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Identifying and Documenting Expert Knowledge, A Practical Study of Design Patterns

Globalization, powered by digitization, is increasing technology growth and knowledge transfer rates to levels not seen in the previous 3500 years, obscuring absolute truth and accelerating rates of innovation and production. Competing,or remaining competitive, in this global marketplace requires a learning organization adopt a method of capture, retention, and reuse for demonstrated tacit knowledge to accelerate the development of increasingly complex systems of high quality at a reasonable cost. The architectural theory of Patterns and Pattern Language is a validated methodology for mining tacit domain knowledge from a proven system. This work applies architectural theory to a multi-year development experiment and captures exposed knowledgeas a design patternin a model based systems engineering tool, demonstrating applicability ofdigital engineering initiativesin thedescription and reuse of expert design knowledge.By creating and archiving model based expressions of expert knowledge,a learning organization canimprovepractical decision making and avoid uninformed concept phase decision making

systems engineering↗

Climate model projections from the Scenario Model Intercomparison Project (ScenarioMIP) of CMIP6

Abstract. The Scenario Model Intercomparison Project (ScenarioMIP) defines and coordinates the main set of future climate projections, based on concentration-driven simulations, within the Coupled Model Intercomparison Project phase 6 (CMIP6). This paper presents a range of its outcomes by synthesizing results from the participating global coupled Earth system models. We limit our scope to the analysis of strictly geophysical outcomes: mainly global averages and spatial patterns of change for surface air temperature and precipitation. We also compare CMIP6 projections to CMIP5 results, especially for those scenarios that were designed to provide continuity across the CMIP phases, at the same time highlighting important differences in forcing composition, as well as in results. The range of future temperature and precipitation changes by the end of the century (2081–2100) encompassing the Tier 1 experiments based on the Shared Socioeconomic Pathway (SSP) scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0 and SSP5-8.5) and SSP1-1.9 spans a larger range of outcomes compared to CMIP5, due to higher warming (by close to 1.5 ∘C) reached at the upper end of the 5 %–95 % envelope of the highest scenario (SSP5-8.5). This is due to both the wider range of radiative forcing that the new scenarios cover and the higher climate sensitivities in some of the new models compared to their CMIP5 predecessors. Spatial patterns of change for temperature and precipitation averaged over models and scenarios have familiar features, and an analysis of their variations confirms model structural differences to be the dominant source of uncertainty. Models also differ with respect to the size and evolution of internal variability as measured by individual models' initial condition ensemble spreads, according to a set of initial condition ensemble simulations available under SSP3-7.0. These experiments suggest a tendency for internal variability to decrease along the course of the century in this scenario, a result that will benefit from further analysis over a larger set of models. Benefits of mitigation, all else being equal in terms of societal drivers, appear clearly when comparing scenarios developed under the same SSP but to which different degrees of mitigation have been applied. It is also found that a mild overshoot in temperature of a few decades around mid-century, as represented in SSP5-3.4OS, does not affect the end outcome of temperature and precipitation changes by 2100, which return to the same levels as those reached by the gradually increasing SSP4-3.4 (not erasing the possibility, however, that other aspects of the system may not be as easily reversible). Central estimates of the time at which the ensemble means of the different scenarios reach a given warming level might be biased by the inclusion of models that have shown faster warming in the historical period than the observed. Those estimates show all scenarios reaching 1.5 ∘C of warming compared to the 1850–1900 baseline in the second half of the current decade, with the time span between slow and fast warming covering between 20 and 27 years from present. The warming level of 2 ∘C of warming is reached as early as 2039 by the ensemble mean under SSP5-8.5 but as late as the mid-2060s under SSP1-2.6. The highest warming level considered (5 ∘C) is reached by the ensemble mean only under SSP5-8.5 and not until the mid-2090s.

