating layer and then connects with the patch above one-third of the radial distance from the center. The modified feed configuration of the innovative approach is an inductive-short-circuit configuration that provides impedance matching and that has been used for many years on other antennas but not on microstrip-style monopole antennas. In this configuration, the pin is connected to both the conductive patch and the ground plane. As before, the shield of the coaxial cable is connected to the ground plane, but now the central conductor is connected to a point on the pin between the ground plane and the conductive plate (see figure). The location of the connection point on the pin is chosen so that together, the inductive short circuit and the conductive plate or patch act as components of a lumped-element resonant circuit that radiates efficiently at the resonance frequency and, at the resonance frequency, has an impedance that matches that of the coaxial cable. It should be noted that the innovative design entails two significant disadvantages. One disadvantage is that the frequency bandwidth for efficient operation is only about 1/20 to 1/15 that of a whip antenna designed for the same nominal frequency. The other disadvantage is that the estimated gain is between 3-1/2 and 4-1/2 dB below that of the whip antenna. However, if an affected radio-communication system used only a few adjacent frequency channels and the design of the components of the system other than the antenna provided adequate power or gain margin, then these disadvantages could be overcome.

Young, W. Robert↗

NASA NTRS2003

Quad-Tree Visual-Calculus Analysis of Satellite Coverage

An improved method of analysis of coverage of areas of the Earth by a constellation of radio-communication or scientific-observation satellites has been developed. This method is intended to supplant an older method in which the global-coverage-analysis problem is solved from a ground-to-satellite perspective. The present method provides for rapid and efficient analysis. This method is derived from a satellite-to-ground perspective and involves a unique combination of two techniques for multiresolution representation of map features on the surface of a sphere.

Lo, Martin W.↗

NASA NTRS2011

Software Displays Data on Active Regions of the Sun

The Solar Active Region Display System is a computer program that generates, in near real time, a graphical display of parameters indicative of the spatial and temporal variations of activity on the Sun. These parameters include histories and distributions of solar flares, active region growth, coronal mass ejections, size, and magnetic configuration. By presenting solar-activity data in graphical form, this program accelerates, facilitates, and partly automates what had previously been a time-consuming mental process of interpretation of solar-activity data presented in tabular and textual formats. Intended for original use in predicting space weather in order to minimize the exposure of astronauts to ionizing radiation, the program might also be useful on Earth for predicting solar-wind-induced ionospheric effects, electric currents, and potentials that could affect radio-communication systems, navigation systems, pipelines, and long electric-power lines. Raw data for the display are obtained automatically from the Space Environment Center (SEC) of the National Oceanic and Atmospheric Administration (NOAA). Other data must be obtained from the NOAA SEC by verbal communication and entered manually. The Solar Active Region Display System automatically accounts for the latitude dependence of the rate of rotation of the Sun, by use of a mathematical model that is corrected with NOAA SEC active-region position data once every 24 hours. The display includes the date, time, and an image of the Sun in H light overlaid with latitude and longitude coordinate lines, dots that mark locations of active regions identified by NOAA, identifying numbers assigned by NOAA to such regions, and solar-region visual summary (SRVS) indicators associated with some of the active regions. Each SRVS indicator is a small pie chart containing five equal sectors, each of which is color-coded to provide a semiquantitative indication of the degree of hazard posed by one aspect of the activity at the indicated location. The five aspects in question are the history of solar flares, the history of coronal mass ejections, the growth or decay of activity, the overall size, and the magnetic configuration. Mouse-clicking on an active-region-marking dot, SRVS indicator, or NOAA region number causes the program to generate a solar-region summary table (SRT) for the active region in question. The SRT contains additional quantitative and qualitative data, beyond those contained in the SRVS: These data include the solar coordinates of the region, the area of the region and its change in area during the past 24 hours, the change in the number of sunspots in the region during the past 24 hours, the magnetic configuration, and the types, dates, and times of the most recent flare and coronal mass ejection.

