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16 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

SCExAO: First Results and On-Sky Performance

We present new on-sky results for the Subaru Coronagraphic Extreme Adaptive Optics imager (SCExAO) verifying and quantifying the contrast gain enabled by key components: the closed-loop coronagraphic low-order wavefront sensor (CLOWFS) and focal plane wavefront control ("speckle nulling"). SCExAO will soon be coupled with a high-order, Pyramid wavefront sensor which will yield greater than 90% Strehl ratio and enable 10(exp 6) -10(exp 7) contrast at small angular separations allowing us to image gas giant planets at solar system scales. Upcoming instruments like VAMPIRES, FIRST, and CHARIS will expand SCExAO's science capabilities.

Subaru Coronagraphic Extreme Adaptive Optics image↗
NASA NTRS2019

Multi-epoch Direct Imaging and Time-variable Scattered Light Morphology of the HD 163296 Protoplanetary Disk

We present H-band polarized scattered light imagery and JHK high-contrast spectroscopy of the protoplanetary disk around HD 163296 observed with the High-Contrast Coronographic Imager for Adaptive Optics (HiCIAO) and Subaru Coronagraphic Extreme Adaptive Optics (SCExAO)/Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS) instruments at Subaru Observatory. The polarimetric imagery resolve a broken ring structure surrounding HD 163296 that peaks at a distance along the major axis of 0 65 (66 au) and extends out to 0 98 (100 au) along the major axis. Our 2011 H-band data exhibit clear axisymmetry, with the NW and SE side of the disk exhibiting similar intensities. Our data are clearly different from 2016 epoch H-band observations of the Very Large Telescope (VLT)/Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE), which found a strong 2.7 x asymmetry between the NW and SE side of the disk. Collectively, these results indicate the presence of time-variable, non-azimuthally symmetric illumination of the outer disk. While our SCExAO/CHARIS data are sensitive enough to recover the planet candidate identified from NIRC2 in the thermal infrared (IR), we fail to detect an object with JHK brightness nominally consistent with this object. This suggests that the candidate is either fainter in JHK bands than model predictions, possibly due to extinction from the disk or atmospheric dust/ clouds, or that it is an artifact of the data set/data processing, such as a residual speckle or partially subtracted disk feature. Assuming standard hot-start evolutionary models and a system age of 5Myr, we set new, direct mass limits for the inner (outer) Atacama Large Millimeter/submillimeter Array (ALMA)-predicted protoplanet candidate along the major (minor) disk axis of of 1.5 (2) M(J).

Evan A. Rich↗
NASA NTRS2015

The CHARIS IFS for high contrast imaging at Subaru

The Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS) is an integral field spectrograph (IFS) being built for the Subaru telescope. CHARIS will take spectra of brown dwarfs and hot Jovian planets in the coronagraphic image provided by the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) and AO188 adaptive optics systems. The system is designed to detect objects five orders of magnitude dimmer than their parent star down to an 80 milliarcsecond inner working angle. For characterization, CHARIS has a high-resolution prism providing an average spectral resolution of R82, R69, and R82 in J, H, and K bands respectively. The so-called discovery mode uses a second low-resolution prism with an average spectral resolution of R19 spanning 1.15-2.37 microns (J+H+K bands). This is unique compared to other high contrast IFS designs. It augments low inner working angle performance by reducing the separation at which we can rely on spectral differential imaging. The principal challenge for a high-contrast IFS is quasi-static speckles, which cause undue levels of spectral crosstalk. CHARIS has addressed this through several key design aspects that should constrain crosstalk between adjacent spectral features to be below 1%. Sitting on the Nasmyth platform, the alignment between the lenslet array, prism, and detector will be highly stable, key for the performance of the data pipeline. Nearly every component has arrived and the project is entering its final build phase. Here we review the science case, the resulting design, status of final construction, and lessons learned that are directly applicable to future exoplanet instruments.

