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Gamma-ray and millimeter-wave emissions from the 1991 June X-class solar flares

We have studied the spectacular 1991 June X-class flares using gamma-ray data from the Charged Particle Detectors (CPDs) of the Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory (CGRO) and 80 GHz millimeter data from Nobeyama, Japan. The CPDs were the only CGRO instrument that did not saturate during the extremely intense 1991 June 4 flare. We have shown that for this flare the CPDs respond to MeV photons, most of which are due to bremsstrahlung produced by relativistic electrons at the Sun. We have further shown that the gamma-ray and millimeter observations agree numerically if the 80 GHz radiation is gyrosynchrotron radiation produced by trapped electrons and the gamma rays are thick-target bremsstrahlung due to electrons precipitating out of the trap. The requirement that the trapping time obtained from the numerical comparison be consistent with the observed time profiles implies a magnetic field between about 200 and 300 G and an electron spectral index between about 3 to 5. By comparing the CPD observations with both the 80 GHz data and nuclear line data from the Energetic Gamma Ray Experiment Telescope (EGRET) and the Oriented Scintillation Spectroscopy Experiment (OSSE) on CGRO for the flares of June 4, 6, 9, and 11, we found that the ratio of the CPD counts to both the millimeter flux densities and the nuclear line fluences decreases with decreasing flare heliocentric angle. All of these flares were produced in the same active region. We interpreted this result in terms of a loop model in which the gyrosynchrotron emission is produced in the coronal portion of the loop where the electrons are kept isotropic by pitch angle scattering due to plasma turbulence, while the bremsstrahlung is produced by precipitating electrons that interact anisotropically. We found that the trapping time in the coronal portion is time dependent, reaching a minimum of about 10 s at the peak of the CPD count rate. We suggested the damping of the turbulence as a possible reason for the variation of the trapping time. turbulence as a possible reason for the variation of the trapping time.

Ramaty, Reuven↗

Investigation of Passive Atmospheric Sounding Using Millimeter- and Submillimeter- Wavelength Channels

This report summarizes progress made during the period from July 1, 1994 through June 30, 1996 on the development of satellite-based observational techniques for high resolution imaging of precipitation and sounding of atmospheric ice and water vapor using passive microwave radiometers in the millimeter (MMW)- and submillimeter (SMMW)-wavelength. This is being achieved by radiative transfer modeling a millimeter and submillimeter wave frequencies and by the development and operation of an airborne millimeter wave imaging radiometer (MIR). The MIR has been used in both airborne and ground-based experiments. Its primary application is to provide calibrated radiometric imagery to verify MMW and SMMW radiative transfer models in clear air, cloud, and precipitation and to develop retrieval techniques using MMW and SMMW channels. The MIR imagery over convective storm cells has been used to illustrate the potentially useful cloud and water vapor sensing and storm-cell mapping capabilities of SMMW channels. The radiometric data has also been used to analyze radiative transfer model discrepancies caused by water vapor errors in radiosondes. The MMW and SMMW channels can be used to extend the altitude that water vapor sounding can be performed up into the lower stratosphere. Together, the use of both SMMW and MMW channels are expected to provide additional observational degrees of freedom related to cloud ice particle size.

Gasiewski, Albin J.↗

Correlation Between Radio-Millimeter and Gamma Ray Fluxes from Blazars

Using multifrequency databases, we have plotted radio (5 GHz, 22 GHz, and 37 GHz) and millimeter (90 GHz and 230 GHz) fluxes versus MeV and gamma-ray fluxes of the EGRET blazar sample. Strong correlations have been found between the emissions at the radio-millimeter wavelengths and they-rays. These correlations have been explained in the frame work of Synchrotron Self-Compton (SSC) processes between the radio-millimeter synchrotron emissions and the shock-accelerated electrons in the jets of blazars. Using this SSC model we are able to explain the GeV spectra of the EGRET blazars. The present model will also explain the physics of TeV flares in blazars and the time lag between the TeV and GeV photons from a blazar.

