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At least 1,369 records · Page 76

Instrument Performance of GISMO, a 2 Millimeter TES Bolometer Camera used at the IRAM 30 m Telescope

In November of 2007 we demonstrated a monolithic Backshort-Under-Grid (BUG) 8x16 array in the field using our 2 mm wavelength imager GISMO (Goddard IRAM Superconducting 2 Millimeter Observer) at the IRAM 30 m telescope in Spain for astronomical observations. The 2 mm spectral range provides a unique terrestrial window enabling ground-based observations of the earliest active dusty galaxies in the universe and thereby allowing a better constraint on the star formation rate in these objects. The optical design incorporates a 100 mm diameter silicon lens cooled to 4 K, which provides the required fast beam yielding 0.9 lambda/D pixels. With this spatial sampling, GISMO will be very efficient at detecting sources serendipitously in large sky surveys, while the capability for diffraction limited imaging is preserved. The camera provides significantly greater detection sensitivity and mapping speed at this wavelength than has previously been possible. The instrument will fill in the spectral energy distribution of high redshift galaxies at the Rayleigh-Jeans part of the dust emission spectrum, even at the highest redshifts. Here1 will we present early results from our observing run with the first fielded BUG bolometer array. We have developed key technologies to enable highly versatile, kilopixel, infrared through millimeter wavelength bolometer arrays. The Backshort-Under-Grid (BUG) array consists of three components: 1) a transition-edge-sensor (TES) based bolometer array with background-limited sensitivity and high filling factor, 2) a quarter-wave reflective backshort grid providing high optical efficiency, and 3) a superconducting bump-bonded large format Superconducting Quantum Interference Device (SQUID) multiplexer readout. The array is described in more detail elsewhere (Allen et al., this conference). In November of 2007 we demonstrated a monolithic 8x 16 array with 2 mm-pitch detectors in the field using our 2 mm wavelength imager GISMO (Goddard IRAM Superconducting 2 Millimeter Observer) at the IRAM 30 m telescope in Spain for astronomical observations. The 2 mm spectral range provides a unique terrestrial window enabling ground-based observations of the earliest active dusty galaxies in the universe and thereby allowing a better constraint on the star formation rate in these objects. The optical design incorporates a 100 mm diameter silicon lens cooled to 4 K, which provides the required fast beam yielding 0.9 lambda1D pixels. With this spatial sampling, GISMO will be very efficient at detecting sources serendipitously in large sky surveys, while the capability for diffraction limited imaging is preserved. The camera provides significantly greater detection sensitivity and mapping speed at this wavelength than has previously been possible. The instrument will fill in the spectral energy distribution of high redshift galaxies at the Rayleigh-Jeans part of the dust emission spectrum, even at the highest redshifts. Here I will we present early results from our observing run with the first fielded BUG bolometer array.

Staguhn, Johannes↗

A New Optical Aerosol Spectrometer

An optical particle spectrometer capable of measuring aerosol particle size distributions from 0.02 to 100 micrometers has been developed. This instrument combines several optical methods in one, in-situ configuration; it can provide continuous data collection to encompass the wide dynamic size ranges and concentrations found in studies of modeled planetary atmospheres as well as terrestrial air quality research. Currently, the system is incorporated into an eight liter capacity spherical pressure vessel that is appropriate both for flowthrough and for in-situ particle generation. The optical sizing methods include polarization ratio, The scattering, and forward scattering detectors, with illumination from a fiber-coupled, Argon-ion laser. As particle sizes increase above 0.1 micrometer, a customized electronics and software system automatically shifts from polarization to diffraction-based measurements as the angular scattering detectors attain acceptable signal-to-noise ratios. The number concentration detection limits are estimated to be in the part-per-trillion (ppT by volume) range, or roughly 1000 submicron particles per cubic centimeter. Results from static experiments using HFC134A (approved light scattering gas standard), flow-through experiments using sodium chloride (NaCl) and carbon particles, and dynamic 'Tholin' (photochemical produced particles from ultraviolet (UV)-irradiated acetylene and nitrogen) experiments have been obtained. The optical spectrometer data obtained with particles have compared well with particle sizes determined by electron microscopy. The 'Tholin' tests provided real-time size and concentration data as the particles grew from about 30 nanometers to about 0.8 micrometers, with concentrations ranging from ppT to ppB, by volume. Tests are still underway, to better define sizing accuracy and concentration limits, these results will be reported.