54 ENVIRONMENTAL SCIENCES↗

Data fusion with artificial neural networks (ANN) for classification of earth surface from microwave satellite measurements

A data fusion system with artificial neural networks (ANN) is used for fast and accurate classification of five earth surface conditions and surface changes, based on seven SSMI multichannel microwave satellite measurements. The measurements include brightness temperatures at 19, 22, 37, and 85 GHz at both H and V polarizations (only V at 22 GHz). The seven channel measurements are processed through a convolution computation such that all measurements are located at same grid. Five surface classes including non-scattering surface, precipitation over land, over ocean, snow, and desert are identified from ground-truth observations. The system processes sensory data in three consecutive phases: (1) pre-processing to extract feature vectors and enhance separability among detected classes; (2) preliminary classification of Earth surface patterns using two separate and parallely acting classifiers: back-propagation neural network and binary decision tree classifiers; and (3) data fusion of results from preliminary classifiers to obtain the optimal performance in overall classification. Both the binary decision tree classifier and the fusion processing centers are implemented by neural network architectures. The fusion system configuration is a hierarchical neural network architecture, in which each functional neural net will handle different processing phases in a pipelined fashion. There is a total of around 13,500 samples for this analysis, of which 4 percent are used as the training set and 96 percent as the testing set. After training, this classification system is able to bring up the detection accuracy to 94 percent compared with 88 percent for back-propagation artificial neural networks and 80 percent for binary decision tree classifiers. The neural network data fusion classification is currently under progress to be integrated in an image processing system at NOAA and to be implemented in a prototype of a massively parallel and dynamically reconfigurable Modular Neural Ring (MNR).

Lure, Y. M. Fleming↗

Ground-based studies of ionospheric convection associated with substorm expansion

The instantaneous patterns of electric fields and currents in the high-latitude ionosphere are deduced by combining satellite and radar measurements of the ionospheric drift velocity, along with ground-based magnetometer observations for October 25, 1981. The period under study was characterized by a relatively stable southward interplanetary magnetic field (IMF), so that the obtained electric field patterns do reflect, in general, the state of sustained and enhanced plasma convection in the magnetosphere. During one of the satellite passes, however, an intense westward electrojet caused by a substorm intruded into the satellite (DE2) and radar (Chatanika, Alaska) field of view in the premidnight sector, providing a unique opportunity to differentiate the enhanced convection and substorm expansion fields. The distributions of the calculated electric potential for the expansion and maximum phases of the substorm show the first clear evidence of the coexistence of two physically different systems in the global convection pattern. The changes in the convection pattern during the substorm indicate that the large-scale potential distributions are indeed of general two-cell patterns representing the southward IMF status, but the night-morning cell has two positive peaks, one in the midnight sector and the other in the late morning hours, corresponding to the substorm expansion and the convection enhancement, respectively.

Kamide, Y.↗

A comparative study of solute trapping in Fe-(33–45 at%) Cu alloys manufactured by laser directed energy deposition

The high cooling rates in laser directed energy deposition (DED-LB) of alloys lead to substantial amounts of solute trapping as solute atoms cannot diffuse away from the solid/liquid interface before it advances. In some concentrated alloys, this results in supersaturated solid phases that form nanoscale hierarchical microstructures when the solute atoms precipitate out during reheating from subsequent laser passes. We choose the Iron-Copper (Fe-Cu) binary alloy as model system as it is chemically homogeneous in the liquid phase and has negligible solid solubility at room temperature. Two alloys with nominal compositions in atomic (at.) %, Fe67Cu33 and Fe55Cu45, were manufactured using DED-LB. Scanning transmission electron microscopy (STEM), energy dispersive spectroscopy (EDS) and wavelength dispersive spectroscopy (WDS) were used to characterize the nanostructures and heterogeneous chemical compositions. A non-equilibrium solute partitioning model was used to compute the supersaturated chemistries of the constituent phases and validated with experimentally measured compositions. The measured phase compositions of the two alloys were very similar, at roughly 12 at.% Cu and 4 at.% Fe in the α(bcc)-Fe and ε(fcc)-Cu phases respectively, despite having different processing parameters and mechanical behavior. This indicates that the total thermal history, that depends on both the processing parameters and laser scan pattern, plays a stronger role on the final microstructure evolution than just the initial quantity of trapped solute. In addition, we find that current non-equilibrium solute partitioning models applied on the continuum scale fall short of predicting accurate quantitative phase compositions in concentrated alloys, although the qualitative trends are captured correctly.

