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At least 1,693 records · Page 94

Ground-based measurements of galactic cosmic ray fragmentation in shielding

The mean free path for nuclear interactions of galactic cosmic-rays is comparable to shielding and tissue thicknesses present in human interplanetary exploration, resulting in a significant fraction of nuclear reaction products at depth. In order to characterize the radiation field, the energy spectrum, the angular distribution, and the multiplicity of each type of secondary particles must also be known as a function of depth. Reactions can take place anywhere in a thick absorber; therefore, it is necessary to know these quantities as a function of particle energy for all particles produced. HZE transport methods are used to predict the radiation field; they are dependent on models of the interaction of man-made systems with the space environment to an even greater extent than methods used for other types of radiation. Hence, there is a major need to validate these transport codes by comparison with experimental data. The most cost-effective method of validation is a comparison with ground-based experimental measurements. A research program to provide such validation measurements using neon, iron and other accelerated heavy ion beams will be discussed and illustrated using results from ongoing experiments and their comparison with current transport codes. The extent to which physical measurements yield radiobiological predictions will be discussed.

NASA Discipline Radiation Health↗

Advancing Metasurfaces Towards New Frontiers: Nonvolatile Reconfigurable Optics

The applications of adaptive optics extend across multiple sectors, encompassing areas such as LiDAR, biological and chemical sensing, and free-space communications. In this study, we report on the design, fabrication, testing, and modeling of electrically reconfigurable metasurfaces using a low-loss high contrast phase change material, Ge2Sb2Se4Te integrated with an IR-transparent silicon microheater. Through this work, we introduce a reliable architecture for switching PCM-based metasurfaces within an integrated circuit configuration which is compatible with standard foundry fabrication processes. We demonstrate the capability of controlling the transmission of electromagnetic waves through the precise stimulation of PCM-based pixels, each spanning a few hundred microns, over numerous cycles. By leveraging PCM-based pixels, we unlock the potential to create metasurfaces encompassing a diverse range of functionalities such as dielectric filters, metalens, or beam steering devices, which is governed by the design of the meta-atoms. Further, we perform an in-depth investigation into the failure mechanism utilizing techniques such as Fourier transform IR spectroscopy (FTIR), transmission electron microscopy (TEM), energy dispersive spectroscopy (EDS), and thermal modeling. According to our results, due to a sharp temperature rise at the PCM/heater interface, we observe severe delamination of the PCM from the heater. More uniform PCM deposition, better adhesion at the PCM/heater interface, and a more uniform temperature distribution in the device could potentially mitigate the failure and lead to a longer life-time. By addressing these challenges, we aim to unlock the full potential of PCM-based devices and advance the field of adaptive optics.

Phase change material↗

Photodissociation dynamics of the tert -butyl perthiyl radical

Here, the photodissociation dynamics of the tert-butyl perthiyl (t-BuSS) radical are investigated by fast-beam coincidence translational spectroscopy. A fast (6 keV-8 keV) beam of neutral t-BuSS radicals is produced via photodetachment of the corresponding anion, followed by photodissociation at 248 nm (5.00 eV) or 193 nm (6.42 eV) and coincident detection of the neutral products. Photofragment mass and translational energy distributions are obtained at both wavelengths. At 248 nm, the dominant product channel (90%) is found to be S loss, with a product translational energy distribution that peaks close to the maximum available energy and an anisotropic photofragment angular distribution, indicating dissociation along a repulsive excited state. A minor channel (10%) leading to the formation of S 2 + t-Bu is also observed. At 193 nm, both two- and three-body dissociation are observed. The formation of S 2 + t-Bu is the dominant two-body product channel, with multiple electronic states of the S 2 molecule produced via excited-state dissociation processes. The formation of S + t-BuS is a minor two-body channel at this dissociation energy. The three-body channels are S 2 + H + isobutene, S 2 + CH 3 + propene, and S + SH + isobutene. The first two of these channels result from a sequential dissociation process in which the loss of S 2 from t-BuSS results in ground-state t-Bu with sufficient internal energy to undergo secondary fragmentation. The third three-body channel, S + SH + isobutene, is attributed to the loss of internally excited HS 2 from t-BuSS, which then rapidly dissociates to form S + SH in an asynchronous concerted dissociation process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Doppler radar detection of vortex hazard indicators