Ghosh, K. K.↗

The Effect of Clouds on Water Vapor Profiling from the Millimeter-Wave Radiometric Measurements

Simultaneous measurements with the millimeter-wave imaging radiometer (MIR), cloud lidar system (CLS), and the MODIS airborne simulator (MAS) were made aboard the NASA ER-2 aircraft over the western Pacific Ocean on 17-18 January 1993. These measurements were used to study the effects of clouds on water vapor profile retrievals based on millimeter-wave radiometer measurements. The CLS backscatter measurements (at 0.532 and 1.064 am) provided information on the heights and a detailed structure of cloud layers; the types of clouds could be positively identified. All 12 MAS channels (0.6-13 Am) essentially respond to all types of clouds, while the six MIR channels (89-220 GHz) show little sensitivity to cirrus clouds. The radiances from the 12-/Am and 0.875-gm channels of the MAS and the 89-GHz channel of the MIR were used to gauge the performance of the retrieval of water vapor profiles from the MIR observations under cloudy conditions. It was found that, for cirrus and absorptive (liquid) clouds, better than 80% of the retrieval was convergent when one of the three criteria was satisfied; that is, the radiance at 0.875 Am is less than 100 W/cm.sr, or the brightness at 12 Am is greater than 260 K, or brightness at 89 GHz is less than 270 K (equivalent to cloud liquid water of less than 0.04 g/cm). The range of these radiances for convergent retrieval increases markedly when the condition for convergent retrieval was somewhat relaxed. The algorithm of water vapor profiling from the MIR measurements could not perform adequately over the areas of storm-related clouds that scatter radiation at millimeter wavelengths.

Wang, J. R.↗

Microwave, Millimeter, Submillimeter, and Far Infrared Spectral Databases

The spectrum of most known astrophysical molecules is derived from transitions between a few hundred to a few hundred thousand energy levels populated at room temperature. In the microwave and millimeter wave regions. spectroscopy is almost always performed with traditional microwave techniques. In the submillimeter and far infrared microwave technique becomes progressively more technologically challenging and infrared techniques become more widely employed as the wavelength gets shorter. Infrared techniques are typically one to two orders of magnitude less precise but they do generate all the strong features in the spectrum. With microwave technique, it is generally impossible and rarely necessary to measure every single transition of a molecular species, so careful fitting of quantum mechanical Hamiltonians to the transitions measured are required to produce the complete spectral picture of the molecule required by astronomers. The fitting process produces the most precise data possible and is required in the interpret heterodyne observations. The drawback of traditional microwave technique is that precise knowledge of the band origins of low lying excited states is rarely gained. The fitting of data interpolates well for the range of quantum numbers where there is laboratory data, but extrapolation is almost never precise. The majority of high resolution spectroscopic data is millimeter or longer in wavelength and a very limited number of molecules have ever been studied with microwave techniques at wavelengths shorter than 0.3 millimeters. The situation with infrared technique is similarly dire in the submillimeter and far infrared because the black body sources used are competing with a very significant thermal background making the signal to noise poor. Regardless of the technique used the data must be archived in a way useful for the interpretation of observations.

Pearson, J. C.↗

The Millimeter-Wave Bolometric Interferometer

The Millimeter-wave Bolometric Interferometer (MBI) is a proposed ground-based instrument designed for a wide range of cosmological and astrophysical observations including studies of the polarization of the cosmic microwave background (CMB). MBI combines the advantages of two well-developed technologies - interferometers and bolometric detectors. Interferometers have many advantages over .filled-aperture telescopes and are particularly suitable for high resolution imaging. Cooled bolometers are the highest sensitivity detectors at millimeter and sub-millimeter wavelengths. The combination of these two technologies results in an instrument with both high sensitivity and high angular resolution.

Ali, S.↗

Large Format Arrays for Far Infrared and Millimeter Astronomy

Some of the most compelling questions in modem astronomy are best addressed with submillimeter and millimeter observations. The question of the role of inflation in the early evolution of the universe is best addressed with large sensitive arrays of millimeter polarimeters. The study of the first generations of galaxies requires sensitive submillimeter imaging, which can help us to understand the history of energy release and nucleosynthesis in the universe. Our ability to address these questions is dramatically increasing, driven by dramatic steps in the sensitivity and size of available detector arrays. While the MIPS instrument on the SIRTF mission will revolutionize far infrared astronomy with its 1024 element array of photoconductors, thermal detectors remain the dominant technology for submillimeter and millimeter imaging and polarimetry. The last decade has seen the deployment of increasingly large arrays of bolometers, ranging from the 48 element arrays deployed on the KAO in the late 198Os, to the SHARC and SCUBA arrays in the 1990s. The past years have seen the deployment of a new generation of larger detector arrays in SHARC II (384 channels) and Bolocam (144 channels). These detectors are in operation and are beginning to make significant impacts on the field. Arrays of sensitive submillimeter bolometers on the SPIRE instrument on Herschel will allow the first large areas surveys of the sky, providing important insight into the evolution of galaxies. The next generation of detectors, led by SCUBA II, will increase the focal scale of these instruments by an order of magnitude. Two major missions are being planned by NASA for which further development of long wavelength detectors is essential, The SAFlR mission, a 10-m class telescope with large arrays of background limited detectors, will extend our reach into the epoch of initial galaxy formation. A major goal of modem cosmology is to test the inflationary paradigm in the early evolution of the universe. To this end, a mission is planned to detect the imprint of inflation on the CMB by precision measurement of its polarization. This work requires very large arrays of sensitive detectors which can provide unprecedented control of a wide range of systematic errors, given the small amplitude of the signal of interest. We will describe the current state of large format detector arrays, the performance requirements set by the new missions, and the different approaches being developed in the community to meet these requirements. We are confident that within a decade, these developments will lead to dramatic advances in our understanding of the evolution of the universe.

