Guest Editors Frederick S. Porter and Paul P. Plucinsky introduce the Special Section on the Line Emission Mapper X-ray Observatory.

The line emission mapper (LEM) is a probe-class mission concept that is designed to detect x-ray emission lines from hot ionized gas (T > 10⁶ K) that will enable us to test galaxy evolution theories. It will permit us to study the effects of stellar and black-hole feedback and flows of baryonic matter into and out of galaxies. The key to being able to study the hot gases that are otherwise invisible to current imaging x-ray spectrometers is that the energy resolution is sufficient to use cosmological redshift to separate extragalactic source lines from foreground Milky Way emission. LEM incorporates a large-format microcalorimeter array instrument called the LEM microcalorimeter spectrometer (LMS) with a light-weight x-ray optic with 10” half power diameter angular resolution. The LMS microcalorimeter array has pixels with 15″ pixel pitch over a 33′ field of view (FOV) optimized for the 0.3 to 2 keV energy band. The central 7′ region of the array has an energy resolution of 1.3 eV at 1 keV and the rest of the FOV has 2.5 eV energy resolution at 1 keV. The array will be read out with state-of-the-art time-division multiplexing. We present an overview of the LMS instrument, including details of the entire detection chain, the focal plane assembly, as well as the cooling system and overall mechanical and thermal design. For each of the key technologies, we discuss the current technology readiness level and the plan to advance them to be ready for flight. We also describe the current system design and our estimate for the mass, power, and data rate of the instrument. The design details presented concentrate primarily on the unique aspects of the LMS design compared with prior missions and confirm that the type of microcalorimeter instrument needed for LEM is not only feasible but also technically mature.

The continuous adiabatic demagnetization refrigerator (CADR) described in this paper is a compact, reliable, and highly efficient magnetic cooling system designed for the line emission mapper (LEM), a future x-ray probe mission currently being proposed. Operating at two distinct temperatures of 350 mK (T₁) and 40 mK (T₀), the CADR offers continuous cooling while efficiently rejecting heat to a cryocooler at 4 K. Shielded by ferromagnetic and high-permeability magnetic shields, the CADR minimizes interference on the focal plane assembly. With flight-proven components, the CADR provides precise temperature regulation via its sensitive and large-arrayed transition edge sensor detectors. The CADR system for LEM consists of two modular units. The high-temperature module spans from 4 K to 350 mK, comprising four stages, whereas the low-temperature module spans from 350 to 40 mK, comprising three stages. The system is designed to continuously deliver 174 μW of useful cooling power at 350 mK and 2 μW at 40 mK.

We are developing space-flight room-temperature readout electronics for the Line Emission Mapper (LEM) Microcalorimeter Spectrometer (LMS) of the LEM mission. The LEM mission is an x-ray probe mission designed to study the physics of galaxy formation. The LMS is optimized for low-energy (0.2 to 2 keV) x-ray emission from extremely diffuse gas. The detector is a hybrid transition-edge sensor (TES) microcalorimeter array with a 33′ outer array and a 7 ^′ × 7 ^′ inner subarray. The outer array consists of 12,736 square pixels on a square grid with a 290 μm pitch but in a close-packed hexagonal shape. The inner subarray consists of 784 TES sensors arranged in a square area in the center of the outer array with the same pixel pitch. The outer array uses a sensor with 2 × 2 thermal multiplexing known as “Hydra,” and the inner array consists of a single absorber per TES. The baselined readout technology for the 3968 TES sensors is time-division multiplexing (TDM), which divides the sensors into 69 columns × 60 rows. The components of the room temperature readout electronics are the three boxes of the warm front-end electronics (WFEE) and the six boxes of the digital electronics and event processor (DEEP). The WFEE is an interface between the cold electronics and the DEEP, and the DEEP generates signals for the TDM and processes x-ray events. We present the detailed designs of the WFEE and DEEP. We also show the estimated power, mass, and size of the WFEE and DEEP flight electronics. Finally, we describe the performance of the TRL-6 prototypes for the WFEE and DEEP electronics.