Wake vortex experiments were conducted at White Sands Missile Range, NM using the AN/MPS-39 Multiple Object Tracking Radar (MOTR). The purpose of these experiments was twofold. The first objective was to verify that radar returns from wake vortex are observed for some time after the passage of an aircraft. The second objective was to verify that other vortex hazard indicators such as ambient wind speed and direction could also be detected. The present study addresses the Doppler characteristics of wake vortex and clear air returns based upon measurements employing MOTR, a very sensitive C-Band phased array radar. In this regard, the experiment was conducted so that the spectral characteristics could be determined on a dwell to-dwell basis. Results are presented from measurements of the backscattered power (equivalent structure constant), radial velocity and spectral width when the aircraft flies transverse and axial to the radar beam. The statistics of the backscattered power and spectral width for each case are given. In addition, the scan strategy, experimental test procedure and radar parameters are presented.

Nespor, Jerald D.↗

Extended Acceleration in Slot Gaps and Pulsar High-Energy Emission

We revise the physics of primary electron acceleration in the "slot gap" (SG) above the pulsar polar caps (PCs), a regime originally proposed by Arons and Scharlemann (1979) in their electrodynamic model of pulsar PCs. We employ the standard definition of the SG as a pair-free space between the last open field lines and the boundary of the pair plasma column which is expected to develop above the bulk of the PC. The rationale for our revision is that the proper treatment of primary acceleration within the pulsar SGs should take into account the effect of the narrow geometry of the gap on the electrodynamics within the gap and also to include the effect of inertial frame dragging on the particle acceleration. We show that the accelerating electric field within the gap, being significantly boosted by the effect of frame dragging, becomes reduced because of the gap geometry by a factor proportional to the square of the SG width. The combination of the effects of frame dragging and geometrical screening in the gap region naturally gives rise to a regime of extended acceleration, that is not limited to favorably curved field lines as in earlier models, and the possibility of multiple-pair production by curvature photons at very high altitudes, up to several stellar radii. We present our estimates of the characteristic SG thickness across the PC, energetics of primaries accelerated within the gap, high-energy bolometric luminosities emitted from the high altitudes in the gaps, and maximum heating luminosities produced by positrons returning from the elevated pair fronts. The estimated theoretical high-energy luminosities are in good agreement with the corresponding empirical relationships for gamma-ray pulsars. We illustrate the results of our modeling of the pair cascades and gamma-ray emission from the high altitudes in the SG for the Crab pulsar. The combination of the frame-dragging field and high-altitude SG emission enables both acceleration at the smaller inclination angles and a larger emission beam, both necessary to produce widely-spaced double-peaked profiles.

White, Nicholas E.↗

Test of Harmonic Coil Accuracy Using a Multi Vertex Probe

Magnets are integral components of particle accelerators, with different multipoles used to perform various beam conditioning functions, like steering and focusing. Testing accelerator magnets to ensure compliance with specification is a crucial step of fabrication. One of the most popular techniques for verifying magnetic field strength and integrity is the harmonic coil probe. Harmonic coil probes are comprised of passive loops that are rotated around the aperture of a magnet and are used to measure magnetic flux. Oftentimes the measurements of the harmonic coil probe are affected by transverse vibrations along the axis of rotation and torsional vibrations of the position closure sensor, both causing spurious harmonics. To make matters challenging, it is difficult to distinguish between the real harmonics of the magnet and the spurious harmonics during analysis. This research explores the use of a novel configuration of harmonic coil probe, Multi-Vertex Probe (MVP), to address multiple factors that affect the accuracy and repeatability of harmonic coil probe measurement. Most of the results are based on simulation data, in which artificial torsional distortions are introduced and removed with the proposed processing method. In addition to implementing torsional vibration removal in simulation, laboratory analysis regarding the source of vibrations was performed using a pre-fabricated MVP. More specifically, various mechanical conditions were used to explore the standard deviation of main harmonic’s flux amplitude. The conditions included: coupling type (rigid or soft), rotation speed, probe starting position within magnetic field, and cabling location inside the magnetic field. Along with this, the MVP’s measured noise floor in and outside a magnetic field was quantified.

