Deformable Mirror Research Articles

Automatic Compressive Sensing of Shack–Hartmann Sensors Based on the Vision Transformer

Shack–Hartmann wavefront sensors (SHWFSs) are crucial for detecting distortions in adaptive optics systems, but the accuracy of wavefront reconstruction is often hampered by low guide star brightness or strong atmospheric turbulence. This study introduces a new method of using the Vision Transformer model to process image information from SHWFSs. Compared with previous traditional methods, this model can assign a weight value to each subaperture by considering the position and image information of each subaperture of this sensor, and it can process to obtain wavefront reconstruction results. Comparative evaluations using simulated SHWFS light intensity images and corresponding deformable mirror command vectors demonstrate the robustness and accuracy of the Vision Transformer under various guide star magnitudes and atmospheric conditions, compared to convolutional neural networks (CNNs), represented in this study by Residual Neural Network (ResNet), which are widely used by other scholars. Notably, normalization preprocessing significantly improves the CNN performance (improving Strehl ratio by up to 0.2 under low turbulence) while having a varied impact on the Vision Transformer, improving its performance under a low turbulence intensity and high brightness (Strehl ratio up to 0.8) but deteriorating under a high turbulence intensity and low brightness (Strehl ratio reduced to about 0.05). Overall, the Vision Transformer consistently outperforms CNN models across all tested conditions, enhancing the Strehl ratio by an average of 0.2 more than CNNs.

An optimization method for deformable mirror configuration in multi-conjugate adaptive optics systems

Multi-conjugate adaptive optics (MCAO) is a crucial technology for achieving high-resolution imaging over a wide field of view with modern ground-based optical telescopes. The configuration of deformable mirrors (DMs) is a key component in the analysis and optimization of MCAO performance. Currently, the search for the optimal DM configuration often relies on iterative and time-consuming Monte Carlo simulations. This issue arises from the lack of an appropriate optimization method for DM configurations. The primary objective of this paper is to establish an optimization method for DM configurations in MCAO systems. We established a quantitative criterion for evaluating DM configurations by analyzing their correction capabilities for turbulence aberrations at different altitudes. Then, we optimized the DM configurations based on this criterion. This method provides a new theoretical foundation and practical tool for the design and performance optimization of MCAO systems. Based on the pupil phase structure function, we established a DM configuration evaluation criterion, namely the non-conjugate correction index (NCCI). Using NCCI as the optimal criterion, combined with the particle swarm optimization algorithm, we searched for the optimal solution across different DM configuration spaces. We conducted simulations based on the turbulence profiles of typical telescope sites. We validated our proposed theoretical model against Monte Carlo simulation models and find that the NCCI error ranges from 0.05 to 0.1. For optimizing DM conjugate heights, the results of our optimization algorithm differ by less than 1 km from those obtained via Monte Carlo simulations. Regarding the performance of the DM optimization algorithm, the average convergence accuracy error is less than 0.1 km, and the average convergence speed is approximately ten iterations. Additionally, our optimization method runs in just a few minutes; Monte Carlo simulations, in comparison, require several dozen hours.

Development of piezo-actuated x-ray deformable mirror for vertical focusing of synchrotron radiation at Indus-2

Piezo-actuated x-ray deformable mirrors (PXDMs) can effectively control the surface profile with sub-nanometre accuracy for adaptive focusing and correct the wavefront distortion generated due to imperfections in optical components or other extraneous effects like heat load, minor misalignments of synchrotron radiation beamline. Generating and controlling the desired shape of PXDMs with sub-nanometre accuracy is very challenging due to the presence of a large number of actuators and constraints related to nonlinearity of piezoactuator, boundary conditions, fabrication related limitations and the requirement for ex-situ as well as in-situ characterization of PXDM. To accomplish this, a PXDM of zerodur with multiple electrodes on a piezoactuator has been developed for vertical focusing of synchrotron x-rays for the first time in India. The PXDM has been fabricated and characterized by in-house developed technologies. The iterative piezo response function-based optimization technique is used to optimize the electric fields of individual piezoactuators in order to achieve the desired parabolic shape of the PXDM. The ex-situ characterization showed that the PXDM can achieve the target parabolic profile with 42 nm root-mean-square error. Furthermore, in-situ characterization at a beamline, BL-12, of Indus-2 synchrotron radiation source using PXDM has confirmed the focusing of collimated x-ray beam in the vertical direction from FWHM 235 μm to FWHM 83 μm.