Golightly, Mike↗

NASA NTRS2012

Tooling Techniques Enhance Medical Imaging

They can release as much energy as tens of billions of hydrogen bombs exploding at the same time. They send protons and electrons rocketing at near the speed of light. They heat gas in the Sun s atmosphere to tens of millions of degrees Celsius. They send a blast of gas and particles toward Earth, posing a danger to spacecraft and astronauts outside the planet s magnetosphere, in rare cases even knocking out radio communications and power grids on the ground. They are so-called solar eruptive events, made up of solar flares and the often associated coronal mass ejections. Because of the scientific mystery of how these solar eruptions are produced on the Sun with such scale and force, and also the major role they play in space weather that can impact life on Earth, NASA researchers have innovated new methods of gathering information about these violent events. One NASA mission, the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) has significantly advanced understanding of solar flares since its launch in 2002. RHESSI scientists use the spacecraft s imaging spectrometer to piece together pictures of solar flares from the high-energy X-ray and gamma-ray radiation they emit. While there is still much to be learned, data gathered by RHESSI has revealed how magnetic fields in the vast expanse of the solar atmosphere may be the force that drives the immense explosions. The instrument has imaged around 50,000 flares to date, providing information that may explain not only the workings of solar flares but also of much more massive energy releases from distant objects like black holes and quasars. We have been able to make images from X-rays with much finer resolution and greater sensitivity than have ever been made before, says Brian Dennis, RHESSI Mission Scientist and astrophysicist in the Solar Physics Laboratory at Goddard Space Flight Center. The key to RHESSI s unprecedented capabilities lie in a set of essential components a NASA partner created for the mission. The manufacturing techniques developed to create the components have yielded innovations advancing medical imaging, transportation security, and even energy efficiency.

Source record↗

NASA NTRS2013

Crew Roles and Interactions in Scientific Space Exploration

Future piloted space exploration missions will focus more on science than engineering, a change which will challenge existing concepts for flight crew tasking and demand that participants with contrasting skills, values, and backgrounds learn to cooperate as equals. In terrestrial space flight analogs such as Desert Research And Technology Studies, engineers, pilots, and scientists can practice working together, taking advantage of the full breadth of all team members training to produce harmonious, effective missions that maximize the time and attention the crew can devote to science. This paper presents, in a format usable as a reference by participants in the field, a successfully tested crew interaction model for such missions. The model builds upon the basic framework of a scientific field expedition by adding proven concepts from aviation and human spaceflight, including expeditionary behavior and cockpit resource management, cooperative crew tasking and adaptive leadership and followership, formal techniques for radio communication, and increased attention to operational considerations. The crews of future spaceflight analogs can use this model to demonstrate effective techniques, learn from each other, develop positive working relationships, and make their expeditions more successful, even if they have limited time to train together beforehand. This model can also inform the preparation and execution of actual future spaceflights.

Love, Stanley G.↗

NASA NTRS2014

Deployable Fresnel Rings

Deployable Fresnel rings (DFRs) significantly enhance the realizable gain of an antenna. This innovation is intended to be used in combination with another antenna element, as the DFR itself acts as a focusing or microwave lens element for a primary antenna. This method is completely passive, and is also completely wireless in that it requires neither a cable, nor a connector from the antenna port of the primary antenna to the DFR. The technology improves upon the previous NASA technology called a Tri-Sector Deployable Array Antenna in at least three critical aspects. In contrast to the previous technology, this innovation requires no connector, cable, or other physical interface to the primary communication radio or sensor device. The achievable improvement in terms of antenna gain is significantly higher than has been achieved with the previous technology. Also, where previous embodiments of the Tri-Sector antenna have been constructed with combinations of conventional (e.g., printed circuit board) and conductive fabric materials, this innovation is realized using only conductive and non-conductive fabric (i.e., "e-textile") materials, with the possible exception of a spring-like deployment ring. Conceptually, a DFR operates by canceling the out-of-phase radiation at a plane by insertion of a conducting ring or rings of a specific size and distance from the source antenna, defined by Fresnel zones. Design of DFRs follow similar procedures to those outlined for conventional Fresnel zone rings. Gain enhancement using a single ring is verified experimentally and through computational simulation. The experimental test setup involves a microstrip patch antenna that is directly behind a single-ring DFR and is radiating towards a second microstrip patch antenna. The first patch antenna and DFR are shown. At 2.42 GHz, the DFR improves the transmit antenna gain by 8.6 dB, as shown in Figure 2, relative to the wireless link without the DFR. A figure illustrates the relative strength of power coupling between the first and second microstrip antennas with and without the DFR. Typically, a DFR is designed for use at a particular frequency; however, testing of a DFR indicated a relatively wide operational bandwidth of approximately 8.2%. Wider bandwidth operation and multi-band operation are anticipated by extending the known art of conventional Fresnel rings to the DFRs. Increasing the number of rings used to construct a DFR antenna increases the gain, with the upper bound limited often by the largest practical dimensions that can be tolerated for a given application. The maximum theoretical improvement in gain for a single ring is 9.5 dB. Experimental results are within 0.9 dB of this theoretical value. Adding rings increases gain, and theoretically, improvements of 10 to 13 dB above that of the primary antenna gain can be achieved with two- and three-ring versions.