Lofquist, Claire [Northern Illinois U.]↗

Design of a nonlinear, thin-film Mach-Zehnder interferometer

A Mach-Zehnder interferometer consists of a 3 db splitter to create the two separate beams, an optical path difference to control the interference between the two beams and another 3 db coupler to reconstruct the output signal. The performance of each of its components has been investigated. Since an optical path difference is required for its function, the performance of a Mach-Zehnder interferometer is not very sensitive to construction parameters. In designing an interferometer for this work, the following considerations must be observed: the interferometer is to be made of phthalocyanine or polydiacetylene thin films; in order to avoid thermal effects which are slower, the wavelength chosen must not be absorbed in either one or two photon processes; the wavelength chosen must be easily generated (laser line); the spacing between the interferometer arms must be large enough to allow attachment of external electrodes; the vapor deposition apparatus can accept disks no larger than 0.9 inches; and the design must allow multiple layer coating in order to determine the optimum film thickness or to change to another substance.

Pearson, Earl F.↗

System-Level Integrated Circuit (SLIC) Technology Development for Phased Array Antenna Applications

This report documents the efforts and progress in developing a 'system-level' integrated circuit, or SLIC, for application in advanced phased array antenna systems. The SLIC combines radio-frequency (RF) microelectronics, digital and analog support circuitry, and photonic interfaces into a single micro-hybrid assembly. Together, these technologies provide not only the amplitude and phase control necessary for electronic beam steering in the phased array, but also add thermally-compensated automatic gain control, health and status feedback, bias regulation, and reduced interconnect complexity. All circuitry is integrated into a compact, multilayer structure configured for use as a two-by-four element phased array module, operating at 20 Gigahertz, using a Microwave High-Density Interconnect (MHDI) process. The resultant hardware is constructed without conventional wirebonds, maintains tight inter-element spacing, and leads toward low-cost mass production. The measured performances and development issues associated with both the two-by-four element module and the constituent elements are presented. Additionally, a section of the report describes alternative architectures and applications supported by the SLIC electronics. Test results show excellent yield and performance of RF circuitry and full automatic gain control for multiple, independent channels. Digital control function, while suffering from lower manufacturing yield, also proved successful.

Windyka, John A.↗

Scanning Laser Infrared Molecular Spectrometer (SLIMS)

This prototype innovation is a novel design that achieves very long, effective laser path lengths that are able to yield ppb (parts per billion) and sub-ppb measurements of trace gases. SLIMS can also accommodate multiple laser channels covering a wide range of wavelengths, resulting in detection of more chemicals of interest. The mechanical design of the mirror cell allows for the large effective path length within a small footprint. The same design provides a robust structure that lends itself to being immune to some of the alignment challenges that similar cells face. By taking a hollow cylinder and by cutting an elliptically or spherically curved surface into its inner wall, the basic geometry of a reflecting ring is created. If the curved, inner surface is diamond-turned and highly polished, a surface that is very highly reflective can be formed. The surface finish can be further improved by adding a thin chrome or gold film over the surface. This creates a high-quality, curved, mirrored surface. A laser beam, which can be injected from a small bore hole in the wall of the cylinder, will be able to make many low-loss bounces around the ring, creating a large optical path length. The reflecting ring operates on the same principle as the Herriott cell. The difference exists in the mirror that doesn't have to be optically aligned, and which has a relatively large, internal surface area that lends itself to either open air or evacuated spectroscopic measurements. This solid, spherical ring mirror removes the possibility of mirror misalignment caused by thermal expansion or vibrations, because there is only a single, solid reflecting surface. Benefits of the reflecting ring come into play when size constraints reduce the size of the system, especially for space missions in which mass is at a premium.

