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NASA NTRS2018

Norton-Thevenin Receptance Coupling (NTRC) as a Payload Analysis Tool

The NASA Engineering and Safety Center (NESC) has funded a study of a new method formulated by NASA Engineers called Norton-Thevenin Receptance Coupling (NTRC) to perform coupled loads analysis (CLA). The problem that NTRC attempts to solve is the dependency of the payload organization to high CLA costs, long schedules, lack of standard capabilities to evaluate multiple configurations and unavailability of loads when needed. NTRC solves the problem by providing a tool that payload developers can use to obtain loads at a fraction of the cost of a CLA at any time that it is required. While NTRC is not intended to replace the formal load cycles performed by the launch vehicle (LV) provider, it will provide the ability to reduce the conservatism in defining preliminary design loads, assess the impact of design changes between formal load cycles, perform trade studies and perform parametric loads analysis where many different design configurations can be evaluated with a minimum amount of data required from the LV provider. NTRC condenses all the necessary information into the launch vehicle to payload/s connection points or boundary degrees of freedom (BD). The launch vehicle model is represented by its impedance at its BDs; its forcing functions are represented by the acceleration at those BDs when the payload is absent and the latter is represented by its impedance at the same BDs. Payload responses are represented by transfer functions of selected response to interface BDs. The methodology has contributed to the Loads and Dynamics discipline advancement and successfully passed Peer Reviews. NTRC is exact in the frequency domain. Time domain replication and accuracy is outstanding. A second phase is envisioned to benchmark the whole set of CLA events for the Agency's most utilized Launch Vehicles, and ready it for operational deployment at NASA.

Kaufman, Daniel↗

NASA NTRS2018

Coupled Radiative Thermal and Nonlinear Stress Analysis for Thermal Deformation in Large Space Structures

Large space structures are capable of large thermal deformations in the space environment. A case of large-scale thermal deformation was observed in the analysis of the Near Earth Asteroid Scout solar sail, with predicted tip displacements of more than one meter in seven-meter booms. Experimental data supports the broad conclusions of the analysis, but shows poor agreement on the details of the thermal deformation. Prediction that is precise enough to drive engineering decisions will require coupled thermal-stress analysis with features that are not found in current multiphysics codes. This paper describes a simple method for stepwise coupling between commercial nonlinear stress analysis software and radiative thermal analysis software. Results are presented for a round stainless steel tube, which is a common case in existing literature.

Stohlman, Olive R.↗

NASA NTRS2017

A Path to High Efficiency Optical Coupling for HIRMES

The high-resolution mid-infrared spectrometer (HIRMES) under development for SOFIA (Stratospheric Observatory for Infrared Astronomy) is an instrument operating in the 25-122 μm spectral range with a spectral resolution R= Δ ʎ /ʎ ~100,000 and has two absorber-coupled transition edge sensor (TES) bolometric detector focal planes. We have developed novel NbTiN low stress absorber coatings which have the required optical impedance across the HIRMES operating band. The low intrinsic stress of these coatings allow for a peak-to-valley corrugation amplitude < 5 μm of the 450 nm thick, 1.4 mm x 1.7 mm detector pixels. Furthermore, these coatings have a superconducting transition temperature ~ 10 K, which allows them to simultaneously serve as an absorber in the desired signal band and a rejection filter at long wavelengths. This attribute makes them especially attractive for ultrasensitive absorber-coupled bolometric detector applications, because it helps in controlling the optical loading from out-of band radiation. We also discuss a novel method for integrating a wedged reflective absorber-termination to the detector array.

bolometers↗

NASA NTRS2018

The SMAP Level-4 ECO Project: Improving Terrestrial Flux Estimates Through Coupled Hydrology-Vegetation Data Assimilation

