Correction Of Wavefront Errors Research Articles

Next-generation active telescope for space astronomy

We present a design for an active telescope for space astronomy. The telescope is capable of both exoplanet work and general astronomy over wavelengths from ∼100 nm up to 5 μm. The primary mirror is 6 m in diameter, formed by 16 mirror segments that are precisely phased and supported on rigid body actuators and with segment optical surface figures fine-tuned using surface figure actuators. The active primary forms a large deformable mirror (DM) with wavefront error (WFE) correction at the entrance pupil. Thus the largest source of WFE can be removed at the source and is corrected over the entire field of view. This enables diffraction-limited performance at 400 nm and a more efficient optical system over a broader wavelength range than could be achieved by a small DM at a downstream relayed pupil. The telescope is passively cooled to below 100 K at Sun–Earth L2, enabling astronomical-background-limited observations out to 5 μm. Launched on a SpaceX Starship or alternatively National Aeronautics and Space Administration’s Space Launch System, the telescope requires minimal deployments. A 72-m-diameter starshade provides a contrast ratio better than 10 − 10 for exoplanet science. Near the visible region, with a 108% working bandwidth from 300 to 1000 nm, a working distance of 120 Mm provides a 51-mas inner working angle (IWA). This band can be moved to shorter or longer wavelengths by adjusting the starshade range from the telescope. Our first-ever thermal analysis of such a starshade shows that a temperature below 100 K can be achieved over a broad range of observing directions, permitting the possibility of working into the infrared. We model the yield in exoplanets that can be observed. A starshade and associated spectrograph offer significant advantages for exoplanet characterization. They enable a much broader instantaneous spectral bandwidth (here 108%) than current coronagraphs (∼10 % to 20% bandwidth), allow both polarizations to be observed simultaneously, and have higher throughput. The IWA is twice as small as can be achieved with a coronagraph and there is no outer working angle. These differences are particularly pronounced in the UV, where coronagraph performance would be strongly affected by throughput losses, wavefront aberrations, Fresnel polarization effects at surfaces, and thermal instability.

Flight designs and pupil error mitigation for the bowtie shaped pupil coronagraph on the Nancy Grace Roman Space Telescope

The Nancy Grace Roman Space Telescope will carry a coronagraph instrument (CGI) that will serve as a demonstrator for technologies needed for future high-contrast imaging missions in space, including deformable mirrors (DMs) to correct high-order wavefront errors that would otherwise limit the achievable contrast. The CGI has three baselined interchangeable observing configurations, one of which is a bowtie shaped pupil coronagraph for high-contrast spectroscopy. We present the flight designs for two closely related mask configurations of the bowtie shaped pupil coronagraph: a baseline 0-deg mask configuration for the technology demonstration and a 60-deg mask configuration contributed by the NASA Exoplanet Exploration Program. The shaped pupil mask and Lyot stop for each mask configuration result from an iterative process that maximizes the core throughput subject to constraints on other performance metrics, such as the contrast: a linear program optimizes the shaped pupil mask for a given Lyot stop, and the optimization repeats for various Lyot stops until the highest-throughput combination is identifiable. The flight designs for the baseline and rotated mask configurations have core throughputs of 4.50% and 3.89%, respectively, at 4 λD and are robust to conservative estimates of potential pupil errors such as misalignments and manufacturing errors. If these estimates are exceeded in flight, the DMs can be used to mitigate the effects of the excess error.

Optical calibration and first light for the deformable mirror demonstration mission CubeSat (DeMi)

Microelectromechanical systems (MEMS) deformable mirrors (DMs) can provide high-precision wavefront control with a small form-factor, low power device. This makes them a key technology option for future space telescopes requiring adaptive optics for high-contrast imaging of exoplanets with a coronagraph instrument. The Deformable Mirror Demonstration Mission (DeMi) CubeSat payload is a miniature space telescope designed to demonstrate MEMS DM technology in space for the first time. The DeMi payload contains a 50-mm primary mirror, an internal calibration laser source, a 140-actuator MEMS DM from Boston Micromachines Corporation, an image plane wavefront sensor, and a Shack–Hartmann wavefront sensor (SHWFS). The key DeMi payload requirements are to measure individual actuator wavefront displacement contributions to a precision of 12 nm and correct both static and dynamic wavefront errors in space to less than 100-nm RMS error. The DeMi mission will raise the technology readiness level of MEMS DM technology from a five to at least a seven for future space telescope applications. We summarize the DeMi optical payload design, calibration, optical diffraction model, alignment, integration, environmental testing, and preliminary data from in-space operations. Ground testing data show that the DeMi SHWFS can measure individual actuator deflections on the MEMS DM to within 10 nm of interferometric calibration measurements and can meet the 12-nm precision mission requirement for actuator deflection voltages between 0 and 120 V. Payload data from throughout environmental testing show that the MEMS DM and DeMi payload survived environmental testing and provides a valuable baseline to compare with space data. Initial data from space operations show the MEMS DM actuating in space with a median agreement between individual actuator measurements from space and equivalent ground testing data of 12 nm.