Kennedy, Timothy F.↗

NASA NTRS2015

Small Unmanned Aircraft Systems Integration into the National Airspace System Visual-Line-of-Sight Human-in-the-Loop Experiment

As part of the Unmanned Aircraft Systems (UAS) in the National Airspace System (NAS) project, research on integrating small UAS (sUAS) into the NAS was underway by a human-systems integration (HSI) team at the NASA Langley Research Center. Minimal to no research has been conducted on the safe, effective, and efficient manner in which to integrate these aircraft into the NAS. sUAS are defined as aircraft weighing 55 pounds or less. The objective of this human system integration team was to build a UAS Ground Control Station (GCS) and to develop a research test-bed and database that provides data, proof of concept, and human factors guidelines for GCS operations in the NAS. The objectives of this experiment were to evaluate the effectiveness and safety of flying sUAS in Class D and Class G airspace utilizing manual control inputs and voice radio communications between the pilot, mission control, and air traffic control. The design of the experiment included three sets of GCS display configurations, in addition to a hand-held control unit. The three different display configurations were VLOS, VLOS + Primary Flight Display (PFD), and VLOS + PFD + Moving Map (Map). Test subject pilots had better situation awareness of their vehicle position, altitude, airspeed, location over the ground, and mission track using the Map display configuration. This configuration allowed the pilots to complete the mission objectives with less workload, at the expense of having better situation awareness of other aircraft. The subjects were better able to see other aircraft when using the VLOS display configuration. However, their mission performance, as well as their ability to aviate and navigate, was reduced compared to runs that included the PFD and Map displays.

Trujillo, Anna C.↗

NASA NTRS2015

Securing the Global Airspace System Via Identity-Based Security

Current telecommunications systems have very good security architectures that include authentication and authorization as well as accounting. These three features enable an edge system to obtain access into a radio communication network, request specific Quality-of-Service (QoS) requirements and ensure proper billing for service. Furthermore, the links are secure. Widely used telecommunication technologies are Long Term Evolution (LTE) and Worldwide Interoperability for Microwave Access (WiMAX) This paper provides a system-level view of network-centric operations for the global airspace system and the problems and issues with deploying new technologies into the system. The paper then focuses on applying the basic security architectures of commercial telecommunication systems and deployment of federated Authentication, Authorization and Accounting systems to provide a scalable, evolvable reliable and maintainable solution to enable a globally deployable identity-based secure airspace system.

Communications↗

NASA NTRS2017

The Scintillation Prediction Observations Research Task (SPORT) Mission

SPORT is a science mission using a 6U CubeSat and integrated ground network that will (1) advance understanding and (2) enable improved predictions of scintillation occurrence that impact GPS signals and radio communications. This is the science of Space Weather. SPORT is an international partnership with NASA, U.S. institutions, the Brazilian National Institute for Space Research (INPE), and the Technical Aeronautics Institute under the Brazilian Air Force Command Department (DCTA/ITA).

SPORT↗

NASA NTRS2017

UAV Inspection of Electrical Transmission Infrastructure with Path Conformance Autonomy and Lidar-Based Geofences NASA Report on UTM Reference Mission Flights at Southern Company Flights November 2016