Advanced Phase Diversity Method for telescope static aberration compensation

Accurate calibration is essential for high-performance Adaptive Optics (AO) systems in astronomy. This paper presents a novel methodology for AO systems calibration that preserves the optical path integrity while achieving high-quality results. By eliminating the need for optical modifications, this approach simplifies system complexity and accounts for all static aberrations. The main novelty of this proposal is an advanced Phase Diversity (PD) method for estimating static optical aberrations. Unlike conventional PD techniques, this approach uses the AO system’s deformable mirror to introduce different diversities, eliminating the need for additional calibration hardware. Furthermore, the optimizer Adam is introduced for the first time in this field to estimate the optical aberrations. To evaluate the performance of this new methodology, a set of experiments under varying operating conditions and optimization parameters has been conducted. Results demonstrated that the presented methodology is capable of providing diffraction-limited corrected images with a Strehl Ratio (SR) exceeding 0.80 within 2 min. Furthermore, employing a Manhattan distance-based error function effectively balanced estimation speed and accuracy. The method demonstrated effectiveness across a wide range of aberration magnitudes, achieving an error of 3 nm in the best scenarios. This proposal represents an advancement in the identification and correction of static aberrations in telescope optical systems, directly improving the acquisition of high-quality references for AO sensing.

Optical design of a 5× zoom afocal telescope with deformable mirrors

All-reflective zoom afocal telescopes can be integrated with existing imaging systems as foreoptics, enabling flexible imaging with adjustable resolution. This paper proposes an approach to designing a 5× zoom afocal telescope using deformable mirrors. Based on matrix optics, the first-order parameters for a coaxial reflective 5× zoom afocal telescope with a fixed primary mirror and three deformable mirrors are determined. To prevent obscuration, the mirrors are tilted at their vertices, which introduces asymmetric aberrations. To correct these aberrations, XY polynomial surfaces are employed on the primary mirror and an additional flat fold mirror. The final design and image simulations indicate that the system achieves good image quality across all zoom positions, enabling 5× zoom imaging with a maximum root mean square wavefront error of less than 0.125λ (λ = 632.8 nm), thereby validating the efficacy of the proposed design methodology.

High fidelity adaptive mirror simulations with reduced order models

In the design process of large adaptive mirrors numerical simulations represent the first step to evaluate the system design compliance in terms of performance, stability and robustness. For the next generation of Extremely Large Telescopes increased system dimensions and bandwidths lead to the need of modeling not only the deformable mirror alone, but also all the system supporting structure or even the full telescope. The capability to perform the simulations with an acceptable amount of time and computational resources is highly dependent on finding appropriate methods to reduce the size of the resulting dynamic models. In this paper we present a framework developed together with the company Microgate to create a reduced order structural model of a large adaptive mirror as a preprocessing step to the control system simulations. The reduced dynamic model is then combined with the remaining system components allowing to simulate the full adaptive mirror in a computationally efficient way. We analyze the feasibility of our reduced models for Microgate’s prototype of the adaptive mirror of the Giant Magellan Telescope.

Hybrid approach for deformable mirror online system identification using RLS algorithm and adaptive forgetting factor optimization

Hybrid approach for deformable mirror online system identification using RLS algorithm and adaptive forgetting factor optimization

Light control and optical path design method for stabilized zoom systems based on deformable mirrors

We extend the design methodology for stabilized zoom systems by analyzing the stable convergence of singular points in the solution region for image plane shift compensation and continuous zooming. Using lens group magnification as key parameters, we analyze the stability of singular points related to the descending gradient of the zoom equation and the positions of extremum points within the solution region. These singular points and their solution regions are identified and correspond to solutions of specific optical path structures. With the acquired solution region clusters, we can ensure the performance of stabilized zoom systems and prevent optical performance degradation, especially when a specific zoom ratio is required.