Scott, David C.↗

Optimized Biasing of Pump Laser Diodes in a Highly Reliable Metrology Source for Long-Duration Space Missions

Optical metrology system reliability during a prolonged space mission is often limited by the reliability of pump laser diodes. We developed a metrology laser pump module architecture that meets NASA SIM Lite instrument optical power and reliability requirements by combining the outputs of multiple single-mode pump diodes in a low-loss, high port count fiber coupler. We describe Monte-Carlo simulations used to calculate the reliability of the laser pump module and introduce a combined laser farm aging parameter that serves as a load-sharing optimization metric. Employing these tools, we select pump module architecture, operating conditions, biasing approach and perform parameter sensitivity studies to investigate the robustness of the obtained solution.

808 mm diode pumps↗

Effect of coaxial nozzle wear on catchment efficiency in direct energy deposition built components

Laser based Direct Energy Deposition (DED) systems using metallic powder feedstock are recognized as a promising manufacturing method for their ability to shorten production cycles and create complex part geometries. Components are built by generating a melt pool with a high-power laser beam while material is coaxially injected and left to solidify. An impediment to large scale use of DED lies in poor powder catchment efficiency, the condition in which a portion of injected powder escapes the melt pool resulting in a ratio of decreased printed material mass to mass of supplied feedstock. The wear state of a coaxial nozzle on a DED system within a hybrid manufacturing machine tool has been observed to decrease catchment efficiency over time. Herein this study investigates this effect by adapting flow visualization techniques to an in-situ process monitoring format, the implementation of a Computational Fluid Dynamics (CFD) simulation, and deposition testing. Nozzle geometric defects due to wear are identified and categorized, and the impact of nozzle tip wear, resulting in axial tip reduction, on powder catchment efficiency is proven by multiple calculation methods. A linear correlation between catchment efficiency and powder stream diameter is identified, causing a 15–20% loss in efficiency sustained over incremental nozzle tip reduction up to − 1 mm. These results provide a foundation for further study of wear effects and Zero defect manufacturing solutions for powder fed DED systems.

42 ENGINEERING↗

Multi-Differential Charged Current $\nu_{\mu}$ - Argon Cross Section without Pions in the Final State Measurement in MicroBooNE

MicroBooNE, an 85-tonne liquid argon time projection chamber (LArTPC) detector is on-axis to the Booster Neutrino Beam (BNB) beamline facility at Fermi National Accelerator Laboratory. MicroBooNE is elucidating neutrino interactions with argon through cross-section measurements to refine interaction models and reduce uncertainties. In this poster, we present the status of the single and double multi-differential charged current (CC) cross section with zero pions in the final state (CC-0$\pi$) as a function of muon momentum ($0.1<p_\mu<2.0\,\mathrm{GeV/c}$) and the cosine of the muon angle ($-1<\cos\theta_\mu<1$). We present the details of the event selection and cross section extraction along with a set of tests using fake data to establish the robustness of the analysis methodology. We also discuss prospects for a future combined measurement with the Gd-H$_2$O target at the ANNIE experiment, to explore MicroBooNE’s proton multiplicity alongside ANNIE’s neutron multiplicity.

43 PARTICLE ACCELERATORS↗

Application of impact dampers in vibration control of flexible structures

Impact dampers belong to the category of passive vibration devices used to attenuate the vibration of discrete and continuous systems. An impact damper generally consists of a mass which is allowed to travel freely between two defined stops. Under the right conditions, the vibration of the structure to which the impact damper is attached will cause the mass of the impact damper to strike the structure. Previous analytical and experimental research work on the effect of impact dampers in attenuating the vibration of discrete and continuous systems have demonstrated their effectiveness. It has been shown in this study that impact dampers can increase the intrinsic damping of a lightly-damped flexible structure. The test structure consists of a slender flexible beam supported by a pin-type support at one end and supported by a linear helical flexible spring at another location. Sinusoidal excitation spanning the first three natural frequencies was applied in the horizontal plane. The orientation of the excitation and the test structure in the horizontal plane minimizes the effect of gravity on the behavior of the test structure. The excitation was applied using a linear sine sweep technique. The span of the test structure, the mass of the impact damper, the distance of travel, and the location of the impact damper along the span of the test structure were varied. The damping ratio are estimated for sixty test configurations. The results show that the impact damper significantly increases the damping ratio of the test structure. Statistical analysis of the results using the method of multiple linear regression indicates that a reasonable fit has been accomplished. It is concluded that additional experimental analysis of flexible structures in microgravity environment is needed in order to achieve a better understanding of the behavior of impact damper under conditions of microgravity. Numerical solution of the behavior of flexible structures equipped with impact dampers is also needed to predict stresses and deformations under operating conditions of microgravity in space applications.

