Future space-based coronagraphs will rely critically on focal-plane wavefront sensing and control with deformable mirrors (DMs) to reach deep contrast by mitigating optical aberrations in the primary beam path. Until now, most focal-plane wavefront control algorithms have been formulated in terms of Jacobian matrices, which encode the predicted effect of each DM actuator on the focal-plane electric field. A disadvantage of these methods is that Jacobian matrices can be cumbersome to compute and manipulate, particularly when the number of DM actuators is large. Recently, we proposed a new class of focal-plane wavefront control algorithms that utilize gradient-based optimization with algorithmic differentiation to compute wavefront control solutions while avoiding the explicit computation and manipulation of Jacobian matrices entirely. In simulations using a coronagraph design for the proposed Large UV/Optical/Infrared Surveyor, we showed that our approach reduces overall CPU time and memory consumption compared to a Jacobian-based algorithm. Here, we expand on these results by implementing the proposed algorithm on the High-contrast Imager for Complex Aperture Telescopes tested at the Space Telescope Science Institute and present initial experimental results, demonstrating contrast suppression capabilities equivalent to Jacobian-based methods.
Due to the limited number of photons, directly imaging planets requires long integration times with a coronagraphic instrument. The wavefront must be stable on the same time scale, which is often difficult in space due to time-varying wavefront errors from thermal gradients and other mechanical instabilities. We discuss a laboratory demonstration of a photon-efficient dark zone maintenance (DZM) algorithm in the presence of representative wavefront error drifts. The DZM algorithm allows for simultaneous estimation and control while obtaining science images and removes the necessity of slewing to a reference star to regenerate the dark zone mid-observation of a target. The experiments are performed on the high-contrast imager for complex aperture telescopes at the Space Telescope Science Institute. The testbed contains an IrisAO segmented primary surrogate, a pair of continuous Boston Micromachine (BMC) kilo deformable mirrors (DMs), and a Lyot coronagraph. Both types of DMs are used to inject synthetic high-order wavefront aberration drifts into the system, possibly similar to those that would occur on telescope optics in a space observatory, which are then corrected by the BMC DMs via the DZM algorithm. In the presence of BMC, IrisAO, and all DM wavefront error drift, we demonstrate maintenance of the dark zone contrast (5.8−9.8 λ/Dlyot) at monochromatic levels of 8.5×10−8, 2.5×10−8, and 5.9×10−8, respectively. In addition, we show multiwavelength maintenance at a contrast of 7.0×10−7 over a 3% band centered at 650 nm (BMC drift). We demonstrate the potential of adaptive wavefront maintenance methods for future exoplanet imaging missions, and our demonstration significantly advances their readiness.
KEYWORDS: Signal to noise ratio, Photons, Coronagraphy, Exoplanets, Electron multiplying charge coupled devices, Wavefronts, Space telescopes, Space operations
Directly imaging exoplanets requires long integration times when using a space-based coronagraphic instrument due to the small number of photons. Wavefront stability on the same timescale is of the utmost importance; a difficult feat in the presence of thermal and mechanical instabilities. In this paper, we demonstrate that dark zone maintenance (DZM) functions in the low signal-to-noise (SNR) regime similar to that expected for the Roman Space Telescope (RST) and the “large (∼6 m aperture) infrared/optical/ultraviolet (IR/O/UV) space telescope” recommended by the 2021 decadal survey. We develop low-photon experiments with tunable noise properties to provide a representative extrapolation. The experiments are performed on the High-contrast Imager for Complex Aperture Telescopes (HiCAT) at the Space Telescope Science Institute (STScI). High-order wavefront error drifts are injected using a pair of kilo-deformable mirrors (DMs). The drifts are corrected using the DMs via the DZM algorithm; note that the current limiting factor for the DZM results is the air environment. We show that DZM can maintain a contrast of 5.3 × 10−8 in the presence of DM random walk drift with a low SNR.