Simulations of hydrologic and vegetation states as well as water, energy and carbon fluxes from the land surface to the atmosphere are crucial for a wide range of applications, including agricultural advisories, forecasts of (short-term) atmospheric behavior and seasonal weather predictions including forecasts of extreme events, such as heatwaves or droughts. The NASA Soil Moisture Active Passive (SMAP) mission Level-4 Eco-Hydrology (L4-ECO) project aims to improve modeled estimates of the terrestrial water, energy and carbon fluxes and states by developing a fully-coupled hydrology-vegetation data assimilation system. This system is developed around the NASA Goddard Earth Observing System (GEOS) Catchment-CN land surface model, which combines land hydrology and energy balance components of the GEOS Catchment model with dynamic vegetation components of the Community Land Model version 4. Catchment-CN fully couples the terrestrial water, energy and carbon cycles, allowing feedbacks from the land hydrology to the biosphere and vice versa.Here, we implement a calibration of the Catchment-CN vegetation parameterization against observations of the fraction of absorbed photosynthetically active radiation (FPAR) from the Moderate Resolution Imaging Spectroradiometer (MODIS) to improve the model's standalone skill. Later, the DA algorithm used to produce the SMAP L4 soil moisture product will be adapted to Catchment-CN to assimilate SMAP brightness temperatures and inform the model's land hydrology component. Finally, the DA system will be further extended to assimilate MODIS FPAR observations in order to constrain the model's dynamic vegetation component.In this presentation, we demonstrate that the Catchment-CN parameter calibration leads to more realistic vegetation simulations and reduces the root mean squared error between modeled and observed vegetation states across the model's various plant functional types. We also show that the assimilation of SMAP observations is able to improve the average correlation, bias and unbiased RMSE between the modeled surface and root zone soil moisture estimates, and ground observations from the SMAP core validation sites.

Kolassa, Jana↗

NASA NTRS2018

Coupled Thermomechanical Micromechanics Modeling of the Influence of Thermally Grown Oxide Layer in an Environmental Barrier Coating System

Environmental Barrier Coatings (EBCs) have emerged as a promising means of protecting critical components for high temperature applications (e.g., aircraft engines). EBCs are often used to protect an underlying material (substrate) from extreme thermal/chemical environments. However, systems that utilize EBCs are susceptible to a number of failure modes including oxidation/delamination. Environmental Barrier Coatings (EBCs) have emerged as a promising means of protecting silicon based ceramic matrix composite (CMC) components for high temperature applications (e.g., aircraft engines). EBCs are often used to protect an underlying material (substrate) such as silicon carbide from extreme thermal/chemical environments. In a typical CMC/EBC system, an EBC may or may not be adhered to an underlying substrate with a bond coat (e.g., silicon). Irrespective, systems that utilize EBCs are susceptible to a number of failure modes including oxidation/delamination, recession, chemical attack and dissolution, thermo-mechanical degradation, erosion, and foreign object damage. Current work at NASA Glenn Research Center is aimed at addressing these failure modes in EBC systems and developing robust analysis tools to aid in the design process. The Higher-Order Theory for Functionally Graded Materials (HOTFGM), a precursor to the High-Fidelity Generalized Method of Cells micromechanics approach, was developed to investigate the coupled thermo-mechanical behavior of functionally graded composites and will be used herein to assess the development and growth of a low-stiffness thermally grown oxide (TGO) layer in EBC/CMC systems without a silicon bond coat. To accomplish this a sensitivity study is conducted to examine the influence of uniformly and non-uniformly grown oxide layer on the associated driving forces leading to mechanical failure (spallation) of EBC layer when subjected to isothermal loading, recession, chemical attack and dissolution, thermomechanical degradation, erosion, and foreign object damage. Current work at NASA Glenn Research Center is aimed at addressing these failure modes in EBC systems and developing robust analysis tools to aid in the design process. The Higher-Order Theory for Functionally Graded Materials (HOTFGM), a precursor to the High-Fidelity Generalized Method of Cells micromechanics approach, was developed to investigate the coupled thermo-mechanical behavior of functionally graded composites (Aboudi et al., 1999, Composites B). For example, HOTFGM was previously used (Arnold et al, 1995, NASA CP 10178, paper 34), to assess interlaminar stresses (including free edge effects) in a substrate with a thermal barrier coating (TBC). In this study, HOTFGM micromechanics analyses will be used to assess the development and growth of a low-stiffness thermally grown oxide (TGO) layer between a silicon carbide substrate and a ytterbium disilicate EBC. In order to realistically simulate TGO growth, an evolution law will be incorporated into HOTFGM. In addition, the effect of TGO roughness will be explored consistent with previous TBC work (Pindera et al., 2000. Material Science and Engineering, A284, pp. 158-175). This model represents a first step in developing a robust analysis tool that can ultimately be used to design durable EBC systems. Additional failure modes will be considered as part of a future work.

