The Roman Space Telescope Grism and Prism assemblies will allow the wide-field instrument (WFI) to perform slitless, multi-object spectroscopy across the complete field of view. These optical elements play a critical role in the High Latitude Wide Area and High Latitude Time Domain Surveys, which are designed to produce robust spectroscopic redshifts for millions of objects over the mission lifetime. To facilitate the characterization of these assemblies, a dedicated test bed was designed and utilized to perform a wide variety of spectroscopic measurements over the full range of operational wavelengths and field angles. Characterized features include, but are not limited to dispersion magnitude, dispersion clocking, encircled energy, total throughput, and bandpass edges. We present the results of this experimental campaign in which the Grism and Prism assemblies met or exceeded many of their design requirements and discuss measurement limitations.
The Nancy Grace Roman Space Telescope (“Roman”) was prioritized by the 2010 Decadal Survey in Astronomy & Astrophysics and is NASA’s next flagship observatory. Launching no earlier than 2026, Roman will explore the nature of dark energy, as well as expand the census of exoplanets in our galaxy via microlensing. Roman will also demonstrate key technology needed to image and spectrally characterize extra-solar planets. Roman’s large field of view, agile survey capabilities, and excellent stability enable these scientific objectives, yet present unique challenges for the design, test, and verification of its optical system. The Roman optical system comprises an optical telescope assembly (OTA) and two instruments: the primary science wide-field instrument (WFI) and a technology demonstration coronagraph instrument (CGI), and the instrument carrier (IC), which meters the OTA to each instrument. This paper presents a status of the optical system hardware as it begins integration and test (I&T), as well as describes key optical test, alignment, and verification activities as part of the I&T program.
The Wide-Field instrument (WFI) for the Roman Space Telescope (RST) features an imaging camera that comprises the Wide-Field Channel (WFC) with several bandpass filters, a spectroscopic dispersion unit called the Grism, and a Prism Assembly (PA), which took the place of the descoped Integral-Field Channel (IFC) assembly. The PA system consists of two prism elements made from S-TIH1 glass (P1) and CaF2 substrate (P2) that together will provide slitless low resolution spectroscopy with a spectral resolution R < 70 at all wavelengths, and R < 170 for wavelengths λ < 0.8 μm, across the full field. One key feature of the P1 element is the application of a bandpass coating that operates in the 0.75-1.8 μm spectral region. The extension of the bandpass towards short wavelengths greatly enhances the capabilities of RST for studies of stellar populations that provides additional means of testing in supernova studies. We have used spectroscopic techniques such as a double-beam monochromator and Fourier Transform InfraRed (FTIR) spectroscopy to characterize the spectral performance of the bandpass coatings of the P1 element. The coating technology used to produce these bandpass optical coatings has been demonstrated in the successful mission of the Mars Perseverance Rover in February of 2021.
We have published the optical design and early test results of the Roman Space Telescope grism spectrometer in previous SPIE proceedings. We report the follow-on activity of the spectral and radiometric calibrations, including the calibration methods, experiment designs, and test equipment calibration, such as the light source and detectors used in the test. The grism calibration includes the throughput versus wavelength, which is largely determined by the diffraction efficiency of the two diffractive surfaces. It also includes spectral resolution, point spread function, and relative radiometric measurements. The measured results are presented. The comparisons between the test data and the theoretical simulations are also presented. The tests and results presented are from the engineering test unit in ambient room temperature environment. The thermal/vacuum tests are planned to verify the results when the flight unit is ready.
We have presented the optical design and early test result of WFIRST grism spectrometer in previous SPIE conferences. This paper reports the follow-on activity of the spectral and radiometric calibrations, including the calibration methods, experiment designs, and the light source and detector calibration. The real grism calibration includes the throughput versus wavelength, which is largely determined by the diffraction efficiency of the two diffractive surfaces. It also includes spectral resolution, point spread function, and encircle energy measurements. The measured data are presented. The comparisons between the test data and the simulation from theory, or optical model, are also presented.