36 MATERIALS SCIENCE↗

Efficient use of bit planes in the generation of motion stimuli

The production of animated motion sequences on computer-controlled display systems presents a technical problem because large images cannot be transferred from disk storage to image memory at conventional frame rates. A technique is described in which a single base image can be used to generate a broad class of motion stimuli without the need for such memory transfers. This technique was applied to the generation of drifting sine-wave gratings (and by extension, sine wave plaids). For each drifting grating, sine and cosine spatial phase components are first reduced to 1 bit/pixel using a digital halftoning technique. The resulting pairs of 1-bit images are then loaded into pairs of bit planes of the display memory. To animate the patterns, the display hardware's color lookup table is modified on a frame-by-frame basis; for each frame the lookup table is set to display a weighted sum of the spatial sine and cosine phase components. Because the contrasts and temporal frequencies of the various components are mutually independent in each frame, the sine and cosine components can be counterphase modulated in temporal quadrature, yielding a single drifting grating. Using additional bit planes, multiple drifting gratings can be combined to form sine-wave plaid patterns. A large number of resultant plaid motions can be produced from a single image file because the temporal frequencies of all the components can be varied independently. For a graphics device having 8 bits/pixel, up to four drifting gratings may be combined, each having independently variable contrast and speed.

Mulligan, Jeffrey B.↗

Timing based clustering of childhood BMI trajectories reveals differential maturational patterns; Study in the Northern Finland Birth Cohorts 1966 and 1986

Children’s biological age does not always correspond to their chronological age. In the case of BMI trajectories, this can appear as phase variation, which can be seen as shift, stretch, or shrinking between trajectories. With maturation thought of as a process moving towards the final state - adult BMI, we assessed whether children can be divided into latent groups reflecting similar maturational age of BMI. The groups were characterised by early factors and time-related features of the trajectories. We used data from two general population birth cohort studies, Northern Finland Birth Cohorts 1966 and 1986 (NFBC1966 and NFBC1986). Height (n = 6329) and weight (n = 6568) measurements were interpolated in 34 shared time points using B-splines, and BMI values were calculated between 3 months to 16 years. Pairwise phase distances of 2999 females and 3163 males were used as a similarity measure in k-medoids clustering. We identified three clusters of trajectories in females and males (Type 1: females, n = 1566, males, n = 1669; Type 2: females, n = 1028, males, n = 973; Type 3: females, n = 405, males, n = 521). Similar distinct timing patterns were identified in males and females. The clusters did not differ by sex, or early growth determinants studied. Trajectory cluster Type 1 reflected to the shape of what is typically illustrated as the childhood BMI trajectory in literature. However, the other two have not been identified previously. Type 2 pattern was more common in the NFBC1966 suggesting a generational shift in BMI maturational patterns.

60 APPLIED LIFE SCIENCES↗

Low-Cost Phased Array Antenna for Sounding Rockets, Missiles, and Expendable Launch Vehicles

A low-cost beamformer phased array antenna has been developed for expendable launch vehicles, rockets, and missiles. It utilizes a conformal array antenna of ring or individual radiators (design varies depending on application) that is designed to be fed by the recently developed hybrid electrical/mechanical (vendor-supplied) phased array beamformer. The combination of these new array antennas and the hybrid beamformer results in a conformal phased array antenna that has significantly higher gain than traditional omni antennas, and costs an order of magnitude or more less than traditional phased array designs. Existing omnidirectional antennas for sounding rockets, missiles, and expendable launch vehicles (ELVs) do not have sufficient gain to support the required communication data rates via the space network. Missiles and smaller ELVs are often stabilized in flight by a fast (i.e. 4 Hz) roll rate. This fast roll rate, combined with vehicle attitude changes, greatly increases the complexity of the high-gain antenna beam-tracking problem. Phased arrays for larger ELVs with roll control are prohibitively expensive. Prior techniques involved a traditional fully electronic phased array solution, combined with highly complex and very fast inertial measurement unit phased array beamformers. The functional operation of this phased array is substantially different from traditional phased arrays in that it uses a hybrid electrical/mechanical beamformer that creates the relative time delays for steering the antenna beam via a small physical movement of variable delay lines. This movement is controlled via an innovative antenna control unit that accesses an internal measurement unit for vehicle attitude information, computes a beam-pointing angle to the target, then points the beam via a stepper motor controller. The stepper motor on the beamformer controls the beamformer variable delay lines that apply the appropriate time delays to the individual array elements to properly steer the beam. The array of phased ring radiators is unique in that it provides improved gain for a small rocket or missile that uses spin stabilization for stability. The antenna pattern created is symmetric about the roll axis (like an omnidirectional wraparound), and is thus capable of providing continuous coverage that is compatible with very fast spinning rockets. For larger ELVs with roll control, a linear array of elements can be used for the 1D scanned beamformer and phased array, or a 2D scanned beamformer can be used with an NxN element array.