Differential wavefront sensing and control using radio-frequency optical demodulation.

Differential wavefront sensing is an essential technique for optimising the performance of many precision interferometric experiments. Perhaps the most extensive application of this is for alignment sensing using radio-frequency beats measured with quadrant photodiodes. Here we present a new technique that uses optical demodulation to measure such optical beats at high resolutions using commercial laboratory equipment. We experimentally demonstrate that the images captured can be digitally processed to generate wavefront error signals and use these in a closed loop control system for correct wavefront errors for alignment and mode-matching a beam into an optical cavity to 99.9%. This experiment paves the way for the correction of even higher order errors when paired with higher order wavefront actuators. Such a sensing scheme could find use in optimizing complex interferometers consisting of coupled cavities, such as those found in gravitational wave detectors, or simply just for sensing higher order wavefront errors in heterodyne interferometric table-top experiments.

Microelectromechanical deformable mirror development for high-contrast imaging, part 2: the impact of quantization errors on coronagraph image contrast

Stellar coronagraphs rely on deformable mirrors (DMs) to correct wavefront errors and create high contrast images. Imperfect control of the DM limits the achievable contrast and, therefore, the DM control electronics must provide fine surface height resolution and low noise. Here, we study the impact of quantization errors due to the DM electronics on the image contrast using experimental data from the High Contrast Imaging Testbed (HCIT) facility at NASA's Jet Propulsion Laboratory (JPL). We find that the simplest analytical model gives optimistic predictions compared to real cases, with contrast up to 3 times better, which leads to DM surface height resolution requirements that are incorrectly relaxed by 70%. We show that taking into account the DM actuator shape, or influence function, improves the analytical predictions. However, we also find that end-to-end numerical simulations of the wavefront sensing and control process provide the most accurate predictions and recommend such an approach for setting robust requirements on the DM control electronics. From our experimental and numerical results, we conclude that a surface height resolution of approximately 6pm is required for imaging temperate terrestrial exoplanets around Solar-type stars at wavelengths as small as 450nm with coronagraph instruments on future space telescopes. Finally, we list the recognizable characteristics of quantization errors that may help determine if they are a limiting factor.

Fast-modulation imaging with the self-coherent camera

Context. Direct detection of exoplanets requires imaging in a highly dynamic range and exquisite image quality and stability. Wavefront error (atmospheric errors, manufacturing errors on optics, cophasing residuals, temperature variations, etc.) will limit the efficiency of this endeavor by creating various flavors of speckles that evolve with different timescales. Active wavefront-error correction using a deformable mirror requires measuring the wavefront aberrations in the science image with high accuracy and in a shorter time than the duration of the dominant speckle lifetime. Aims. The self-coherent camera (SCC) is a focal plane wavefront sensor exploiting the coherence of light to generate Fizeau fringes in the image plane to spatially encode speckles. The SCC combines a coronagraph and a modified Lyot stop to which a reference channel is added. The conventional SCC is restricted to long-exposure measurements because the light transmitted through the reference channel is limited. The SCC can correct quasi-static aberrations but precludes short-lived atmospheric aberrations from the measurement. Methods. I propose an alternative to the conventional SCC that I call the fast-modulated SCC. It uses a simplified Lyot stop design and an adequate Fourier filtering algorithm. The theory is established and confirmed by means of numerical simulations. Results. The SCC theory dictates that the separation between the classical Lyot stop and the reference channel must be larger than 1.5 times the Lyot stop diameter. The fast-modulated SCC allows for the reference channel to be placed anywhere, in particular in the vicinity of the pupil where the maximum of diffracted light is found. This alternative represents a complete game changer for the sensor: full compatibility with any type of coronagraph, easy installation in existing instruments, and versatility by accessing short- and long-time exposure measurements. Conclusions. While the conventional SCC can almost not be implemented in existing instruments because the optical beam footprint in the instrument must be wide enough to illuminate the reference channel, which is often seen as a significant shortcoming, the fast-modulated SCC does not require any constraint on this. The fast-modulated SCC also relaxes the high sampling requirement to resolve the fringes, which is usually incompatible with the observation of fainter targets because the fringes are larger. The fast-modulated SCC simultaneously counteracts the two original shortcomings of the SCC concept.

