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NASA NTRS1993

Rover imaging system for the Mars rover/sample return mission

In the past year, the conceptual design of a panoramic imager for the Mars Environmental Survey (MESUR) Pathfinder was finished. A prototype camera was built and its performace in the laboratory was tested. The performance of this camera was excellent. Based on this work, we have recently proposed a small, lightweight, rugged, and highly capable Mars Surface Imager (MSI) instrument for the MESUR Pathfinder mission. A key aspect of our approach to optimization of the MSI design is that we treat image gathering, coding, and restoration as a whole, rather than as separate and independent tasks. Our approach leads to higher image quality, especially in the representation of fine detail with good contrast and clarity, without increasing either the complexity of the camera or the amount of data transmission. We have made significant progress over the past year in both the overall MSI system design and in the detailed design of the MSI optics. We have taken a simple panoramic camera and have upgraded it substantially to become a prototype of the MSI flight instrument. The most recent version of the camera utilizes miniature wide-angle optics that image directly onto a 3-color, 2096-element CCD line array. There are several data-taking modes, providing resolution as high as 0.3 mrad/pixel. Analysis tasks that were performed or that are underway with the test data from the prototype camera include the following: construction of 3-D models of imaged scenes from stereo data, first for controlled scenes and later for field scenes; and checks on geometric fidelity, including alignment errors, mast vibration, and oscillation in the drive system. We have outlined a number of tasks planned for Fiscal Year '93 in order to prepare us for submission of a flight instrument proposal for MESUR Pathfinder.

Source record↗
NASA NTRS1993

Real-time dynamics simulation of the Cassini spacecraft using DARTS. Part 1: Functional capabilities and the spatial algebra algorithm

This paper describes the Dynamics Algorithms for Real-Time Simulation (DARTS) real-time hardware-in-the-loop dynamics simulator for the National Aeronautics and Space Administration's Cassini spacecraft. The spacecraft model consists of a central flexible body with a number of articulated rigid-body appendages. The demanding performance requirements from the spacecraft control system require the use of a high fidelity simulator for control system design and testing. The DARTS algorithm provides a new algorithmic and hardware approach to the solution of this hardware-in-the-loop simulation problem. It is based upon the efficient spatial algebra dynamics for flexible multibody systems. A parallel and vectorized version of this algorithm is implemented on a low-cost, multiprocessor computer to meet the simulation timing requirements.

Jain, A.↗
NASA NTRS1993

Aerodynamic control of NASP-type vehicles through vortex manipulation, volume 4

Forebody Vortex Control (FVC) is an emerging technology that has received widespread and concentrated attention by many researchers for application on fighter aircraft to enhance aerodynamic controllability at high angles of attack. This research explores potential application of FVC to a NASP-type configuration. The configuration investigated is characterized by a slender, circular cross-section forebody and a 78 deg swept delta wing. A man-in-the-loop, six-degress-of-freedom, high-fidelity simulation was developed that demonstrates the implementation and advantages of pneumatic forebody vortex control. Static wind tunnel tests were used as the basis for the aerodynamic characteristics modeled in the simulation. Dynamic free-to-roll wind tunnel tests were analyzed and the wing rock motion investigated. A non-linear model of the dynamic effects of the bare airframe and the forebody vortex control system were developed that closely represented the observed behavior. Multiple state-of-the-art digital flight control systems were developed that included different utilizations of pneumatic vortex control. These were evaluated through manned simulation. Design parameters for a pneumatic forebody vortex control system were based on data collected regarding the use of blowing and the mass flow required during realistic flight maneuvers.

Smith, Brooke C.↗
NASA NTRS1993

Fabrication techniques for very fast diffractive lenses

Aspheric lenses with arbitrary phase functions can be fabricated on thin light weight substrates via the binary optics fabrication technique. However, it is difficult and costly to fabricate a fast lens (f/number less than 1) for use as the shorter wavelengths. The pitch of the masks and the alignment accuracy must be very fine. For a large lens, the space-bandwidth product of the element can also become impractically large. In this paper, two alternate approaches for the fabrication of fast aspheric diffractive lenses are described. The first approach fabricates the diffractive lens interferometrically, utilizing a spherical wavefront to provide the optical power of the lens and a computer generated hologram to create the aspheric components. The second approach fabricates the aspheric diffractive lens in the form if a higher order kinoform which trades groove profile fidelity for coarser feature size. The design and implementation issues for these two fabrication techniques are discussed.

