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Conduct of the International Multigrid Conference

The 1983 International Multigrid Conference was held at Colorado's Copper Mountain Ski Resort, April 5-8. It was organized jointly by the Institute for Computational Studies at Colorado State University, U.S.A., and the Gasellschaft fur Mathematik und Datenverarbeitung Bonn, F.R. Germany, and was sponsored by the Air Force Office of Sponsored Research and National Aeronautics and Space Administration Headquarters. The conference was attended by 80 scientists, divided by institution almost equally into private industry, research laboratories, and academia. Fifteen attendees came from countries other than the U.S.A. In addition to the fruitful discussions, the most significant factor of the conference was of course the lectures. The lecturers include most of the leaders in the field of multigrid research. The program offered a nice integrated blend of theory, numerical studies, basic research, and applications. Some of the new areas of research that have surfaced since the Koln-Porz conference include: the algebraic multigrid approach; multigrid treatment of Euler equations for inviscid fluid flow problems; 3-D problems; and the application of MG methods on vector and parallel computers.

Mccormick, S.↗

Fusion for Space Propulsion

There is little doubt that humans will attempt to explore and develop the solar system in this century. A large amount of energy will be required for accomplishing this. The need for fusion propulsion is discussed. For a propulsion system, there are three important thermodynamical attributes: (1) The absolute amount of energy available, (2) the propellant exhaust velocity, and (3) the jet power per unit mass of the propulsion system (specific power). For human exploration and development of the solar system, propellant exhaust velocity in excess of 100 km/s and specific power in excess of 10 kW/kg are required. Chemical combustion can produce exhaust velocity up to about 5 km/s. Nuclear fission processes typically result in producing energy in the form of heat that needs to be manipulated at temperatures limited by materials to about 2,800 K. Using the energy to heat a hydrogen propellant increases the exhaust velocity by only a factor of about two. Alternatively the energy can be converted into electricity which is then used to accelerate particles to high exhaust velocity. The necessary power conversion and conditioning equipment, however, increases the mass of the propulsion system for the same jet power by more than two orders of magnitude over chemical system, thus greatly limits the thrust-to-weight ratio attainable. The principal advantage of the fission process is that its development is relatively mature and is available right now. If fusion can be developed, fusion appears to have the best of all worlds in terms of propulsion - it can provide the absolute amount, the propellant exhaust velocity, and the high specific jet power. An intermediate step towards pure fusion propulsion is a bimodal system in which a fission reactor is used to provide some of the energy to drive a fusion propulsion unit. The technical issues related to fusion for space propulsion are discussed. The technical priorities for developing and applying fusion for propulsion are somewhat different from those for terrestrial electrical power generation. Thus fusion schemes that are initially attractive for electrical power generation might not necessarily be attractive also for propulsion and vice versa, though the underlying fusion science and engineering enjoy much overlap. Parallel efforts to develop these qualitatively differently fusion schemes for the two applications could benefit greatly from each other due to the synergy in the underlying physics and engineering. Pulsed approaches to fusion have not been explored to the same degree as steady-state or long-pulse approaches to fusion in the fusion power research program. The concerns early on were several. One was that the pulsed power components might not have the service lifetimes meeting the requirements of a practical power generating plant. Another was that, for many pulsed fusion schemes, it was not clear whether the destruction of hardware per pulse could be minimized or eliminated or recycled to such an extent as to make economical electrical power generation feasible, Significant development of the underlying pulsed power component technologies have occurred in the last two decades because of defense and other energy requirements. The state of development of the pulsed power technologies are sufficiently advanced now to make it compelling to visit or re-visit pulsed fusion approaches for application to propulsion where the cost of energy is not so demanding a factor as in the case of terrestrial power application. For propulsion application, the overall mass of the fusion system is the critical factor. Producing fusion reactions require extreme states of matter. Conceptually, these extreme states of matter are more readily realizable in the pulsed states, at least within appropriate bounds, than in the steady states. Significant saving in system mass may result in such systems. Magnetic fields are effective in confining plasma energy, whereas inertial compression is an effective way of heating and containing the plasma. Intensive research in developing magnetic energy containment and inertial plasma compression are being pursued in distinctively different fusion experiments in the terrestrial fusion power program. Fusion schemes that attempt to combine the favorable attributes of these two aspects into one single integrated fusion scheme appear to have benefits that are worth exploring for propulsion application.

