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Rémi Soummer

Publications and source records attributed to Rémi Soummer.

At least 19 recordsLinked to original sources

Modal estimation of high-order wavefront drifts on coronagraphic testbeds for high-contrast direct imaging of exoplanets

Long-term wavefront stability will be critical for the upcoming Habitable Worlds Observatory which aims to directly image exo-Earths. Mechanical and thermal instabilities induce slow, high-order wavefront errors which can degrade the contrast and in turn, the scientific yield of the observatory. Dark zone maintenance (DZM) has been proposed as a high-order wavefront sensing and control strategy to maintain contrast despite wavefront error drifts. This approach uses an Extended Kalman Filter (EKF) to estimate the electric field at each pixel in the dark zone of the science camera. However, relying on individual pixel information to estimate wavefront errors can discard information stored in the underlying wavefront. This is a fundamental limitation on the best achieved contrast compared to the model based theoretical bounds derived from photon noise. An alternative EKF can incorporate more holistic information by estimating the drifting wavefront modes present in the system. In this work we analyze the performance of this Modal EKF on the High-contrast Imager for Complex Aperture Telescopes (HiCAT) simulator at the Space Telescope Science Institute. A parameter scan is performed across key variables: deformable mirror (DM) drift, the direct photon rate at the telescope aperture governing the mean number of photons in the dark zone (DZ), and the dither magnitude used to provide phase diversity. While prior studies explored a range of dither magnitudes, this work introduces a covariance-based approach within the Extended Kalman Filter (EKF) framework to optimally determine the probe magnitude required. Results from the modal EKF demonstrate a 15-fold improvement in contrast relative to the single-pixel DZM experiments, reducing the gap to within a factor of 2-3 of the theoretical bounds.

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JWST telemetry combined with active coronagraphy: raw contrast predictions for exoplanet imaging with the Habitable Worlds Observatory

We provide a quantification of the technological gap between the James Webb Space Telescope (JWST) and the Habitable Worlds Observatory (HWO) for the goal of exo-Earth imaging around Sun-like stars at the $10^{-10}$ raw contrast level. We use JWST's in-flight telemetry of the primary segmented mirror to simulate a JWST-like telescope equipped with a modern coronagraph instrument, inspired by the Roman Space Telescope (RST) Coronagraphic Instrument (CGI), featuring an Apodized Pupil Lyot Coronagraph and active deformable mirror wavefront control on a segmented, unobstructed, off-axis telescope. We show that it can achieve around $10^{-10}$ raw contrast for very bright stars (brighter than magnitude 4) for fast control frequencies of 100 Hz, but that this level of control still lacks sufficient signal to correct JWST-amplitude errors for fainter stars. We show that an improvement of a factor of ten in wavefront stability is sufficient to extend this capability to a $10^{-10}$ raw contrast across all considered control frequencies (1 Hz to 100 Hz), assuming no reaction wheel vibrations, for stars up to a magnitude of 11. These results establish a new quantitative benchmark linking JWST's demonstrated thermo-mechanical stability to HWO's requirements, showing that active wavefront control relaxes the structural stability demands on the observatory, and identifying wavefront stability as the critical technological gap that must be closed for HWO to achieve its exo-Earth imaging goals.

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Calibration of MEMS DM actuator gains using a Zernike wavefront sensor on the HiCAT testbed and implications for Habitable Worlds Observatory operations

Deformable mirrors (DMs) are a key component of coronagraph instruments performing adaptive optics on the ground, and for future space observatories such as HWO and Roman CGI. Here, they will be used as part of the wavefront sensing and control system to "dig a dark zone'' - remove residual stellar light to create a high-contrast region in the focal plane where faint companions can be detected. To reach the deep contrasts needed to directly image cool or reflected light planets (<1e-8) accurate calibration of the DM actuator gain is essential as picometer differences between the expected and realized DM surface can significantly degrade dark zone (DZ) digging efficiency. This increases the overheads needed to achieve a DZ and critically places more stringent requirements on observatory stability. Furthermore, DM gain varies with actuator stroke, necessitating rapid, in situ gain map recalculations to maintain DZ digging efficiency over time. Zernike wavefront sensors (ZWFS) are well-suited for this task as they efficiently provide picometer-level sensitivity and will likely already be included on board as part of a low order wavefront sensor for HWO. Here we present results from the HiCAT testbed at STScI where we calibrated gain maps for our Boston Micromachines 952-actuator micro electromechanical (MEMS) DMs using both a Fizeau interferometer and a ZWFS to compare performance. With the ZWFS we compute a gain map using both local linear fits around a given DM solution, and present a formalism for deriving more complex quadratic solutions which are more computationally intensive, but accurate over most of the dynamic range of each actuator. We then use these techniques to calibrate the DMs on the HiCAT testbed and show increased DZ digging efficiency with the new gain map and better contrast performance moving from 14 to 16 bit control electronics as enabled by these calibrations.