Approach for deformable mirror wavefront error correction

Adaptive optics (AO) is receiving wide applications for diffraction-limited imaging in astronomical observations and biomedical research. In an AO system, the deformable mirror (DM) is commanded to correct wavefront errors (WFEs) and is a key component. However, a DM may not be perfect, and it may have strong static WFEs, which may be inherited from the DM manufacturing process or be induced by external factors such as the vibration during the transportation of delivery, which must be corrected before it is integrated into an AO system. To correct this static WFE, we introduce a simple approach. Our approach is based on a two-beam Michelson interferometer configuration, in which a high-quality flat mirror is used as a reference mirror whose surface wavefront can be copied to that of the DM, and thus the DM WFEs can be effectively corrected through an optimization procedure. Our experiments demonstrated that this approach is simple to conduct. Using an iteration optimization approach, the Strehl ratio of the DM can be improved from the initial 0.198 to the 0.997, within 30 min of the optimization run.

First on-sky demonstration of the piezoelectric adaptive secondary mirror.

We propose using a piezoelectric adaptive secondary mirror (PASM) in the medium-sized adaptive telescopes with a 2-4m aperture for structure and control simplification by utilizing the piezoelectric actuators in contrast with the voice-coil adaptive secondary mirror. A closed-loop experimental setup was built for on-sky demonstration of the 73-element PASM developed by our laboratory. In this Letter, the PASM and the closed-loop adaptive optics system are introduced. High-resolution stellar images were obtained by using the PASM to correct high-order wavefront errors in May 2016. To the best of our knowledge, this is the first successful on-sky demonstration of the PASM. The results show that with the PASM as the deformable mirror, the angular resolution of the 1.8m telescope can be effectively improved.

Controlling X-ray deformable mirrors during inspection.

The X-ray deformable mirror (XDM) is becoming widely used in the present synchrotron/free-electron laser facilities because of its flexibility in correcting wavefront errors or modification of the beam size at the sample location. Owing to coupling among the N actuators of an XDM, (N + 1) or (2N + 1) scans are required to learn the response of each actuator one by one. When the mirror has an important number of actuators (N) and the actuator response time including stabilization or the necessary metrology time is long, the learning process can be time consuming. In this work, a fast and accurate method is presented to drive an XDM to a target shape usually with only three or four measurements during inspection. The metrology data are used as feedback to calculate the curvature discrepancy between the current and the target shapes. Three different derivative estimation methods are introduced to calculate the curvature from measured data. The mirror shape is becoming close to the target through iterative compensations. The feasibility of this simple and effective approach is demonstrated by a series of experiments.

Detection and correction of wavefront errors caused by slight reference tilt in two-step phase-shifting digital holography.

A simple and convenient method, without the need for any additional optical devices and measurements, is suggested to improve the quality of the reconstructed object wavefront in two-step phase-shifting digital holography by decreasing the errors caused by reference beam tilt, which often occurs in practice and subsequently introduces phase distortion in the reconstructed wave. The effects of reference beam tilt in two-step generalized interferometry is analyzed theoretically, showing that this tilt incurs no error either on the extracted phase shift or on the retrieved real object wave amplitude on the recording plane, but causes great deformation of the recovered object wavefront. A corresponding error detection and correction approach is proposed, and the formulas to calculate the tilt angle and correct the wavefront are deduced. A series of computer simulations to find and remove the wavefront errors caused by reference beam tilt demonstrate the effectiveness of this method.

Optically addressed deformable mirror for low-light applications

A microelectromechanical deformable mirror device that is optically addressed and designed to actuate at extremely low-light levels for wavefront error correction is fabricated and theoretically described. The device consists of an optically transparent substrate, a photoconductive detector, a thin-film resistor, and insulating posts that support a mirror. The mirror is suspended over the detector by the insulating posts and is deformed when the detector is illuminated through the substrate. The actuation of the device is theoretically modeled as a capacitor in series with a photoconductor under an external dc bias. Under an external 6.3 V dc bias and when back-illuminated with 501 μW∕cm2 light at 539 nm, a total mirror deformation of 474.3 nm was obtained and substantiated by numerical modeling. This represents the highest actuation sensitivity to date that results in mirror deflection values in hundreds of nanometers.

Unimorph deformable mirror for space telescopes: design and manufacturing.