environmental barrier coating↗

NASA NTRS2019

Optimizing a Coupled Solution for the Orion MPCV Using DPLR and NEQAIR

The goal of this project is to study the convective and radiative heat flux predictions using computational fluid dynamics (CFD) on a smooth body representation of the NASA Orion Multi-Purpose Crew Vehicle (MPCV). The Orion MPCV is designed for long duration missions in space and will play a crucial role in transporting astronauts in the upcoming Artemis missions. With Orion's aim for cost-effective reusability comes a need to study its Thermal Protection System (TPS), which allows for safe entry into the atmospheres of the Earth, Moon, and Mars. In order to study the effects of the TPS on test flights and better understand the aerothermal environment, CFD is a necessary tool used to create simulations of entry vehicles and calculate the heat load and heat flux. However, solutions are often performed using an uncoupled approach between the flow and the radiation solver. This leads to an overestimation of the overall heating effects because they do not consider radiative cooling. Furthermore, the effects of radiation on the aft-body is an area of research with significant uncertainty. Through the use of codes developed at NASA Ames, DPLR and NEQAIR, a coupled solution can be attained for the Orion capsule which will more accurately solve for the effects of radiation in both the fore and aft-body regions. This yields more accurate design margins for the TPS, which produces a better estimate of the thickness required. By developing an accurate coupled solution of the TPS on the Orion MPCV, planners will have greater flexibility in carrying out future missions to the Moon and beyond.

Design↗

NASA NTRS2019

Evolving HPC and Application Design Toward a Coupled Data Assimilation System at NASA Suitable for Emerging Exascale Platforms

The prediction capabilities of global models have continuously evolved from the traditional medium-range global weather prediction application to span scales in support of hourly prediction of convective scale storms to seasonal Earth system prediction. This evolution has increased the demands on the system infrastructure design and workflow to achieve the required performance on modern high-performance computing (HPC) platforms. The planned evolution of the Goddard Earth Observing System (GEOS) modeling and assimilation system will stress the capabilities of conventional HPC overwhelming the available compute cycles at the NASA Center for Climate Simulation (NCCS) at the NASA Goddard Space Flight Center in the coming 5-10 years. This has led to the re-design of key elements of the assimilation and modeling systems to achieve significant gains in performance on anticipated Exacale platforms. The transition of the assimilation system to the Joint Effort for Data assimilation Integration (JEDI) framework has positioned GEOS to exploit new efficient algorithms for data assimilation (DA) in a fully-coupled Earth system context. The suitability of the GEOS model to leverage a domain specific language (DSL) approach and artificial intelligence (AI) is being explored to accelerate computational performance and data exchange efficiency of the coupled Earth system model. The storage and processing of large data volumes produced by these advance systems is being redesigned with a data-centric cloud-based approach. We will highlight the recent efforts in these areas and emphasize the demand for further development and re-design to achieve the science objectives in support of NASA's Earth system modeling and assimilation missions.

Putman, Bill↗

NASA NTRS2019

Fully-Coupled Fluid-Structure Interaction Simulations of a Supersonic Parachute

A validated computational fluid-structure interaction method for simulating the complex interaction between the large deformation of very thin, highly deformable structures and compressible flows is extended to consider large-scale problems in supersonic flows using parallel computing. The coupled fluid-structure interaction system is solved in a partitioned, or weakly-coupled, manner. The foundations of the applied fluid-structure interaction method are a higher-order, block-structured Cartesian, sharp immersed boundary method for the compressible Navier-Stokes equations and a computational structural dynamics solver employing a geometrically nonlinear 3-node shell element based on the mixed interpolation of tensorial components formulation. The method is applied to large deformation fluid-structure interaction validation cases before being applied to the inflation of a supersonic parachute in the upper Martian atmosphere where the goal is to demonstrate the capabilities of the solver when considering large-scale problems in supersonic flows.