Subaru Coronagraphic Extreme Adaptive Optics (SCEx↗
DOE OSTI2020

SCExAO/CHARIS Near-infrared Integral Field Spectroscopy of the HD 15115 Debris Disk

We present new, near-infrared (1.1–2.4 μm) high-contrast imaging of the debris disk around HD 15115 with the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system coupled with the Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS). The SCExAO/CHARIS resolves the disk down to ρ ∼ 0.″2 (r {sub proj} ∼ 10 au), a factor of ∼3–5 smaller than previous recent studies. We derive a disk position angle of PA ∼ 279.°4–280.°5 and an inclination of i ∼ 85.°3–86.2.°. While recent SPHERE/IRDIS imagery of the system could suggest a significantly misaligned two-ring disk geometry, CHARIS imagery does not reveal conclusive evidence for this hypothesis. Moreover, optimizing models of both one- and two-ring geometries using differential evolution, we find that a single ring having a Hong-like scattering phase function matches the data equally well within the CHARIS field of view (ρ ≲ 1″). The disk’s asymmetry, well evidenced at larger separations, is also recovered; the west side of the disk appears, on average, around 0.4 mag brighter across the CHARIS bandpass between 0.″25 and 1″. Comparing Space Telescope Imaging Spectrograph (STIS) 50CCD optical photometry (2000–10500 Å) with CHARIS near-infrared photometry, we find a red (STIS/50CCD−CHARIS broadband) color for both sides of the disk throughout the 0.″4–1″ region of overlap, in contrast to the blue color reported at similar wavelengths for regions exterior to ∼2″. Further, this color may suggest a smaller minimum grain size than previously estimated at larger separations. Finally, we provide constraints on planetary companions and discuss possible mechanisms for the observed inner disk flux asymmetry and color.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2020

SCExAO/CHARIS Near-infrared Integral Field Spectroscopy of the HD 15115 Debris Disk

We present new, near-infrared (1.1–2.4 μm) high-contrast imaging of the debris disk around HD 15115 with the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system coupled with the Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS). The SCExAO/CHARIS resolves the disk down to ρ ∼ 0."2 (r(proj) ∼ 10 au), a factor of ∼3–5 smaller than previous recent studies. We derive a disk position angle of PA ∼ 279.°4–280.°5 and an inclination of i ∼ 85.°3–86.2.°. While recent SPHERE/IRDIS imagery of the system could suggest a significantly misaligned two-ring disk geometry, CHARIS imagery does not reveal conclusive evidence for this hypothesis. Moreover, optimizing models of both one- and two-ring geometries using differential evolution, we find that a single ring having a Hong-like scattering phase function matches the data equally well within the CHARIS field of view (ρ ≲ 1''). The disk's asymmetry, well evidenced at larger separations, is also recovered; the west side of the disk appears, on average, around 0.4 mag brighter across the CHARIS bandpass between 0farcs25 and 1''. Comparing Space Telescope Imaging Spectrograph (STIS) 50CCD optical photometry (2000–10500 Å) with CHARIS near-infrared photometry, we find a red (STIS/50CCD−CHARIS broadband) color for both sides of the disk throughout the 0farcs4–1'' region of overlap, in contrast to the blue color reported at similar wavelengths for regions exterior to ∼2''. Further, this color may suggest a smaller minimum grain size than previously estimated at larger separations. Finally, we provide constraints on planetary companions and discuss possible mechanisms for the observed inner disk flux asymmetry and color.

Kellen Lawson↗
NASA NTRS2016

Laboratory Testing and Performance Verification of the CHARIS Integral Field Spectrograph

The Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS) is an integral field spectrograph (IFS) that has been built for the Subaru telescope. CHARIS has two imaging modes; the high-resolution mode is R82, R69, and R82 in J, H, and K bands respectively while the low-resolution discovery mode uses a second low-resolution prism with R19 spanning 1.15-2.37 microns (J+H+K bands). The discovery mode is meant to augment the low inner working angle of the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) adaptive optics system, which feeds CHARIS a coronagraphic image. The goal is to detect and characterize brown dwarfs and hot Jovian planets down to contrasts five orders of magnitude dimmer than their parent star at an inner working angle as low as 80 milliarcseconds. CHARIS constrains spectral crosstalk through several key aspects of the optical design. Additionally, the repeatability of alignment of certain optical components is critical to the calibrations required for the data pipeline. Specifically the relative alignment of the lens let array, prism, and detector must be highly stable and repeatable between imaging modes. We report on the measured repeatability and stability of these mechanisms, measurements of spectral crosstalk in the instrument, and the propagation of these errors through the data pipeline. Another key design feature of CHARIS is the prism, which pairs Barium Fluoride with Ohara L-BBH2 high index glass. The dispersion of the prism is significantly more uniform than other glass choices, and the CHARIS prisms represent the first NIR astronomical instrument that uses L-BBH2as the high index material. This material choice was key to the utility of the discovery mode, so significant efforts were put into cryogenic characterization of the material. The final performance of the prism assemblies in their operating environment is described in detail. The spectrograph is going through final alignment, cryogenic cycling, and is being delivered to the Subaru telescope in April 2016. This paper is a report on the laboratory performance of the spectrograph, and its current status in the commissioning process so that observers will better understand the instrument capabilities. We will also discuss the lessons learned during the testing process and their impact on future high-contrast imaging spectrographs for wavefront control.

Coronagraphic High Angular Resolution Imaging Spec↗
NASA NTRS2019

A Chromaticity Analysis and PSF Subtraction Techniques for SCExAO/CHARIS Data

We present an analysis of instrument performance using new observations taken with the Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS) instrument and the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system. In a correlation analysis of our data sets (which use the broadband mode covering the J band through the K band in a single spectrum), we find that chromaticity in the SCExAO/CHARIS system is generally worse than temporal stability. We also develop a point-spread function (PSF) subtraction pipeline optimized for the CHARIS broadband mode, including a forward modeling-based exoplanet algorithmic throughput correction scheme. We then present contrast curves using this newly developed pipeline. An analogous subtraction of the same data sets using only the H-band slices yields the same final contrasts as the full JHK sequences; this result is consistent with our chromaticity analysis, illustrating that PSF subtraction using spectral differential imaging (SDI) in this broadband mode is generally not more effective than SDI in the individual J, H, or K bands. In the future, the data processing framework and analysis developed in this paper will be important to consider for additional SCExAO/CHARIS broadband observations and other ExAO instruments which plan to implement a similar integral field spectrograph broadband mode.

Benjamin L. Gerard↗
NASA NTRS2019

No Clear, Direct Evidence for Multiple Protoplanets Orbiting LkCa 15: LkCa 15 bcd are Likely Inner Disk Signals

Two studies utilizing sparse aperture-masking (SAM) interferometry and Hα differential imaging have reported multiple Jovian companions around the young solar-mass star, LkCa 15 (LkCa 15 bcd): thefirst claimed direct detection of infant, newly formed planets (“protoplanets”). We present new near-infrared direct imaging/spectroscopy from the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system coupled with Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS) integral field spectrograph and multi-epoch thermal infrared imaging from Keck/ NIRC2 of LkCa 15 at high Strehl ratios. These data provide the first direct imaging look at the same wavelengths and in the same locations where previous studies identified the LkCa 15 protoplanets,and thus offer the first decisive test of their existence.The data do not reveal these planets. Instead,we resolve extended emission tracing adust disk with a brightness and location comparable to that claimed for LkCa 15 bcd. Forward-models attributing this signal to orbiting planets are inconsistent with the combined SCExAO/CHARIS and Keck/NIRC2 data. An inner disk provides a more compelling explanation for the SAM detections and perhaps also the claimed Hα detection of LkCa 15 b. We conclude that there is currently no clear, direct evidence for multiple protoplanets orbiting LkCa 15, although the system likely contains at least one unseen Jovian companion. To identify Jovian companions around LkCa 15 from future observations, the inner disk should be detected and its effect modeled, removed, and shown to be distinguishable from planets. Protoplanet candidates identified from similar systems should likewise be clearly distinguished from disk emission through modeling.