Thio, Y. C. Francis↗

The evolution of concepts of vestibular peripheral information processing: toward the dynamic, adaptive, parallel processing macular model

In a letter to Robert Hooke, written on 5 February, 1675, Isaac Newton wrote "If I have seen further than certain other men it is by standing upon the shoulders of giants." In his context, Newton was referring to the work of Galileo and Kepler, who preceded him. However, every field has its own giants, those men and women who went before us and, often with few tools at their disposal, uncovered the facts that enabled later researchers to advance knowledge in a particular area. This review traces the history of the evolution of views from early giants in the field of vestibular research to modern concepts of vestibular organ organization and function. Emphasis will be placed on the mammalian maculae as peripheral processors of linear accelerations acting on the head. This review shows that early, correct findings were sometimes unfortunately disregarded, impeding later investigations into the structure and function of the vestibular organs. The central themes are that the macular organs are highly complex, dynamic, adaptive, distributed parallel processors of information, and that historical references can help us to understand our own place in advancing knowledge about their complicated structure and functions.

Review, Tutorial↗

NASA Project Constellation Systems Engineering Approach

NASA's Office of Exploration Systems (OExS) is organized to empower the Vision for Space Exploration with transportation systems that result in achievable, affordable, and sustainable human and robotic journeys to the Moon, Mars, and beyond. In the process of delivering these capabilities, the systems engineering function is key to implementing policies, managing mission requirements, and ensuring technical integration and verification of hardware and support systems in a timely, cost-effective manner. The OExS Development Programs Division includes three main areas: (1) human and robotic technology, (2) Project Prometheus for nuclear propulsion development, and (3) Constellation Systems for space transportation systems development, including a Crew Exploration Vehicle (CEV). Constellation Systems include Earth-to-orbit, in-space, and surface transportation systems; maintenance and science instrumentation; and robotic investigators and assistants. In parallel with development of the CEV, robotic explorers will serve as trailblazers to reduce the risk and costs of future human operations on the Moon, as well as missions to other destinations, including Mars. Additional information is included in the original extended abstract.

Dumbacher, Daniel L.↗

Guidelines for Selection, Screening and Qualification of Low-Voltage Commercial Multilayer Ceramic Capacitors for Space Programs

This document has been developed in the course of NASA Electronic Parts and Packaging (NEPP) program and is not an official endorsement of the insertion of commercial capacitors in space programs or an established set of requirements for their testing. The purpose of this document is to suggest possible ways for selection, screening, and qualification of commercial capacitors for NASA projects and open discussions in the parts engineering community related to the use of COTS ceramic capacitors. This guideline is applicable to commercial surface mount chip, simple parallel plate design, multi-layer ceramic capacitors (MLCCs) rated to voltages of 100V and less. Parts with different design, e.g. low inductance ceramic capacitors (LICA), land grid array (LGA) etc., might need additional testing and tailoring of the requirements described in this document. Although the focus of this document is on commercial MLCCs, many procedures discussed below would be beneficial for military-grade capacitors

Teverovsky, Alexander A.↗

Strategies for the GPU Implementation of the OVERFLOW CFD Code

Wondering how to port a large, computational fluid dynamics (CFD) solver, written in Fortran, to run effectively on GPUs? Join this talk to learn about the strategies NASA’s OVERFLOW CFD code has used to effectively utilize GPUs to greatly improve the time to solution compared to CPUs. OVERFLOW is an overset, structured grid, computational fluid dynamics (CFD) flow solver developed by NASA and widely used by government, US industry, and academia. It is known for its effective use of CPU hardware, but this talk will discuss recent efforts to modify the code to run efficiently on GPUs. We will describe our use of OpenACC, CUDA Fortran, and CUDA C++, discussing why and how we use each to map our problem onto NVIDIA GPUs. We will also describe structural changes we made in the code to expose enough parallelism to effectively use the GPU hardware. Finally, we will present the performance benefits from running OVERFLOW on GPUs compared to the well optimized CPU version of the code.