Moseley, Harvey↗

Remote Measurements of Snowfalls in Wakasa Bay, Japan with Airborne Millimeter- wave Imaging Radiometer and Cloud Radar

In this paper we explore the application of combined millimeter-wave radar and radiometry to remotely measure snowfall. During January-February of 2003, a field campaign was conducted with the NASA P-3 aircraft in Wakasa Bay, Japan for the validation of the AMSRE microwave radiometer on board the Aqua satellite. Among the suite of instruments-on board the P-3 aircraft were the Millimeter-wave Imaging Radiometer (MIR) from the NASA Goddard Space Flight Center and the 94 GHz Airborne Cloud Radar (ACR) which is co-owned and operated by NASA Jet Propulsion Laboratory/University of Massachusetts. MIR is a total power, across-track scanning radiometer that measures radiation at the frequencies of 89, 150, 183.3 +/- 1, 183.3 +/- 3, 183.3 +/-7, 220, and 340 GHz. The MIR has flown many successful missions since its completion in May 1992. ACR is a newer instrument and flew only a few times prior to the Wakasa Bay deployment. These two instruments which are particularly well suited for the detection of snowfall functioned normally during flights over snowfall and excellent data sets were acquired. On January 14, 28, and 29 flights were conducted over snowfall events. The MIR and ACR detected strong signals during periods of snowfall over ocean and land. Results from the analysis of these concurrent data sets show that (1) the scattering of millimeter-wave radiation as detected by the MIR is strongly correlated with ACR radar reflectivity profiles, and (2) the scattering is highly frequency-dependent, the higher the frequency the stronger the scattering. Additionally, the more transparent channels of the MIR (e.g., 89, 150, and 220 GHz) are found to display ambiguous signatures of snowfall because of their exposure to surface features. Thus, the snowfall detection and retrievals of snowfall parameters, such as the ice water path (IWP) and median mass diameter (D(me)) are best conducted at the more opaque channels near 183.3 GHz and 340 GHz. Retrievals of IWP and D(me) using the MIR measurements at 183.3 and 340 GHZ are currently in progress, and the results will be compared with those derived from the ACR reflectivity profiles. Implication from this comparison will be discussed.

Wang, J. R.↗

Millimeter Wave Detection of Localized Anomalies in the Space Shuttle External Fuel Tank Insulating Foam and Acreage Heat Tiles

The Space Shuttle Columbia's catastrophic accident emphasizes the growing need for developing and applying effective, robust and life-cycle oriented nondestructive testing (NDT) methods for inspecting the shuttle external fuel tank spray on foam insulation (SOFI) and its protective acreage heat tiles. Millimeter wave NDT techniques were one of the methods chosen for evaluating their potential for inspecting these structures. Several panels with embedded anomalies (mainly voids) were produced and tested for this purpose. Near-field and far-field millimeter wave NDT methods were used for producing millimeter wave images of the anomalies in SOFI panel and heat tiles. This paper presents the results of an investigation for the purpose of detecting localized anomalies in two SOFI panels and a set of heat tiles. To this end, reflectometers at a relatively wide range of frequencies (Ka-band (26.5 - 40 GHz) to W-band (75 - 110 GHz)) and utilizing different types of radiators were employed. The results clearly illustrate the utility of these methods for this purpose.

Kharkovsky, S.↗

Microwave and Millimeter Wave Testing for the Inspection of the Space Shuttle Spray on Foam Insulations (SOFI) and the Acreage Heat Tiles

The utility of microwave and millimeter wave nondestructive testing and evaluation (NDT&E) methods, for testing the Space Shuttle's external he1 tank spray on foam insulation (SOFI) and the acreage heat tiles has been investigated during the past two years. Millimeter wave NDE techniques are capable of producing internal images of SOFI. This paper presents the results of testing several diverse panels with embedded voids and debonds at millimeter wave frequencies. Additionally, the results of testing a set of heat tiles are also presented. Finally, the attributes of these methods as well as the advantageous features associated with these systems are also provided.