Large space telescopes made of deployable and lightweight structures suffer from aberrations caused by thermal deformations, gravitational release, and alignment errors which occur during the deployment procedure. An active optics system would allow on-site correction of wave-front errors, and ease the requirements on thermal and mechanical stability of the optical train. In the course of a project funded by the European Space Agency we have developed and manufactured a unimorph deformable mirror based on piezoelectric actuation. The mirror is able to work in space environment and is designed to correct for large aberrations of low order with high surface fidelity. This paper discusses design, manufacturing and performance results of the deformable mirror.

Wavefront error correction with adaptive optics in diabetic retinopathy.

To determine the effects of diabetic retinopathy (DR), increased foveal thickness (FT), and adaptive optics (AO) on wavefront aberrations and Shack-Hartmann (SH) image quality. Shack-Hartmann aberrometry and wavefront error correction were performed with a bench-top AO retinal imaging system in 10 healthy control and 19 DR subjects. Spectral domain optical coherence tomography was performed and central FT was measured. Based on the FT data in the control group, subjects in the DR group were categorized into two subgroups: those with normal FT and those with increased FT. Shack-Hartmann image quality was assessed based on spot areas, and high-order (HO) root mean square (RMS) and total RMS were calculated. There was a significant effect of DR on HO and total RMS (p = 0.01), and RMS decreased significantly after AO correction (p < 0.001). Shack-Hartmann spot area was significantly affected by DR (p < 0.001), but it did not change after AO correction (p = 0.6). High-order RMS, total RMS, and SH spot area were higher in DR subjects both before and after AO correction. In DR subgroups, HO and total RMS decreased significantly after AO correction (p < 0.001), whereas the effect of increased FT on HO and total RMS was not significant (p ≥ 0.7). There were no significant effects of increased FT and AO on SH spot area (p = 0.9). Diabetic retinopathy subjects had higher wavefront aberrations and less compact SH spots, likely attributable to pathological changes in the ocular optics. Wavefront aberrations were significantly reduced by AO, although AO performance was suboptimal in DR subjects as compared with control subjects.

Coherent Beam Combination Using a General Model-Based Method

Coherent beam combination techniques can increase the output laser power from a single gain medium. We demonstrate coherent beam combination using the general model-based wavefront error correction method. The experiments for wavefront error correction are performed by using a 7-segment deformable mirror. Both the general model-based method and the stochastic parallel gradient descent algorithm are used to correct the wavefront error generated by a turbulent simulator. The experimental results show that the residual error is obviously reduced in comparison with that by using the SPGD method.

Registration Tolerance of a Custom Correction to Maintain Visual Acuity

To present a predictive model of the registration tolerance for wavefront-guided correction to maintain acuity within fixed limits and demonstrate the potential utility using two typical keratoconic eyes. Change in log visual Strehl was plotted as a function of translation error for a series of rotations of a wavefront-guided correction. Contour lines were added at Δlog visual Strehl levels predicted to induce one- and two-line losses of logMAR visual acuity. The model was validated by regressing measured acuity loss from subjects viewing acuity charts that were degraded by the residual wavefront error resulting from the movement of wavefront-guided correction against the model's predicted acuity. The model's predicted change in acuity can be substituted for measured change in acuity (R² = 0.91) within measurement error (±0.1 logMAR). Translation and/or rotation of a wavefront-guided correction induced asymmetric optical tolerance to movement. Induced errors depended on the wavefront error being corrected, the wavefront-guided correction design, and the amount of registration error. Change in log visual Strehl can be used to determine the registration tolerance necessary to keep the variation in acuity within user-defined limits. This tolerance is unique for each wavefront error and wavefront-guided correction design.

Correction of wave-front retrieval errors caused by the imperfect collimation of reference beam in phase-shifting interferometry

In phase-shifting interferometry (PSI) the standard wave retrieval formulae are usually derived based on the condition of a plane reference beam normal to the recording plane. In practice, however, the reference wave may be a spherical wave of large radius or even have a slight inclination at the same time due to the imperfect collimation and coaxality of the optical system, and this fact will introduce phase distortion for the reconstructed object wave-front. A simple digital processing algorithm without any additional measurements is proposed to determine the unknown parameters of the spherical reference wave and then correct the object wave errors reconstructed with standard wave retrieval formulae. The effectiveness of this method is verified by a series of computer simulations, and its limitation is also discussed.