Tai, Anthony M.↗
NASA NTRS1993

Characterization of fluid physics effects on cardiovascular response to microgravity (G-572)

The recognition and understanding of cardiovascular adaptation to spaceflight has experienced substantial advancement in the last several years. In-flight echocardiographic measurements of astronaut cardiac function on the Space Shuttle have documented a 15 percent reduction in both left ventricular volume index and stroke volume with a compensatory increase in heart rate to maintain cardiac output. To date, the reduced cardiac size and stroke volume have been presumed to be the consequence of the reduction in circulating fluid volume following diuresis and other physiological processes to reduce blood volume within a few days after orbital insertion. However, no specific mechanism for the reduced stroke volume has been elucidated. The following investigation proposes the use of a hydraulic model of the cardiovascular system to examine the possibility that the observed reduction in stroke volume may, in part, be related to fluid physics effects on heart function. The automated model is being prepared to fly as a GAS payload. The experimental apparatus consists of a pneumatically actuated, elliptical artificial ventricle connected to a closed-loop, hydraulic circuit with compliance and resistance elements to create physiologic pressure and flow conditions. The ventricle is instrumented with high-fidelity, acceleration-insensitive, catheter-tip pressure transducers (Millar Instruments) in the apex and base to determine the instantaneous ventricular pressures and (delta)P(sub LV) across the left ventricle (LVP(sub apex)-LVP(sub base). The ventricle is also instrumented with a flow probe and pressure transducers immediately upstream of the inflow valve and downstream of the outflow valve. The experiment will be microprocessor controlled with analog signals stored on the FM data tape recorder. By varying the circulating fluid volume, ventricular function can be determined for varying preload pressures with fixed afterload pressure. Pilot experiments on board the NASA KC-135 aircraft have demonstrated proof-of-concept and provided early support for the proposed hypothesis. A review of the pilot experiments and developmental progress on the GAS version of this experiment will be presented.

Pantalos, George M.↗
NASA NTRS1993

Semi-span model testing in the National Transonic Facility

A semi-span testing technique has been proposed for the NASA Langley Research Center's National Transonic Facility (NTF). Semi-span testing has several advantages including (1) larger model size, giving increased Reynolds number capability; (2) improved model fidelity, allowing ease of flap and slat positioning which ultimately improves data quality; and (3) reduced construction costs compared with a full-span model. In addition, the increased model size inherently allows for increased model strength, reducing aeroelastic effects at the high dynamic pressure levels necessary to simulate flight Reynolds numbers. The Energy Efficient Transport (EET) full-span model has been modified to become the EET semi-span model. The full-span EET model was tested extensively at both NASA LRC and NASA Ames Research Center. The available full-span data will be useful in validating the semi-span test strategy in the NTF. In spite of the advantages discussed above, the use of a semi-span model does introduce additional challenges which must be addressed in the testing procedure. To minimize the influence of the sidewall boundary layer on the flow over the semi-span model, the model must be off-set from the sidewall. The objective is to remove the semi-span model from the sidewall boundary layer by use of a stand-off geometry. When this is done however, the symmetry along the centerline of the full-span model is lost when the semi-span model is mounted on the wind tunnel sidewall. In addition, the large semi-span model will impose a significant pressure loading on the sidewall boundary layer, which may cause separation. Even under flow conditions where the sidewall boundary layer remains attached, the sidewall boundary layer may adversely effect the flow over the semi-span model. Also, the increased model size and sidewall mounting requires a modified wall correction strategy. With these issues in mind, the semi-span model has been well instrumented with surface pressure taps to obtain data on the expected complex flow field in the near wall region. This status report summarizes the progress to date on developing the semi-span geometry definition suitable for generating structured grids for the computational research. In addition, the progress on evaluating three state-of-the-art Navier-Stokes codes is presented.