Flights at low altitudes in close proximity to electrical transmission infrastructure present serious navigational challenges: GPS and radio communication quality is variable and yet tight position control is needed to measure defects while avoiding collisions with ground structures. To advance unmanned aerial vehicle (UAV) navigation technology while accomplishing a task with economic and societal benefit, a high voltage electrical infrastructure inspection reference mission was designed. An integrated air-ground platform was developed for this mission and tested in two days of experimental flights to determine whether navigational augmentation was needed to successfully conduct a controlled inspection experiment. The airborne component of the platform was a multirotor UAV built from commercial off-the-shelf hardware and software, and the ground component was a commercial laptop running open source software. A compact ultraviolet sensor mounted on the UAV can locate 'hot spots' (potential failure points in the electric grid), so long as the UAV flight path adequately samples the airspace near the power grid structures. To improve navigation, the platform was supplemented with two navigation technologies: lidar-to-polyhedron preflight processing for obstacle demarcation and inspection distance planning, and trajectory management software to enforce inspection standoff distance. Both navigation technologies were essential to obtaining useful results from the hot spot sensor in this obstacle-rich, low-altitude airspace. Because the electrical grid extends into crowded airspaces, the UAV position was tracked with NASA unmanned aerial system traffic management (UTM) technology. The following results were obtained: (1) Inspection of high-voltage electrical transmission infrastructure to locate 'hot spots' of ultraviolet emission requires navigation methods that are not broadly available and are not needed at higher altitude flights above ground structures. (2) The sensing capability of a novel airborne UV detector was verified with a standard ground-based instrument. Flights with this sensor showed that UAV measurement operations and recording methods are viable. With improved sensor range, UAVs equipped with compact UV sensors could serve as the detection elements in a self-diagnosing power grid. (3) Simplification of rich lidar maps to polyhedral obstacle maps reduces data volume by orders of magnitude, so that computation with the resultant maps in real time is possible. This enables real-time obstacle avoidance autonomy. Stable navigation may be feasible in the GPS-deprived environment near transmission lines by a UAV that senses ground structures and compares them to these simplified maps. (4) A new, formally verified path conformance software system that runs onboard a UAV was demonstrated in flight for the first time. It successfully maneuvered the aircraft after a sudden lateral perturbation that models a gust of wind, and processed lidar-derived polyhedral obstacle maps in real time. (5) Tracking of the UAV in the national airspace using the NASA UTM technology was a key safety component of this reference mission, since the flights were conducted beneath the landing approach to a heavily used runway. Comparison to autopilot tracking showed that UTM tracking accurately records the UAV position throughout the flight path.

Moore, Andrew J.↗

NASA NTRS2016

Demonstration of Mars Crosslink Occultation Measurements for Future Small Spacecraft Constellations

Future planetary atmospheric profiling via radio occultations (RO) benefits significantly from increased received signal-to-noise ratio as well as geometrical coverage of links between two or more spacecraft in orbit around a target planet. These can be small spacecraft, possibly dedicated to quality radio-metrics with precision clock reference. Motivated by long-term research investigating the optimum SNR for the science performance, the optimum reference clock stability, the number and combination of wavelengths driving the number of transmitters and antennas, the optimum number and orbital spacecraft configuration, and design modifications to existing radio communication systems that would allow these new science objectives on future missions, three crosslink occultation experiments have been acquired between the Mars Odyssey and Mars Reconnaissance Orbiter spacecraft to probe the Martian atmosphere. While crosslink occultations between Earth orbiting satellites have long been used to profile the Earth’s atmosphere, this represents the first demonstration of crosslink occultation measurements at another planet. These measurements leverage the proximity link telecommunication payloads on each orbiter, which were designed to provide relay communication and navigation services to Mars landers and rovers. Analysis of the observed Doppler shift on each crosslink measurement reveals a clear signature of the Martian atmosphere, primarily the ionosphere. Inversion of the observed Doppler data yields vertical profiles of the Martian refractivity and electron density. The electron density profiles show the presence of two layers with peak densities and peak heights that are consistent with empirical models.

Asmar, Sami↗

NASA NTRS2008

Radiometric tracking for deep space navigation

Metric information derived from radio communication links between Earth and spacecraft are used for navigation of interplanetary probes. This paper summarizes radiometric techniques and their error budgets.

Shin, Dong K.↗

NASA NTRSDate not supplied

Biosentinel: Update on Extended Mission Operations

BioSentinel has achieved unprecedented performance of an SLS secondary payload due to preparation, planning, and a robust design. Following the conclusion of the primary science mission in April 2023, the Linear Energy Transfer (LET) Spectrometer has continued to collect solar and galactic radiation data from its unique location in heliocentric orbit. The free space dataset offered by the BioSentinel LET is a valuable source of data for both model validation and future mission planning. As the spacecraft travels farther from Earth it is poised to provide longitudinally distributed measurements of solar particle events during solar maximum. Flight heritage has now been gained on many of the novel spacecraft components. The spacecraft bus continues to operate within the design envelope. The 3D-printed cold gas propulsion system provides momentum unloading from the reaction wheels. The power system has maintained power positive levels during flight. The IRIS radio communicates on a weekly basis with the Deep Space Network. The extended mission operations are allowing the team to characterize the performance of the spacecraft components over longer durations of operations. NASA Ames led development of the BioSentinel spacecraft and mission operations. The novel subsystems and COTS components that comprise the BioSentinel bus can serve as a template for future deep space missions. With over a year of continuous operations, the data will inform the next generation of interplanetary smallsat missions.