Boustani, Jonathan↗

NASA NTRS2019

Assessment of Satellite Sea Surface Salinity Products Using a Coupled ENSO Prediction Model

Much work has gone into revising and updating algorithms for converting satellite-measured radiances to useful ocean variables like sea surface salinity (e.g. SMOS - Boutin et al., 2017, SMAP - Fore et al., 2016 and Aquarius - Meissner et al., 2018). As part of our Ocean Salinity Science Team work, we utilize an intermediate-complexity air/sea coupled model as a transfer function to test if more mature satellite SSS model algorithms actually improve ENSO forecast skill. For initialization of the coupled forecast, we demonstrate that the positive impact of SSS assimilation is brought about by surface freshening near the eastern edge of the western Pacific warm pool and density changes that lead to shallower mixed layer between 10S-5N. In addition, salting near the ITCZ leads to a deepening of the mixed layer and thermocline near 8N. These patterns together provide the background state to amplify equatorial Kelvin waves and improve ENSO hindcasts (Hackert et al., 2019). Here we extend this work to compare the impact of various pairs of original and improved satellite SSS algorithms. For instance we compare SMAP V4.1 with the latest, SMAP V4.2, to see what impact algorithm improvements may have on ENSO forecasts. SSS observations are tested on seasonal to interannual variability of tropical Indo-Pacific Ocean dynamics as well as on dynamical ENSO forecasts by initializing twelve-month forecasts for each month of available data. All experiments assimilate satellite sea level (SL), sea surface temperature (SST), and in situ subsurface temperature and salinity observations (Tz, Sz). Additionally various satellite, blended, and in-situ SSS products are assimilated. We find that including satellite SSS significantly improves NiÃ±o3.4 sea surface temperature anomaly validation, more mature SSS model algorithms are generally improving ENSO forecasts over time, and more satellite SSS data coverage helps to extend useful forecasts.

Ocean↗

NASA NTRS2019

MERRA-2 Ocean: The NASA Global Modeling and Assimilation Office's Weakly Coupled Atmosphere-Ocean Reanalysis Using GEOS-S2S Version 3

The NASA Modern Era Reanalysis for Research and Applications (MERRA2) has been a respected and widely used reanalysis that has so far been restricted to the atmosphere. Now a newly released version of the atmosphere/ocean coupled data assimilation system (AODAS) has been developed by the NASA/Goddard Global Modeling and Assimilation Office to perform a retrospective ocean reanalysis from 1982 to present. In addition to assimilating all available in situ data (e.g. Argo, mooring, XBT and CTD data) and altimetry information into the ocean, the new version (GEOS-S2S Version 3) model includes a higher resolution, eddy-permitting ocean model than previous versions, a more realistic implementation of the atmosphere-ocean interface layer, and an improved coupling between glacier and ocean (among other improvements). In addition, this ocean data assimilation was expanded to include the assimilation of satellite sea surface salinity. The MERRA-2 AODAS will be described, and preliminary results will be shown from the assimilation reanalysis and from retrospective forecasts issued using a new ensemble strategy. Following the Global Ocean Data Assimilation Experiment (GODAE) protocols, we will present Class 1 through Class 4 validation results from the ocean reanalysis. Results indicate an improved ocean mixed layer depth, improved salinity near Greenland, an improved diurnal cycle of the sea surface skin temperature, an improved estimate of ocean evaporation, and better representation of western boundary currents (e.g. Gulf Stream) from our new ocean reanalysis. One of the motivations of this project is to provide optimal initial states for ENSO forecasting. Therefore, we will also present some preliminary results of retrospective ENSO forecasts. After thorough testing, it is expected that the GEOS-S2S Version 3 will replace our contributions to North American Multi-Model Ensemble (NMME), WCRP Subseasonal to Seasonal (S2S), and IRI seasonal prediction forecast projects.

Molod, Andrea↗

NASA NTRS2020

Modeling and Control of Robot-Structure Coupling During In-Space Structure Assembly

This paper considers the problem of robot-structure coupling dynamics during in-space robotic assembly of large flexible structures. A two-legged walking robot is used as a construction agent, whose primary goal is to stably walking on the flexible structure while carrying a substructure component to a designated location. The reaction forces inserted by the structure to the walking robot are treated as bounded disturbance inputs, and a trajectory tracking robotic controller is proposed that combines the standard full state feedback motion controller and an adaptive controller to account for the disturbance inputs. In this study, a reduced-order Euler-Bernoulli beam structure model is adapted, and a finite number of co-located sensors and actuators are distributed along the span of the beam structure. The robot-structure coupling forces are treated as a bounded external forcing function to the structure, and hence an output covariance constraint problem can be formulated, in terms of linear matrix inequality, for optimal structure control by utilizing the direct output feedback controllers. The numerical simulations show the effectiveness of the proposed robot-structure modeling and control methodology.