The Line Emission Mapper (LEM) is an x-ray probe mission concept that is designed to provide unprecedented insight into the physics of galaxy formation, including stellar and black-hole feedback and flows of baryonic matter into and out of galaxies. LEM incorporates a light-weight x-ray optic with a large-format microcalorimeter array. The LEM detector utilizes a 14k pixel array of transition-edge sensors (TESs) that will provide <2.5 eV spectral resolution over the energy range 0.2 to 2 keV, along with a field-of-view of 30 arcmin. The microcalorimeter array and readout builds upon the technology developed for the European Space Agency’s (ESA’s) Athena/x-ray Integral Field Unit. Here, we present a detailed overview of the baseline microcalorimeter design, its performance characteristics, including a detailed energy resolution budget and the expected count-rate capability. In addition, we outline the current status and plan for continued technology maturation. Behind the LEM array sits a high-efficiency TES-based anticoincidence (antico) detector that will reject cosmic-ray background events. We will briefly describe the design of the antico and plan for continued development.

The Line Emission Mapper (LEM) is a proposed x-ray probe mission to study the physics of galaxy formation through spectral and spatial measurements of x-rays in the energy band of 0.2 to 2 keV. The LEM Microcalorimeter Spectrometer instrument on LEM will have a hybrid transition-edge sensor (TES) microcalorimeter array made up of an inner array of single-pixels with one x-ray absorber connected to one TES and an outer array of multi-absorber microcalorimeters, or “hydras,” with four absorbers connected to a single TES, each with a different thermal conductance. Here, we characterize the first hybrid array of single-pixel and multi-absorber microcalorimeters designed for LEM. We present the fundamental transition, noise, and detector performance properties to demonstrate their suitability for the mission. We also show that the spectral resolution at the Al K_α line is 1.92 ± 0.02 eV for the 4-pixel hydra (coadded) and 0.90 ± 0.02 eV for the single-pixels. This is significantly better resolution than the LEM mission level requirement. Finally, we demonstrate that the position discrimination between the four pixels of the hydra can be achieved down to 200 eV when measured with a time-division multiplexed readout using timings representative of the anticipated LEM requirements.

The line emission mapper x-ray microcalorimeter instrument requires a 4 K cryogenic system to precool a continuous adiabatic demagnetization refrigerator enabling high-resolution x-ray spectroscopy. The cryogenic system described in this work provides the required structural and thermal environments using mature cooling and structural technologies. The system is comprised of a dewar design based on heritage manufacturing processes and an efficient four-stage pulse tube cryocooler with supporting control electronics.

In the 2020 Astrophysics Decadal Survey, the National Academies identified cosmic feedback and structure formation as a key question that should drive research in the upcoming decade. In response to this recommendation, NASA released a call for X-ray and IR probe-class missions, with a $1B cost cap. The line emission mapper (LEM) is a mission concept designed in response to this call. LEM is a single-instrument X-ray telescope that consists of a Wolter–Schwarzschild type I X-ray optic with a 4 m focal length, coupled with an X-ray microcalorimeter with a 30′ field of view (FoV), 15″ angular resolution, and 2.5 eV energy resolution [full-width half maximum (FWHM)], with a 1.3 eV FWHM energy resolution central subarray. The high throughput X-ray mirror combined with the large FoV and excellent energy resolution allows for efficient mapping of extended emission-line dominated astrophysical objects from megaparsecs to sub-pc scales to study cosmic ecosystems and unveil the physical drivers of galaxy formation.

Visible emission line coronagraph (VELC) is the prime payload on board India’s first space solar observatory Aditya-L1. VELC is a unique payload with simultaneous observational capabilities in imaging, spectroscopy, and spectro polarimetry modes. VELC is capable of achieving high spatial, spectral, and temporal resolution closer to the solar limb 1.05 R _⊙ compared to the existing space and ground-based solar coronagraphs. VELC consists of a total of 44 optical elements in 18 groups, which are custom designed and developed to meet the desired performance requirements. In addition, it consists of four mechanisms out of which two are multioperational with expected life cycle of million operations. Four detectors (three sCMOS and one InGaAs) are used to record the data. The performance of the payload depends on the performance of individual element, subsystems, and the system level performance of all the elements (such as optics, mechanism, and detectors) together. To ensure the desired performance levels are achieved, each element/subsystem should be tested prior to integrating them together. Evaluation of performance of the integrated system is essential to validate the payload capabilities to meet the proposed science goals. This paper summarizes the calibration tests carried out on the integrated system and compares the results obtained with respect to the design requirements to meet the proposed science goals.