Mullinix, Daniel↗

Building a Framework to Understand Transition Metals' Behavior in Euxinic Conditions (Final Technical Report)

This project focuses first and foremost on metal sulfide geochemistry and mineralogy as controlled by a complex matrix of environmental factors. The principal investigator’s group aim to illuminate the metal-sulfide reaction mechanisms, rates, and pathways through systematic experimentation and data collection and analyzing the relationships between the characteristics of the produced metal sulfide solid-phase/aqueous complexes and the environmental factors. This understanding is essential for obtaining a full picture of the complex cycling patterns of single or multi metal species in sulfidic environments ranging from deep-see basins, hydrothermal vents, inland seas, terrestrial water bodies, to engineered remediation systems. The specific goal of this past project was to illuminate the reaction mechanisms and kinetics of metal anions and sulfide in mixed metal cation-metal anion-sulfide systems under various aqueous conditions (which resembled a range of naturally occurring euxinic settings). For the period of this contract, we investigated the molybdenum-iron-sulfide system, with an emphasis on the conditions that caused solid phase formation. We focused on quantifying the mobility/sequestration of molybdenum under each experimental condition and identified the changes of valence states for each involved element (i.e., Mo, Fe, and S) in the precipitate. We also proposed pathways for the electron transfer that occurred in aqueous chemistry. The major analytical tools used for this study include UV-visible light spectroscopy, transmission electron microscopy, X-ray photoelectron spectroscopy, and synchrotron-based X-ray absorption spectroscopy (access gained through facility proposals to the Canadian Light Source). The biggest finding of this project was that besides pH, the iron-sulfur chemistry has a dominant control of the thiolation kinetics and subsequent reduction of Mo(VI), which are likely prerequisites of molybdenum sequestration in anoxic conditions. The results have been written up as manuscript by the end of this project (see Phillips et al.). The experimental results of this project may be critical for advancing our understanding of (1) basic chemistry involving transition metals and reduced sulfur species, (2) the validity of certain geochemical proxies, and (3) the stability and evolution of euxinic geochemical environments. It is noted that the basic results obtained through this project also have implications for Mo-S cluster-based catalyst development in inorganic chemistry and materials sciences.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cecropin P1 antimicrobial peptide modulates differential expression of immune relevant genes in rainbow trout ( Oncorhynchus mykiss ) gill cell line, RTgill-W1

Accumulated evidence indicates that antimicrobial peptides modulate immune activities in fish. In this study, we profiled the differential expression patterns of representative immune relevant genes in an epithelial-like cell line of rainbow trout gill, RTgill-W1, in response to exposure of cecropin P1 antimicrobial peptide. RTgill-W1 cells were treated with synthetic cecropin P1 over time (0, 2, 4 and 24 h) with or without the present of lipopolysaccharide (LPS) or polyinosinic polycytidylic acid (PolyI:C). The relative abundances of each mRNA were measured by real-time quantitative PCR. The dose-response study revealed significant perturbations of mRNA levels of genes related to pro-inflammation, acute phase, surface proteins and transcription factors at 30 μM of cecropin P1. In addition, cecropin P1 altered the differential expression patterns that were induced by LPS or PolyI:C, at different time points in RTgill-W1. Overall, our results indicate that cecropin P1 exhibits pro-inflammation activity, modulate cell-cell interaction and cytokine signal transduction in rainbow trout gill cell, and may suggest a potential application of this peptide as an immune adjuvant for disease control in aquaculture.

59 BASIC BIOLOGICAL SCIENCES↗

Response of Global Lightning Activity Observed by the TRMM/LIS During Warm and Cold ENSO Phases