Fonda, Mark↗

Design and Optimization of the SPOT Primary Mirror Segment

The 3m Spherical Primary Optical Telescope (SPOT) will utilize a single ring of 0.86111 point-to-point hexagonal mirror segments. The f2.85 spherical mirror blanks will be fabricated by the same replication process used for mass-produced commercial telescope mirrors. Diffraction-limited phasing will require segment-to-segment radius of curvature (ROC) variation of approx.1 micron. Low-cost, replicated segment ROC variations are estimated to be almost 1 mm, necessitating a method for segment ROC adjustment & matching. A mechanical architecture has been designed that allows segment ROC to be adjusted up to 400 microns while introducing a minimum figure error, allowing segment-to-segment ROC matching. A key feature of the architecture is the unique back profile of the mirror segments. The back profile of the mirror was developed with shape optimization in MSC.Nastran(TradeMark) using optical performance response equations written with SigFit. A candidate back profile was generated which minimized ROC-adjustment-induced surface error while meeting the constraints imposed by the fabrication method. Keywords: optimization, radius of curvature, Pyrex spherical mirror, Sigfit

Budinoff, Jason G.↗

Optical Control of Adaptive Nanoscale Domain Networks

Adaptive networks can sense and adjust to dynamic environments to optimize their performance. Understanding their nanoscale responses to external stimuli is essential for applications in nanodevices and neuromorphic computing. However, it is challenging to image such responses on the nanoscale with crystallographic sensitivity. Here, the evolution of nanodomain networks in (PbTiO 3 ) n /(SrTiO 3 ) n superlattices (SLs) is directly visualized in real space as the system adapts to ultrafast repetitive optical excitations that emulate controlled neural inputs. The adaptive response allows the system to explore a wealth of metastable states that are previously inaccessible. Their reconfiguration and competition are quantitatively measured by scanning x-ray nanodiffraction as a function of the number of applied pulses, in which crystallographic characteristics are quantitatively assessed by assorted diffraction patterns using unsupervised machine-learning methods. The corresponding domain boundaries and their connectivity are drastically altered by light, holding promise for light-programable nanocircuits in analogy to neuroplasticity. Phase-field simulations elucidate that the reconfiguration of the domain networks is a result of the interplay between photocarriers and transient lattice temperature. The demonstrated optical control scheme and the uncovered nanoscopic insights open opportunities for the remote control of adaptive nanoscale domain networks.

36 MATERIALS SCIENCE↗

Polymorphism and Phase Control in Dion–Jacobson 2D 3-(Aminomethyl)piperidinium-Based Metal Iodide Perovskites

Two-dimensional halide perovskites exhibit rich structural diversity and tunable optoelectronic properties, making them promising materials for energy, sensing, and photonic applications. In this work, we report the structural mapping of four distinct polymorphs, γ (P2 1 /c), β (P4/mbm), α (P4/mmm), and δ (Cmcm) in the two-dimensional iodoplumbate, iodostannate, and iodogermanate perovskite so-called Dion-Jacobson series (3AMP)MI4 (M = Sn, Pb, Ge), where 3AMP is 3-(aminomethyl)piperidinium. The phases exhibit systematic evolution in octahedral distortion, lattice symmetry, and metal–halide geometry, enabling structural control over optoelectronic properties. Notably, the α-phase of (3AMP)SnI 4 represents a rare, ambient-stable, high-symmetry structure for Sn-based perovskites, without a phase transition down to 100 K. Variable-temperature single-crystal diffraction, powder x-ray diffraction (PXRD), and calorimetry reveal metal- and temperature-dependent polymorph interconversions, including the emergence of long range supercell reflections in Pb-rich compositions at low temperature. Optical spectroscopy and photoelectron yield spectroscopy confirm band gap tunability and band alignment trends, highlighting symmetry-dependent shifts and anomalous band gap bowing in mixed-metal systems, verified by electronic structure calculations. Calculations additionally indicate that the higher symmetry phases have reduced electron and hole effective masses compared to the lower symmetry phases.