We present a publicly available software package developed for exploring apodized pupil Lyot coronagraph (APLC) solutions for various telescope architectures. In particular, the package optimizes the apodizer component of the APLC for a given focal-plane mask and Lyot stop geometry to meet a set of constraints (contrast, bandwidth etc.) on the coronagraph intensity in a given focal-plane region (i.e. dark zone). The package combines a high-contrast imaging simulation package (HCIPy) with a third-party mathematical optimizer (Gurobi) to compute the linearly optimized binary mask that maximizes transmission. We provide examples of the application of this toolkit to several different telescope geometries, including the Gemini Planet Imager (GPI) and the High-contrast imager for Complex Aperture Telescopes (HiCAT) testbed. Finally, we summarize the results of a preliminary design survey for the case of a ∼6 m aperture off-axis space telescope, as recommended by the 2020 NASA Decadal Survey, exploring APLC solutions for different segment sizes. We then use the Pair-based Analytical model for Segmented Telescope Imaging from Space (PASTIS) to perform a segmented wavefront error tolerancing analysis on these solutions.
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.
The characterization of exoplanets’ atmospheres using direct imaging spectroscopy requires high-contrast over a wide wavelength range. We study a recently proposed focal plane wavefront estimation algorithm that exclusively uses broadband images to estimate the electric field. This approach therefore reduces the complexity and observational overheads compared to traditional single wavelength approaches. The electric field is estimated as an incoherent sum of monochromatic intensities with the pair-wise probing technique. This paper covers the detailed implementation of the algorithm and an application to the High-contrast Imager for Complex Aperture Telescopes (HiCAT) testbed with the goal to compare the performance between the broadband and traditional narrowband filter approaches.
Future large segmented space telescopes and their coronagraphic instruments are expected to provide the resolution and sensitivity to observe Earth-like planets with a 1010 contrast ratio at less than 100 mas from their host star. Advanced coronagraphs and wavefront control methods will enable the generation of high-contrast dark holes in the image of an observed star. However, drifts in the optical path of the system will lead to pointing errors and other critical low-order aberrations that will prevent maintenance of this contrast. To measure and correct for these errors, we explore the use of a Zernike wavefront sensor (ZWFS) in the starlight rejected and filtered by the focal plane mask of a Lyot-type coronagraph. In our previous work, the analytical phase reconstruction formalism of the ZWFS was adapted for a filtered beam. We now explore strategies to actively compensate for these drifts in a segmented pupil setup on the High-contrast imager for Complex Aperture Telescopes (HiCAT). This contribution presents laboratory results from closed-loop compensation of bench internal turbulence as well as known introduced aberrations using phase conjugation and interaction matrix approaches. We also study the contrast recovery in the image plane dark hole when using a closed loop based on the ZWFS.
Due to the limited number of photons, directly imaging planets requires long integration times with a coronagraphic instrument. The wavefront must be stable on the same time scale, which is often difficult in space due to thermal variations and other mechanical instabilities. In this paper, we discuss the implications on future space mission observing conditions of our recent laboratory demonstration of a dark hole maintenance (DHM) algorithm. The experiments are performed on the High-contrast imager for Complex Aperture Telescopes (HiCAT) at the Space Telescope Science Institute (STScI). The testbed contains a segmented aperture, a pair of deformable mirrors (DMs), and a lyot coronagraph. The segmented aperture injects high order zernike wavefront aberration drifts into the system which are then corrected by the DMs downstream via the DHM algorithm. We investigate various drift modes including segmented aperture drift, all DMs drift, and drift correction at multiple wavelengths.