The WFIRST wide field instrument (WFI) includes a slitless spectrometer, which plays an important role in the WFIRST mission for the survey of emission-line galaxies. WFI is building engineering design and environmental test (EDU and ETU) units to reduce risk for the flight grism unit. We report here on successful build and test of the EDU grism. The four-element EDU grism consists of two prism elements and two diffractive elements that provide R700 dispersion. The elements were fabricated with alignment fiducials and integral flats to allow opto-mechanical alignment in six-degrees of freedom. Each element in turn, was installed onto a hexapod and positioned to its nominal orientation relative to the grism deck, then bonded into individual cells. Alignment measurements were performed in situ using theodolites to set tip/tilt and a Micro-vu non-contact Multisensor Measurement System was used to set despace, decenter and clocking of each element using the hexapod. After opto-mechanical alignment, the grism wavefront was measured using an Infrared ZYGO interferometer at various field points extending over a 20 by 14- degree (local) field of view. Using modeled alignment sensitivities, we determined the alignment correction required on our Element 2 prism compensator and successfully minimized the field dependent wavefront error and confocality. This paper details the alignment and testing of the EDU grism at ambient and cold operating temperatures.
Now in Phase-B, the architecture of the Wide-Field Infra-Red Survey Telescope (WFIRST) payload has matured since 2013 to accommodate various opto-mechanical constraints. Based on a 2.4-meter aperture Forward Optical Assembly (FOA), the Imaging Optics Assembly (IOA) provides corrected optical fields to each on-board instrument. Using a Three Mirror Anastigmat (TMA) optical design, the Wide-Field Channel (WFC) provides ~1/3-square degree of instantaneous field coverage at 0.11 arcsecond pixel scale. The WFC as-built predictive analysis anticipates near diffraction-limited imaging over a focal plane of 300.8 million pixels, operating in seven panchromatic bands between 0.48 – 2.0μm, or a 1-octive multi-spectral imaging mode from ~0.95-1.93μm. The IOA provides the Coronagraph Instrument (CGI) a collimated beam with very specific wavefront constraints. We present configuration changes since 2013 that improved interfaces, improved testability, and reduced technical risk. We provide an overview of our Integrated Modeling results, performed at an unprecedented level for a phase-A study, to illustrate performance margins with respect to static wavefront error, jitter, and thermal drift.
Interferometers using computer-generated holograms (CGHs) have become the industry standard to accurately measure aspheric optics. The CGH is a diffractive optical element that can create a phase or amplitude distribution and can be manufactured with low uncertainty using modern lithographic techniques. However, these CGHs have conventionally been used with visible light and piezo-shifting interferometers. Testing the performance of transmissive optics in the infrared requires infrared CGHs and an infrared interferometer. Such an instrument is used in this investigation, which introduces its phase shift via wavelength-tuning. A procedure on how to design and manufacture infrared CGHs and how these were successfully used to model and measure the Wide-Field Infrared Survey Telescope grism elements is provided. Additionally, the paper provides a parametric model, simulation results, and calculations of the errors and measurements that come about when interferometers introduce a phase variation via wavelength-tuning interferometry to measure precision aspheres.
NASA’s Wide Field Infrared Survey Telescope (WFIRST) is being designed to deliver unprecedented capability in dark energy and exoplanet science, and to host a technology demonstration coronagraph for exoplanet imaging and spectroscopy. The observatory design has matured since 2013 [“WFIRST 2.4m Mission Study”, D. Content, SPIE Proc Vol 8860, 2013] and we present a comprehensive description of the WFIRST observatory configuration as refined during formulation phase (AKA the phase-A study). The WFIRST observatory is based on an existing, repurposed 2.4m space telescope coupled with a 288 megapixel near-infrared (0.6 to 2 microns) HgCdTe focal plane array with multiple imaging and spectrographic modes. Together they deliver a 0.28 square degree field of view, which is approximately 100 times larger than the Hubble Space Telescope, and a sensitivity that enables rapid science surveys. In addition, the technology demonstration coronagraph will prove the feasibility of new techniques for exoplanet discovery, imaging, and spectral analysis. A composite truss structure meters both instruments to the telescope assembly, and the instruments and the spacecraft are on-orbit serviceable. We present the current design and summarize key Phase-A trade studies and configuration changes that improved interfaces, improved testability, and reduced technical risk. We provide an overview of our Integrated Modeling results, performed at an unprecedented level for a phase-A study, to illustrate performance margins with respect to static wavefront error, jitter, and thermal drift. Finally, we summarize the results of technology development and peer reviews, demonstrating our progress towards a low-risk flight development and a launch in the middle of the next decade.
