A high-contrast coronagraph for direct imaging of Earth-like exoplanets: design and test

A high-contrast coronagraph for direct imaging of an Earth-like exoplanet at the visible band needs a contrast of 10^-10 at a small angular separation of 4λ/D or less. Here we report our recent laboratory experiment that approaches these lim- its. Our test of a high-contrast imaging coronagraph is based on our step-transmission apodized filter. To achieve this goal, we use a liquid crystal array as a phase correc- tor to create a dark hole based on our dedicated algorithm. We have suppressed the diffraction and speckle noise near the point image of a star to a level of 1.68 × 10^-9 at 4λ/D, which can be used for direct imaging of Jupiter-like exoplanets. This demon- strates that a telescope incorporating a high-contrast coronagraph in space has the potential to detect and characterize Earth-like planets.

Stochastic parallel gradient descent based adaptive optics used for a high contrast imaging coronagraph

An adaptive optics （AO） system based on a stochastic parallel gradient descent （SPGD） algorithm is proposed to reduce the speckle noises in the optical system of a stellar coronagraph in order to further improve the contrast. The principle of the SPGD algorithm is described briefly and a metric suitable for point source imaging optimization is given. The feasibility and good performance of the SPGD algorithm is demonstrated by an experimental system featured with a 140-actuator deformable mirror and a Hartrnann-Shark wavefront sensor. Then the SPGD based AO is applied to a liquid crystal array （LCA） based coronagraph to improve the contrast. The LCA can modulate the incoming light to generate a pupil apodization mask of any pattern. A circular stepped pattern is used in our preliminary experiment and the image contrast shows improvement from 10^-3 to 10^-4.5 at an angular distance of 2A/D after being corrected by SPGD based AO.

Design and calibration of a high-sensitivity and high-accuracy polarimeter based on liquid crystal variable retarders

Polarimetry plays an important role in the measurement of solar magnetic fields. We devel- oped a high-sensitivity and high-accuracy polarimeter （HHP） based on nematic liquid crystal variable retarders （LCVRs）, which has a compact setup and no mechanical moving parts. The system design and calibration methods are discussed in detail. The azimuth error of the transmission axis of the polarizer as well as the fast axes of the two LCVRs and the quarter-wave plate were determined using dedicated procedures. Linearly and circularly polarized light were employed to evaluate the performance of the HHP. The experimental results indicate that a polarimetric sensitivity of better than 5.7 × 10-3 can be achieved by using a single short-exposure image, while an accuracy on the order of 10-5 can be reached by using a large number of short-exposure images. This makes the HHP a high-performance system that can be used with a ground-based solar telescope for high-precision solar magnetic field investigations.

High-contrast coronagraph for ground-based imaging of Jupiter-like planets

We propose a high-contrast coronagraph for direct imaging of young Jupiter-like planets orbiting nearby bright stars. The coronagraph employs a step- transmission filter in which the intensity is apodized with a finite number of steps with identical transmission in each step. It should be installed on a large ground-based telescope equipped with a state-of-the-art adaptive optics system. In this case, contrast ratios around 10-6 should be accessible within 0.1 arcsec of the central star. In recent progress, a coronagraph with a circular apodizing filter has been developed, which can be used for a ground-based telescope with a central obstruction and spider structure. It is shown that ground-based direct imaging of Jupiter-like planets is promising with current technology.

A low-cost and high-performance technique for adaptive optics static wavefront correction

Non-Common Path Error(NCPE) is one of the factors that limit an Adaptive Optics(AO)system from delivering ultra-high performance. To correct the NCPE associated static aberration, we propose a simple but robust and high-performance pupil-plane based wavefront measurement and correction technique, which can copy a single-mode fiber generated perfect wavefront to the AO system via an iteration optimization process, and the NCPE can be effectively corrected by directly commanding the Deformable Mirror(DM) of the AO system. Compared with the previous focal-plane based approach that uses focal plane based Point Spread Function(PSF) for correction evaluation, the pupil-plane based approach can be reliably and rapidly converged to a global optimization result and provides better performance, in particular for an AO system with a large initial static wavefront error. This technique we proposed can be implemented in astronomical AO systems where extremely high performance is required.

Numerical analysis of modal tomography for solar multi-conjugate adaptive optics

Multi-conjugate adaptive optics （MCAO） can considerably extend the cor- rected field of view with respect to classical adaptive optics, which will benefit solar observation in many aspects. In solar MCAO, the Sun structure is utilized to provide multiple guide stars and a modal tomography approach is adopted to implement three- dimensional wavefront restorations. The principle of modal tomography is briefly re- viewed and a numerical simulation model is built with three equivalent turbulent lay- ers and a different number of guide stars. Our simulation results show that at least six guide stars are required for an accurate wavefront reconstruction in the case of three layers, and only three guide stars are needed in the two layer case. Finally, eigen- mode analysis results are given to reveal the singular modes that cannot be precisely retrieved in the tomography process.