Zoughi, R.↗

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↗

Millimeter Wave Synthetic Aperture Imaging System with a Unique Rotary Scanning System

In recent years, millimeter wave imaging techniques, using synthetic aperture focusing and holographical approaches, have shown tremendous potential for nondestructive testing applications, involving materials and structures used in space vehicles, including the space shuttle external fuel tank spray on foam insulation and its acreage heat tiles. The ability of signals at millimeter wave frequencies (30 - 300 GHz) to easily penetrate inside of low loss dielectric materials, their relatively small wavelengths, and the possibility of detecting coherent (magnitude and phase) reflections make them suitable for high resolution synthetic aperture focused imaging the interior of such materials and structures. To accommodate imaging requirements, commonly a scanning system is employed that provides for a raster scan of the desired structure. However, most such scanners, although simple in design and construction, are inherently slow primarily due to the need to stop and start at the beginning and end of each scan line. To this end, a millimeter wave synthetic aperture focusing system including a custom-designed transceiver operating at 35 - 45 GHz (Q-band) and unique and complex rotary scanner was designed and developed. The rotary scanner is capable of scanning an area with approximately 80 cm in diameter in less than 10 minutes at step sizes of 3 mm and smaller. The transceiver is capable of producing accurate magnitude and phase of reflected signal from the structure under test. Finally, a synthetic aperture focusing algorithm was developed that translates this rotary-obtained magnitude and phase into a synthetic aperture focusing image of inspected structures. This paper presents the design of the transceiver and the rotary scanning system along with showing several images obtained with this system from various complicated structures.

Ghasr, M. T.↗

Millimeter Wave Holographical Inspection of Honeycomb Composites

Multi-layered composite structures manufactured with honeycomb, foam or balsa wood cores are finding increasing utility in a variety of aerospace, transportation, and infrastructure applications. Due to the low conductivity and inhomogeneity associated with these composites standard nondestructive testing (NDT) methods are not always capable of inspecting their interior for various defects caused during the manufacturing process or as a result of in-service loading. On the contrary, microwave and millimeter wave NDT methods are well-suited for inspecting these structures since signals at these frequencies readily penetrate through these structures and reflect from different interior boundaries revealing the presence of a wide range of defects such as disbond, delamination, moisture and oil intrusion, impact damage, etc. Millimeter wave frequency spectrum spans 30 GHz - 300 GHz with corresponding wavelengths of 10 - 1 mm. Due to the inherent short wavelengths at these frequencies, one can produce high spatial resolution images of these composites either using real-antenna focused or synthetic-aperture focused methods. In addition, incorporation of swept-frequency in the latter method (i.e., holography) results in high-resolution three-dimensional images. This paper presents the basic steps behind producing such images at millimeter wave frequencies and the results of two honeycomb composite panels are demonstrated at Q-band (33-50 GHz). In addition, these results are compared to previous results using X-ray computed tomography.

Case, J. T.↗

Sub-millimeter wave frequency heterodyne detector system

The present invention relates to sub-millimeter wave frequency heterodyne imaging systems. More specifically, the present invention relates to a sub-millimeter wave frequency heterodyne detector system for imaging the magnitude and phase of transmitted power through or reflected power off of mechanically scanned samples at sub-millimeter wave frequencies.

Siegel, Peter H.↗

Sub-millimeter wave frequency heterodyne detector system

The present invention relates to sub-millimeter wave frequency heterodyne imaging systems. More specifically, the present invention relates to a sub-millimeter wave frequency heterodyne detector system for imaging the magnitude and phase of transmitted power through or reflected power off of mechanically scanned samples at sub-millimeter wave frequencies.

Siegel, Peter H.↗

Modeling of LEO Orbital Debris Populations in Centimeter and Millimeter Size Regimes