Future space-based coronagraphs will rely critically on focal-plane wavefront sensing and control with deformable mirrors to reach deep contrast by mitigating optical aberrations in the primary beam path. Until now, most focal-plane wavefront control algorithms have been formulated in terms of Jacobian matrices, which encode the predicted effect of each deformable mirror actuator on the focal-plane electric field. A disadvantage of these methods is that Jacobian matrices can be cumbersome to compute and manipulate, particularly when the number of deformable mirror actuators is large. Recently, we proposed a new class of focal-plane wavefront control algorithms that utilize gradient-based optimization with algorithmic differentiation to compute wavefront control solutions while avoiding the explicit computation and manipulation of Jacobian matrices entirely. In simulations using a coronagraph design for the proposed Large UV/Optical/Infrared Surveyor (LUVOIR), we showed that our approach reduces overall CPU time and memory consumption compared to a Jacobian-based algorithm. Here, we expand on these results by implementing the proposed algorithm on the High Contrast Imager for Complex Aperture Telescopes (HiCAT) testbed at the Space Telescope Science Institute (STScI) and present initial experimental and numerical results.
We present recent laboratory results demonstrating high-contrast coronagraphy for future space-based large segmented telescopes such as the Large UV, Optical, IR telescope (LUVOIR) mission concept studied by NASA. 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 36 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 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. 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 by comparing against our end-to-end models.
Due to the limited number of photons, directly imaging planets requires long integration times. The wavefront must be stable on the same time scale which is often difficult in space due to thermal variations and vibrations. In this paper, we discuss the results of implementing a dark hole maintenance (DHM) algorithm (Pogorelyuk et. al. 2019)1 on the High-contrast imager for Complex Aperture Telescopes (HiCAT) at the Space Telescope Science Institute (STScI). The testbed contains a pair of deformable mirrors (DMs) and a lyot coronagraph. The algorithm uses an Extended Kalman Filter (EKF) and DM dithering to predict the drifting electric field in the dark hole along with Electric Field Conjugation to cancel out the drift. The DM dither introduces phase diversity which ensures the EKF converges to the correct value. The DHM algorithm maintains an initial contrast of 8.5 x 10-8 for 6 hrs in the presence of the DM actuator random walk drift with a standard deviation of 1:7 x 10-3 nm/s..
Modern coronagraph design relies on advanced, large-scale optimization processes that require an ever increasing amount of computational resources. In this paper, we restrict ourselves to the design of Apodized Pupil Lyot Coronagraphs (APLCs). To produce APLC designs for future giant space telescopes, we require a fine sampling for the apodizer to resolve all small features, such as segment gaps, in the telescope pupil. Additionally, we require the coronagraph to operate in broadband light and be insensitive to small misalignments of the Lyot stop. For future designs we want to include passive suppression of low-order aberrations and finite stellar diameters. The memory requirements for such an optimization would exceed multiple terabytes for the problem matrix alone. We therefore want to reduce the number of variables and constraints to minimize the size of the problem matrix. We show how symmetries in the pupil and Lyot stop are expressed in the complete optimization problem, and allow removal of both variables and constraints. Each mirror symmetry reduces the problem size by a factor of four. Secondly, we introduce progressive refinement, which uses low-resolution optimizations as a prior for higher resolutions. This lets us remove the majority of variables from the high-resolution optimization. Together these two improvements require up to 256x less computer memory, with a corresponding speed increase. This allows for greater exploration of the phase space of the focal-plane mask and Lyot-stop geometry, and easier simulation of sensitivity to Lyot-stop misalignments. Moreover, apodizers can now be optimized at their native manufactured resolution.