Realizing accurate positioning with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) closed-loop system depends on accurate high-precision calibration of the visual measurement system, which has a great impact on collision avoidance and accurate positioning. We designed fiducial fibers for the calibration of the LAMOST closed-loop system to provide accurate fiducial positions for visual measurement. The benchmark position accuracy of the fiducial fibers is a key factor affecting the accuracy of the visual measurement system; the more accurate the fiducial fiber positions are, the higher the visual measurement correction accuracy. In this study, three measurement methods were used to obtain the fiducial fiber positions, namely, measuring the hole positions using a coordinate measuring machine, imaging the fiducial fibers using a calibrated photographic system, and directly measuring the fiducial fiber spatial positions using a laser tracker. By evaluating the fiber positions obtained via the three methods, we can obtain a stable and reliable fiducial fiber position benchmark. A fiducial fiber positions evaluation method based on an optimal residual criterion is proposed, and the optimal residual solution for a small calibration target (SCT) is used to evaluate the optimal fiducial fiber measurement method. Specifically, the fiducial positions obtained via each of the three methods are used to invert the camera calibration parameters, which are then used to calculate the physical position of an SCT. Finally, the residual value between the calculated and theoretical positions is taken as the standard for evaluating the fiducial fiber measurement benchmark performance. The results show that the fiducial fiber positions measured using the laser tracker can be applied to effectively calibrate the photographic system, enabling the LAMOST vision measurement system to achieve a positioning accuracy of nearly 10 μm with the camera 20 m from the focal surface, whereas the accuracy is within 20 μm for ∼95 % of the measurement points.

In the past few years, there has been a resurgence in studies of space-based optical/infrared interferometry, particularly with the vision to use the technique to discover and characterize temperate Earth-like exoplanets around solar analogs. One of the key technological leaps needed to make such a mission feasible is demonstrating that formation flying precision at the level needed for interferometry is possible. Here, we present Pyxis, a ground-based demonstrator for a future small satellite mission with the aim to demonstrate the precision metrology needed for space-based interferometry. We describe the science potential of such a ground-based instrument and detail the various subsystems: three six-axis robots, a multi-stage metrology system, an integrated optics beam combiner, and the control systems required for the necessary precision and stability. We conclude by looking toward the next stage of Pyxis: a collection of small satellites in Earth orbit.

The Roman Space Telescope will have the first advanced coronagraph in space, with deformable mirrors (DMs) for wavefront control (WFC), low-order wavefront sensing and maintenance, and a photon-counting detector. It is expected to be able to detect and characterize mature, giant exoplanets in reflected visible light. Over the past decade, the performance of the coronagraph in its flight environment has been simulated with increasingly detailed diffraction and structural/thermal finite-element modeling. With the instrument now being integrated in preparation for launch within the next few years, the present state of the end-to-end modeling, including the measured flight components such as DMs, is described. The coronagraphic modes, including characteristics most readily derived from modeling, are thoroughly described. The methods for diffraction propagation, WFC, and structural and thermal finite-element modeling are detailed. The techniques and procedures developed for the instrument will serve as a foundation for future coronagraphic missions, such as the Habitable Worlds Observatory.

