Optimal dark hole generation via two deformable mirrors with stroke minimization

Future space-based observatories such as WFIRST will be equipped with high contrast imaging instruments designed to study extrasolar planets and disks in the absence of atmospheric perturbations. One of the most efficient techniques to achieve this goal is the combination of wavefront control and broadband coronagraphy. Being able to achieve a high contrast over a wide spectral bandwidth allows us to characterize the chemical composition of exoplanet atmospheres using an integral field spectrograph (IFS). In this paper, we report on the development of such an IFS for the High Contrast Imaging Lab (HCIL) at Princeton University, downstream of a Shaped Pupil coronagraph. Our final lensletbased design calls for the light in an 18% band around 660 nm to be dispersed with a spectral resolution of 50. We also present our new laboratory control software written in Python, allowing the import of open-source packages such as CRISPY to ultimately reconstruct 3D datacubes from IFS spatio-spectral science images. Finally, we show and discuss our preliminary first light results, reaching a contrast of ~10-5 using in-house focal-plane wavefront control and estimation algorithms with two deformable mirrors.

For direct imaging of faint exoplanets, coronagraphs are widely used to suppress light and achieve a high contrast. Wavefront correction algorithms based on adaptive optics are introduced simultaneously to mitigate aberrations in the optical system. Stroke minimization is one of the primary control algorithms used for high-contrast wavefront control. This technique calculates the minimum deformation across the deformable mirrors' surface under the constraint that a targeted average contrast level in the search areas, namely the dark holes, is achieved. In this paper we present a modified linear constraint stroke minimization algorithm. Instead of using a single constraint on intensity averaged over all pixels, we constrain the electric field's real and imaginary part of each pixel in the dark holes. The new control algorithm can be written into a linear programming problem. Model reduction methods, including pixel binning and singular value decomposition (SVD), are further employed to avoid over-constraining the problem and to speed up computation. In numerical simulation, we find that the revised algorithm leads to more uniform dark holes and faster convergence.

The high‐contrast imaging group at Princeton University has been at the forefront of the adaptive optics community. In this paper, we present advances made in both the correction and estimation of aberrated wavefronts. We show experimental results in the use of two sequential deformable mirrors (DMs) for the creation of a symmetric dark hole in the image plane. In addition, we present results of the two‐camera wavefront estimation scheme that is less dependent on knowledge of the DM surface than traditional estimation by diversity on the DM.

The goal of directly imaging Earth-like planets in the habitable zone of other stars has motivated the design of coronagraphs for use with large segmented aperture space telescopes. In order to achieve an optimal trade-off between planet light throughput and diffracted starlight suppression, we consider coronagraphs comprised of a stage of phase control implemented with deformable mirrors (or other optical elements), pupil plane apodization masks (gray scale or complex valued), and focal plane masks (either amplitude only or complex-valued, including phase only such as the vector vortex coronagraph). The optimization of these optical elements, with the goal of achieving 10 or more orders of magnitude in the suppression of on-axis (starlight) diffracted light, represents a challenging non-convex optimization problem with a nonlinear dependence on control degrees of freedom. We develop a new algorithmic approach to the design optimization problem, which we call the ”Auxiliary Field Optimization” (AFO) algorithm. The central idea of the algorithm is to embed the original optimization problem, for either phase or amplitude (apodization) in various planes of the coronagraph, into a problem containing additional degrees of freedom, specifically fictitious ”auxiliary” electric fields which serve as targets to inform the variation of our phase or amplitude parameters leading to good feasible designs. We present the algorithm, discuss details of its numerical implementation, and prove convergence to local minima of the objective function (here taken to be the intensity of the on-axis source in a ”dark hole” region in the science focal plane). Finally, we present results showing application of the algorithm to both unobscured off-axis and obscured on-axis segmented telescope aperture designs. The application of the AFO algorithm to the coronagraph design problem has produced solutions which are capable of directly imaging planets in the habitable zone, provided end-to-end telescope system stability requirements can be met. Ongoing work includes advances of the AFO algorithm reported here to design in additional robustness to a resolved star, and other phase or amplitude aberrations to be encountered in a real segmented aperture space telescope.

Hardware-in-the-loop testing of formation flying control and sensing algorithms for starshade missions

In this paper, we propose an active vision system which has variable PSF. The system consists of a deformable mirror, an aperture stop and four lenses. The deformable mirror is placed at the pupil plane and its effective size is determined by the aperture stop at the conjugate position of the mirror. We try to enhance the image resolution using this system. We make four different mirror surface shapes to take four regularly shifted images and use super-resolution algorithm to synthesize higher resolution image from the low resolution observations. It is demonstrated that our method can be used to enhance image resolution which is limited by CCD cell size. We compare the result with the real image and some discussion about algorithmic parameters follows.