Swei, Sean↗

NASA NTRS2020

A Coupled Analysis of Atmospheric Mass Loss and Tidal Evolution in XUV Irradiated Exoplanets: The TRAPPIST-1 Case Study

Exoplanets residing close to their stars can experience evolution of both their physical structures and their orbits due to the influence of their host stars. In this work, we present a coupled analysis of dynamical tidal dissipation and atmospheric mass loss for exoplanets in X-ray and ultraviolet (XUV) irradiated environments. As our primary application, we use this model to study the TRAPPIST-1 system and place constraints on the interior structure and orbital evolution of the planets. We start by reporting on an ultraviolet continuum flux measurement (centered around ∼1900 Å) for the star TRAPPIST-1, based on 300 ks of Neil Gehrels Swift Observatory data, and which enables an estimate of the XUV-driven thermal escape arising from XUV photodissociation for each planet. We find that the X-ray flaring luminosity, measured from our X-ray detections, of TRAPPIST-1 is 5.6 × 10(exp −4) L(*), while the full flux including non-flaring periods is 6.1 × 10(exp −5) L*, when L(*) is TRAPPIST-1ʼs bolometric luminosity. We then construct a model that includes both atmospheric mass loss and tidal evolution and requires the planets to attain their present-day orbital elements during this coupled evolution. We use this model to constrain the ratio Q' = 3Q/2k2 for each planet. Finally, we use additional numerical models implemented with the Virtual Planet Simulator VPLanet to study ocean retention for these planets using our derived system parameters.

Juliette Becker↗

NASA NTRSDate not supplied

Autonomous Measurement of Electrochemical Redox Couples for In-Situ Characterization of Enceladus Plume Samples

A 3D-printed microfluidic electrochemical cell with integrated electrodes was developed to demonstrate autonomous in-situ electrochemical characterization of terrestrial seawater samples. The system is designed to extend the capabilities of the 2008 Phoenix Lander’s Wet Chemistry Laboratory (WCL) that analyzed the soluble chemistry of the Martian soil, by miniaturizing its fluidic architecture for analysis of µL-volume samples as expected from an Enceladus fly-by mission. The microfluidic device has a total fluid volume of 48 µL and includes dual channels each populated with 7 electrodes. Measurement of pH was measured using an iridium oxide electrode. Cyclic voltammetry with Au, Pt, and glassy carbon working electrodes was used to measure redox couples in synthetic seawater that contained inorganic and bio-organic molecules. Glassy carbon was found to have minimal risk of interference from constituents of synthetic seawater when measuring molecular organic redox species; however, care must be used to prevent interference due to potential oxidation or dissolution in the case of Au working electrodes. A completely autonomous end-to-end run including sample delivery was performed, to demonstrate the feasibility of microfluidic-based cyclic voltammetry measurements for in-situ characterization of redox couples in Ocean World samples.

Planetary Instruments↗

NASA NTRS2020

Soil Evaporation Stress Determines Soil Moisture‐Evapotranspiration Coupling Strength in Land Surface Modeling

Model‐based estimates of soil moisture (SM)‐evapotranspiration (ET) coupling strength(ρ) vary widely and are prone to bias. Here we apply numerical modeling and remote sensing to identify the process‐level source of modeledρbias with the goal of improving the fidelity of current Earth system models. Results illustrate that modeledρis most strongly determined by soil evaporation (E) stress, and (generally positive)ρmodeling bias is attributable to the oversimplification of soil texture impacts on E stress. Based on new remotely sensed estimates ofρ, we demonstrate that removingρbias via a single optimized E stress parameter leads to improved ET accuracy and resolves a well‐known modeling bias in the partitioning of ET into E and T. As such, we highlight the importance of the stress function relating E and SM and its central role in regulating land‐atmosphere coupling processes impacting local climate.