The Institute for Astrophysics and Geophysics solar observatory is producing high-fidelity, ultra-high-resolution spectra (R > 500000) of the spatially resolved surface of the Sun using a Fourier transform spectrometer (FTS). The radial velocity (RV) calibration of these spectra is currently performed using absorption lines from Earth’s atmosphere, limiting the precision and accuracy. To improve the frequency calibration precision and accuracy, we use a Fabry–Pérot etalon (FP) setup that is an evolution of the CARMENES FP design and an iodine cell in combination. To create an accurate wavelength solution, the iodine cell is measured in parallel with the FP. The FP is then used to transfer the accurate wavelength solution provided by the iodine via a simultaneous calibration of solar observations. To verify the stability and precision of the FTS, we perform parallel measurements of the FP and an iodine cell. The measurements show an intrinsic stability of the FTS of a level of 1 m s ^{− 1} over 90 h. The difference between the FP RVs and the iodine cell RVs show no significant trends during the same time span. The root mean square of the RV difference between the FP and iodine cell is 10.7 cm s ^{− 1}, which can be largely attributed to the intrinsic RV precisions of the iodine cell and the FP (10.2 and 1.0 cm s ^{− 1}, respectively). This shows that we can calibrate the FTS to a level of 10 cm s ^{− 1}, competitive with current state-of-the-art precision RV instruments. Based on these results, we argue that the spectrum of iodine can be used as an absolute reference to reach an RV accuracy of 10 cm s ^{− 1}.

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.

CIS221-X is a prototype complementary metal-oxide-semiconductor (CMOS) image sensor, optimized for soft x-ray astronomy and developed for the proposed ESA Transient High Energy Sky and Early Universe Surveyor (THESEUS) mission. The sensor features 40 μm pitch square pixels built on a 35 μm thick, high-resistivity epitaxial silicon that is fully depleted by reverse substrate bias. Backside illumination processing has been used to achieve high x-ray quantum efficiency, and an optical light-blocking filter has been applied to mitigate the influence of stray light. A comprehensive electro-optical characterization of CIS221-X has been completed. The median readout noise is 3.3 e ⁻ RMS with 90% of pixels reporting a value <3.6 e ⁻ RMS. At −40 ° C, the dark current is 12.4 ± 0.06 e ⁻ / pixel / s. The pixel photo-response is linear to within 1% for 0.3 to 5 keV photons (82 to 1370 e ⁻ ) with <0.1 % image lag. Following per-pixel gain correction, an energy resolution of 130.2 ± 0.4 eV has been measured at 5898 eV. In the 0.3 to 1.8 keV energy range, CIS221-X achieves >80 % quantum efficiency. With the exception of dark current, these results either meet or outperform the requirements for the THESEUS mission, strongly supporting the consideration of CMOS technology for soft x-ray astronomy.

Future x-ray observatories will require imaging detectors with fast readout speeds that simultaneously achieve or exceed the other high-performance parameters of x-ray charge-coupled devices used in many missions over the past three decades. Fast readout will reduce the impact of pile-up in missions with large collecting areas while improving the performance in other respects, such as timing resolution. Event-driven readout, in which only pixels with charge from x-ray events are read out, can be used to achieve these faster operating speeds. Speedster-EXD550 detectors are hybrid complementary metal-oxide semiconductor detectors capable of event-driven readout that were developed by Teledyne Imaging Sensors and Penn State University. We present the initial results from measurements of the first of these detectors, demonstrating their capabilities and performance in both full-frame and event-driven readout modes. These include dark current, read noise, gain variation, and energy resolution measurements from the first two engineering-grade devices.

Complementary metal-oxide-semiconductor (CMOS) sensors are a competitive choice for future X-ray astronomy missions. Typically, CMOS sensors on space astronomical telescopes are exposed to a high dose of irradiation. We investigate the impact of irradiation on the performance of two scientific CMOS (sCMOS) sensors between −^{30 °} C and 20 ^° C at high gain mode (7.5 × ), including the bias map, readout noise, dark current, conversion gain, and energy resolution. The two sensors are irradiated with 50 MeV protons with a total dose of 5.3 × 10¹⁰ p · cm ^{− 2}. After the exposure, the bias map, readout noise, and conversion gain at various temperatures are not significantly degraded, nor is the energy resolution at −^{30 °} C. However, after the exposure the dark current has increased by hundreds of times, and for every ^{20 °} C increase in temperature, the dark current also increases by an order of magnitude. Therefore, at room temperature, the fluctuations of the dark currents dominate the noise and lead to a serious degradation of the energy resolution. Moreover, among the 4 k × 4 k pixels, there are about 100 pixels whose bias at 50 ms has changed by more than 10 DN ( ∼ 18 e ⁻ ), and about 10 pixels whose readout noise has increased by over 15 e ⁻ at −^{30 °} C. Fortunately, the influence of the dark current can be reduced by decreasing the integration time, and the degraded pixels can be masked by regular analysis of the dark images. Some future X-ray missions will likely operate at −30 ^° C, under which the dark current is too small to significantly affect the X-ray performance. Our investigations show the high tolerance of the sCMOS sensors for proton radiation and prove their suitability for X-ray astronomy applications.