GPU Programming↗

Aviation System Capacity Program Terminal Area Productivity Project: Ground and Airborne Technologies

Ground and airborne technologies were developed in the Terminal Area Productivity (TAP) project for increasing throughput at major airports by safely maintaining good-weather operating capacity during bad weather. Methods were demonstrated for accurately predicting vortices to prevent wake-turbulence encounters and to reduce in-trail separation requirements for aircraft approaching the same runway for landing. Technology was demonstrated that safely enabled independent simultaneous approaches in poor weather conditions to parallel runways spaced less than 3,400 ft apart. Guidance, control, and situation-awareness systems were developed to reduce congestion in airport surface operations resulting from the increased throughput, particularly during night and instrument meteorological conditions (IMC). These systems decreased runway occupancy time by safely and smoothly decelerating the aircraft, increasing taxi speed, and safely steering the aircraft off the runway. Simulations were performed in which optimal trajectories were determined by air traffic control (ATC) and communicated to flight crews by means of Center TRACON Automation System/Flight Management System (CTASFMS) automation to reduce flight delays, increase throughput, and ensure flight safety.

Giulianetti, Demo J.↗

The Shuttle inertial system

The Space Shuttle inertial system is built around a sensor assembly called the inertial measurement unit (IMU). The system includes a redundant set of three structurally integrated IMU's that operate in conjunction with parallel strung data system computers to provide precise attitude and velocity information to user system functions. The inertial system is actually a separate subsystem function integrated into the overall avionics system. Software resident in the system computers is the final link in the inertial system. The inertial software is comprised of two major sets, including a subsystem operating program (SOP) called the IMU SOP and redundancy management. Attention is given to system applications, systems performance, attitude sensitivities, the IMU platform, IMU thermal management, aspects of IMU calibration, and Shuttle program experience.

Swingle, W. L.↗

New Experiment to Measure the Electron Electric Dipole Moment

An electron can possess an electric dipole moment (edm) only if time reversal symmetry (T) is violated. No edm of any particle has yet been discovered. CP-violation, equivalent to T-violation by the CPT theorem, does occur in Kaon decays and can be accounted for by the standard model. However, this mechanism leads to an electron edm d(sub e) of the order of 10(exp -38) e cm, whereas the current experimental bound on d(sub e) is about 10(exp -27) e cm. However, well-motivated extensions of the standard model such as supersymmetric theories do predict that de could be as large as the current bound. In addition, CP violation in the early universe is required to explain the preponderance of matter over anti-matter, but the exact mechanism of this CP violation is unclear. For these reasons, we are undertaking a new experimental program to determine de to an improved accuracy of 10(exp -29) e cm. Our experiment will use laser-cooled, trapped Cesium atoms to measure the atomic edm d(sub Cs) that occurs if d(sub e) is not zero. In order to do this, we will measure the energy splitting between the atoms spin states in parallel electric and magnetic fields. The signature of an edm would be a linear dependence of the splitting on the electric field E due to the interaction - d(sub Cs) dot E. Our measurement will be much more sensitive than previous measurements because atoms can be stored in the trap for tens of seconds, allowing for much narrower Zeeman resonance linewidths. Also, our method eliminates the most important systematic errors, proportional to atomic velocity, which have limited previous experiments. In this presentation, we will describe the design of our new apparatus, which is presently under construction. An important feature of our experimental apparatus is that magnetic field noise will be suppressed to a very low value of the order of 1 fT/(Hz)1/2. This requires careful attention to the Johnson noise currents in the chamber, which have not been important in previous experiments. In addition we will present estimates of the limits of the various errors that we expect for our experiment.

Kittle, Melanie↗

Testing of 30-GHz low noise receivers

NASA-sponsored studies of the growth in communications traffic have indicated that the frequency spectrum allocated to fix-service satellites at the C and Ku bands will reach saturation by the early 1990's. The next higher frequency bands allocated for communications satellties are 27.5 to 30 GHz for the uplink and 17.7 to 20.2 GHz for the downlink. Current plans for developing satellite systems that use these bands include a NASA demonstration satellite (ACTS). One of the components identified as critical to the success of that mission is a 27.5 to 30 GHz satellite receiver. In response to that identification, NASA has sponsored the development of such a receiver to the proof-of-concept (POC) level. Design and fabrication of such POC model receivers was carried out under parallel contracts awarded to LNR Communications, Inc. of Hauppauge, New York and to ITT Defense Communications Division of Nutley, New Jersey. The most significant of the performance goals were a 5 db maximum noise figure, a 2.5 GHz passband, and e0 dB Rf to If gain. Following delivery of hardware from each of the contractors, an in-house test program was undertaken at NASA's Lewis Research Center in order to verify the contractor-reported performance and to provide a comparison of the two receivers under identical test conditions. The present paper reports the results of those tests.