Design and qualification of an aluminum deformable mirror for spaceborne electro-optical payloads

Design and qualification of an aluminum deformable mirror for spaceborne electro-optical payloads

End-to-end simulations of photonic phase correctors for adaptive optics systems

Optical beams and starlight distorted by atmospheric turbulence can be corrected with adaptive optics systems to enable efficient coupling into single-mode fibers. Deformable mirrors, used to flatten the wavefront in astronomical telescopes, are costly, sensitive, and complex mechanical components that require careful calibration to enable high-quality imaging in astronomy, microscopy, and vision science. They are also impractical to deploy in large numbers for non-imaging applications like free-space optical communication. Here, we propose a photonic integrated circuit capable of spatially sampling the wavefront collected by the telescope and co-phasing the subapertures to maximize the flux delivered to an output single-mode fiber as the integrated photonic implementation of a deformable mirror. We present the results of end-to-end simulations to quantify the performance of the proposed photonic solution under varying atmospheric conditions toward realizing an adaptive optics system without a deformable mirror for free-space optical receivers.

A piston and tilt wavefront sensor dedicated to the cophasing of segmented optics in low light level conditions

We present a new interferometer to measure piston, tip and tilt of segmented mirrors, using the combination of an optical grating and a microlens array. Since this interferometer is able to collect all the incident light and to operate with a large spectra bandwidth, it is particularly suitable to operate in low light level conditions, for example for the co-phasing of segmented primary mirrors like James Webb Space Telescope. We tested our new device on a 37-segment deformable mirror and obtained an accuracy better than λ/100. The measurement is self-referenced and errors can be estimated on the measurement itself thanks to closure relationships.

Adaptive optics in an oblique plane microscope.

Adaptive optics (AO) can restore diffraction-limited performance when imaging beyond superficial cell layers in vivo and in vitro, and as such, is of interest for advanced 3D microscopy methods such as light-sheet fluorescence microscopy (LSFM). In a typical LSFM system, the illumination and detection paths are separate and subject to different optical aberrations. To achieve optimal microscope performance, it is necessary to sense and correct these aberrations in both light paths, resulting in a complex microscope system. Here, we show that in an oblique plane microscope (OPM), a type of LSFM with a single primary objective lens, the same deformable mirror can correct both illumination and fluorescence detection. Besides reducing the complexity, we show that AO in OPM also restores the relative alignment of the light-sheet and focal plane, and that a projection imaging mode can stabilize and improve the wavefront correction in a sensorless AO format. We demonstrate OPM with AO on fluorescent nanospheres and by imaging the vasculature and cancer cells in zebrafish embryos embedded in a glass capillary, restoring diffraction limited resolution and improving the signal strength twofold.

High contrast at small separation – III. Impact on the dark hole of MEMS deformable mirror control electronics

ABSTRACT The creation of a dark hole (DH) region in the science image for exoplanet direct detection depends on deformable mirrors (DMs), where the imperfect control of DM limits the achievable contrast. The mirror surface height resolution is set by the DM drive electronics, and the quantization errors in DM impact the contrast in the DH. Consequently, determining the optimal voltage value for the flattening map of DM is essential, as it involves balancing dynamic and accuracy considerations. We conduct a numerical study to examine the impact of these parameters on microelectromechanical DM within the high-contrast field of view of several DHs with various characteristics and optical configurations. Our analysis includes an exploration of their influence on both small and moderate angular separations. We compare our numerical results with a formula available in the literature that aims to capture the dependence of contrast on DM quantization errors. We show that the formula accuracy to predict the contrast limit when the DM deflection curves follow the as-manufactured quadratic power law is dependent on the DM flattening map voltage domain, regardless of DH size and angular separations. Further these results appear to be insensitive to factors such as actuator number, coronagraph type, set-up architecture, and science objective (small or moderate angular separations). We provide guidelines for determining the optimal voltage for the DM flattening map, discuss the domain validity of the formula used to predict DM quantization errors on the contrast, and provide insights into balancing DM actuator density and mirror surface height resolution.