Chokani, Ndaona↗
NASA NTRS1993

Plasma-puff initiation of high Coulomb transfer switches

The plasma-puff triggering mechanism based on a hypocycloidal pinch geometry was investigated to determine the optimal operating conditions for an azimuthally uniform surface flashover which initiates plasma-puff under wide ranges of fill gas pressures of Ar, He and N2. The optimal fill gas pressures for the azimuthally uniform plasma-puff were about 120 mTorr less than P(opt) less than 450 Torr for He and N2. For Argon 120 mTorr less than P(opt) less than 5 Torr for argon. The inverse pinch switch was triggered with the plasma-puff and the switching capability under various electrical parameters and working gas pressures of Ar, He and N2 was determined. It was also shown that the azimuthally uniform switching discharges were dependent on the type of fill gas and its fill pressure. A new concept of plasma-focus driven plasma-puff was also discussed in comparison with hypocycloidal pinch plasma-puff triggering. The main discharge of the inverse pinch switch with the plasma-focus driven plasma-puff trigger is found to be more azimuthally uniform than that with the hypocycloidal pinch plasma-puff trigger in a gas pressure region between 80 mTorr and 1 Torr. In order to assess the effects of plasma current density on material erosion of electrodes, emissions from both an inverse-pinch plasma switch (INPIStron) and from a spark gap switch under test were studied with an optical multichannel analyzer (OMA). The color temperature of the argon plasma was approximately 4,000 K which corresponded with the peak continuum emission near 750 nm. There are the strong line emissions of argon in the 650 - 800 nm range and a lack of line emissions of copper and other solid material used in the switch. This indicates that the plasma current density during closing is low and the hot spot or hot filament in the switch is negligible. This result also indicates considerable reduction of line emission with the INPIStron switch over that of a spark-gap switch. However, a strong carbon line emission exists due to vaporization of the plastic insulator used. In order to reduce the vaporization of the insulator, the plexiglass insulating material of INPIStron was replaced with Z-9 material. A comparative study of the INPIStron and a spark gap also reveals that the INPIStron, with a low impedance of Z equals 9 ohms, can transfer a high voltage pulse with a superior pulse-shape fidelity over that of a spark gap with Z equals 100 ohms.

Venable, D. D.↗
NASA NTRS1993

An investigation of fighter aircraft agility

This report attempts to unify in a single document the results of a series of studies on fighter aircraft agility funded by the NASA Ames Research Center, Dryden Flight Research Facility and conducted at the University of Kansas Flight Research Laboratory during the period January 1989 through December 1993. New metrics proposed by pilots and the research community to assess fighter aircraft agility are collected and analyzed. The report develops a framework for understanding the context into which the various proposed fighter agility metrics fit in terms of application and testing. Since new metrics continue to be proposed, this report does not claim to contain every proposed fighter agility metric. Flight test procedures, test constraints, and related criteria are developed. Instrumentation required to quantify agility via flight test is considered, as is the sensitivity of the candidate metrics to deviations from nominal pilot command inputs, which is studied in detail. Instead of supplying specific, detailed conclusions about the relevance or utility of one candidate metric versus another, the authors have attempted to provide sufficient data and analyses for readers to formulate their own conclusions. Readers are therefore ultimately responsible for judging exactly which metrics are 'best' for their particular needs. Additionally, it is not the intent of the authors to suggest combat tactics or other actual operational uses of the results and data in this report. This has been left up to the user community. Twenty of the candidate agility metrics were selected for evaluation with high fidelity, nonlinear, non real-time flight simulation computer programs of the F-5A Freedom Fighter, F-16A Fighting Falcon, F-18A Hornet, and X-29A. The information and data presented on the 20 candidate metrics which were evaluated will assist interested readers in conducting their own extensive investigations. The report provides a definition and analysis of each metric; details of how to test and measure the metric, including any special data reduction requirements; typical values for the metric obtained using one or more aircraft types; and a sensitivity analysis if applicable. The report is organized as follows. The first chapter in the report presents a historical review of air combat trends which demonstrate the need for agility metrics in assessing the combat performance of fighter aircraft in a modern, all-aspect missile environment. The second chapter presents a framework for classifying each candidate metric according to time scale (transient, functional, instantaneous), further subdivided by axis (pitch, lateral, axial). The report is then broadly divided into two parts, with the transient agility metrics (pitch lateral, axial) covered in chapters three, four, and five, and the functional agility metrics covered in chapter six. Conclusions, recommendations, and an extensive reference list and biography are also included. Five appendices contain a comprehensive list of the definitions of all the candidate metrics; a description of the aircraft models and flight simulation programs used for testing the metrics; several relations and concepts which are fundamental to the study of lateral agility; an in-depth analysis of the axial agility metrics; and a derivation of the relations for the instantaneous agility and their approximations.