Conroy, M. J.↗

Testing of 30-GHz low noise receivers

NASA-sponsored studies of the growth in communications traffic have indicated that the frequency spectrum allocated to fix-service satellites at the C and Ku bands will reach saturation by the early 1990's. The next higher frequency bands allocated for communications satellites are 27.5 to 30 GHz for the uplink and 17.7 to 20.2 GHz for the downlink. Current plans for developing satellite systems that use these bands include a NASA demonstration satellite (ACTS). One of the components identified as critical to the success of that mission is a 27.5 to 30 GHz satellite receiver. In response to that identification, NASA has sponsored the development of such a receiver to the proof-of-concept (POC) level. Design and fabrication of such POC model receivers was carried out under parallel contracts awarded to LNR Communications, Inc. of Hauppauge, New York and to ITT Defense Communications Division of Nutley, New Jersey. The most significant of the performance goals were a 5 dB maximum noise figure, a 2.5 GHz passband, and 20 dB RF to IF gain. Following delivery of hardware from each of the contractors, an in-house test program was undertaken at NASA's Lewis Research Center in order to verify the contractor-reported performance and to provide a comparison of the two receivers under identical test conditions. The present paper reports the results of those tests.

Conroy, M. J.↗

Effects of ethylene on the kinetics of curvature and auxin redistribution in gravistimulated roots of Zea mays

We tested the involvement of ethylene in maize (Zea mays L.) root gravitropism by measuring the kinetics of curvature and lateral auxin movement in roots treated with ethylene, inhibitors of ethylene synthesis, or inhibitors of ethylene action. In the presence of ethylene the latent period of gravitropic curvature appeared to be increased somewhat. However, ethylene-treated roots continued to curve after control roots had reached their final angle of curvature. Consequently, maximum curvature in the presence of ethylene was much greater in ethylene-treated roots than in controls. Inhibitors of ethylene biosynthesis or action had effects on the kinetics of curvature opposite to that of ethylene, i.e. the latent period appeared to be shortened somewhat while total curvature was reduced relative to that of controls. Label from applied 3H-indole-3-acetic acid was preferentially transported toward the lower side of stimulated roots. In parallel with effects on curvature, ethylene treatment delayed the development of gravity-induced asymmetric auxin movement across the root but extended its duration once initiated. The auxin transport inhibitor, 1-N-naphthylphthalamic acid reduced both gravitropic curvature and the effect of ethylene on curvature. Since neither ethylene nor inhibitors of ethylene biosynthesis or action prevented curvature, we conclude that ethylene does not mediate the primary differential growth response causing curvature. Because ethylene affects curvature and auxin transport in parallel, we suggest that ethylene modifies curvature by affecting gravity-induced lateral transport of auxin, perhaps by interfering with adaptation of the auxin transport system to the gravistimulus.

Non-NASA Center↗

Modeling of Transient Flow Mixing of Streams Injected into a Mixing Chamber

Ignition is recognized as one the critical drivers in the reliability of multiple-start rocket engines. Residual combustion products from previous engine operation can condense on valves and related structures thereby creating difficulties for subsequent starting procedures. Alternative ignition methods that require fewer valves can mitigate the valve reliability problem, but require improved understanding of the spatial and temporal propellant distribution in the pre-ignition chamber. Current design tools based mainly on one-dimensional analysis and empirical models cannot predict local details of the injection and ignition processes. The goal of this work is to evaluate the capability of the modern computational fluid dynamics (CFD) tools in predicting the transient flow mixing in pre-ignition environment by comparing the results with the experimental data. This study is a part of a program to improve analytical methods and methodologies to analyze reliability and durability of combustion devices. In the present paper we describe a series of detailed computational simulations of the unsteady mixing events as the cold propellants are first introduced into the chamber as a first step in providing this necessary environmental description. The present computational modeling represents a complement to parallel experimental simulations' and includes comparisons with experimental results from that effort. A large number of rocket engine ignition studies has been previously reported. Here we limit our discussion to the work discussed in Refs. 2, 3 and 4 which is both similar to and different from the present approach. The similarities arise from the fact that both efforts involve detailed experimental/computational simulations of the ignition problem. The differences arise from the underlying philosophy of the two endeavors. The approach in Refs. 2 to 4 is a classical ignition study in which the focus is on the response of a propellant mixture to an ignition source, with emphasis on the level of energy needed for ignition and the ensuing flame propagation issues. Our focus in the present paper is on identifying the unsteady mixing processes that provide the propellant mixture in which the ignition source is to be placed. In particular, we wish to characterize the spatial and temporal mixture distribution with a view toward identifying preferred spatial and temporal locations for the ignition source. As such, the present work is limited to cold flow (pre-ignition) conditions