In astronomy and microscopy, distortions in the wavefront affect the dynamic range of a high-contrast imaging system. These aberrations are either imposed by a turbulent medium such as the atmosphere, by static or thermal aberrations in the optical path, or by imperfectly phased subapertures in a segmented mirror. Active and adaptive optics (AO), consisting of a wavefront sensor and a deformable mirror, are employed to address this problem. Nevertheless, the non-common-path between the wavefront sensor and the science camera leads to persistent quasi-static speckles that are difficult to calibrate and which impose a floor on the image contrast. In this paper, we present the first experimental demonstration of a novel wavefront sensor requiring only a minor asymmetric obscuration of the pupil, using the science camera itself to detect high-order wavefront errors from the speckle pattern produced. We apply this to correct errors imposed on a deformable microelectromechanical segmented mirror in a closed loop, restoring a high-quality point spread function and residual wavefront errors of the order of ∼10 nm using 1600 nm light, from a starting point of ∼300 nm in piston and ∼0.3 mrad in tip–tilt. We recommend this as a method for measuring the non-common-path error in AO-equipped ground based telescopes, as well as an approach to phasing difficult segmented mirrors such as on the James Webb Space Telescope primary and as a future direction for extreme AO.

Supercontinuum laser, as a new type of laser source, compared with monochromatic or quasi-monochromatic light, has incandescent wide spectra and the brightness of the laser. However,the beam quality in high power is usually bad and greatly affected by atmospheric turbulence in the transmission process. Therefore, how to improve the beam quality to ensure the energy transmission and image quality has become a popular topic. According to the measurement results of the near field wavefront characteristics of the supercontinuum laser in different wavelength, we know that the wavefront phase of the light source is relatively stable and change slowly over time. The types of wavefront distortion at each wavelength are basically the same, mainly made up of defocus and astigmatism. In order to conform to the wavefront characteristics of supercontinuum laser, the input of simulation is low-order static distortion wavefront generated by using Zernike polynomia with defocus and astigmatism. Stochastic Parallel Gradient Descent (SPGD) algorithm with the thorlabs DMP40 deformable mirror and CCD camera as the imaging sensor, is used to construct a simulation model for wavefront correction of low-order static distortion aberrations. Since B-SPGD algorithm is superior to U-SPGD in terms of convergence speed and correction effect, as well as adaptability to the near field wavefront distortion [1], we use B-SPGD algorithm to construct the simulation program for wavefront correction simulation research. The ability and convergence of SPGD algorithm to correct wavefront distortion are studied, mainly about the random disturbance amplitude and influence coefficient of the core parameters. In order to get close to the evaluation standard of laser in practical application, Strehl Ratio(SR) is selected as the performance evaluation function. According to the effective diameter of deformable mirror and the distance between electrodes, the influence function of deformable mirror is normalized to the unit circle to meet the requirements of simulation calculation. In order to improve the stability of SPGD algorithm and reduce the possibility of SPGD algorithm falling into local extreme values, we use Hessian matrix to optimize SPGD algorithm. After simulation and analysis of distortion correction of Supercontinuum laser wavefront, deformable mirror controlled by SPGD algorithm has good correction capability for low-order static aberration.

A major component of the estimation and correction of starlight at very high contrasts is the creation of a dark hole: a region in the vicinity of the core of the stellar point spread function (PSF) where speckles in the PSF wings have been greatly attenuated, up to a factor of 10¹⁰ for the imaging of terrestrial exoplanets. At these very high contrasts, removing these speckles requires distinguishing between light from the stellar PSF scattered by instrument imperfections, which may be partially corrected across a broad band using deformable mirrors in the system, from light from other sources which generally may not. These other sources may be external or internal to the instrument (e.g. planets, exozodiacal light), but in either case, their distinguishing characteristic is their inability to interfere coherently with the PSF. In the following we discuss the estimation, structure, and expected origin of this incoherent" signal, primarily in the context of a series of experiments made with a linear band-limited mask in Jan-Mar 2013. We find that the incoherent" signal at moderate contrasts is largely estimation error of the coherent signal, while at very high contrasts it represents a true floor which is stable over week-timescales.

We demonstrate increases in contrast sensitivity and letter acuity in white light and in monochromatic light when adaptive optics corrects the eye’s higher order monochromatic aberrations. The contrast sensitivity and visual acuity when correcting most monochromatic aberrations with a deformable mirror are higher than when defocus and astigmatism alone are corrected. Moreover, correcting both monochromatic and chromatic aberrations provides an even larger increase in contrast sensitivity and visual acuity. These results are in good agreement with the theoretical visual benefit from the optical modulation transfer function based on the measured eye’s aberration with a Hartmann-Shack wavefront sensor.