WFIRST is one of NASA’s Decadal Survey Missions and is currently in Phase-A development. The optical design of the WFIRST Integral Field Channel (IFC), one of three main optical channels of WFIRST, is presented, and the evolution of the IFC channel since the Mission Concept Review (MCR, end of Pre-Phase A) is discussed. The IFC has two subchannels: Supernova (IFC-S) and Galaxy (IFC-G) channels, with Fields of View of 3”x4.5” and 4.2”x9” respectively, and ~R 100 spectral analysis over waveband 0.42–2.0 μm. The Phase-A IFC optical design meets image quality requirements over the field of view (FOV) while balancing cost and volume constraints.
The WFIRST Wide-Field Infrared Survey Telescope TMA optical design provides 0.28-sq° FOV at 0.11” pixel scale to the Wide Field Instrument, operating between 0.48-2.0μm, including a spectrograph mode (1.0-2.0μm.) An Integral Field Channel provides 2-D discrete spectroscopy at 0.15” and 0.3” sampling from 0.42-2.0μm.
KEYWORDS: Space telescopes, Telescopes, Mirrors, Infrared telescopes, Space operations, Optical telescopes, Coronagraphy, Monte Carlo methods, Infrared astronomy, Infrared radiation
The Wide-Field Infrared Survey Telescope (WFIRST) mission[1] is the top-ranked large space mission in the New Worlds, New Horizon (NWNH) Decadal Survey of Astronomy and Astrophysics. WFIRST will settle essential questions in both exoplanet and dark energy research and will advance topics ranging from galaxy evolution to the study of objects within the galaxy. The WFIRST mission uses a repurposed 2.4-m Forward Optical Telescope assembly (FOA), which, when completed with new aft optics will be an Integrated Optical Assembly (IOA). WFIRST is equipped with a Wide Field Instrument (WFI) and a Coronagraph Instrument (CGI). An Instrument Carrier (IC) meters these payload elements together and to the spacecraft bus (S/C). A distributed ground system receives the data, uploads commands and software updates, and processes the data. After transition from the study phase, Pre-Phase-A (a.k.a., “Cycle 6”) design to NASA Phase A formulation, a significant change to the IOA was initiated; including moving the tertiary mirror from the instrument package to a unified three-mirror anastigmat (TMA) placement, that provides a wide 0.28-sq° instrumented field of view to the Wide Field Instrument (WFI). In addition, separate relays from the primary and secondary mirror feed the Wide Field Instrument (WFI) and Coronagraph Instrument (CGI). During commissioning the telescope is aligned using wavefront sensing with the WFI[2]. A parametric and Monte-Carlo analysis was performed, which determined that alignment compensation with the secondary mirror alone degraded performance in the other instruments. This led to the addition of a second compensator in the WFI optical train to alleviate this concern. This paper discusses the trades and analyses that were performed and resulting changes to the WFIRST telescope architecture.
The slitless spectrometer plays an important role in the WFIRST mission for the survey of emission-line galaxies. This
will be an unprecedented very wide field, HST quality 3D survey of emission line galaxies1. The concept of the
compound grism as a slitless spectrometer has been presented previously. The presentation briefly discusses the
challenges and solutions of the optical design, and recent specification updates, as well as a brief comparison between
the prototype and the latest design. However, the emphasis of this paper is the progress of the grism prototype: the
fabrication and test of the complicated diffractive optical elements and powered prism, as well as grism assembly
alignment and testing. Especially how to use different tools and methods, such as IR phase shift and wavelength shift
interferometry, to complete the element and assembly tests. The paper also presents very encouraging results from
recent element tests to assembly tests. Finally we briefly touch the path forward plan to test the spectral characteristic,
such as spectral resolution and response.
The PISCES (Prototype Imaging Spectrograph for Coronagraphic Exoplanet Studies) is a lenslet array based integral field spectrograph (IFS) designed to advance the technology readiness of the WFIRST-AFTA high contrast Coronagraph Instrument. We present the end to end optical simulator and plans for the data reduction pipeline (DRP). The optical simulator was created with a combination of the IDL-based PROPER library and Zemax, while the data reduction pipeline is a modified version of the Gemini Planet Imager's (GPI) IDL pipeline. The simulations of the propagation of light through the instrument are based on Fourier transform algorithms. The DRP enables transformation of the PISCES IFS data to calibrated spectral data cubes.