Receding-horizon adaptive control of aero-optical wavefronts

A new method for adaptive prediction and correction of wavefront errors in adaptive optics (AO) is introduced. The new method is based on receding-horizon control design and an adaptive lattice filter. Experimental results presented illustrate the capability of the new adaptive controller to predict and correct aero-optical wavefronts derived from recent flight-test data. The experimental results compare the performance of the new adaptive controller the performance of a minimum-variance adaptive controller previously used in AO. These results demonstrate the reduced sensitivity of the receding-horizon adaptive controller to high-frequency sensor noise

High-aspect-ratio MEMS deformable mirrors for next-generation telescopes

The next generation of extremely large telescopes (ELTs) that will be built on a scale of 30–50 meters in diameter necessarily require an increased ability to correct wavefront errors. Currently, wavefront correction is achieved through the use of a deformable mirror (DM). The degree and amount of correction depends on amechanical displacement of segments of themirror (stroke), and the number of actuators in the mirror surface (order). An effective ELTwill require a high-stroke (10microns) and high-order (100X100 actuators) mirror, a costly prospect using current technology.1 Lowering the cost while improving the performance of DMs is possible using microelectromechanical systems (MEMS) technology. However, current surface machining processes used to fabricate MEMS deformable mirrors, such as the Sandia ultra-planar multilevel MEMS technology (SUMMiT) and MEMSCAP’s PolyMUMPS process, limit a DM’s stroke due to the use of thin-film sacrificial layers (which are dissolved away after the etching process to free up micromechanical components in the actuators).2, 3 Commercially available surface micromachined MEMS mirrors are limited in stroke to approximately 5.5 microns, about half of the stroke required by ELTs. A high aspect ratio fabrication process capable of depositing thick layers will allow the DM’s to provide both high-stroke and highorder corrections, thus bypassing the need for a complex dual woofer (high stroke, low order)/tweeter (high order, low stroke) DM configuration.4 In our work, we tested different actuator designs with a bonded faceplate constructed using the LIGA (German acronym for lithography, electroplating, and molding) process, enabling multilayer fabrication of MEMS devices.5 Various types of high-stroke gold actuators consisting of folded springs with Figure 1. Diagram showing the final release of the monolithic fabricated structure created using our technique. The gap for the Xbeam electrostatic actuators is 20 microns, enabling a mirror stroke of 10 microns. WMS-15: specific glass-ceramic substrate. Not to scale.

Self-coherent camera as a focal plane wavefront sensor: simulations

Direct detection of exoplanets requires high dynamic range imaging. Coronagraphs could be the solution, but their performance in space is limited by wavefront errors (manufacturing errors on optics, temperature variations, etc.), which create quasi-static stellar speckles in the final image. Several solutions have been suggested for tackling this speckle noise. Differential imaging techniques substract a reference image to the coronagraphic residue in a post-processing imaging. Other techniques attempt to actively correct wavefront errors using a deformable mirror. In that case, wavefront aberrations have to be measured in the science image to extremely high accuracy. We propose the self-coherent camera sequentially used as a focal-plane wavefront sensor for active correction and differential imaging. For both uses, stellar speckles are spatially encoded in the science image so that differential aberrations are strongly minimized. The encoding is based on the principle of light incoherence between the hosting star and its environment. In this paper, we first discuss one intrinsic limitation of deformable mirrors. Then, several parameters of the self-coherent camera are studied in detail. We also propose an easy and robust design to associate the self-coherent camera with a coronagraph that uses a Lyot stop. Finally, we discuss the case of the association with a four-quadrant phase mask and numerically demonstrate that such a device enables the detection of Earth-like planets under realistic conditions. The parametric study of the technique lets us believe it can be implemented quite easily in future instruments dedicated to direct imaging of exoplanets.

Changes of higher‐order aberrations with the use of various mydriatics

Advances in corneal refractive surgery have allowed ophthalmologists to correct ocular higher-order aberrations. To obtain more information on the ocular aberrations generated from the optical axis, mydriasis is required. The aim of this study is to evaluate the changes in higher-order aberrations with the use of various mydriatics. Higher-order aberrations were measured in 21 eyes of 21 subjects (age range 24-37 years; 13 males, 8 females). Repeated measurements were conducted before and after the installation of three different mydriatics: 10% phenylephrine, 1% tropicamide, or 1% cyclopentolate. At a pupil size of 6 mm, the average root mean square value of higher-order aberrations (HO-RMS) was 0.430 mum in undilated eyes, and 0.413, 0.410, and 0.477 mum after installation of phenylephrine, tropicamide, and cyclopentolate, respectively. There were no statistically significant differences in the HO-RMS between the four conditions. There was a significant difference in the spherical aberration between the undilated or phenylephrine-treated eyes, compared to those treated with tropicamide or cyclopentolate. Cycloplegic mydriatics seemed to shift spherical aberration in a positive direction. These results suggest that mydriatics may affect higher-order aberrations, especially spherical aberration, and this should be considered when performing wavefront analysis and when correcting wavefront errors.