36 MATERIALS SCIENCE↗

Octahedral oxide glass network in ambient pressure neodymium titanate

Abstract Rare-earth titanates form very fragile liquids that can be made into glasses with useful optical properties. We investigate the atomic structure of 83TiO 2 -17Nd 2 O 3 glass using pair distribution function (PDF) analysis of X-ray and neutron diffraction with double isotope substitutions for both Ti and Nd. Six total structure factors are analyzed (5 neutron + 1 X-ray) to obtain complementary sensitivities to O and Ti/Nd scattering, and an empirical potential structure refinement (EPSR) provides a structural model consistent with the experimental measurements. Glass density is estimated as 4.72(13) g cm −3 , consistent with direct measurements. The EPSR model indicates nearest neighbor interactions for Ti-O at $$\overline{r}_{TiO}$$ r ¯ TiO = 1.984(11) Å with coordination of $$n_{TiO}$$ n TiO = 5.72(6) and for Nd-O at $$\overline{r}_{NdO}$$ r ¯ NdO = 2.598(22) Å with coordination of $$n_{NdO}$$ n NdO = 7.70(26), in reasonable agreement with neutron first order difference functions for Ti and Nd. The titanate glass network comprises a mixture of distorted Ti-O 5 and Ti-O 6 polyhedra connected via 71% corner-sharing and 23% edge-sharing. The O-Ti coordination environments include 15% nonbridging O-Ti 1 , 51% bridging O-Ti 2 , and 32% tricluster O-Ti 3 . This structure is highly unusual for oxide glasses melt-quenched at ambient pressure, as it consists of Ti-O x predominantly in octahedral (with nearly no tetrahedral) coordination.

36 MATERIALS SCIENCE↗

Determining the oxidation stability of SnSe under atmospheric exposure

Abstract Understanding surface stability becomes critical as 2D materials like SnSe are developed for piezoelectric and optical applications. SnSe thin films deposited by molecular beam epitaxy showed no structural changes after a two-year exposure to atmosphere, as confirmed by X-ray diffraction and Raman spectroscopy. X-ray photoelectron spectroscopy and reflectivity show a stable 3.5 nm surface oxide layer, indicating a self-arresting oxidative process. Resistivity measurements show an electrical response dominated by SnSe post-exposure. This work shows that SnSe films can be used in ambient conditions with minimal risk of long-term degradation, which is critical for the development of piezoelectric or photovoltaic devices. Graphical Abstract

Chin, Jonathan R. (ORCID:0000000273205678)↗

Extending in situ X-ray Temperature Diagnostics to Internal Components

Time-resolved X-ray thermometry is an enabling technology for measuring temperature and phase change of components. However, current diagnostic methods are limited in their ability due to the invasive nature of probes or the requirement of coatings and optical access to the component. Our proposed developments overcome these challenges by utilizing X-rays to directly measure the objects temperature. Variable-Temperature X-ray Diffraction (VT-XRD) was performed over a wide range of temperatures and diffraction angles and was performed on several materials to analyze the patterns of the bulk materials for sensitivity. "High-speed" VT-XRD was then performed for a single material over a small range of diffraction angles to see how fast the experiments could be performed, whilst still maintaining peaks sufficiently large enough for analysis.

36 MATERIALS SCIENCE↗

Using High-Performance Cameras for Advanced Plasma Diagnostics

We will present insights, challenges, and recent progress on using a multi-megapixel deep-depletion CCD camera for quantitative X-ray spectra in a single-hit exposure mode in order to optimize X-ray diffraction experiments. We will also present some applications of Sandia’s in-house developed hybrid CMOS (hCMOS) sensors, which can record up to four full frames of optical or X-ray images in sequences with only a few nanoseconds interframe timing in a single line-of-sight.

Geissel, Matthias [Sandia National Laboratories (S↗

High-pressure phase diagram and equation of state of solid helium from single-crystal X-ray diffraction to 23.3 GPa

Single-crystal X-ray diffraction measurements have been performed on solid He-4 from 15.6 to 23.3 GPa at 300 K with synchrotron radiation. The diffraction patterns demonstrate that the structure of the solid is hexagonal close packed over this pressure-temperature range, contrary to both the interpretation of high-pressure optical studies and to theoretical predictions. The solid is more compressible than is indicated by equations of state calculated with recently determined helium pair potentials. The results suggest that a significant revision of current views of the phase diagram and energetics of dense solid helium is in order.