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Segment-level thermal sensitivity analysis for exo-Earth coronagraphy with segmented space telescopes

Direct imaging and characterization of Earth-like planets require ultra-stable wavefronts to achieve a starlight suppression level of 100 parts per trillion (ppt) in the coronagraphic dark region of the host star. Thermal drifts in the telescope may affect the wavefront stability. In this context, we present a segment-level thermal stability error budget for segmented space telescopes crucial to Earth-like planet detection and specify requirements for an ultra-stable telescope. Our study utilizes multiple segmented primary mirror architectures, each with their respective apodizer solution developed by the Segmented Coronagraph Design & Analysis research team at the Space Telescope Science Institute, tailored to an off-axis ~6 m-aperture space telescope design. Using a detailed finite element model provided by L3Harris Technologies, we relate the temperature gradient at the location of the primary mirror to wavefront variations on each segment. We allocate both static and dynamic thermal tolerances for each segment using the Pair-based Analytical model for Segmented Telescope Imaging from Space sensitivity approach, and a batch-estimation algorithm respectively. Our analysis shows a non-uniform tolerance allocation across all segments of the primary mirror, as a result of apodization, and generally, with an increase in segment numbers, the tolerances for outer segments become less stringent. We observe trade-offs between segment size, tolerance relaxation and optimal wavefront sensing time to achieve a desired dark-hole contrast.

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First high-contrast results on THD2 testbed after infrastructure upgrade

We present the first scientific results delivered by the upgraded THD2 high-contrast imaging testbed. We report two advances enabled by its improved stability and broadband performance. First, for the Roman Space Telescope, we demonstrate that Gaussian-shaped diversity probes outperform the baseline sinc probes by reducing non-linearities, supporting higher probe amplitudes, and improving electric field estimation efficiency. These results have led to their prioritization as an enhanced early observation for Roman. Second, within ESA's SUPPPPRESS project, we test new polarization-independent Vector Vortex Coronagraphs and design them to high-contrast performance approaching 1e-10 over a 20% bandwidth. We assess their behavior in narrow- and broadband light with active focal-plane wavefront control. Together, these results show how THD2 strengthens Europe's capability in high-contrast imaging, providing a unique platform reaching contrasts of 1e-8 to 1e-9 for developing next-generation coronagraphic technologies.

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Enhanced wavefront sensing for the Roman Coronagraph Instrument: Gaussian probes and compact model validation

The Coronagraph Instrument on the Roman Space Telescope will be the first space-based system to demonstrate closed-loop focal-plane wavefront sensing and control, a key step towards the Habitable Worlds Observatory. Beyond the baseline Hybrid Lyot Coronagraph, "enhanced modes" are being developed to improve efficiency and science yield. One such mode uses Gaussian probes for electric field estimation, extending the linear regime and allowing higher probe amplitudes. This may increase signal-to-noise, reduce exposure time, accelerate dark hole convergence, and extend operation to stars as faint as $V\sim5$. For those reasons, it was selected by the Coronagraph Community Participation Program's Hardware Working Group as the first technology demonstration carried out on Roman in early 2027. We present numerical simulations using a noise-free compact software model, which demonstrate the benefits of replacing the nominal probes with Gaussian probes.