Jianzhi Dong↗

NASA NTRS2021

Impacts of Fully Coupling Land Surface and Flood Models on the Simulation of Large Wetlands’ Water Dynamics: The Case of the Inner Niger Delta

It is known that representing wetland dynamics in land surface modeling improves models ‘capacity to reproduce fluxes and land surface boundary conditions for atmospheric modeling in general circulation models. This study presents the development of the full coupling between the Noah-MP land surface model (LSM) and the HyMAP flood model in the NASA Land Information System and its application over the Inner Niger Delta (IND), a well-known hot-spot of strong land surface-atmosphere interactions in West Africa. Here, we define two experiments at 0.02o spatial resolution over 2002-2018 to quantify the impacts of the proposed developments on simulating IND dynamics. One represents the one-way approach for simulating land surface and flooding processes (1-WAY), i.e., Noah-MP neglects surface water availability, and the proposed two-way coupling (2-WAY), where Noah-MP takes surface water availability into account in the vertical water and energy balance. Results show that accounting for two-way interactions between Noah- MP and HyMAP over IND improves simulations of all selected hydrological variables. Compared to 1-WAY, evapotranspiration derived from 2-WAY over flooding zones doubles, increased by 0.8mm/day, resulting in an additional water loss rate of ~18,900km(exp 3)/year, ~40% drop of wetland extent during wet seasons and major improvement in simulated water level variability at multiple locations. Significant soil moisture increase and surface temperature drop were also observed. Wetland outflows decreased by 35%, resulting in a substantial a Nash-Sutcliffe coefficient improvement, from -0.73 to 0.79. It is anticipated that future developments in water monitoring and water-related disaster warning systems will considerably benefit from these findings.

Augusto Getirana↗

NASA NTRSDate not supplied

Fully Coupled Aeroelastic Stability Analysis of Adaptive Shape Memory Alloy Structural Technologies for Airframe Noise Reduction

The objective of this work is the development of computational models and analysis of the coupled fluid-structure response of a slat gap filler (SGF) noise treatment applied to the leading-edge-slat component of a high-lift system typical of modern transport aircraft. The representative airframe chosen for this work is NASA’s High-lift Common Research Model (CRM-HL) in a baseline high-lift configuration. Superelastic shape memory alloys (SMAs) have been identified as enabling materials for these structural treatments. Since the technology elements rely upon having a highly reconfigurable structure, designs must be assessed for static aeroelastic deflection as well as dynamic aeroelastic stability using coupled computational fluid dynamics (CFD) and nonlinear computational structural dynamics (NL CSD) tools. The technical approach consists of solving for the flow field around the entire vehicle using a global CFD model, followed by extraction of relevant local subdomain data for CFD and NL-CSD co-simulations. The SGF design is assessed using both 2D and 3D co-simulations to predict quasi-static aeroelastic deformations and to assess dynamic aeroelastic stability.

Fluid structure interaction↗

NASA NTRSDate not supplied

Performance of Coupled Physics Solvers for Multidisciplinary Hypersonic Flow Simulations on Several Classes of Computer Architectures

The application of hypersonic flow simulation tools to realistic flight scenarios will require the coupling of multiple physical effects to the baseline fluid dynamics. Such multiphysics effects can include the aerooelastic response of the airframe or engine components, dynamic transport of atmospheric particles, the deformation of solid-fluid interfaces that can ablate, pyrolyze, or erode, as well as a host of other processes, all of which are governed by unique sets of physical equations and models. Coupling multiple (and potentially disparate) physics solvers to a robust compressible flow solver poses additional challenges related to the stability, performance and scalability of the combined solver. The choices made during the software design process can therefore lead to a variation in simulation efficiency across different computer architectures. In this paper, we will consider two representative multiphysics hypersonic flow scenarios: the interaction of solid particulates with the flow field created by a hypersonic lifting body and the aerooelastic deformation of a model airframe under high-Mach-number flow conditions. For these simulations we explore the behavior of several hypersonic simulation tools, including Kestrel, FUN3D, US3D, and JENRE multiphysics framework, on several high performance computing systems containing various CPU and GPU architectures.

architecture↗

NASA NTRS2022

Numerical phase space optics methods and applications to the analysis of fiber coupling efficiency in atmospheric turbulence

A fundamental requirement of free-space optical communication is the ability to efficiently couple atmospherically distorted light from a telescope to a detector. A numerical method is presented for modeling fiber-based receiver performance in atmospheric conditions based on phase space optics which does not rely on Monte Carlo methods. This method is employed to analyze the waveguide insertion loss and optimal coupling geometry in atmospheric conditions for step-index fibers, graded-index fibers, and photonic lanterns with and without tilt compensation and central obscurations in the telescope.

free-space optical communication↗