Imaging exo-Earths is an exciting but challenging task because of the 10-10 contrast ratio between these planets and their host star at separations narrower than 100 mas. Large segmented aperture space telescopes enable the sensitivity needed to observe a large number of planets. Combined with coronagraphs with wavefront control, they present a promising avenue to generate a high-contrast region in the image of an observed star. Another key aspect is the required stability in telescope pointing, focusing, and co-phasing of the segments of the telescope primary mirror for long-exposure observations of rocky planets for several hours to a few days. These wavefront errors should be stable down to a few tens of picometers RMS, requiring a permanent active correction of these errors during the observing sequence. To calibrate these pointing errors and other critical low-order aberrations, we propose a wavefront sensing path based on Zernike phase-contrast methods to analyze the starlight that is filtered out by the coronagraph at the telescope focus. In this work we present the analytical retrieval of the incoming low order aberrations in the starlight beam that is filtered out by an Apodized Pupil Lyot Coronagraph, one of the leading coronagraph types for starlight suppression. We implement this approach numerically for the active control of these aberrations and present an application with our first experimental results on the High-contrast imager for Complex Aperture Telescopes (HiCAT) testbed, the STScI testbed for Earth-twin observations with future large space observatories, such as LUVOIR and HabEx, two NASA flagship mission concepts.
This paper presents the setup for empirical validations of the Pair-based Analytical model for Segmented Telescope Imaging from Space (PASTIS) tolerancing model for segmented coronagraphy. We show the hardware configuration of the High-contrast imager for Complex Aperture Telescopes (HiCAT) testbed on which these experiments will be conducted at an intermediate contrast regime between 10-6 and 10-8. We describe the optical performance of the testbed with a classical Lyot coronagraph and describe the recent hardware upgrade to a segmented mode, using an IrisAO segmented deformable mirror. Implementing experiments on HiCAT is made easy through its top-level control infrastructure that uses the same code base to run on the real testbed, or to invoke the optical simulator. The experiments presented in this paper are run on the HiCAT testbed emulator, which makes them ready to be performed on actual hardware. We show results of three experiments with results from the emulator, with the goal to demonstrate PASTIS on hardware next. We measure the testbed PASTIS matrix, and validate the PASTIS analytical propagation model by comparing its contrast predictions to simulator results. We perform the tolerancing analysis on the optical eigenmodes (PASTIS modes) and on independent segments, then validate these results in respective experiments. This work prepares and enables the experimental validation of the analytical segment-based tolerancing model for segmented aperture coronagraphy with the specific application to the HiCAT testbed.
The goal of the High-contrast imager for Complex Aperture Telescopes (HiCAT) testbed is to demonstrate coronagraphic starlight suppression solutions for future segmented aperture space telescopes such as the Large UV, Optical, IR telescope (LUVOIR) mission concept being studied by NASA. The testbed design has the flexibility to enable studies with increasing complexity for telescope aperture geometries starting with off-axis telescopes, then on-axis telescopes with central obstruction and support structures. The testbed implements the Apodized Pupil Lyot Coronagraph (APLC) optimized for the HiCAT aperture, which is similar to one of the possible geometries considered for LUVOIR. Wavefront can be controlled using continuous deformable mirrors, and wavefront sensing is performed using the imaging camera, or a dedicated phase retrieval camera, and also in a low-order wavefront sensing arm. We present a progress update of the testbed in particular results using two deformable mirror control to produce high-contrast dark zone, and preliminary results using the testbed’s low order Zernike wavefront sensor.
Direct imaging of exo-Earths and search for life is one of the most exciting and challenging objectives for future space observatories. Segmented apertures in space will be required to reach the needed large diameters beyond the capabilities of current or planned launch vehicles. These apertures present additional challenges for high-contrast coronagraphy, not only in terms of static phasing but also in terms of their stability. The Pair-based Analytical model for Segmented Telescope Imaging from Space (PASTIS) was developed to model the effects of segment-level optical aberrations on the final image contrast. In this paper, we extend the original PASTIS propagation model from a purely analytical to a semi-analytical method, in which we substitute the use of analytical images with numerically simulated images. The inversion of this model yields a set of orthonormal modes that can be used to determine segment-level wavefront tolerances. We present results in the case of segment-level piston error applied to the baseline coronagraph design of LUVOIR A, with minimum and maximum wavefront error constraint between 56 pm and 290 pm per segment. The analysis is readily generalizable to other segment-level aberrations modes, and can also be expanded to establish stability tolerances for these missions.
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