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CATKit2-HCI: a collaborative framework for advancing high-contrast coronagraph testbeds

High-contrast exoplanet imaging requires dedicated laboratory testbeds for the development and validation of coronagraph architectures, wavefront sensing and control methods, calibration strategies, and system-level observing concepts. These testbeds often share similar software needs, yet many tools are developed independently at each institution. The CATKit2-High-Contrast-Imaging collaboration, or CATKit2-HCI, addresses this gap by providing a shared software framework for reusable HCI infrastructure. Built on top of CATKit2, an open-source hardware control and synchronization framework originally developed for the High-contrast Imager for Complex Aperture Telescopes (HiCAT) testbed at the Space Telescope Science Institute, CATKit2-HCI provides the collaborative layer for HCI-specific algorithms, calibration tools, diagnostics, visualization, and performance metrics. The collaboration currently includes multiple coronagraph testbeds in the United States and Europe. Its goals are to reduce duplicated software development, improve code quality through shared review, enable more direct comparison of results across facilities, and facilitate the movement of students, postdoctoral researchers, and collaborators between laboratories. We describe the motivation, architecture, collaboration model, shared technical capabilities, and early cross-testbed examples of CATKit2-HCI as a framework for accelerating coronagraph technology development.

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JWST-TST High Contrast: First Direct Spectroscopy of GJ 504 b reveals Clouds and Possible Metal Enrichment

Characterizing the coldest directly imaged companions through direct spectroscopy has only recently become possible with the James Webb Space Telescope. We present moderate-resolution (R $\sim$ 2,700) spectroscopic observations of the directly imaged planetary-mass companion (PMC), GJ 504 b, using the $JWST$/NIRSpec. As the coldest imaged PMC of the pre-JWST era GJ 504 b is too faint for ground-based spectroscopy, with only photometric observations possible. Leveraging advanced post-processing techniques with a forward modeling framework, we detect the companion at high signal-to-noise (S/N$>$300). We also present the first successful PSF subtraction with angular differential imaging (ADI) in the NIRSpec point cloud, detecting GJ 504 b at S/N$>10$ and reaching contrast limits $<10^{-4}$. The extracted 2.9--5.3 $μm$ spectra show strong signatures of several molecular species, including H$_2$O, $^{12}$C$^{16}$O, CH$_4$, CO$_2$, NH$_3$, H$_2$S, $^{13}$C$^{16}$O, and $^{12}$C$^{18}$O. Atmospheric modeling of the spectra using \texttt{petitRADTRANS}, yields an effective temperature = 564$\pm$4 K, surface gravity $\log{g}$ = 4.87$^{+0.13}_{-0.12}$, metallicity [M/H] = 0.67$^{+0.13}_{-0.12}$, C/O ratio = 0.64$^{+0.02}_{-0.02}$, interstellar $^{12}$C/$^{13}$C and $^{16}$O/$^{18}$O isotopologue ratios, and strong evidence of disequilibrium chemistry and salt clouds. The retrieved parameters indicate a mass 25.2$^{+8.4}_{-6.0}$ $M_\mathrm{Jup}$, which is in agreement with the mass range (19--27 $M_\mathrm{Jup}$) obtained from ATMO evolutionary models, implying an age of 2.5--4.0 Gyr. Lastly, we compare the abundances of GJ 504 b to its primary, obtaining a stellar abundance of sulfur (S), super-stellar carbon (C), and possibly, oxygen (O). The observed metal enrichment tentatively supports planet-like formation, but does not entirely exclude stellar abundances for GJ 504 b.

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Impact of segmented deformable mirrors on high-contrast testbeds for exoplanet imaging with future large space telescopes: contrast stability assessment on the HiCAT bench

We investigate the stability of a segmented deformable mirror (DM) on high-contrast testbeds and its impact on the images produced with coronagraphs. Segmented apertures are promising to obtain large primary mirrors for future missions with starlight suppression capabilities. Cophased at the sub-nanometer level, segments can be slightly misaligned by small drifts, proving harmful for exoplanet observations. We study the impact of misalignments on contrast using the High-contrast Imager for Complex Aperture Telescopes (HiCAT), a testbed which includes a 37-segment DM and produces coronagraphic images with 2.5e-8 contrast in narrowband light. Temporal wavefront errors due to the segmented DM are estimated with a Zernike wavefront sensor. Our in-lab results show aberrations at the sub-nanometer level, proving encouraging for contrast stability studies. We then use a digital twin of HiCAT to simulate coronagraphic images with an initial 0.5e-8 contrast and the segments in flat position. By injecting known perturbations on the segments, we observe a contrast degradation by a factor of 2.5, nearly corresponding to the typical contrast observed on HiCAT. These results highlight the importance of segment cophasing sensing and control strategies to ensure the required contrasts for exo-Earth imaging with a large segmented aperture for the Habitable Worlds Observatory mission.