Prototype Imaging Spectrograph for Coronagraphic Exoplanet Studies (PISCES) is a lenslet array based integral field spectrometer (IFS) designed for high contrast imaging of extrasolar planets. PISCES will be used to advance the technology readiness of the high contrast IFS baselined on the Wide-Field InfraRed Survey Telescope/Astrophysics Focused Telescope Assets (WFIRST-AFTA) coronagraph instrument. PISCES will be integrated into the high contrast imaging testbed (HCIT) at the Jet Propulsion Laboratory (JPL) and will work with both the Hybrid Lyot Coronagraph (HLC) and the Shaped Pupil Coronagraph (SPC) configurations. We discuss why the lenslet array based IFS was selected for PISCES. We present the PISCES optical design, including the similarities and differences of lenslet based IFSs to normal spectrometers, the trade-off between a refractive design and reflective design, as well as the specific function of our pinhole mask on the back surface of the lenslet array to reduce the diffraction from the edge of the lenslets. The optical analysis, alignment plan, and mechanical design of the instrument will be discussed.
The recommended design approach for the 3D Tropospheric Winds mission is a hybrid Doppler lidar which combines the best elements of both a coherent aerosol Doppler lidar operating at 2 μm and a direct detection molecular Doppler lidar operating at 0.355 μm. In support of the mission, we built a novel, compact, light-weighted multi-field of view transceiver where multiple telescopes are used to cover the required four fields of view. A small mechanism sequentially selects both the “transmit” and “receive” fields of view. The four fields are combined to stimulate both the 0.355 μm receiver and the 2 μm receiver. This version is scaled (0.2 m diameter aperture) from the space-based version but still demonstrates the feasibility of the hybrid approach. The primary mirrors were conventionally light-weighted and coated with dielectric, high reflectivity coatings with high laser damage thresholds at both 2 μm and 0.355 μm. The mechanical structure and mounts were fabricated from composites to achieve dimensional stability while significantly reducing the mass. In the laboratory, we demonstrated the system level functionality at 0.355 μm and at 2 μm, raising the Technology Readiness Level (TRL) from 2 to 4.
The Goddard IRAM Superconducting Millimeter Observer (GISMO) is a new superconducting bolometer array camera
for the IRAM 30 Meter Telescope on Pico Veleta, Spain. GISMO uses a 3He/4He cooler mounted to a liquid He/LN2
cryostat to cool the bolometer array and SQUID electronics to an operating temperature of 260mK. The bolometer array
is based on the backshort-under-grid architecture and features 128 2mm square absorbing pixels. A 101mm diameter
anti-reflection coated silicon lens is used to define the beam. A single cold pupil stop prevents warm radiation from
reaching the array, but no other stops are used. In the beam, filters and a cold baffling and stray light suppression system
were used to define the bandpass and prevent out-of-band radiation to a very high level, including out-of-band radiation
leaking through the metal-mesh filters from extreme angles. We present a detailed description of this optical design and
its performance. A comprehensive report of the electronics and cryogenic integration are also included.
We are building a bolometer camera (the Goddard-Iram Superconducting 2-Millimeter Observer, GISMO) for operation in the 2 mm atmospheric window to be used at the IRAM 30 m telescope. The instrument uses a 8x16 planar array of multiplexed TES bolometers which incorporates our newly designed Backshort Under Grid (BUG) architecture. Due to the size and sensitivity of the detector array (the NEP of the detectors is 4×10-17 W/√Hz), this instrument will be unique in that it will be capable of providing significantly greater imaging sensitivity and mapping speed at this wavelength than has previously been possible. The major scientific driver for this instrument is to provide the IRAM 30 m telescope with the capability to rapidly observe galactic and extragalactic dust emission, in particular from high-z ULIRGs and quasars, even in the summer season. The 2 mm spectral range provides a unique window to observe the earliest active dusty galaxies in the universe and is well suited to better confine the star formation rate in these objects. The instrument will fill in the SEDs of high redshift galaxies at the Rayleigh-Jeans part of the dust emission spectrum, even at the highest redshifts. The observational efficiency of a 2 mm camera with respect to bolometer cameras operating at shorter wavelengths increases for objects at redshifts beyond z ~ 1 and is most efficient at the highest redshifts, at the time when the first stars were re-ionizing the universe. Our models predict that at this wavelength one out of four serendipitously detected galaxies will be at a redshift of z > 6.5.