Single-frame fringe pattern analysis with synchronous phase-shifting based on polarization interferometry phase measuring deflectometry (PIPMD)

In the domain of phase measuring deflectometry (or fringe projection profilometry), utilizing only a single-frame fringe pattern to achieve high-precision three-dimensional reconstruction has emerged as a focal point of ongoing research. To achieve four-step phase-shifting demodulation from a single-frame fringe pattern, this paper proposes a Polarization Interferometry Phase Measuring Deflectometry (PIPMD). This method primarily relies on a Michelson polarization interferometry structure to produce projected polarization interference fringes, which are then captured by a polarization camera as modulated single-frame deformed fringe patterns. These single-frame fringe patterns enable pixelated four-step phase shifting with adjacent 2 × 2 pixel units. To validate the proposed method, a series of experiments has been conducted, including surface shape detection of a concave spherical mirror and an off-axis parabolic mirror, as well as dynamic deformation measurements of a deformable mirror. All experimental results consistently indicate that the polarization interference-based fringe projection technique can achieve synchronized phase-shifting demodulation of single-frame fringe patterns, thereby facilitating high-precision reconstruction of the fringe patterns captured in a single frame. This synchronous phase-shifting technique can overcome the influence of air disturbances in traditional four-step phase-shifting methods, thereby enhancing the accuracy of phase demodulation. Additionally, this polarization interference-based Phase Measuring Deflectometry exhibits promising application prospects in dynamic measurements.

Estimation of the lateral mis-registrations of the GRAVITY+ adaptive optics system

Context. The GRAVITY+ upgrade implies a complete renewal of its adaptive optics (AO) systems. Its complex design, featuring moving components between the deformable mirrors and the wavefront sensors, requires the monitoring and auto-calibrating of the lateral mis-registrations of the system while in operation. Aims. For preset and target acquisition, large lateral registration errors must be assessed in open loop to bring the system to a state where the AO loop closes. In closed loop, these errors must be monitored and corrected, without impacting the science. Methods. With respect to the first requirement, our method is perturbative, with two-dimensional modes intentionally applied to the system and correlated to a reference interaction matrix. For the second requirement, we applied a non-perturbative approach that searches for specific patterns in temporal correlations in the closed loop telemetry. This signal is produced by the noise propagation through the AO loop. Results. Our methods were validated through simulations and on the GRAVITY+ development bench. The first method robustly estimates the lateral mis-registrations, in a single fit and with a sub-subaperture resolution while in an open loop. The second method is not absolute, but it does successfully bring the system towards a negligible mis-registration error, with a limited turbulence bias. Both methods proved to robustly work on a system still under development and not fully characterised. Conclusions. Tested with Shack-Hartmann wavefront sensors, the proposed methods are versatile and easily adaptable to other AO instruments, such as the pyramid, which stands as a baseline for all future AO systems. The non-perturbative method, not relying on an interaction matrix model and being sparse in the Fourier domain, is particularly suitable to the next generation of AO systems for extremely large telescopes that will present an unprecedented level of complexity and numbers of actuators.

Direct observation of atmospheric turbulence with a video-rate wide-field wavefront sensor

Turbulence is a complex and chaotic state of fluid motion. Atmospheric turbulence within the Earth’s atmosphere poses fundamental challenges for applications such as remote sensing, free-space optical communications and astronomical observation due to its rapid evolution across temporal and spatial scales. Conventional methods for studying atmospheric turbulence face hurdles in capturing the wide-field distribution of turbulence due to its transparency and anisoplanatism. Here we develop a light-field-based plug-and-play wide-field wavefront sensor (WWS), facilitating the direct observation of atmospheric turbulence over 1,100 arcsec at 30 Hz. The experimental measurements agreed with the von Kármán turbulence model, further verified using a differential image motion monitor. Attached to an 80 cm telescope, our WWS enables clear turbulence profiling of three layers below an altitude of 750 m and high-resolution aberration-corrected imaging without additional deformable mirrors. The WWS also enables prediction of the evolution of turbulence dynamics within 33 ms using a convolutional recurrent neural network with wide-field measurements, leading to more accurate pre-compensation of turbulence-induced errors during free-space optical communication. Wide-field sensing of dynamic turbulence wavefronts provides new opportunities for studying the evolution of turbulence in the broad field of atmospheric optics.