BioSentinel↗

NASA NTRSDate not supplied

Scalar Atomic Defect-Based Solid-State Self-calibrating Magnetometer (3SM) for Space Plasma Analysis

The Earth’s magnetosphere is a system of multiple, co-located particle populations interacting via plasma waves. Things to understand are driving processes, radiation belt and ring current issues, auroral physics, internal plasma processes, and magnetosphere-ionosphere mapping issues. These plasma-physics processes enable the Earth’s magnetosphere to evolve in response to temporal changes in the solar wind and they underlie the phenomena of space weather, which impacts spacecraft systems, astronauts, radio communications, and ground based electric-power grids. The objective of 3SM is to measure magnetic field strength and to calibrate the Vector Magnetometer (VM) device to maintain absolute accuracy during a mission. The 3SM features make the instrument preferably suited not only for the traditional role of scalar magnetometers as absolute references for the calibration of the on-board vector instruments, but also for extended operational capacities, such as higher frequency scalar measurements (of potential interest for magnetosphere studies for the low frequency part of the spectrum) or autonomous scalar / vector operations. Diamond has been the solid-state platform of choice for quantum device technologies for some time, however, it suffers from difficulties such as scalability, integration, and cost. While the diamond platform is very useful for quantum technologies, further development is needed to make it viable. The material platform of choice for NASA Glenn’s Quantum Sensing And Spin Physics (Q-SASP) is silicon carbide (SiC). This is due to the much higher industry development of the SiC material platform for high-power and high-temperature electronics. It leverages both the decades-long SiC development expertise and infrastructure at NASA Glenn and its growing capabilities in quantum metrology. To make SiC devices usable for quantum technologies such as quantum sources, a much deeper understanding of defects is needed. Q-SASP is developing quantum metrology capabilities to evaluate the energy structure, defect formation energy, band structure augmentation, generation/recombination rates, and limits of dipole-dipole coupling in non-metal implanted SiC devices. This can be achieved by analysis of zero-field splitting, low-field resonance, and singlet-triplet mixing through various forms of Electrically Detectable Magnetic Resonance (EDMR) and Near-Zero Field Magnetic Resonance (NZFMR) spectroscopy. This work will discuss recent system developments, device developments, computational modeling, and spectroscopy results and analysis of defects created by non-metal implantations in SiC devices. The defect formation energies of V Si ,V C , V C V Si , N C V Si , N Si , N C in 4H-SiC are previously reported values in other research [2]-[3]. The defect formation energies of PSi and PC were calculated in GPAW [fig 1A]. The basic underlying mechanism of the zero-field phenomenon is the mixing of singlet and triplet states [4]-[5]. In most spin-dependent transport, two electron spins are involved, and thus one must consider each of their interactions with the field. We investigated the electronic and magnetic properties of 4H-SiC and 6H-SiC. The defect formation energy helps us determine what types of defects we are observing in the SiC EDMR experiment. They have very low formation energy (it is negative). The phosphorus substitution in 4H-SiC is a very stable defect. The band diagrams provide us with vital information about how the electronic properties of SiC (such as band gap) change as we add non-metal defects. The zero-field splitting parameters allow us to study the inflection point in the NZFMR [fig 1B]. We clearly observed zero-field splitting. We also noted that the zero-field splitting remained constant with changing bias. We aspect it zero-field splitting to remain constant while the hyperfine and exchange interaction perturbations shift under the influence of an external magnetic field. This is the essence of quantum magnetometry and self-calibration.

space plasma↗

NASA NTRS1973

Coordination procedure for radio relay and communication satellite services

A global rain rate statistic model is used to link microwave propagation statistics to measurable rain statistics in order to develop international telecommunication site criteria for radio relay and communication satellite services that minimize interference between receivers and transmitters. This rain coordination procedure utilizes a rain storm cell size, a statistical description of the rainfall rate within the cell valid for most of the earth's surface, approximations between Raleigh scatter and constancy of precipitation with altitude, and an analytic relation between radar reflectivity and rain rate.

Eckerman, J.↗

NASA NTRS2020

Integrated Radio and Optical Communications (iROC) Primary, Secondary, and Tertiary Optics Alignment Procedure

This Technical Memorandum (TM) describes a procedure and associated equipment for performing an initial, relative alignment of a multiple-element optical system. The specific system of interest motivating this procedure arises from the Integrated Radio and Optical Communications (iROC) project, but is applicable to the more general configuration of a two-element folded, reflective telescope. Each step of the procedure includes a description of the particular degree of freedom (DOF) being addressed, and the associated equipment required, including both commercially available items and those fabricated specifically for this purpose.

Paul S Greenberg↗