Valasek, John↗
NASA NTRS1993

Current capabilities for simulating the extreme distortion of thin structures subjected to severe impacts

The explicit transient dynamics technology in use today for simulating the impact and subsequent transient dynamic response of a structure has its origins in the 'hydrocodes' dating back to the late 1940's. The growth in capability in explicit transient dynamics technology parallels the growth in speed and size of digital computers. Computer software for simulating the explicit transient dynamic response of a structure is characterized by algorithms that use a large number of small steps. In explicit transient dynamics software there is a significant emphasis on speed and simplicity. The finite element technology used to generate the spatial discretization of a structure is based on a compromise between completeness of the representation for the physical processes modelled and speed in execution. That is, since it is expected in every calculation that the deformation will be finite and the material will be strained beyond the elastic range, the geometry and the associated gradient operators must be reconstructed, as well as complex stress-strain models evaluated at every time step. As a result, finite elements derived for explicit transient dynamics software use the simplest and barest constructions possible for computational efficiency while retaining an essential representation of the physical behavior. The best example of this technology is the four-node bending quadrilateral derived by Belytschko, Lin and Tsay. Today, the speed, memory capacity and availability of computer hardware allows a number of the previously used algorithms to be 'improved.' That is, it is possible with today's computing hardware to modify many of the standard algorithms to improve their representation of the physical process at the expense of added complexity and computational effort. The purpose is to review a number of these algorithms and identify the improvements possible. In many instances, both the older, faster version of the algorithm and the improved and somewhat slower version of the algorithm are found implemented together in software. Specifically, the following seven algorithmic items are examined: the invariant time derivatives of stress used in material models expressed in rate form; incremental objectivity and strain used in the numerical integration of the material models; the use of one-point element integration versus mean quadrature; shell elements used to represent the behavior of thin structural components; beam elements based on stress-resultant plasticity versus cross-section integration; the fidelity of elastic-plastic material models in their representation of ductile metals; and the use of Courant subcycling to reduce computational effort.

Key, Samuel W.↗
NASA NTRS1993

Intact capture of hypervelocity particles on Shuttle

The capability for capturing micrometeoroid analogs intact through laboratory simulations in passive underdense media offers a valuable tool for cosmic dust research. However, no amount of laboratory simulations can replace actual space experiments due to the technical inability to launch high fidelity analogs of micrometeoroids in ground laboratories and then reliably simulating high hypervelocities (greater than 7 km/s). Fluffy composite micrometeoroid analogs tend to break up and have not survived laboratory launches at beyond 4 km/s, however, a new technique of launching cluster analogs was developed for the two-stage light-gas gun at NASA Ames Vertical Gun Range. Plasma drag or electrostatic accelerators may be able to achieve higher speeds than two-stage light-gas guns but only with very limited projectile compositions and may result in severe projectile deformation. Consequently, a space demonstration of intact capture was sought since 1983. Initial results from our STS-47 flight, which carried the first Shuttle Sample Return Experiment (SRE) with silica aerogel capture media, are reported.