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JWST-TST High Contrast: Living on the Wedge, or, NIRCam Bar Coronagraphy Reveals CO$_2$ in the HR 8799 and 51 Eri Exoplanets' Atmospheres

High-contrast observations with JWST can reveal key composition and vertical mixing dependent absorption features in the spectra of directly imaged planets across the 3-5 $μ$m wavelength range. We present novel coronagraphic images of the HR 8799 and 51 Eri planetary systems using the NIRCam Long Wavelength Bar in an offset "narrow" position. These observations have revealed the four known gas giant planets encircling HR 8799, even at spatial separations challenging for a 6.5 m telescope in the mid-infrared, including the first ever detection of HR 8799 e at 4.6 $μ$m. The chosen filters constrain the strength of CO, CH4, and CO2 absorption in each planet's photosphere. The planets display a diversity of 3-5 $μ$m colors that could be due to differences in composition and ultimately be used to trace their formation history. They also show stronger CO2 absorption than expected from solar metallicity models, indicating that they are metal enriched. We detected 51 Eri b at 4.1 $μ$m and not at longer wavelengths, which, given the planet's temperature, is indicative of out-of-equilibrium carbon chemistry and an enhanced metallicity. Updated orbits fit to the new measurement of 51 Eri b validate previous studies that find a preference for high eccentricities ($e{=}0.57_{-0.09}^{+0.03}$), which likely indicates some dynamical processing in the system's past. These results present an exciting opportunity to model the atmospheres and formation histories of these planets in more detail in the near future, and are complementary to future higher-resolution, continuum-subtracted JWST spectroscopy.

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A parameter scan of dark zone maintenance for high-contrast imaging of exoplanets using theoretical and experimental implementations

Maintaining wavefront stability while directly imaging exoplanets over long exposure times is an ongoing problem in the field of high-contrast imaging. Robust and efficient high-order wavefront sensing and control systems are required for maintaining wavefront stability to counteract mechanical and thermal instabilities. Dark zone maintenance (DZM) has been proposed to address quasi-static optical aberrations and maintain high levels of contrast for coronagraphic space telescopes. To further experimentally test this approach for future missions, such as the Habitable Worlds Observatory, this paper quantifies the differences between the theoretical closed-loop contrast bounds and DZM performance on the High-contrast Imager for Complex Aperture Telescopes(HiCAT) testbed. The quantification of DZM is achieved by traversing important parameters of the system, specifically the total direct photon rate entering the aperture of the instrument, ranging from $1.85 \times 10^6$ to $1.85 \times 10^8$ photons per second, and the wavefront error drift rate, ranging from $σ_{drift}$ = 0.3 - 3 $nm/\sqrt{iteration}$, injected via the deformable mirror actuators. This is tested on the HiCAT testbed by injecting random walk drifts using two Boston Micromachines kilo deformable mirrors (DMs). The parameter scan is run on the HiCAT simulator and the HiCAT testbed where the corresponding results are compared to the model-based theoretical contrast bounds to analyze discrepancies. The results indicate an approximate one and a half order of magnitude difference between the theoretical bounds and testbed results.

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High-contrast imager for complex aperture telescopes (HiCAT): 8. Dark zone demonstration with simultaneous closed-loop low-order wavefront sensing and control

We present recent laboratory results demonstrating high-contrast coronagraphy for the future space-based large IR/Optical/Ultraviolet telescope recommended by the Decadal Survey. The High-contrast Imager for Complex Aperture Telescopes (HiCAT) testbed aims to implement a system-level hardware demonstration for segmented aperture coronagraphs with wavefront control. The telescope hardware simulator employs a segmented deformable mirror with 37 hexagonal segments that can be controlled in piston, tip, and tilt. In addition, two continuous deformable mirrors are used for high-order wavefront sensing and control. The low-order sensing subsystem includes a dedicated tip-tilt stage, a coronagraphic target acquisition camera, and a Zernike wavefront sensor that is used to measure and correct low-order aberration drifts. We explore the performance of a segmented aperture coronagraph both in static operations (limited by natural drifts and instabilities) and in dynamic operations (in the presence of artificial wavefront drifts added to the deformable mirrors), and discuss the estimation and control strategies used to reach and maintain the dark-zone contrast using our low-order wavefront sensing and control. We summarize experimental results that quantify the performance of the testbed in terms of contrast, inner/outer working angle and bandpass, and analyze limiting factors.