This paper investigates the response of global lightning activity to the transition from the warm (January February March-JFM 1998) to the cold (JFM 1999) ENSO phase. The nine-year global lightning climatology for these months from the Tropical Rainfall Measuring Mission (TRMM) Lightning Imaging Sensor (LIS) provides the observational baseline. Flash rate density is computed on a 5.0x5.0 degree lat/lon grid within the LIS coverage area (between approx.37.5 N and S) for each three month period. The flash rate density anomalies from this climatology are examined for these months in 1998 and 1999. The observed lightning anomalies spatially match the documented general circulation features that accompany the warm and cold ENSO events. During the warm ENSO phase the dominant positive lightning anomalies are located mostly over the Western Hemisphere and more specifically over Gulf of Mexico, Caribbean and Northern Mid-Atlantic. We further investigate specifically the Northern Mid-Atlantic related anomaly features since these show strong relation to the North Atlantic Oscillation (NAO). Furthermore these observed anomaly patterns show strong spatial agreement with anomalous upper level (200 mb) cold core cyclonic circulations. Positive sea surface temperature anomalies during the warm ENSO phase also affect the lightning activity, but this is mostly observed near coastal environments. Over the open tropical oceans, there is climatologically less lightning and the anomalies are less pronounced. Warm ENSO related anomalies over the Eastern Hemisphere are most prominent over the South China coast. The transition to the cold ENSO phase illustrates the detected lightning anomalies to be more pronounced over East and West Pacific. A comparison of total global lightning between warm and cold ENSO phase reveals no significant difference, although prominent regional anomalies are located over mostly oceanic environments. All three tropical "chimneys" (Maritime Continent, Central Africa, and Amazon Basin) do not show any particular response to this transition.

Chronis, Themis G.↗

Wettability and capillary effects: Dynamics of pinch-off in unconstricted straight capillary tubes

We study the interfacial evolution of immiscible two-phase flow within a capillary tube in the partial wetting regime using direct numerical simulation. We investigate the flow patterns resulting from the displacement of a more viscous fluid by a less viscous one under a wide range of wettability conditions. We find that beyond a wettability dependent critical capillary number, a uniform displacement by a less viscous fluid can transition into a growing finger that eventually breaks up into discrete blobs by a series of pinch-off events for both wetting and non-wetting contact angles. This study validates previous experimental observations of pinch-off for wetting contact angles and extends those to non-wetting contact angles. We find that the blob length increases with the capillary number. We observe that the time between consecutive pinch-off events decreases with the capillary number and is greater for more wetting conditions in the displaced phase. Here, we further show that the blob separation distance as a function of the difference between the inlet velocity and the contact line speed collapses into two monotonically decreasing curves for wetting and non-wetting contact angles. For the phase separation in the form of pinch-off, this work provides a quantitative study of the emerging length and time scales and their dependence on the wettability conditions, capillary effects, and viscous forces.

42 ENGINEERING↗

Laser diagnostics for microgravity droplet studies

Rapid advances have recently been made in numerical simulation of droplet combustion under microgravity conditions, while experimental capabilities remain relatively primitive. Calculations can now provide detailed information on mass and energy transport, complex gas-phase chemistry, multi-component molecular diffusion, surface evaporation and heterogeneous reaction, which provides a clearer picture of both quasi-steady as well as dynamic behavior of droplet combustion. Experiments concerning these phenomena typically result in pictures of the burning droplets, and the data therefrom describe droplet surface regression along with flame and soot shell position. With much more precise, detailed, experimental diagnostics, significant gains could be made on the dynamics and flame structural changes which occur during droplet combustion. Since microgravity experiments become increasingly more expensive as they progress from drop towers and flights to spaceborne experiments, there is a great need to maximize the information content from these experiments. Sophisticated measurements using laser diagnostics on individual droplets and combustion phenomena are now possible. These include measuring flow patterns and temperature fields within droplets, vaporization rates and vaporization enhancement, radical species profiling in flames and gas-phase flow-tagging velocimetry. Although these measurements are sophisticated, they have undergone maturation to the degree where with some development, they are applicable to studies of microgravity droplet combustion. This program beginning in September of 1992, will include a series of measurements in the NASA Learjet, KC-135 and Drop Tower facilities for investigating the range of applicability of these diagnostics while generating and providing fundamental data to ongoing NASA research programs in this area. This program is being conducted in collaboration with other microgravity investigators and is aimed toward supplementing their experimental efforts.