Akl, Fred A.↗

The Gamma-Ray Emitting Radio-Loud Narrow-Line Seyfert 1 Galaxy PKS 2004-447 II. The Radio View

Context. gamma-ray-detected radio-loud narrow-line Seyfert 1 (gamma-NLS1) galaxies constitute a small but interesting sample of the gamma-ray-loud AGN. The radio-loudest gamma-NLS1 known, PKS2004447, is located in the southern hemisphere and is monitored in the radio regime by the multiwavelength monitoring programme TANAMI. Aims. We aim for the first detailed study of the radio morphology and long-term radio spectral evolution of PKS2004447, which are essential for understanding the diversity of the radio properties of gamma-NLS1s. Methods. The TANAMI VLBI monitoring program uses the Australian Long Baseline Array (LBA) and telescopes in Antarctica, Chile, New Zealand, and South Africa to monitor the jets of radio-loud active galaxies in the southern hemisphere. Lower resolution radio flux density measurements at multiple radio frequencies over four years of observations were obtained with the Australia Telescope Compact Array (ATCA). Results. The TANAMI VLBI image at 8.4GHz shows an extended one-sided jet with a dominant compact VLBI core. Its brightness temperature is consistent with equipartition, but it is an order of magnitude below other gamma-NLS1s with the sample value varying over two orders of magnitude. We find a compact morphology with a projected large-scale size 11 kpc and a persistent steep radio spectrum with moderate flux-density variability. Conclusions. PKS2004447 appears to be a unique member of the gamma-NLS1 sample. It exhibits blazar-like features, such as a flat featureless X-ray spectrum and a core-dominated, one-sided parsec-scale jet with indications for relativistic beaming. However, the data also reveal properties atypical for blazars, such as a radio spectrum and large-scale size consistent with compact-steep-spectrum (CSS) objects, which are usually associated with young radio sources. These characteristics are unique among all gamma-NLS1s and extremely rare among gamma-ray-loud AGN.

galaxies: active / galaxies: individual: PKS 2004-↗

Photo- and Electro-Induced Hadron Production from Nuclei at Jefferson Laboratory

Understanding many-body knockout processes is crucial for nuclear physics, particularly in photo- and electro-induced reactions. In turn, understanding two- and three-body forces, including higher-order forces, is vital for a complete understanding of atoms. We present photo-induced many-proton knockout processes, with multiplicities from 1 to 6, using 12C, CH2, and C4H9OH targets in the g9a FROST dataset. Our analysis covers photon energies from 600 to 4500 MeV, significantly expanding current world data. Comparing our experimental data to the state-of-the-art GiBUU model offers a new challenge in the model’s theoretical description of many-body processes. GiBUU reasonably describes the data at lower photon energies but struggles at higher energies and missing masses, likely due to missing processes, such as initial 3-pion photoproduction. Our results will inform future developments in describing proton knockout processes, indicating GiBUU’s overall reasonable description of many-proton knockout data up to around 2.2 GeV. We also assess various electro-induced reactions using 2D, 12C, and 40Ar targets in the RGM dataset. Our results, obtained at electron beam energies of 2, 4, and 6 GeV, are compared in detail to GENIE and GiBUU, two widely used theory models in neutrino oscillation experiments. Discrepancies between model predictions and experimental data underscore the need for refining the two theoretical models. Despite discrepancies, GiBUU provides a more accurate modelling of electro-induced reactions, especially for 40Ar - crucial for future neutrino oscillation facilities such as DUNE. Understanding the fundamental nuclear physics involved in neutrino-nuclei interactions is essential for reducing the systematic uncertainties in extracting neutrino oscillation parameters. Many-body processes significantly contribute to the background processes observed in neutrino-nuclei interactions, hence the results from both analyses are crucial for developing the theoretical framework for the underlying nuclear physics.