The development of technology to measure and correct the eye's higher-order aberrations, i.e., those beyond defocus and astigmatism, raises the issue of how much visual benefit can be obtained by providing such correction. We demonstrate improvements in contrast sensitivity and visual acuity in white light and in monochromatic light when adaptive optics corrects the eye's higher-order monochromatic aberrations. In white light, the contrast sensitivity and visual acuity when most monochromatic aberrations are corrected with a deformable mirror are somewhat higher than when defocus and astigmatism alone are corrected. Moreover, viewing conditions in which monochromatic aberrations are corrected and chromatic aberrations are avoided provides an even larger improvement in contrast sensitivity and visual acuity. These results are in reasonable agreement with the theoretical improvement calculated from the eye's optical modulation transfer function.

As an active device, deformable mirror has been successfully used in adaptive optical systems to compensate phase aberrations and improve beam quality. However, it is often limited to correcting the phase aberrations for a flat reference wavefront. In this paper we present a new adaptive beam intensity profiles control technique based on the combination of a 19-element deformable mirror and a global genetic algorithm. This algorithm can adaptively adjust the voltages of the 19 actuators on the deformable mirror to reduce the difference between the target beam shape and the actual beam shape. The numerical simulations results show that within the mechanical constraints of the deformable mirror, this technique can create the given beam intensity profiles in a focal plane.

We present a direct slope-based correction algorithm to simultaneously control two deformable mirrors (DMs) in a woofer-tweeter adaptive optics system. A global response matrix was derived from the response matrices of each deformable mirror and the voltages for both deformable mirrors were calculated simultaneously. This control algorithm was tested and compared with a 2-step sequential control method in five normal human eyes using an adaptive optics scanning laser ophthalmoscope. The mean residual total root-mean-square (RMS) wavefront errors across subjects after adaptive optics (AO) correction were 0.128 ± 0.025 μm and 0.107 ± 0.033 μm for simultaneous and 2-step control, respectively (7.75-mm pupil). The mean intensity of reflectance images acquired after AO convergence was slightly higher for 2-step control. Radially-averaged power spectra calculated from registered reflectance images were nearly identical for all subjects using simultaneous or 2-step control. The correction performance of our new simultaneous dual DM control algorithm is comparable to 2-step control, but is more efficient. This method can be applied to any woofer-tweeter AO system.

(abridged) Extreme adaptive optics (XAO) encounters severe difficulties to cope with the high speed (>1kHz), high accuracy and high order requirements for future extremely large telescopes. An innovative high order adaptive optics system using a self-referenced Mach-Zehnder wavefront sensor (MZWFS) allows counteracting these limitations. This sensor estimates very accurately the wavefront phase at small spatial scale by measuring intensity differences between two outputs, with a $\lambda /4$ path length difference between its two legs, but is limited in dynamic range due to phase ambiguity. During the past few years, such an XAO system has been studied by our team in the framework of 8-meter class telescopes. In this work, we report on our latest results with the XAO testbed recently installed in our lab, and dedicated to high contrast imaging with 30m-class telescopes (such as the E-ELT or the TMT). After reminding the principle of a MZWFS and describing the optical layout of our experiment, we will show the results of the assessment of the woofer-tweeter phase correctors, i.e., a Boston Micromachine continuous membrane deformable mirror (DM) and a Boulder Nonlinear Systems liquid crystal spatial light modulator (SLM). In particular, we will detail the calibration of the DM using Zygo interferometer metrology. Our method consists in the precise measurement of the membrane deformation while applying a constant deformation to 9 out of 140 actuators at the same time. By varying the poke voltage across the DM operating range, we propose a simple but efficient way of modeling the DM influence function using a Gaussian model. Finally, we show the DM flattening on the MZWFS allowing to compensate for low order aberrations.

We compare the broadband contrast performances of several Phase Induced Amplitude Apodization (PIAA) coronagraph configurations through modeling and simulations. The basic optical design of the PIAA coronagraph is the same as NASA's High Contrast Imaging Testbed (HCIT) setup at the Jet Propulsion Laboratory (JPL). Using a deformable mirror and a broadband wavefront sensing and control algorithm, we create a dark hole in the broadband point-spread function (PSF) with an inner working angle (IWA) of 2(f lambda/D)(sub sky). We evaluate two systems in parallel. One is a perfect system having a design PIAA output amplitude and not having any wavefront error at its exit-pupil. The other is a realistic system having a design PIAA output amplitude and the measured residual wavefront error. We also investigate the effect of Lyot stops of various sizes when a postapodizer is and is not present. Our simulations show that the best 7.5%-broadband contrast value achievable with the current PIAA coronagraph is approximately 1.5x10(exp -8).