Thayne Currie↗
NASA NTRS2017

Subaru SCExAO First-Light Direct Imaging of a Young Debris Disk around HD 36546

We present H-band scattered light imaging of a bright debris disk around the A0 star HD 36546 obtained from the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system with data recorded by the HiCIAO camera using the vector vortex coronagraph. SCExAO traces the disk from r approximately 0 3 to r approximately 0".3 to r approximately 1" (34-114 au). The disk is oriented in a near east west direction (PA approximately 75deg), is inclined by I approximately 70deg-75deg, and is strongly forward-scattering(g greater than 0.5). It is an extended disk rather than a sharp ring; a second, diffuse dust population extends from the disks eastern side. While HD 36546 intrinsic properties are consistent with a wide age range (t approximately 1-250 Myr), its kinematics and analysis of coeval stars suggest a young age (310 Myr) and a possible connection to Taurus-Aurigas star formation history. SCExAOs planet-to-star contrast ratios are comparable to the first-light Gemini Planet Imager contrasts; for an age of 10 Myr, we rule out planets with masses comparable to HR 8799 b beyond a projected separation of 23 au. A massive icy planetesimal disk or an unseen super-Jovian planet at r greater than 20 au may explain the disks visibility. The HD 36546 debris disk may be the youngest debris disk yet imaged, is the first newly identified object from the now-operational SCExAO extreme AO system, is ideally suited for spectroscopic follow-up with SCExAO/CHARIS in 2017, and may be a key probe of icy planet formation and planet disk interactions.

Subaru Coronagraphic Extreme Adaptive Optics (SCEx↗
NASA NTRS2018

SCExAO/CHARIS Near-IR High-Contrast Imaging and Integral Field Spectroscopy of the HIP 79977 Debris Disk

We present new, near-infrared (1.1–2.4 μm) high-contrast imaging of the bright debris disk surrounding HIP 79977 with the Subaru Coronagraphic Extreme Adaptive Optics system (SCExAO) coupled with the CHARIS integral field spectrograph. SCExAO/CHARIS resolves the disk down to smaller angular separations of (0".11; r ∼ 14 au) and at a higher significance than previously achieved at the same wavelengths. The disk exhibits a marginally significant east–west brightness asymmetry in H band that requires confirmation. Geometrical modeling suggests a nearly edge-on disk viewed at a position angle of ∼114°.6 east of north. The disk is best-fit by scattered-light models assuming strongly forward-scattering grains (g ∼ 0.5–0.65) confined to a torus with a peak density at r0 ∼ 53–75 au. We find that a shallow outer density power law of α(sub out) = −1 to −3 and flare index of β = 1 are preferred. Other disk parameters (e.g., inner density power law and vertical scale height) are more poorly constrained. The disk has a slightly blue intrinsic color and its profile is broadly consistent with predictions from birth ring models applied to other debris disks. While HIP 79977ʼs disk appears to be more strongly forward- scattering than most resolved disks surrounding 5–30 Myr old stars, this difference may be due to observational biases favoring forward-scattering models for inclined disks versus lower inclination, ostensibly neutral-scattering disks like HR 4796A’s. Deeper, higher signal-to-noise SCExAO/CHARIS data can better constrain the disk’s dust composition.

Goebel, Sean↗
NASA NTRSDate not supplied

Multi-Star Wavefront Control with SCExAO Instrument: Demonstration with an Internal Source