Mao, H. K.↗

Robust Quantitative Measurement of Flows and Transparent or Highly Reflective Objects

The liquid crystal point diffraction interferometer (LCPDI) is a new instrument that has been developed for the measurement of phase objects. The LCPDI uses the compact, robust design of Linnik's point diffraction interferometer and adds to it phase stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wave-fronts. A solid state camera provides very high data density and automated data reduction. The instrument can measure either transparent objects like fluids and lenses, or highly reflective opaque objects like mirrors. In the former case, the refractive index distribution is measured and then related to various properties like temperature, density, chemical composition, or thickness. In the latter case, the measured phase distribution is related to the object shape. The objects measured must be stationary or quasisteady state because the measurement requires the acquisition of several frames of image data during which time the object's properties must not have changed. The data acquisition time depends on the speed of the frame grabber and the required number of data frames. Typically, three to five frames taking 1 to 2 seconds are required. The potential for faster data acquisition exists.

Mercer, Carolyn R.↗

GISMO

The 2 mm (1 50 GHz) atmospheric window enables unparalleled ground-based observations of the earliest active dusty galaxies in the universe. We have undertaken the development of a bolometer camera, GISMO (the Goddard-IRAM Superconducting 2-Millimeter Observer), which will obtain large and sensitive sky maps at this wavelength. The instrument will be used at the IRAM 30 m telescope, where we hope to have a trial observing run in Spring of 2007. The innovative element in this camera is its 8x1 6 fully sampled planar array of multiplexed superconducting transition edge sensor bolometers. This array is based on our recently demonstrated Backshort Under Grid architecture, designed to be scaled to kilopixel arrays with high sensitivity (of around 4 * 10 (exp -17)/ W* square root of Hz at T(sub c) approximates 450mK). A compact cryogenic optical system provides a wide field of view, (almost 2'x4') enabling GISMO to be very efficient at detecting sources serendipitously in large sky surveys, while retaining diffraction-limited imaging performance. GISMO will provide significantly greater imaging sensitivity and mapping speed at this wavelength than has previously been possible. The major scientific driver for the instrument is to detect dust emission from high-z Ultraluminous Infrared Galaxies (ULIRGs) and quasars. The instrument provides an important portion of the spectrum of high redshift galaxies at the Rayleigh-Jeans part of the dust emission spectrum, even at the highest redshifts. Models of galaxy evolution predict that GISMO will serendipitously detect one galaxy in every four hours of observing blank sky, and that one quarter of these galaxies will be at a redshift of z > 6.5.

Benford, Dominic↗

A Sounding Rocket Mission Concept to Acquire High-Resolution Radiometric Spectra Spanning the 9 nm - 31 nm Wavelength Range

When studying Solar Extreme Ultraviolet (EUV) emissions, both single-wavelength, two- dimensional (2D) spectroheliograms and multi-wavelength, one-dimensional (1D) line spectra are important, especially for a thorough understanding of the complex processes in the solar magnetized plasma from the base of the chromosphere through the corona. 2D image data are required for a detailed study of spatial structures, whereas radiometric (i.e., spectral) data provide information on relevant atomic excitation/ionization state densities (and thus temperature). Using both imaging and radiometric techniques, several satellite missions presently study solar dynamics in the EUV, including the Solar Dynamics Observatory (SDO), Hinode, and the Solar-Terrestrial Relations Observatory (STEREO). The EUV wavelengths of interest typically span 9 nm to 31 nm, with the shorter wavelengths being associated with the hottest features (e.g., intense flares and bright points) and the longer wavelengths associated with cooler features (e.g., coronal holes and filaments). Because the optical components of satellite instruments degrade over time, it is not uncommon to conduct sounding rocket underflights for calibration purposes. The authors have designed a radiometric sounding rocket payload that could serve as both a calibration underflight for and a complementary scientific mission to the upcoming Solar Ultraviolet Imager (SUVI) mission aboard the GOES-R satellite (scheduled for a 2015 launch). The challenge to provide quality radiometric line spectra over the 9-31 nm range covered by SUVI was driven by the multilayer coatings required to make the optical components, including mirrors and gratings, reflective over the entire range. Typically, these multilayers provide useful EUV reflectances over bandwidths of a few nm. Our solution to this problem was to employ a three-telescope system in which the optical components were coated with multilayers that spanned three wavelength ranges to cover the three pairs of SUVI bands. The complete system was designed to fit within the Black Brandt-IX 22.-diameter payload skin envelope. The basic optical path is that of a simple parabolic telescope in which EUV light is focused onto a slit and shutter assembly and imaged onto a normal-incidence diffraction grating, which then disperses the light onto a 2048 2048 CCD sensor. The CCD thus records 1D spatial information along one axis and spectral information along the other. The slit spans 40 arc-minutes in length, thus covering a solar diameter out to +/- 1.3 solar radii. Our operations concept includes imaging at three distinct positions: the north-south meridian, the northeast-southwest diagonal, and real-time pointing at an active region. Six 10-second images will be obtained at each position. Fine pointing is provided by the SPARCS-VII attitude control system typically employed on Black Brandt solar missions. Both before and after launch, all three telescopes will be calibrated with the EUV line emission source and monochromater system at NASA's Stray Light Facility at Marshall Spaceflight Center. Details of the payload design, operations concept, and data application will be presented.