Prior to launch, the Spitzer Space Telescope (SST) secondary focus mechanism was set to a predicted desired in-orbit focus value. This predicted setting, determined from double-pass cold chamber measurements and calculated ground-to-orbit corrections, had an uncertainty greater than the required in-orbit focus accuracy. Because of concern about the potential for failure in a cryogenic mechanism affecting all Spitzer instruments, it was required that any focus correction be made in a set of moves directly from the initial to the desired setting. The task of determining the required focus moves fell to IRAC (Infrared Array Camera), the instrument most affected by and sensitive to defocus. To determine the focus directly from examining images at a fixed focus, we developed two methods, "Simfit" and "Focus Diversity" (W. F. Hoffmann, et. al.1). Simfit finds the focus by obtaining the best match between observed images and families of simulated images at a range of focus settings. Focus Diversity utilizes the focal plane curvature to find the best fit of the varied image blur over the focal plane to a model defocus curve. Observations of a single star at many field locations in each of the four IRAC bands were analyzed before and during the refocus activity. The resulting refocus moves brought the focus close to the specified requirement of within 0.3 mm from the desired IRAC optimum focus. This is less than a "Diffraction Focus Unit" (λx(f/2)) of 0.52 mm at the SST focus at the shortest IRAC band (3.58 microns). The improvement in focus is apparent in both the appearance and the calculated noise-pixels of star images.
The Infrared Array Camera (IRAC) is one of three focal plane instruments on board the Spitzer Space Telescope. IRAC is a four-channel camera that obtains simultaneous broad-band images at 3.6, 4.5, 5.8, and 8.0 μm in two nearly adjacent fields of view. We summarize here the in-flight scientific, technical, and operational performance of IRAC.
The Infrared Array Camera (IRAC) on board the Spitzer Space Telescope uses two dichroic beamsplitters, four interference filters, and four detector arrays to acquire images in four different channels with nominal wavelengths of 3.6, 4.5, 5.8, and 8 μm for channels 1 through 4 respectively. A ray-tracing analysis of the IRAC optical system indicates a distribution of angles that is position-dependent at each optical element and the focal-plane arrays. For the band-pass filters in channels 1 and 2, the angle distribution relative to the filter surface normal is 0-28°, whereas for channels 3 and 4, the distribution is from 30° to 58°. Since these angle variations will cause changes in the center-band wavelengths for these interference filters that needed to be accounted for, we performed spectral performance measurements as a function of the angle of incidence on witness samples corresponding to each of the four filters and the two beamsplitters in the IRAC instrument. These
measurements were done in the 2-10 μm wavelength range and at the temperature of 5 K, which is near the operating temperature of IRAC. Based on these filter measurements, we also performed an analysis of the pass-band wavelength distributions as a function of position on the instrument focal-plane array detectors. This information is necessary to attain the highest possible photometric accuracy when using IRAC for astronomical observations.
KEYWORDS: Sensors, Space telescopes, Telescopes, Mirrors, Digital signal processing, Beam splitters, Interferometers, Wavefronts, Control systems, Prototyping
The Earth Atmospheric Solar-Occultation Imager (EASI) is a proposed interferometer with 5 telescopes on an 8-meter boom in a 1D Fizeau configuration. Placed at the Earth-Sun L2 Lagrange point, EASI would perform absorption spectroscopy of the Earth’s atmosphere occulting the Sun. Fizeau interferometers give spatial resolution comparable to a filled aperture but lower collecting area. Even with the small collecting area the high solar flux requires most of the energy to be reflected back to space. EASI will require closed loop control of the optics to compensate for spacecraft and instrument motions, thermal and structural transients and pointing jitter. The Solar Viewing Interferometry Prototype (SVIP) is a prototype ground instrument to study the needed wavefront control methods. SVIP consists of three 10 cm aperture telescopes, in a linear configuration, on a 1.2-meter boom that will estimate atmospheric abundances of O2, H2O, CO2, and CH4 versus altitude and azimuth in the 1.25 - 1.73 micron band. SVIP measures the Greenhouse Gas absorption while looking at the sun, and uses solar granulation to deduce piston, tip and tilt misalignments from atmospheric turbulence and the instrument structure. Tip/tilt sensors determine relative/absolute telescope pointing and operate from 0.43 - 0.48 microns to maximize contrast. Two piston sensors, using a robust variation of dispersed fringes, determine piston shifts between the baselines and operate from 0.5 - 0.73 microns. All sensors are sampled at 800 Hz and processed with a DSP computer and fed back at 200 Hz (3 dB) to the active optics. A 4 Hz error signal is also fed back to the tracking platform. Optical performance will be maintained to better than λ/8 rms in closed-loop.