Although only a small fraction of currently known exoplanets was found in binary and multiple systems, studies show that such stars do form planets, with an efficiency that is smaller, but within an order of magnitude of single stars. However, binaries are rarely considered as targets for exoplanet imaging space missions because of challenges of removing light from the second binary component. In our previous works it was shown how to solve two main issues that make exoplanet imaging in multiple systems impossible, namely, the mutual incoherence of speckles created by different binary components, and inability of a deformable mirror (DM) to control the starlight beyond the DM outer working angle/Nyquist limit. Feasibility of the developed Multi-Star Wavefront Control (MSWC) and Super-Nyquist Wavefront Control(SNWC) algorithms was demonstrated at the Ames Coronagraph Experiment (ACE) laboratory using a simple imaging system with a DM and no coronagraph. In this paper, we report the results our MSWC experiments using the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) instrument that is part of our technology development effort. The main goal of these experiments is to validate MSWC on a real coronagraphic system by using an internal source to simulate at least one real representative binary target. In our demonstration narrow-band contrast of 4.1×10−6has been reached by using MSWC in a 12×6λ/D dark zone separated from the primary component of the simulated binary star (STF 3121 AB) by 4λ/D. This contrast is better by a factor of 13.2 than the contrast floor reached by standard single-star wavefront control (SSWC). We also discuss the main limiting factors that affect the MSWC performance in our experiments.

Binary stars↗
DOE OSTI2021

SCExAO/MEC and CHARIS Discovery of a Low-mass, 6 au Separation Companion to HIP 109427 Using Stochastic Speckle Discrimination and High-contrast Spectroscopy

We report the direct imaging discovery of a low-mass companion to the nearby accelerating A star, HIP 109427, with the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) instrument coupled with the Microwave Kinetic Inductance Detector Exoplanet Camera (MEC) and CHARIS integral field spectrograph. CHARIS data reduced with reference star point spread function (PSF) subtraction yield 1.1–2.4 μm spectra. MEC reveals the companion in Y and J band at a comparable signal-to-noise ratio using stochastic speckle discrimination, with no PSF subtraction techniques. Combined with complementary follow-up L {sub p} photometry from Keck/NIRC2, the SCExAO data favors a spectral type, effective temperature, and luminosity of M4–M5.5, 3000–3200 K, and log{sub 10}(L/L{sub ⊙})=−2.28{sub −0.04}{sup +0.04}, respectively. Relative astrometry of HIP 109427 B from SCExAO/CHARIS and Keck/NIRC2, and complementary Gaia–Hipparcos absolute astrometry of the primary favor a semimajor axis of 6.55{sup +3.0} {sub −0.48} au, an eccentricity of 0.54{sub −0.15}{sup +0.28}, an inclination of 66.7{sub −14}{sup +8.5} degrees, and a dynamical mass of 0.280{sub −0.059}{sup +0.18} M {sub ⊙}. This work shows the potential for extreme AO systems to utilize speckle statistics in addition to widely used postprocessing methods to directly image faint companions to nearby stars near the telescope diffraction limit.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2017

The CHARIS High-Contrast Integral-Field Spectrograph

One of the leading direct Imaging techniques, particularly in ground-based imaging, uses a coronagraphic system and integral field spectrograph (IFS). The Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS) is an IFS that has been built for the Subaru telescope. CHARIS has been delivered to the observatory and now sits behind the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system. CHARIS has 'high' and 'low' resolution operating modes. The "high-resolution" mode is used to characterize targets in J, H, and K bands at ~R70. The "low-resolution" prism is meant for discovery and spans J+H+K bands (1.15-2.37 microns) with a spectral resolution of ~R18. This discovery mode has already proven better than 15-sigma detections of HR8799c,d,e when combining ADI+SDI. Using SDI alone, planets c and d have been detected in a single 24 second image. The CHARIS team is optimizing instrument performance and refining ADI+SDI recombination to maximize our contrast detection limit. In addition to the new observing modes, CHARIS has demonstrated a design with high robustness to spectral crosstalk. CHARIS is in the final stages of commissioning, with the instrument open for science observations beginning February 2017. Here we review the science case, design, on-sky performance, engineering observations of exoplanet and disk targets, and specific lessons learned for extremely high contrast imagers. Key design aspects that will be demonstrated are crosstalk optimization, wavefront correction using the IFS image, lenslet tolerancing, the required spectral resolution to fit exoplanet atmospheres, and the utility of the spectrum in achieving higher contrast detection limits.