Krause, L. Habash↗

NASA Work Experience

I have had the opportunity to support the analytical laboratories in chemical analysis of unknown samples, using Optical Microscopy (OM), Polarizing Light Microscopy (PLM), Fourier-Transform Infrared Spectroscopy (FT-IR), Scanning Electron Microscopy with Energy Dispersive Spectroscopy (SEMEDS), and X-ray Powder Diffraction (XPD). I have assisted in characterizing fibers pulled from a spacecraft, a white fibrous residue discovered in a jet refueler truck, brown residue from a plant habitat slated for delivery to the ISS (International Space Station), corrosion on a pipe from a sprinkler, and air filtration material brought back from the ISS. I also conducted my own fiber study in order to practice techniques and further my understanding of background concepts. Furthermore, I had the opportunity to participate in diverse work assignments, where I was assigned to work with other branches of the engineering department for 1-2 days each. The first was in the Materials Science branch where I participated in the construction of the plant habitat intended for use in research aboard the ISS. The second was in the Testing Design branch where I assisted with tensile and hardness testing of over 40 samples. In addition, I have had the privilege to attend multiple tours of the NASA KSC campus, including to the Astronaut Crew Quarters, the VAB (the main area, the Columbia room, and the catwalk), the Visitor Center housing the shuttle Atlantis, the Saturn-V exhibit, the Prototype laboratory, SWAMP WORKS, the Shuttle Landing Facility, the Crawler, and the Booster Fabrication Facility (BFF). Lastly, much of my coursework prepared me for this experience, including numerous laboratory courses with topics diverse as chemistry, physics, and biology.

Florida Tech↗

Habitable Exoplanet Observatory (HabEx) Telescope: Systems Engineering and STOP Modeling

The Habitable Exoplanet Observatory Mission (HabEx) is one of four missions studied for the 2020 Astrophysics Decadal Survey. Its goal is to directly image and spectroscopically characterize planetary systems in the habitable zone around nearby sun-like stars. Additionally, HabEx will perform a broad range of general astrophysics science enabled by 115 to 1700 nm spectral range and 3 x 3 arc-minute FOV. Critical to achieving its science goals is a large, ultra-stable UV/Optical/Near-IR (UVOIR) telescope. The baseline HabEx telescope is a 4-meter off-axis unobscured three-mirror-anastigmatic, diffraction limited at 400 nm with wavefront stability on the order of a few 10s of picometers. This paper summarizes the opto-mechanical design of the baseline optical telescope assembly, including a discussion of how we applied science driven systems engineering to derive the telescope’s engineering specifications from the mission’s science requirements, and presents analysis that the baseline telescope structure meets its specified tolerances.