Voytovych, Dmytro M.↗

A Technology Development Roadmap for a Near-Term Probe-Class X-ray Astrophysics Mission

This document presents a roadmap, including proposed budget and schedule, for maturing the instrumentation needed for an X-ray astrophysics Probe-class mission. The Physics of the Cosmos (PCOS) Program Office was directed to create this roadmap following the December 2012 NASA Astrophysics Implementation Plan (AIP). Definition of this mission is called for in the AIP, with the possibility of selection in 2015 for a start in 2017. The overall mission capabilities and instrument performance requirements were defined in the 2010 Astronomy and Astrophysics Decadal Survey report, New Worlds, New Horizons in Astronomy and Astrophysics (NWNH), in connection with the highly ranked International X-ray Observatory (IXO). In NWNH, recommendations were provided regarding the size of, and instrumentation needed by, the next large X-ray observatory. Specifically, the key instrumental capability would be an X-ray calorimeter spectrometer at the focus of a large mirror with angular resolution of 10 arc seconds (arcsec) or better. If possible, a grating spectrometer should also be incorporated into the instrument complement. In response to these recommendations, four instrumentation technologies are included in this roadmap. Three of these are critical for an X-ray mission designed to address NWNH questions: segmented X-ray mirrors, transition edge sensor calorimeters, and gratings. Two approaches are described for gratings, which represent the least mature technology and thus most in need of a parallel path for risk reduction. Also, while current CCD detectors would likely meet the mission needs for grating spectrum readout, specific improvements are included as an additional approach for achieving the grating system effective area requirement. The technical steps needed for these technologies to attain technology readiness levels (TRL) of 5 and 6 are described, as well as desirable modest risk reduction steps beyond TRL-6. All of the technology development efforts are currently funded through the NASA Physics of the Cosmos (PCOS) Strategic Astrophysics Technology (SAT) program; some through the end of FY13, others though FY14. These technology needs are those identified as critical for a near-term mission and briefly described in the 2012 NASA X-ray Mission Concepts Study. This Technology Development Roadmap (TDR) provides a more complete description of each, updates the status, and describes the steps to mature them. For each technology, a roadmap is presented for attaining TRL-6 by 2020 at the latest, and 2018 for most. The funding required for each technology to attain TRL-5 and TRL-6 is presented and justified through a description of the steps needing completion. The total funding required for these technologies to reach TRL-6 is relatively modest, and is consistent with the planned PCOS SAT funding over the next several years. The approximate annual cost through 2018 is $8M. The total cost for all technologies to be matured is $62M (including funding already awarded for FY13 and FY14). This can be contrasted to the $180M recommended by NWNH for technology development for IXO, primarily for the maturation of the mirror technology. The technology described in Section 3 of this document is exclusively that needed for a near-term Probe-class mission, to start in 2017, or for a mission that can be recommended by the next Decadal survey committee for an immediate start. It is important to note that there are other critical X-ray instrumentation technologies under development that are less mature than the ones discussed here, but are essential for a major X-ray mission that might start in the late 2020s. These technologies, described briefly in Section 4, are more appropriately funded through the Astronomy and Physics Research and Analysis (APRA) program.

Development↗

Energetic particle flux experiment (IMP F and G)

The data reduction procedures and programs for analysis of the IMP F and G energetic particle flux experiments are summarized. The IMP-F experiment contained two thin-window Geiger-Mueller detectors and an ionization chamber. There were two IMP-G experiments: one with six Geiger-Mueller detectors and an ionization chamber, and the other with two funnel mouthed channeltrons in a parallel plate electrostatic analyzer. These experiments measured particles in the energy range above 20 keV (IMP-F) and above approximately 5 keV (IMP-G). A bibliography is presented of papers containing the scientific results. These data were predominantly used for the study of low energy solar particles from flares.