Groff, Tyler D.↗
NASA NTRS2012

SEEDS Moving Groups and CHARIS Status Updates

We present the status update for the SEEDS Moving Groups category. To date, we have observed 59 targets and currently have more than 20 candidates. We also present the expected scientific capabilities of CHARIS, the Coronagraphic High Angular Resolution Imaging Spectrograph, which is being built for the Subaru 8.2 m telescope of the National Astronomical Observatory of Japan. CHARIS will be implemented behind the new extreme adaptive optics system at Subaru, SCExAO, and the existing 188-actuator system AO188. CHARIS will offer three observing modes over near~infrared wavelengths from 0.9 to 2.4 microns (the y-, J-, H-, and K-bands), including a low-spectral-resolution mode covering this entire wavelength range and a high-resolution mode within a single band. With these capabilities, CHARIS will offer exceptional sensitivity for discovering giant exoplanets, and will enable detailed characterization of their atmospheres, CHARIS, the only planned high-contrast integral field spectrograph on an 8m-class telescope in the Northern Hemisphere, will complement the similar instruments such as Project 1640 at Palomar, and GPI and SPHERE in Chile.

McElwain, Michael↗
NASA NTRS2017

Synergies of Subaru and CGI

Given the limited observing time and demanding scenarios of the WFIRST coronagraph instrument (CGI), it is critical to consider how Subaru observations can benefit its observing program. Subaru telescope has a suite of instruments with their adaptive optics (AO) and extreme adaptive optics modules (SCExAO). With SCExAO, the Subaru telescope is capable of detection and spectral characterization of binaries and bright (greater than 5(exp -6) contrast) companions in the near-infrared. This will enable the vetting of targets, disk detection and characterization, and potentially some additional science should CGI identify interesting targets during its technology demonstration and potential guest observer program. Additionally, large companions that are within the inner working angle of the coronagraph can be identified using the VAMPIRES aperture masking interferometer. With highly complementary target brightness and significantly overlapping fields of view, there is a great deal of potential for combined observations with Subaru and CGI. This will represent the first time single observations spanning the visible to near-infrared will be possible for high contrast imaging. We will discuss the overlap of instrumentation over time, the implication of instrument evolution as TMT comes online, and how this can be used to improve both science and technology demonstrations for CGI.

adaptive optics (AO↗
NASA NTRS2018

Laboratory and On-Sky Validation of the Shaped Pupil Coronagraph's Sensitivity to Low-Order Aberrations with Active Wavefront Control

We present early laboratory simulations and extensive on-sky tests validating of the performance of a shaped pupil coronagraph (SPC) behind an extreme-AO (Adaptive Optics) corrected beam of the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system. In tests with the SCExAO internal source/wavefront error simulator, the normalized intensity profile for the SPC degrades more slowly than for the Lyot coronagraph as low-order aberrations reduce the Strehl ratio (S.R.) from extremely high values (S.R. approximately 0.93-0.99) to those characteristic of current ground-based extreme AO systems (S.R. approximately 0.74-0.93) and then slightly lower values down to S.R. approximately 0.57. On-sky SCExAO data taken with the SPC and other coronagraphs for brown dwarf/planet-hosting stars HD 1160 and HR 8799 provide further evidence for the SPC's robustness to low-order aberrations. From H-band Strehl ratios of 80 percent to 70 percent, the Lyot coronagraph's performance versus that of the SPC may degrade even faster on sky than is seen in our internal source simulations. The 5-sigma contrast also degrades faster (by a factor of two) for the Lyot than the SPC. The SPC we use was designed as a technology demonstrator only, with a contrast floor, throughput, and outer working angle poorly matched for SCExAO's current AO performance and poorly tuned for imaging the HR 8799 planets. Nevertheless, we detect HR 8799 cde with SCExAO/CHARIS using the SPC in broadband mode, where the signal-to-noise ratio for planet e is within 30 percent of that obtained using the vortex coronagraph. The shaped-pupil coronagraph is a promising design demonstrated to be robust in the presence of low-order aberrations and may be well-suited for future ground and space-based direct imaging observations, especially those focused on follow-up exoplanet characterization and technology demonstration of deep contrast within well-defined regions of the image plane.

Currie, Thayne↗