Tsou, P.↗
NASA NTRS1993

Plasma-puff initiation of high Coulomb transfer switches

The plasma-puff triggering mechanism based on a hypocycloidal pinch geometry was investigated to determine the optimal operating conditions for an azimuthally uniform surface flashover which initiates plasma-puff under wide ranges of fill gas pressures of Ar, He and N2. The optimal fill gas pressures for the azimuthally uniform plasma-puff were about 120 mTorr less than P(sub opt) less than 450 Torr for He and N2. For Argon 20 mTorr is less than P(sub opt) is less than 5 Torr. The inverse pinch switch was triggered with the plasma-puff and the switching capability under various electrical parameters and working gas pressures of Ar, He and N2 was determined. It was also shown that the azimuthally uniform switching discharges were dependent on the type of fill gas and its fill pressure. A new concept of plasma-focus driven plasma-puff was also discussed in comparison with hypocycloidal pinch plasma-puff triggering. The main discharge of the inverse pinch switch with the plasma-focus driven plasma-puff trigger is found to be more azimuthally uniform than that with the hypocycloidal pinch plasma-puff trigger in a gas pressure region between 80 mTorr and 1 Torr. In order to assess the effects of plasma current density on material erosion of electrodes, emissions from both an inverse-pinch plasma switch (INPIStron) and from a spark gap switch under test were studied with an optical multichannel analyzer (OMA). The color temperature of the argon plasma was approximately 4,000 K which corresponded with the peak continuum emission near 750 nm. There are the strong line emissions of argon in the 650 - 800 nm range and a lack of line emissions of copper and other solid material used in the switch. This indicates that the plasma current density during closing is low and the hot spot or hot filament in the switch is negligible. This result also indicates considerable reduction of line emission with the INPIStron switch over that of a spark-gap switch. However, a strong carbon line emission exists due to vaporization of the plastic insulator used. In order to reduce the vaporization of the insulator, the plexiglass insulating material of INPIStron was replaced with Z-9 material. A comparative study of the INPIStron and a spark gap also reveals that the INPIStron, with a low impedance of Z = 9 ohms, can transfer a high voltage pulse with a superior pulse-shape fidelity over that of a spark gap with Z = 100 ohms.

Han, Kwang S.↗
NASA NTRS1993

Space network scheduling benchmark: A proof-of-concept process for technology transfer

This paper describes a detailed proof-of-concept activity to evaluate flexible scheduling technology as implemented in the Request Oriented Scheduling Engine (ROSE) and applied to Space Network (SN) scheduling. The criteria developed for an operational evaluation of a reusable scheduling system is addressed including a methodology to prove that the proposed system performs at least as well as the current system in function and performance. The improvement of the new technology must be demonstrated and evaluated against the cost of making changes. Finally, there is a need to show significant improvement in SN operational procedures. Successful completion of a proof-of-concept would eventually lead to an operational concept and implementation transition plan, which is outside the scope of this paper. However, a high-fidelity benchmark using actual SN scheduling requests has been designed to test the ROSE scheduling tool. The benchmark evaluation methodology, scheduling data, and preliminary results are described.

Moe, Karen↗
NASA NTRS1993

Atomic oxygen interaction with spacecraft materials: Relationship between orbital and ground-based testing for materials certification

The effects of atomic oxygen on boron nitride (BN), silicon nitride (Si3N4), Intelsat 6 solar cell interconnects, organic polymers, and MoS2 and WS2 dry lubricant, were studied in Low Earth Orbit (LEO) flight experiments and in a ground based simulation facility. Both the inflight and ground based experiments employed in situ electrical resistance measurements to detect penetration of atomic oxygen through materials and Electron Spectroscopy for Chemical Analysis (ESCA) analysis to measure chemical composition changes. Results are given. The ground based results on the materials studied to date show good qualitative correlation with the LEO flight results, thus validating the simulation fidelity of the ground based facility in terms of reproducing LEO flight results. In addition it was demonstrated that ground based simulation is capable of performing more detailed experiments than orbital exposures can presently perform. This allows the development of a fundamental understanding of the mechanisms involved in the LEO environment degradation of materials.

Cross, Jon B.↗
NASA NTRS1993

SIMSAT: An object oriented architecture for real-time satellite simulation

Real-time satellite simulators are vital tools in the support of satellite missions. They are used in the testing of ground control systems, the training of operators, the validation of operational procedures, and the development of contingency plans. The simulators must provide high-fidelity modeling of the satellite, which requires detailed system information, much of which is not available until relatively near launch. The short time-scales and resulting high productivity required of such simulator developments culminates in the need for a reusable infrastructure which can be used as a basis for each simulator. This paper describes a major new simulation infrastructure package, the Software Infrastructure for Modelling Satellites (SIMSAT). It outlines the object oriented design methodology used, describes the resulting design, and discusses the advantages and disadvantages experienced in applying the methodology.