Anderson, K. A.↗

Development of a stereo analysis algorithm for generating topographic maps using interactive techniques of the MPP

A local area matching algorithm was developed on the Massively Parallel Processor (MPP). It is an iterative technique that first matches coarse or low resolution areas and at each iteration performs matches of higher resolution. Results so far show that when good matches are possible in the two images, the MPP algorithm matches corresponding areas as well as a human observer. To aid in developing this algorithm, a control or shell program was developed for the MPP that allows interactive experimentation with various parameters and procedures to be used in the matching process. (This would not be possible without the high speed of the MPP). With the system, optimal techniques can be developed for different types of matching problems.

Strong, James P.↗

Characterization of Aircraft Produced Soot and Contrails Near the Tropopause

Participation in the SUCCESS project primarily involved development and deployment of specific instruments for characterizing jet aircraft exhaust emissions as particulates and their subsequent evolution as contrail particles, either liquid or solid, as cirrus. Observations can be conveniently considered in two categories - close or distant from the aircraft. Thus close to the aircraft the exhaust is mixing through the engine turbulence with a much drier and colder environment and developing water/ ice supersaturation along the trail depending on circumstances (near field), whereas distant from the aircraft (far field) the exhaust has cooled essentially to ambient temperature, the turbulence has decayed and any particle growth or evaporation is controlled by the prevailing ambient conditions. Intermediate between these two regions the main aircraft vortices form (one on each side of the aircraft) which tend to inhibit mixing under some conditions, a region extending from a few aircraft lengths to sometimes a hundred times this distance. Our approach to the problem lay in experience gained in characterizing the smoke from hydrocarbon combustion in terms of its cloud forming properties and its potential influence on the radiation properties of the smoke and subsequent cloud from the viewpoint of reduction (absorbtion and scattering ) of solar radiation flux leading to significant global cooling (Hudson et al 1991; Hallett and Hudson 1991). Engine exhaust contains a much smaller proportion of the fuel carbon than is sometimes present in ordinary combustion (less than 0.01% compared with 10%) and influences condensation in quite different ways, to be characterized by the Cloud Condensation Nucleus, CCN - supersaturation spectrum. The transition to ice is to be related to the dilution of solution droplets to freeze by homogeneous nucleation at temperatures somewhat below -40C (Pueschel et al 1998). The subsequent growth of ice particles depends critically on temperature, supersaturation and to some extent pressure, as is demonstrated in an NSF funded project being carried out in parallel with the work reported here. As will be discussed below, nucleation processes themselves and also exhaust impurities also influence the growth of ice particles and may control some aspects of growth of ice in contrails. Instrumentation was designed to give insight into these questions and to be flown on the NASA DC- 8 as a platform. In addition a modest program was undertaken to investigate the properties of laboratory produced smoke produced under controlled conditions from the viewpoint of forming both CCN and CN. The composition of the smoke could inferred from a thermal characterization technique; larger particles were captured by formvar replicator for detailed analysis; ice particles were captured and evaporated in flight on a new instrument, the cloudscope, to give their mass, density and impurity content.

Hallett, John↗

Software for Verifying Image-Correlation Tie Points

A computer program enables assessment of the quality of tie points in the image-correlation processes of the software described in the immediately preceding article. Tie points are computed in mappings between corresponding pixels in the left and right images of a stereoscopic pair. The mappings are sometimes not perfect because image data can be noisy and parallax can cause some points to appear in one image but not the other. The present computer program relies on the availability of a left- right correlation map in addition to the usual right left correlation map. The additional map must be generated, which doubles the processing time. Such increased time can now be afforded in the data-processing pipeline, since the time for map generation is now reduced from about 60 to 3 minutes by the parallelization discussed in the previous article. Parallel cluster processing time, therefore, enabled this better science result. The first mapping is typically from a point (denoted by coordinates x,y) in the left image to a point (x',y') in the right image. The second mapping is from (x',y') in the right image to some point (x",y") in the left image. If (x,y) and(x",y") are identical, then the mapping is considered perfect. The perfect-match criterion can be relaxed by introducing an error window that admits of round-off error and a small amount of noise. The mapping procedure can be repeated until all points in each image not connected to points in the other image are eliminated, so that what remains are verified correlation data.

Klimeck, Gerhard↗