The building of the NASA Orbital Debris Engineering Model, whether ORDEM2000 or its recently updated version ORDEM2010, uses as its foundation a number of model debris populations, each truncated at a minimum object-size ranging from 10 micron to 1 m. This paper discusses the development of the ORDEM2010 model debris populations in LEO (low Earth orbit), focusing on centimeter (smaller than 10 cm) and millimeter size regimes. Primary data sets used in the statistical derivation of the cm- and mm-size model populations are from the Haystack radar operated in a staring mode. Unlike cataloged objects of sizes greater than approximately 10 cm, ground-based radars monitor smaller-size debris only in a statistical manner instead of tracking every piece. The mono-static Haystack radar can detect debris as small as approximately 5 mm at moderate LEO altitudes. Estimation of millimeter debris populations (for objects smaller than approximately 6 mm) rests largely on Goldstone radar measurements. The bi-static Goldstone radar can detect 2- to 3-mm objects. The modeling of the cm- and mm-debris populations follows the general approach to developing other ORDEM2010-required model populations for various components and types of debris. It relies on appropriate reference populations to provide necessary prior information on the orbital structures and other important characteristics of the debris objects. NASA's LEO-to-GEO Environment Debris (LEGEND) model is capable of furnishing such reference populations in the desired size range. A Bayesian statistical inference process, commonly adopted in ORDEM2010 model-population derivations, changes a priori distribution into a posteriori distribution and thus refines the reference populations in terms of data. This paper describes key elements and major steps in the statistical derivations of the cm- and mm-size debris populations and presents results. Due to lack of data for near 1-mm sizes, the model populations of 1- to 3.16-mm objects are an empirical extension from larger debris. The extension takes into account the results of micro-debris (from 10 micron to 1 mm) population modeling that is based on shuttle impact data, in the hope of making a smooth transition between micron and millimeter size regimes. This paper also includes a brief discussion on issues and potential future work concerning the analysis and interpretation of Goldstone radar data.

Xu, Y.-L.↗

A Three-Frequency Feed for Millimeter-Wave Radiometry

A three-frequency millimeter-wave feed horn was developed as part of an advanced component technology task that provides components necessary for higher-frequency radiometers to meet the needs of the Surface Water and Ocean Topography (SWOT) mission. The primary objectives of SWOT are to characterize ocean sub-mesoscale processes on 10-km and larger scales in the global oceans, and to measure the global water storage in inland surface water bodies, including rivers, lakes, reservoirs, and wetlands. In this innovation, the feed provides three separate output ports in the 87-to- 97-GHz, 125-to-135-GHz, and 161-to-183- GHz bands; WR10 for the 90-GHz channel, WR8 for the 130-GHz channel, and WR5 for the 170-GHz channel. These ports are in turn connected to individual radiometer channels that will also demonstrate component technology including new PIN-diode switches and noise diodes for internal calibration integrated into each radiometer front end. For this application, a prime focus feed is required with an edge taper of approximately 20 dB at an illumination angle of 40 deg. A single polarization is provided in each band. Preliminary requirements called for a return loss of better than 15 dB, which is achieved across all three bands. Good pattern symmetry is also obtained throughout all three-frequency bands. This three-frequency broadband millimeter-wave feed also minimizes mass and provides a common focal point for all three millimeter-wave bands.

Hoppe, Daniel J.↗

Transition-Edge Hot-Electron Microbolometers for Millimeter and Submillimeter Astrophysics

The millimeter and the submillimeter wavelengths of the electromagnetic spectrum hold a wealth of information about the evolution of the universe. In particular, cosmic microwave background (CMB) radiation and its polarization carry the oldest information in the universe, and provide the best test of the inflationary paradigm available to astronomy today. Detecting gravity waves through their imprint on the CMB polarization would have extraordinary repercussions for cosmology and physics. A transition-edge hot-electron micro - bolometer (THM) consists of a superconducting bilayer transition-edge sensor (TES) with a thin-film absorber. Unlike traditional monolithic bolometers that make use of micromachined structures, the THM em ploys the decoupling between electrons and phonons at millikelvin temperatures to provide thermal isolation. The devices are fabricated photolithographically and are easily integrated with antennas via microstrip transmission lines, and with SQUID (superconducting quantum interference device) readouts. The small volume of the absorber and TES produces a short thermal time constant that facilitates rapid sky scanning. The THM consists of a thin-film metal absorber overlapping a superconducting TES. The absorber forms the termination of a superconducting microstripline that carries RF power from an antenna. The purpose of forming a separate absorber and TES is to allow flexibility in the optimization of the two components. In particular, the absorbing film's impedance can be chosen to match the antenna, while the TES impedance can be chosen to match to the readout SQUID amplifier. This scheme combines the advantages of the TES with the advantages of planar millimeter-wave transmission line circuits. Antenna-coupling to the detectors via planar transmission lines allows the detector dimensions to be much smaller than a wavelength, so the technique can be extended across the entire microwave, millimeter, and submillimeter wavelength ranges. The circuits are fabricated using standard microlithographic techniques and are compatible with uniform, large array formats. Unlike traditional monolithic bolometers that make use of micromachined structures, the THM employs the decoupling between electrons and phonons at millikelvin temperatures to provide thermal isolation. There is no fragile membrane in the structure for thermal isolation, which improves the fabrication yield.

Hsieh, Wen-Ting↗