Multi-aperture seeing profiler with multiple guide stars

The daytime atmospheric turbulence profile is crucial for the design of both optical systems and the control algorithm of a solar Multi-Conjugate Adaptive Optics(MCAO) system. The Multi-Aperture Seeing Profiler(MASP) is a portable instrument which can measure the daytime turbulence profile up to^30 km. It consists of two portable small telescopes that can deliver performance similar to a SolarDifferential Image Motion Monitor +(S-DIMM+) on a 1.0 m solar telescope. In the original design of MASP, only two guide stars are used to retrieve the turbulence profile. In this paper, we studied the usage of multiple guide stars in MASP using numerical simulation, and found that there are three main advantages.Firstly, the precision of the turbulence profile can be increased, especially at a height of about 15 km, which is important for characterizing turbulence at the tropopause. Secondly, the equivalent diameter of MASP can be increased up to 30%, which will reduce the cost and weight of the instruments. Thirdly, the vertical resolution of the turbulence profile near the ground increases with the help of multiple guide stars.

Design and experimental test of an optical vortex coronagraph

Using an optical vortex coronagraph （OVC） is one of the most promising techniques for di- rectly imaging exoplanets because of its small inner working angle and high throughput. This paper presents the design and laboratory demonstration performance of an OVC based on liquid crystal polymers （LCPs） at 633 nm and 1520 nm. The OVC can deliver good performance in laboratory tests and achieve a contrast of 10-6 at an angular distance of 3A/D, which can be implemented for imaging young giant exoplanets in combination with extreme adaptive optics.

Solar GLAO and TAO:performance comparisons

Multi-conjugate adaptive optics （MCAO）, consisting of several deformable mirrors （DMs）, can significantly increase the adaptive optics （AO） correction field of view. Current MCAO can be realized by either star-oriented or layer-oriented approaches. For solar AO, ground-layer adaptive optics （GLAO） can be viewed as an extreme case of layer-oriented MCAO in which the DM is conjugated to the ground, while solar tomography adaptive optics （TAO） that we proposed recently can be viewed as star-oriented MCAO with only one DM. Solar GLAO and TAO use the same hardware as conventional solar AO, and therefore it will be important to see which method can deliver better performance. In this article, we compare the performance of solar GLAO and TAO by using end-to-end numerical simulation software. Numerical simulations of TAO and GLAO with different numbers of guide stars are conducted. Our results show that TAO and GLAO produce the same performance if the DM is conjugated to the ground, but TAO can only generate better performance when the DM is conjugated to the best height. This result has important application in existing one-DM solar AO systems.

Two-telescope-based solar seeing profile measurement simulation

Measurements of the daytime seeing profile of the atmospheric turbulence are crucial for evaluating a solar astronomical site so that research on the profile of the atmospheric turbulence as a function of altitude C_(n)^(2)(h_(n))becomes more and more critical for performance estimation and optimization of future adaptive optics(AO)including the multi-conjugate adaptive optics(MCAO)systems.Recently,the S-DIMM+method has been successfully used to measure daytime turbulence profiles above the New Solar Telescope(NST)on Big Bear Lake.However,such techniques are limited by the requirement of using a large solar telescope which is not realistic for a new potential astronomical site.Meanwhile,the AMASP(advanced multiple-aperture seeing profiler)method is more portable and has been proved that can reliably retrieve the seeing profile up to 16 km with the Dunn Solar Telescope(DST)on the National Solar Observatory(Townson,Kellerer et al.).But the turbulence of the ground layer is calculated by combining A-MASP and S-DIMM+(Solar Differential Image Motion Monitor+)due to the limitation of the twoindividual-telescopes structure.To solve these problems,we introduce the two-telescope seeing profiler(TTSP)which consists of two portable individual telescopes.Numerical simulations have been conducted to evaluate the performance of TTSP.We find our TTSP can effectively retrieve seeing profiles of four turbulence layers with a relative error of less than 4%and is dependable for actual seeing measurement.

An active coronagraph using a liquid crystal array for exoplanet imaging:principle and testing

High-contrast imaging coronagraphs, used for the detection of exoplanets, have always adopted passive coronagraph optical components. It is therefore impossible to actively optimize the coronagraphs to achieve their best performance. To solve this problem, we propose a novel high-contrast imaging coronagraph which combines a liquid crystal array （LCA） for active pupil apodization and a deformable mirror （DM） for phase correction. The LCA we use is an amplitude-only spatial light mod- ulator. The LCA is well calibrated and compensates for its amplitude non-uniformity and nonlinear intensity responsivity. We measured the imaging contrasts of the coron- agraph system with the LCA only and without the DM deployed. Imaging contrasts of 10-4 and 10-5 can be reached at an inner working angular distance of 2.5 and 5A/D, respectively. A simulation shows that the phase errors on the coronagraph pupil limit the contrast performance. The contrast could be further improved if a DM is deployed to correct the phase errors induced by the LCA and coronagraph optics.

A high-contrast imaging polarimeter with a stepped-transmission filter based coronagraph

The light reflected from planets is polarized mainly due to Rayleigh scattering, but starlight is normally unpolarized. Thus it provides an approach to enhance the imaging contrast by inducing the imaging polarimetry technique. In this paper, we propose a high-contrast imaging polarimeter that is op- timized for the direct imaging of exoplanets, combined with our recently developed stepped-transmission filter based coronagraph. Here we present the design and calibration method of the polarimetry system and the associated test of its high-contrast performance. In this polarimetry system, two liquid crystal variable retarders （LCVRs） act as a polarization modulator, which can extract the polarized signal. We show that our polarimeter can achieve a measurement accuracy of about 0.2% at a visible wavelength （632.8 nm） with linearly polarized light. Finally, the whole system demonstrates that a contrast of 10 9 at 5A/D is achievable, which can be used for direct imaging of Jupiter-like planets with a space telescope.