Winter, Michael↗

Improved Refractometer for Measuring Temperatures of Drops

The Dual Rainbow refractometer is an enhanced version of the Rainbow refractometer, which is added to, and extends the capabilities of, a phase Doppler particle analyzer (PDPA). A PDPA utilizes pairs of laser beams to measure individual components of velocity and sizes of drops in a spray. The Rainbow-refractometer addition measures the temperatures of individual drops. The designs of prior versions of the Rainbow refractometer have required substantial modifications of PDPA transmitting optics, plus dedicated lasers as sources of illumination separate from, and in addition to, those needed for PDPA measurements. The enhancement embodied in the Dual Rainbow refractometer eliminates the need for a dedicated laser and confers other advantages as described below. A dedicated laser is no longer needed because the Dual Rainbow refractometer utilizes one of the pairs of laser beams already present in a PDPA. Hence, the design of the Dual Rainbow refractometer simplifies the task of upgrading PDPA hardware to enable measurement of temperature. Furthermore, in a PDPA/Dual Rainbow refractometer system, a single argon-ion laser with three main wavelengths can be used to measure the temperatures, sizes, and all three components of velocity (in contradistinction to only two components of velocity in a prior PDPA/Rainbow refractometer system). In order to enable the Dual Rainbow refractometer to utilize a pair of PDPA laser beams, it was necessary to (1) find a location for the refractometer receiver, such that the combined rainbow patterns of two laser beams amount to a pattern identical to that of a single beam, (2) adjust the polarization of the two beams to obtain the strongest rainbow pattern, and (3) find a location for the PDPA receiver to obtain a linear relationship between the measured phase shift and drop size.

Naqwi, Amir A.↗

Modeling NASA’s Procedural Requirement Processes - Implications for Digital Future

The National Aeronautics and Space Administration (NASA) has an ongoing Digital Transformation effort and to leverage and showcase the power of Digital Transformation, an effort is underway to develop an integrated, datacentric, model representing NASA’s key process requirements. The task was divided into three phases: As Is modeling, Analysis, and To Be Planning. As part of this effort, a team has completed the first Phase I of the modeling task and is nearing completion of the second phase. This effort will capture the key elements as requirements, responsibilities, allocations, roles, products, and associated lifecycle elements. The scope of modeling included NASA’s NPR 7120.5 (Project and Program Management), NPR 7123.1 (Systems Engineering) and NPRs 8705.2 (Risk classification for Robotic Missions) and 8705.4 (Human-Rating Requirements for Space Missions). This paper will summarize the approach, scope, parsing patterns applied, metamodel, and associated workflows for the As-Is modeling. It will also summarize the results and insights gleaned during that phase, including the review process. These insights have informed the analysis and will be discussed. The analysis modeling phase will also be summarized including how the stakeholders were engaged, how the common elements were handled and dispositioned, and will also describe some of the plans for the future of NASA NPDs and NPRs.

Systems Engineering↗

High-precision phase control of an optical lattice with up to 50 dB noise suppression

An optical lattice is a periodic light crystal constructed from the standing-wave interference patterns of laser beams. It can be used to store and manipulate quantum degenerate atoms and is an ideal platform for the quantum simulation of many-body physics. A principal feature is that optical lattices are flexible and possess a variety of multidimensional geometries with modifiable band structure. An even richer landscape emerges when control functions can be applied to the lattice by modulation of the position or amplitude with Floquet driving. However, the desire of realizing high-modulation bandwidths while preserving extreme lattice stability has been difficult to achieve. In this paper, we demonstrate an effective solution that consists of overlapping two counterpropagating lattice beams and controlling the phase and intensity of each with independent acousto-optic modulators. Our phase controller mixes sampled light from both lattice beams with a common optical reference. This dual heterodyne locking method allows exquisite determination of the lattice position, while also removing parasitic phase noise accrued as the beams travel along separate paths. Here, we report up to 50 dB suppression in lattice phase noise in the 0.1–1 Hz band, along with significant suppression spanning more than 4 decades of frequency. The absolute phase diffusion of the lattice position is only 10 Å when integrated over 10 s. This method permits precise, high-bandwidth modulation (greater than 50 kHz) of the optical lattice intensity and phase. We demonstrate the efficacy of this approach by executing intricate time-varying phase profiles for atom interferometry.

Atom interferometry↗

Interference in astronomical speckle patterns

Astronomical speckle patterns are examined in an atmospheric-optics context in order to determine what kind of image quality is to be expected from several different imaging techniques. The model used to describe the instantaneous complex field distribution across the pupil of a large telescope regards the pupil as a deep phase grating with a periodicity given by the size of the cell of uniform phase or the refractive index structure function. This model is used along with an empirical formula derived purely from the physical appearance of the speckle patterns to discuss the orders of interference in astronomical speckle patterns.

Breckinridge, J. B.↗