Pandora is an upcoming NASA SmallSat mission that will observe transiting exoplanets to study their atmospheres and the variability of their host stars. Efficient mission planning is critical for maximizing the science achieved with the year-long primary mission. To this end, we have developed a scheduler based on a metaheuristic algorithm that is focused on tackling the unique challenges of time-constrained observing missions, like Pandora. Our scheduling algorithm combines a minimum transit requirement metric, which ensures we meet observational requirements, with a “quality” metric that considers three factors to determine the scientific quality of each observation window around an exoplanet transit (defined as a visit). These three factors are: observing efficiency during a visit, the amount of the transit captured by the telescope during a visit, and how much of the transit captured is contaminated by a coincidental passing of the observatory through the South Atlantic Anomaly (SAA). The importance of each of these factors can be adjusted based on the needs or preferences of the science team. Utilizing this schedule optimizer, we develop and compare a few schedules with differing factor weights for the Pandora SmallSat mission, illustrating trade-offs that should be considered between the three quality factors. We also find that under all scenarios probed, Pandora will not only be able to achieve its observational requirements using the planets on the notional target list but will do so with significant time remaining for ancillary science.

The large side aperture of the Nuclear Spectroscopic Telescope Array (NuSTAR) telescope for unfocused photons (so-called stray light) is a known source of rich astrophysical information. To support many studies based on the NuSTAR stray light data, we present a fully automatic method for determining detector area suitable for background analysis and free from any kind of focused x-ray flux. The method’s main idea is “á trous” wavelet image decomposition, capable of detecting structures of any spatial scale and shape, which makes the method of general use. Applied to the NuSTAR data, the method provides a detector image region with the highest possible statistical quality, suitable for the NuSTAR stray light studies. We developed an open-source Python nuwavdet package, which implements the presented method. The package contains subroutines to generate detector image region for further stray light analysis and/or to produce a list of detector bad-flagged pixels for processing in the NuSTAR Data Analysis Software for conventional x-ray analysis.

The proposed Daksha mission comprises of a pair of highly sensitive space telescopes for detecting and characterizing high-energy transients, such as electromagnetic counterparts of gravitational wave events and gamma-ray bursts (GRBs). Along with spectral and timing analysis, Daksha can also undertake polarization studies of these transients, providing data crucial for understanding the source geometry and physical processes governing high-energy emission. Each Daksha satellite will have 340 pixelated cadmium zinc telluride (CZT) detectors arranged in a quasi-hemispherical configuration without any field-of-view collimation (open detectors). These CZT detectors are good polarimeters in the energy range 100 to 400 keV, and their ability to measure polarization has been successfully demonstrated by the cadmium zinc telluride imager onboard AstroSat. Here, we demonstrate the hard x-ray polarization measurement capabilities of Daksha and estimate the polarization measurement sensitivity (in terms of the minimum detectable polarization: MDP) using extensive simulations. We find that Daksha will have MDP of 30% for a fluence threshold of 10 ^{− 4} erg cm ^{− 2} (in 10 to 1000 keV). We estimate that with this sensitivity, if GRBs are highly polarized, Daksha can measure the polarization of about five GRBs per year.