Active-compensation of systematic error for the 1000 mm aperture flat interferometer

Large-aperture elements would induce unnegligible systematic errors due to material inhomogeneity, manufacturing or gravity, that are difficult to correct in an extreme large aperture flat interferometer and result in reference wavefront distortion. We propose an active-compensation method for systematic errors by employing a deformable mirror into the interferometer to modulate reference wavefront. A mapping relationship between sag of the deformable mirror and reference wavefront error is derived by theory of matrix optics, and two interferometer optical paths are designed for whether the deformable mirror is located at the pupil or not. The algorithm for calculating and controlling the sag of a deformable mirror can eliminate the need for the deformable mirror to be positioned at the pupil in order to achieve controllable modulation of the wavefront. This algorithm has been validated through the intentional introduction of systematic errors into the 1000 mm aperture flat interferometer for effective compensation. Moreover, the optimization algorithm in Ansys Zemax is utilized to calculate the optimal solution for surface shape of the deformable mirror, treating it as a nominal value. The algorithm error is on the order of 10−6 mm, falling within the acceptable tolerance range for the deformable mirror's surface shape.

Phase-diversity-based wavefront sensing for fluorescence microscopy

Fluorescence microscopy is an invaluable tool in biology, yet its performance is compromised when the wavefront of light is distorted due to optical imperfections or the refractile nature of the sample. Such optical aberrations can dramatically lower the information content of images by degrading the image contrast, resolution, and signal. Adaptive optics (AO) methods can sense and subsequently cancel the aberrated wavefront, but they are too complex, inefficient, slow, or expensive for routine adoption by most labs. Here, we introduce a rapid, sensitive, and robust wavefront sensing scheme based on phase diversity, a method successfully deployed in astronomy but underused in microscopy. Our method enables accurate wavefront sensing to less than λ/35 root mean square (RMS) error with few measurements, and AO with no additional hardware besides a corrective element. After validating the method with simulations, we demonstrate the calibration of a deformable mirror >hundredfold faster than comparable methods (corresponding to wavefront sensing on the ∼100ms scale), and sensing and subsequent correction of severe aberrations (RMS wavefront distortion exceeding λ/2), restoring diffraction-limited imaging on extended biological samples.

Accurate optical dispersion identification for linear deformable mirror with spatial-spectral interferometry

In ultrashort laser pulse systems, optical dispersion can cause severe distortion of the spectral phase and thus significantly affect the pulse shape. To address this problem, this study places a linear deformable mirror (LDM) at the Fourier plane of a blazed grating for dispersion control, and reconstructs the spectral phase modulated by the LDM using single-shot spatial-spectral interferometry. An iterative algorithm and closed-loop optimization process are used to drive the LDM to generate orthogonal modes of Legendre polynomials with a signal-to-background ratio (SBR) of more than 10 dB. The identified LDM modes are then used as the basis for spectral phase modulation. It is shown that the group delay dispersion (GDD), third order dispersion (TOD), fourth order dispersion (FOD), and fifth order dispersion (5OD) can be accurately obtained by the linear combination of identified Legendre modes. In addition, the maximum phase error between the generated and target dispersions is less than 0.15 rad, while the error between the pulse widths produced by the generated dispersion and the target dispersion, respectively, is less than 3.5 %. Overall, the results confirm that the linear superposition of the generated Legendre modes enables the accurate dispersion modulation of ultrashort laser pulses.

Topography reconstruction of high aspect ratio silicon trench array via near-infrared coherence scanning interferometry

Topography measurement of high aspect ratio trench array using coherence scanning interferometry presents significant challenges because the numerical aperture of detection light is constrained by the trenches. Altering the detection light to penetrate the sample like near-infrared light for silicon could overcome this obstacle, but the trench array spreads the detection light. This study introduces a coherence scanning interferometry model based on three-dimensional point spread function and assuming sample is transparent to detection light, which is realized by integrating rigorous numerical electromagnetic field solution to quantify the modulation aberrations of detection light by transparent trench arrays, and theoretical angular spectrum diffraction utilized for far-field interference imaging. This model facilitates a thorough analysis of the aberrations introduced by trench arrays, encompassing comparisons between trench arrays and a single trench, as well as between the symmetric region of the array and the asymmetric region at the edge. Additionally, an investigation into the impact of unified compensation for low-order aberrations on the topography reconstruction is presented, and we find the sample-induced aberration compensation method utilizing a deformable mirror that we previously proposed for a single trench is still effective confronting trench array. Experimental measurements are performed on silicon trench arrays with the aspect ratio of up to 20:1 and the period of approximately 10 µm to validate the effectiveness of our model and measurement methods, thus providing valuable insights for enhancing high aspect ratio manufacturing.