Williams, Rhidian↗

DYCAST: A finite element program for the crash analysis of structures

DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors.

Pifko, A. B.↗

Investigating Laser Beam Welding as an In-Space Joining Technique via Thermal Vacuum and Microgravity and Vacuum Experiments

In-space joining technologies are crucial for stimulating an in-space economy and for enabling sustained space exploration by in-space manufacturing and repair of metallic structures. Compared to brazing or soldering, in-space welding (ISW) can provide highly hermetic, strong, and complex joints, potentially without introducing additional material. However, the influence of extreme temperatures, reduced pressure, and reduced gravity on ISW is not yet fully elucidated. Several efforts at NASA are investigating laser beam welding (LBW) as a joining and repair method in both thermal vacuum (TVAC) and combined vacuum & reduced gravity environments. NASA Marshall Space Flight Center (MSFC) shepherded several ISW projects in its past, including the 1973 electron beam welding on Skylab, the 1989 low-power LBW on parabolic flights, and the unflown 1990s-era In-Space Welding Experiment. Recent parabolic flights and 3 degree-of-freedom ground testing build upon this heritage. A collaboration with the Ohio State University using NASA Langley Research Center (LaRC) hardware retrofitted for LBW achieved the first high-powered laser welds under vacuum and low gravity and developed a workforce capable developing such experimental hardware. A ground testing campaign at the MSFC Flat Floor simulated fit-up and welding representative of ISW in 3 degrees of freedom to emulate microgravity effects on inertial systems. One ongoing effort is a NASA Early Career Initiative project – Lunar Assembly and Servicing by Autonomous Robotics (LASAR). Ruggedized LBW components were developed by an external partner for use in TVAC. A TVAC-rated robotic arm was procured by MSFC and used in the first known robotic laser weld where all components save the laser generator were under vacuum. NASA Johnson Space Center (JSC) is advancing supervised autonomy of ISW. NASA LaRC continues to adapt their unique snowflake joint geometry, suitable for connecting segments in trusses and other structures, to LBW. Upcoming TVAC campaigns will focus on testing extreme temperatures, proving out autonomous operations, and demonstrating weld repair. Weld inspection will occur via a non-contact nondestructive evaluation (NDE) technique – electromagnetic acoustic transduction (EMAT). Another ongoing effort based at MSFC is the DISCMAN -- DIsk-Shaped Configurable and Modular vAcuum uNit – which seeks to development a compact, modular payload that can provide a vacuum environment while in a reduced gravity condition. This payload could support multiple in-space manufacturing developmental efforts, with the first demonstration technology being LBW. Currently, the design is targeting operations in the pressurized volume of a space station, but the payload could readily be adapted to other flight platforms such as parabolic or even suborbital vehicles. LASAR elucidates the effects of temperature and vacuum on LBW while DISCMAN probes those of vacuum and gravity. Through these complementary efforts, NASA is addressing the primary challenges of ISW across the space environment while simultaneously developing and maturing technologies including robotic systems and inspection methodologies for future practical implementation on the Moon and beyond. This approach is timely, as upcoming missions requiring sustained human presence in space will depend on reliable ISW capabilities to create robust metallic joints currently unproven in the space environment and to perform repairs in situ .

hypogravity↗

Scannable beam forming interferometer antenna array system

An antenna array is described which comprises three interferometer pairs of antenna elements with selected spacings made to form a single beam which is readily scannable. All spatial frequencies generated by a signal and intercepted by the array are derived from a signal processing technique applied to the array. The array samples space in the spatial frequency domain while the signal processing technique utilizes real time convolution of functions in the spectral frequency domain. Summation of the appropriate spatial frequencies is equilvalent to a Fourier transform operation, yielding the location of the signal source in space. Resolution and freedom from interference of the interferometer system is equal to that of a fully filled array of the same aperture size containing element spacings of one half wavelength. An antenna array system comprising four antenna elements forming six interferometer pairs with a resolution equal to that of a sixteen element array with spacings of one half wavelength is described, as well as other multiples of one quarter wavelength of partial multiples of a wave length.

Kaiser, J. A., Jr.↗