Stahl, H. Philip↗

Atypical phase-change alloy Ga 2 Te 3 : atomic structure, incipient nanotectonic nuclei, and multilevel writing

Emerging brain-inspired computing, including artificial optical synapses, photonic tensor cores, neuromorphic networks, etc., needs phase-change materials (PCMs) of the next generation with lower energy consumption and a wider temperature range for reliable long-term operation. Gallium tellurides with higher melting and crystallization temperatures appear to be promising candidates and enable achieving the necessary requirements. Here, using high energy X-ray diffraction and Raman spectroscopy supported by first-principles simulations, we show that vitreous g-Ga 2 Te 3 films essentially have a tetrahedral local structure and sp 3 hybridization, similar to those in the stable fcc Ga 2 Te 3 polymorph and in contrast to a vast majority of typical PCMs. Nevertheless, optical pump–probe laser experiments revealed high-contrast, fast and reversible multilevel SET-RESET transitions raising a question related to the phase change mechanism. A recently observed nanotectonic compression in bulk glassy Ga–Te alloys seems to be responsible for the PCM performance. Incipient nanotectonic nuclei, reminiscent of monoclinic high-pressure HP-Te II and rhombohedral HP-Ga 2 Te 3 , are present as minorities (2–4%) in g-Ga 2 Te 3 but are suggested to grow dramatically with increasing temperature while interacting with appropriate laser pulses. This leads to co-crystallization of HP-polymorphs amplified by a high internal local pressure reaching 4–8 GPa. The metallic HP-forms provide an increasing optical and electrical contrast, favorable for reliable PCM operations, and higher energy efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part 2: Dependence of absorption and extinction on ice crystal morphology

This study builds upon the microphysical modeling described in Part 1 by deriving formulations for the extinction and absorption coefficients in terms of the size distribution parameters predicted from the micro-physical model. The optical depth and single scatter albedo of a cirrus cloud can then be determined, which, along with the asymmetry parameter, are the input parameters needed by cloud radiation models. Through the use of anomalous diffraction theory, analytical expressions were developed describing the absorption and extinction coefficients and the single scatter albedo as functions of size distribution parameters, ice crystal shapes (or habits), wavelength, and refractive index. The extinction coefficient was formulated in terms of the projected area of the size distribution, while the absorption coefficient was formulated in terms of both the projected area and mass of the size distribution. These properties were formulated as explicit functions of ice crystal geometry and were not based on an 'effective radius.' Based on simulations of the second cirrus case study described in Part 1, absorption coefficients predicted in the near infrared for hexagonal columns and rosettes were up to 47% and 71% lower, respectively, than absorption coefficients predicted by using equivalent area spheres. This resulted in single scatter albedos in the near-infrared that were considerably greater than those predicted by the equivalent area sphere method. Reflectances in this region should therefore be underestimated using the equivalent area sphere approach. Cloud optical depth was found to depend on ice crystal habit. When the simulated cirrus cloud contained only bullet rosettes, the optical depth was 142% greater than when the cloud contained only hexagonal columns. This increase produced a doubling in cloud albedo. In the near-infrared (IR), the single scatter albedo also exhibited a significant dependence on ice crystal habit. More research is needed on the geometrical properties of ice crystals before the influence of ice crystal shape on cirrus radiative properties can be adequately understood. This study provides a way of coupling the radiative properties of absorption, extinction, and single scatter albedo to the microphysical properties of cirrus clouds. The dependence of extinction and absorption on ice crystal shape was not just due to geometrical differences between crystal types, but was also due to the effect these differences had on the evolution of ice particle size spectra. The ice particle growth model in Part 1 and the radiative properties treated here are based on analytical formulations, and thus represent a computationally efficient means of modeling the microphysical and radiative properties of cirrus clouds.

Mitchell, David L.↗

Performance analysis of a noncoherently combined large aperture optical heterodyne receiver

The performance of a noncoherently combined, multiple-mirror heterodyne receiver is analyzed. It is shown that in the absence of atmospheric turbulence, the performance of the noncoherently combined receiver is inferior to that of a monolithic, diffraction-limited receiver with equivalent aperture area. However, when atmospheric turbulence is taken into consideration, the efficiency of a monolithic aperture heterodyne receiver is limited by the phase coherence length of the atmosphere and generally does not improve with increasing aperture size. In constrast, the performance of a noncoherently combined system improves with an increasing number of receivers. Consequently, given a fixed collecting area, the noncoherently combined system can offer superior performance. The performance of the noncoherently combined heterodyne receiver is studied by analyzing the combining loss of the receiver SNR. It is shown that, given the collecting area, the performance of the combined receiver is optimized when the diameter of each of the individual receivers is on the order of the phase coherence length gamma sub 0 of the atmospheric turbulence.

Chen, C.-C.↗