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High-contrast imager for complex aperture telescopes (HiCAT): 11. System-level demonstration of the Apodized Pupil Lyot Coronagraph with a segmented aperture in air

We present the final results of the Apodized Pupil Lyot Coronagraph (APLC) on the High-contrast imager for Complex Aperture Telescopes (HiCAT) testbed, under NASA's Strategic Astrophysics Technology program. The HiCAT testbed was developed over the past decade to enable a system-level demonstration of coronagraphy for exoplanet direct imaging with the future Habitable Wolds Observatory. HiCAT includes an active, segmented telescope simulator, a coronagraph, and metrology systems (Low-order and Mid-Order Zernike Wavefront Sensors, and Phase Retrieval camera). These results correspond to an off-axis (un-obscured) configuration, as was envisioned in the 2020 Decadal Survey Recommendations. Narrowband and broadband dark holes are generated using two continuous deformable mirrors (DM) to control high order wavefront aberrations, and low-order drifts can be further stabilized using the LOWFS loop. The APLC apodizers, manufactured using carbon nanotubes, were optimized for broadband performance and include the calibrated geometric aperture. HiCAT is, to this date, the only testbed facility able to demonstrate high-contrast coronagraphy with a truly segmented aperture, as is required for the Habitable World Observatory, albeit limited to ambient conditions. Results presented here include $6\times 10^{-8}$ (90% CI) contrast in 9% bandpass in a 360 deg dark hole with inner and outer working angles of $4.4 λ/D_{pupil}$ and $11 λ/D_{pupil}$ . Narrowband contrast (3% bandpass) reaches $2.4\times 10^{-8}$ (90% confidence interval).

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ESCAPE project: testing active observing strategies for high-contrast imaging in space on the HiCAT testbed

The Roman Space Telescope will be a critical mission to demonstrate high-contrast imaging technologies allowing for the characterisation of exoplanets in reflected light. It will demonstrate $10^{-7}$ contrast limits or better at 3--9 $λ/ D$ separations with active wavefront control for the first time in space. The detection limits for the Coronagraph Instrument are expected to be set by wavefront variations between the science target and the reference star observations. We are investigating methods to use the deformablel mirrors to methodically probe the impact of such variations on the coronagraphic PSF, generating a PSF library during observations of the reference star to optimise the starlight subtraction at post-processing. We are collaborating with STScI to test and validate these methods in lab using the HiCAT tested, a high-contrast imaging lab platform dedicated to system-level developments for future space missions. In this paper, we will present the first applications of these methods on HiCAT.

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Simulated performance of energy-resolving detectors towards exoplanet imaging with the Habitable Worlds Observatory

One of the primary science goals of the Habitable Worlds Observatory (HWO) as defined by the Astro2020 decadal survey is the imaging of the first Earth-like planet around a Sun-like star. A key technology gap towards reaching this goal are the development of ultra-low-noise photon counting detectors capable of measuring the incredibly low count rates coming from these planets which are at contrasts of $\sim 1 \times 10^{-10}$. Superconducting energy-resolving detectors (ERDs) are a promising technology for this purpose as, despite their technological challenges, needing to be cooled below their superconducting transition temperature ($< 1\mathrm{K}$), they have essentially zero read noise, dark current, or clock-induced charge, and can get the wavelength of each incident photon without the use of additional throughput-reducing filters or gratings that spread light over many pixels. The use of these detectors on HWO will not only impact the science of the mission by decreasing the required exposure times for exo-Earth detection and characterization, but also in a wavefront sensing and control context when used for starlight suppression to generate a dark zone. We show simulated results using both an EMCCD and an ERD to ``dig a dark zone'' demonstrating that ERDs can achieve the same final contrast as an EMCCD in about half of the total time. We also perform a simple case study using an exposure time calculator tool called the Error Budget Software (EBS) to determine the required integration times to detect water for HWO targets of interest using both EMCCDs and ERDs. This shows that once a dark zone is achieved, using an ERD can decrease these exposure times by factors of 1.5--2 depending on the specific host star properties.