For diffraction-limited optical systems, an accurate physical optics model is necessary to properly evaluate instrument performance. Astronomical observatories outfitted with coronagraphs for direct exoplanet imaging require physical optics models to simulate the effects of misalignment and diffraction. Accurate knowledge of the observatory’s point-spread function (PSF) is integral for the design of high-contrast imaging instruments and simulation of astrophysical observations. The state of the art is to model the misalignment, ray aberration, and diffraction across multiple software packages, which complicates the design process. Gaussian beamlet decomposition (GBD) is a ray-based method of diffraction calculation that has been widely implemented in commercial optical design software. By performing the coherent calculation with data from the ray model of the observatory, the ray aberration errors can be fed directly into the physical optics model of the coronagraph, enabling a more integrated model of the observatory. We develop a formal algorithm for the transfer-matrix method of GBD and evaluate it against analytical results and a traditional physical optics model to assess the suitability of GBD for high-contrast imaging simulations. Our GBD simulations of the observatory PSF, when compared to the analytical Airy function, have a sum-normalized RMS difference of ≈10 ^{− 6}. These fields are then propagated through a Fraunhofer model of an exoplanet imaging coronagraph where the mean residual numerical contrast is 4 × ^{10 − 11}, with a maximum near the inner working angle at 5 × 10 ^{− 9}. These results show considerable promise for the future development of GBD as a viable propagation technique in high-contrast imaging. We developed this algorithm in an open-source software package and outlined a path for its continued development to increase the accuracy and flexibility of diffraction simulations using GBD.

Adaptive optics (AO) corrected image restoration is particularly difficult, as it suffers from the lack of knowledge on the point spread function (PSF) in addition to usual difficulties. An efficient approach is to marginalize the object out of the problem and to estimate the PSF and (object and noise) hyperparameters only, before deconvolving the image using these estimates. Recent works have applied this marginal myopic deconvolution method, based on the maximum a posteriori estimator, combined with a parametric model of the PSF, to a series of AO-corrected astronomical and satellite images. However, this method does not enable one to infer global uncertainties on the parameters. We propose a PSF estimation method, which consists in choosing the minimum mean square error estimator and computing the latter as well as the associated uncertainties thanks to a Markov chain Monte Carlo algorithm. We validate our method by means of realistic simulations, in both astronomical and satellite observation contexts. Finally, we present results on experimental images for both applications: an astronomical observation on Very Large Telescope/spectro-polarimetric high-contrast exoplanet research with the Zimpol instrument and a ground-based LEO satellite observation at Côte d’Azur Observatory’s 1.52 m telescope with Office National d'Etudes et de Recherches Aérospatiales’s ODISSEE AO bench.

Photonic technologies have enabled a generation of nulling interferometers, such as the guided light interferometric nulling technology instrument, potentially capable of imaging exoplanets and circumstellar structure at extreme contrast ratios by suppressing contaminating starlight, and paving the way to the characterization of habitable planet atmospheres. But even with cutting-edge photonic nulling instruments, the achievable starlight suppression (null-depth) is only as good as the instrument’s wavefront control and its accuracy is only as good as the instrument’s calibration. Here, we present an approach wherein outputs from non-science channels of a photonic nulling chip are used as a precise null-depth calibration method and can also be used in real time for fringe tracking. This is achieved using a deep neural network to learn the true in-situ complex transfer function of the instrument and then predict the instrumental leakage contribution (at millisecond timescales) for the science (nulled) outputs, enabling accurate calibration. In this method, this pseudo-real-time approach is used instead of the statistical methods used in other techniques (such as null self calibration, or NSC) and also resolves the severe effect of read-noise seen when NSC is used with some detector types.

Photon counting is a mode of processing astronomical observations of low-signal targets that are observed using an electron-multiplying charge-coupled device (EMCCD). In photon counting, the EMCCD amplifies the signal, and a thresholding technique effectively selects for the signal electrons while drastically reducing relative noise sources. Photometric corrections that result in the extraction of a more accurate estimate of the signal of electrons have been developed; the Nancy Grace Roman Telescope will utilize a theoretical expression for the signal-to-noise ratio (SNR) given these corrections based on well-calibrated noise parameters to plan observations taken by its coronagraph instrument. The analytic expressions for the SNR for the method of photon counting, before and after these photometric corrections are applied, are derived.