Williams, Adam P.↗
NASA NTRS1993

Admittance model for the shuttle remote manipulator system in four configurations

A possible scenario for robot task performance in space is to mount two small, dexterous arms to the end of the Shuttle Remote Manipulator System (SRMS). As these small robots perform tasks, the flexibility of the SRMS may cause unsuccessful task executions. In order to simulate the dynamic coupling between the SRMS and the arms, admittance models of the SRMS in four brakes locked configurations were developed. The admittance model permits calculation of the SRMS end-effector response due to end-effector disturbing forces. The model will then be used in conjunction with a Stewart Platform, a vehicle emulation system. An application of the admittance model was shown by simulating the disturbing forces using two SRMS payloads, the Dextrous Orbital Servicing System (DOSS) manipulator and DOSS carrying a 1000 lb. cylinder. Mode by mode comparisons were conducted to determine the minimum number of modes required in the admittance model while retaining dynamic fidelity. It was determined that for all four SRMS configurations studied, between 4 and 6 modes of the SRMS structure (depending on the excitation loads) were sufficient to retain tolerance of 0.01 inches and 0.01 deg. These tolerances correspond to the DOSS manipulator carrying no object. When the DOSS carries the 1000 lb. cylinder, between 15 and 20 modes were sufficient, approximately three or four times as many modes as for the unloaded case.

Papadopoulos, Loukas↗
NASA NTRS1993

Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle

High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.

Adams, Richard J.↗
NASA NTRS1993

Modelling the Shuttle Remote Manipulator System: Another flexible model

High fidelity elastic system modeling algorithms are discussed. The particular system studied is the Space Shuttle Remote Manipulator System (RMS) undergoing full articulated motion. The model incorporates flexibility via a methodology the author has been developing. The technique is based in variational principles, so rigorous boundary condition generation and weak formulations for the associated partial differential equations are realized, yet the analyst need not integrate by parts. The methodology is formulated using vector-dyad notation with minimal use of tensor notation, therefore the technique is believed to be affable to practicing engineers. The objectives of this work are as follows: (1) determine the efficacy of the modeling method; and (2) determine if the method affords an analyst advantages in the overall modeling and simulation task. Generated out of necessity were Mathematica algorithms that quasi-automate the modeling procedure and simulation development. The project was divided into sections as follows: (1) model development of a simplified manipulator; (2) model development of the full-freedom RMS including a flexible movable base on a six degree of freedom orbiter (a rigid-body is attached to the manipulator end-effector); (3) simulation development for item 2; and (4) comparison to the currently used model of the flexible RMS in the Structures and Mechanics Division of NASA JSC. At the time of the writing of this report, items 3 and 4 above were not complete.

Barhorst, Alan A.↗
NASA NTRS1993

Advanced radiometric and interferometric milimeter-wave scene simulations

Smart munitions and weapons utilize various imaging sensors (including passive IR, active and passive millimeter-wave, and visible wavebands) to detect/identify targets at short standoff ranges and in varied terrain backgrounds. In order to design and evaluate these sensors under a variety of conditions, a high-fidelity scene simulation capability is necessary. Such a capability for passive millimeter-wave scene simulation exists at TRW. TRW's Advanced Radiometric Millimeter-Wave Scene Simulation (ARMSS) code is a rigorous, benchmarked, end-to-end passive millimeter-wave scene simulation code for interpreting millimeter-wave data, establishing scene signatures and evaluating sensor performance. In passive millimeter-wave imaging, resolution is limited due to wavelength and aperture size. Where high resolution is required, the utility of passive millimeter-wave imaging is confined to short ranges. Recent developments in interferometry have made possible high resolution applications on military platforms. Interferometry or synthetic aperture radiometry allows the creation of a high resolution image with a sparsely filled aperture. Borrowing from research work in radio astronomy, we have developed and tested at TRW scene reconstruction algorithms that allow the recovery of the scene from a relatively small number of spatial frequency components. In this paper, the TRW modeling capability is described and numerical results are presented.

Hauss, B. I.↗