Because of concern over possible failure of the SIRTF cryogenic focus mechanism in space, the SIRTF Project Office has directed that the focus should be set before launch so that the telescope arrives in orbit as close to optimum focus as possible. Then focus evaluation and determination of any required focus change to achieve best focus must be carried out without the conventional approach of a focus slew. For these tasks we have created two methods: Simfit and Focus Diversity. Simfit is a procedure for comparing an observed stellar image with a family of simulated point-source images with a range of focus settings. With a sufficiently accurate as-built telescope model for creating the simulated images, the focus offset and direction can be accurately and unambiguously determined because of the change in image appearance with defocus. Focus diversity takes advantage of the variation of best-focus setting over the instrument's focal plane due to focal plane curvature and tilt and offsets between different instrument channels. By plotting an image quality parameter, such as noise-pixels, for observed stars at several positions on the focal plane versus a defocus variable, the focus error and direction can be determined. We have developed an efficient program for carrying out these procedures. The validity of this program has been successfully confirmed using point-source images observed with three bands of the IRAC camera during a double-pass optical test of SIRTF in a Ball Aerospace cryogenic test chamber. The two procedures are described and are illustrated with these results
A wide field (6x6 arcmin2) Rapid Infrared-Visible Multi-Object Spectrometer (RIVMOS) has been designed and is being fabricated at NASA's GSFC as part of the Next Generation Space Telescope (NGST) development and new technology demonstration. The primary goal is to demonstrate that the microshutter arrays, currently being designed for the NGST Near Infrared Spectrometer (NIRSpec) as programmable 2D selection masks, can achieve the optical performance required for faint object imaging and spectroscopy.
We developed an original optical design that includes both reflective and refractive optics. The primary goal of the design was to achieve high imaging quality in both imaging and spectroscopy modes over a very wide spectral range with all spherical surfaces. The required optical performance is achieved for both multi-object spectroscopy and camera imaging over the entire field-of-view. The optical design consists of six optical subsystems including (1) an image relay consisting of a three-mirror anastigmat (TMA), (2) the microshutter assembly, (3) a triplet collimating optic, (4) a grism/filter assembly, (5) a pupil imaging optic, and (6) a five element telecentric camera design.
The all-spherical optical design reduces construction costs and facilitates fabrication of the optical assembly while maintaining an encircled energy of 2 pixels within the FOV for wavelengths between 0.6 and 5.0 microns. Three spectral resolution modes (R = 50, 2000, 4000) will be available for multi-object spectroscopy as well as cross-dispersed echelle spectroscopy at the highest spectral resolution. The low resolution mode will be provided by the direct view prism, whereas silicon grisms will be used for higher resolving power. This design provides an extremely wide spectral range, wide field, very compact, high resolution imager-spectrometer with multi-object capability.
The Infrared Array Camera (IRAC) is one of three science instruments that will fly aboard the Space Infrared Telescope Facility mission scheduled for launch in December, 2001. This paper summarizes the `as built' design of IRAC along with important integration and testing results.
The Composite Infrared Spectrometer (CIRS) is an instrument currently under development at NASA Goddard Space Flight Center for the Cassini mission to Saturn. The CIRS optical design heritage extends back to the Infrared Interferometer Spectrometer (IRIS) which flew on Voyager. CIRS is the next logical step in the exploration of the atmosphere of Saturn and Titan. It will obtain more complete sets of data with broader spectral coverage, higher spectral and spatial resolution, and greater sensitivity. The CIRS optical design consists of four subassemblies: (1) a 50.8 cm diameter Cassegrain telescope, (2) a Mid-Infrared (MIR) Michelson interferometer, (3) a Far-Infrared (FIR) polarizing interferometer, and (4) a Reference interferometer (RI).
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