The nonlinear curvature wavefront sensor (nlCWFS) offers improved sensitivity for adaptive optics systems compared with existing WFSs, such as the Shack–Hartmann. The nominal nlCWFS design uses a series of imaging planes offset from the pupil along the optical propagation axis as inputs to a numerically iterative reconstruction algorithm. Research into the nlCWFS has assumed that the device uses four measurement planes configured symmetrically around the optical system pupil. This assumption is not strictly required. In this paper, we perform the first systematic exploration of the location, number, and spatial sampling of measurement planes for the nlCWFS. Our numerical simulations show that the original, symmetric four-plane configuration produces the most consistently accurate results in the shortest time over a broad range of seeing conditions. We find that the inner measurement planes should be situated past the Talbot distance corresponding to a spatial period of r₀. The outer planes should be large enough to fully capture the field intensity and be situated beyond a distance corresponding to a Fresnel-number-scaled equivalent of Z ≈ 50 km for a D = 0.5 m pupil with λ = 532 nm. The minimum spatial sampling required for diffraction-limited performance is 4 to 5 pixels per r₀ as defined in the pupil plane. We find that neither three-plane nor five-plane configurations offer significant improvements compared with the original design. These results can impact future implementations of the nlCWFS by informing sensor design.

We present a method to develop a turbulence emulation bench for low-Earth-orbit satellite-to-ground optical communication links under strong turbulence. We provide guidelines to characterize the spatio–temporal dynamics of phase disturbances and scintillation produced by the emulator on a laser beam. We implemented such an emulator for a link at 10 deg elevation and discuss here its design method and characterization. The characterization results are compared to numerical simulations, and this characterization results in the validation of a digital twin of the emulator. The emulator will serve as a testing platform for adaptive optics systems and other free-space optical communication components under strong turbulence conditions.

Deformable mirrors (DM) are critical components of active optics systems that are used to compensate for wavefront correction in spaceborne electro-optical (EO) payloads. In comparison to glass mirrors, a metal-based mirror is lighter in weight, has more compact design, is less expensive, and can be manufactured quickly. Furthermore, aluminum has higher yield strength than glass, which is advantageous in the event of mirror deformation. We present finite element (FE) optimization of an aluminum mirror’s active surface for the contradictory requirements of flexibility for mirror deformation and stiffness for mirror fabrication. The active surface thickness considered for optimization is 1 to 6 mm for varied mirror diameters ranging from 80 to 100 mm. Aspects related to mirror fabrication on single point diamond turning (SPDT) machine have been considered during the design stage. We compare correction accuracy targeting more than 95%, peak to peak actuator stroke, and root mean square error for various diameters and thicknesses. The optimized mirror was fabricated using SPDT and tested using an interferometer. Later, a DM prototype was built using commercially available piezoelectric actuators, and targeted aberrations/shapes were generated to demonstrate the accuracy of correction.

Consistent operation of adaptive optics (AOs) systems requires the use of a wavefront sensor (WFS) with high sensitivity and low noise. The nonlinear curvature WFS (nlCWFS) has been shown both in simulations and lab experiments to be more sensitive than the industry-standard Shack–Hartmann WFS (SHWFS), but its noise characteristics have yet to be thoroughly explored. In this work, we develop a spatial domain wavefront error budget for the nlCWFS that includes common sources of noise that introduce uncertainty into the reconstruction process (photon noise, finite bit depth, read noise, vibrations, non-common-path errors, servo lag, etc.). We find that the nlCWFS can outperform the SHWFS in a variety of environmental conditions and that the primary challenge involves overcoming speed limitations related to the wavefront reconstructor. The results of this work may be used to inform the design of nlCWFS systems for a broad range of AO applications.

For natural guide star adaptive optics (AO) systems, pyramid wavefront sensors (PWFSs) can provide a significant increase in sensitivity over the traditional Shack–Hartmann but at the cost of a reduced linear range. When using a linear reconstructor, nonlinearities result in wavefront estimation errors, which can have a significant impact on the image quality delivered by the AO system. We simulate a wavefront passing through a PWFS under varying observing conditions to explore the possibility of using a nonlinear machine learning model to estimate wavefront errors and compare with a linear reconstruction. We find significant potential improvements in delivered image quality even with computationally simple models, underscoring the need for further investigation of this approach.