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JWST-TST High Contrast: Achieving direct spectroscopy of faint substellar companions next to bright stars with the NIRSpec IFU

The JWST NIRSpec integral field unit (IFU) presents a unique opportunity to observe directly imaged exoplanets from 3-5 um at moderate spectral resolution (R~2,700) and thereby better constrain the composition, disequilibrium chemistry, and cloud properties of their atmospheres. In this work, we present the first NIRSpec IFU high-contrast observations of a substellar companion that requires starlight suppression techniques. We develop specific data reduction strategies to study faint companions around bright stars, and assess the performance of NIRSpec at high contrast. First, we demonstrate an approach to forward model the companion signal and the starlight directly in the detector images, which mitigates the effects of NIRSpec's spatial undersampling. We demonstrate a sensitivity to planets that are 3e-6 fainter than their stars at 1'', or 3e-5 at 0.3''. Then, we implement a reference star point spread function (PSF) subtraction and a spectral extraction that does not require spatially and spectrally regularly sampled spectral cubes. This allows us to extract a moderate resolution (R~2,700) spectrum of the faint T-dwarf companion HD 19467 B from 2.9-5.2 um with signal-to-noise ratio (S/N)~10 per resolution element. Across this wavelength range, HD~19467~B has a flux ratio varying between 1e-5-1e-4 and a separation relative to its star of 1.6''. A companion paper by Hoch et al. more deeply analyzes the atmospheric properties of this companion based on the extracted spectrum. Using the methods developed here, NIRSpec's sensitivity may enable direct detection and spectral characterization of relatively old (~1 Gyr), cool (~250 K), and closely separated (~3-5 au) exoplanets that are less massive than Jupiter.

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Debris Disk Color with the Hubble Space Telescope

Multi-wavelength scattered light imaging of debris disks may inform dust properties including typical size and mineral composition. Existing studies have investigated a small set of individual systems across a variety of imaging instruments and filters, calling for uniform comparison studies to systematically investigate dust properties. We obtain the surface brightness of dust particles in debris disks by post-processing coronagraphic imaging observations, and compare the multi-wavelength reflectance of dust. For a sample of resolved debris disks, we perform a systematic analysis on the reflectance properties of their birth rings. We reduced the visible and near-infrared images of 23 debris disk systems hosted by A through M stars using two coronagraphs onboard the Hubble Space Telescope: the STIS instrument observations centering at 0.58 $μ$m, and the NICMOS instrument at 1.12 $μ$m or 1.60 $μ$m. For proper recovery of debris disks, we used classical reference differential imaging for STIS, and adopted non-negative matrix factorization with forward modeling for NICMOS. By dividing disk signals by stellar signals to take into account of intrinsic stellar color effects, we systematically obtained and compared the reflectance of debris birth rings at ~90 deg scattering angle. Debris birth rings typically exhibit a blue color at ~90 deg scattering angle. As the stellar luminosity increases, the color tends to be more neutral. A likely L-shaped color-albedo distribution indicates a clustering of scatterer properties. The observed color trend correlates with the expected blow-out size of dust particles. The color-albedo clustering likely suggests different populations of dust in these systems. More detailed radiative transfer models with realistic dust morphology will contribute to explaining the observed color and color-albedo distribution of debris systems.

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Wavefront tolerances of space-based segmented telescopes at very high contrast: Experimental validation

Context: The detection and characterization of Earth-like exoplanets (exoEarths) from space requires exquisite wavefront stability at contrast levels of $10^{-10}$. On segmented telescopes in particular, aberrations induced by cophasing errors lead to a light leakage through the coronagraph, deteriorating the imaging performance. These need to be limited in order to facilitate the direct imaging of exoEarths. Aims: We perform a laboratory validation of an analytical tolerancing model that allows us to determine wavefront error requirements in the $10^{-6} - 10^{-8}$ contrast regime, for a segmented pupil with a classical Lyot coronagraph. We intend to compare the results to simulations, and we aim to establish an error budget for the segmented mirror on the High-contrast imager for Complex Aperture Telescopes (HiCAT) testbed. Methods: We use the Pair-based Analytical model for Segmented Telescope Imaging from Space (PASTIS) to measure a contrast influence matrix of a real high contrast instrument, and use an analytical model inversion to calculate per-segment wavefront error tolerances. We validate these tolerances on the HiCAT testbed by measuring the contrast response of segmented mirror states that follow these requirements. Results: The experimentally measured optical influence matrix is successfully measured on the HiCAT testbed, and we derive individual segment tolerances from it that correctly yield the targeted contrast levels. Further, the analytical expressions that predict a contrast mean and variance from a given segment covariance matrix are confirmed experimentally.

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