Static Aberrations Research Articles

Investigation on a high energy stimulated Brillouin scattering phase-conjugate mirror

A novel dual-cell Brillouin oscillator-amplifier phase conjugate mirror for high energy and high peak power operation in double-pass solid state laser amplifier is described. Correction of static aberration and dynamic aberration induced in single-pass amplifier was achieved in the second passage through the aberrating medium under the condition of using the stimulated Brillouin scattering phase conjugate mirror as reflector. Output energy of 13 J was obtained with input energy of 7.1 J. An energy reflectivity of 65% and a conjugation fidelity of 90% were achieved by the use of this dual-cell phase conjugate mirror. Finally, the performance of this kind of SBS reflector in a double-pass amplifier has been compared to that of a flat mirror. The results show that the SBS reflector is highly effective in correcting the spatial aberrations of laser radiation. Excellent near-and far-field conjugation fidelities were obtained even with high input energy.

Fundamental limitations on Earth-like planet detection with extremely large telescopes

We analyse the fundamental limitations for the detection of extraterrestrial planets with Extremely Large Telescopes. For this task, a coronagraphic device combined with a very high order wavefront correction system is required but is not sufficient to achieve the 10 -10 contrast level needed to detect an Earth-like planet. The stellar residuals left uncorrected by the wavefront correction system need to be calibrated and subtracted. We consider a general model including the dynamic phase aberrations downstream of the wavefront correction system, the static phase aberrations of the instrument and some differential aberrations provided by the calibration unit. A rather optimistic case of a filled circular pupil and of a perfect coronagraph is assumed. As a result of the analytical study, the limitation is found to mostly come from the static aberrations. We confirm this result using numerical simulations and evaluate the requirements in terms of phase aberrations to detect Earth-like planets with Extremely Large Telescopes.

Earth-like planet detection with Extremely Large Telescopes

Direct detection of Earth-like planets is one of the major objectives for the next generation of ground based telescopes (Extremely Large Telescopes, ELT). ELT instruments will be conditionned by such scientific programs. Here, we consider here a system made with an adaptive optics device, a coronagraph and a simultaneous calibration system. We refined this simple model by including static aberrations upstream the coronagraph and differential aberrations downstream. Using numerical simulations, we evaluate how these static aberrations limit the detectability of telluric planets.

Experimental demonstration of phase correction with a 32×32 microelectromechanical systems mirror and a spatially filtered wavefront sensor

A 32 x 32 microelectromechanical systems deformable mirror is controlled in closed loop with a spatially filtered Shack-Hartmann wavefront sensor and a Fourier-transform wavefront reconstruction algorithm. A phase plate based on atmospheric turbulence statistics is used to generate a 1 microm peak-valley static phase aberration. Far-field images and direct phase measurements of the residual are used to compare performance with and without the spatial filter. Use of the spatial filter reduces error in the controllable band from 20 to 6 nm rms. Residual phase power is reduced by more than a factor of 5 for all spatial frequencies up to 0.85 x 1/2d, with a maximum attenuation factor of 37.

Spatial frequency analytical modeling of adaptive optics for diffraction limited coronagraphs studies on extremely large segmented telescopes

In this paper, we briefly describe the principle of analytical modelization of the adaptive optics (AO) corrected point spread function in the spatial frequency domain, both for the turbulent and the telescope static aberrations, and demonstrate how this can be used for simulating AO corrected phase screens on extremely large hexagonal segmented telescopes, required for performance analysis of diffraction limited coronagraphs.

Fundamental limitations on Earth-like planet detection with ELTs

A forthcoming step in the study of extrasolar planetary systems is the direct detection and characterization of Earth-like planets. An asset of the ELTs in that context is their very high angular resolution and their collecting area. The luminosity ratio between a terrestrial planet and its star ( $10^{-10}$ ) is such an ambitious goal that a thorough study needs to be carried out. We started with a simple analysis of the fundamental limitations for the detection of extraterrestrial planets with ELTs. Here, we considered an extreme adaptive optics device upstream of a perfect coronagraph. Even with high Strehl ratios, the coronagraphic halo level is only $10^{-6}$ to $10^{-7}$ at typical exo-Earth angular distances. A calibration device is therefore mandatory to reach the contrast between a terrestrial planet and its star in the near infra-red. We considered a simple but realistic model taking into account dynamic aberrations left uncorrected by the adaptive optics system, static aberrations of optical system and differential static aberrations due to the calibration channel itself. Numerical simulations prove that, after the calibration, the limitations are set by the static aberrations which cannot be neglected anymore.

Alignment and wavefront control systems of the National Ignition Facility

The National Ignition Facility (NIF) at the Lawrence Livermore National Laboratory is a stadium-sized facility containing a 192-beam Nd glass laser. Its 1.053-µm output is frequency converted to produce 1.8-MJ, 500-TW pulses in the ultraviolet. Refer to the companion overview articles in this issue for more information. High-energy-density and inertial confinement fusion physics experiments require the ability to precisely align and focus pulses with single-beam energy up to 20 KJ and durations of a few nanoseconds onto millimeter-sized targets. NIF's alignment control system now regularly provides automatic alignment of the four commissioned beams prior to every NIF shot in approximately 45 min, and speed improvements are being implemented. NIF utilizes adaptive optics for wavefront control, which significantly improves the ability to tightly focus each laser beam onto a target. Multiple sources of both static and dynamic aberration are corrected. This article provides an overview of the NIF automatic alignment and wavefront control systems, and provides data to show that the facility is expected to meet its primary requirements to position beams on the target with an accuracy of 50-µm rms over the 192 beams and to focus the pulses into a 600-µm spot.

Analysis of the Naval Observatory Flagstaff Station 1-m telescope using annular Zernike polynomials

The Naval Observatory Flagstaff Station 1-m telescope is evaluated for the addition of adaptive optics capabilities to its instrumentation suite. Zernike decomposition of the optical system based on phase diversity measurements shows that the static optical aberrations are small enough that they will not degrade the performance of the deformable optical element. The analysis makes use of annular pupil Zernike polynomial reconstruction of the wavefront to accommodate the large obscuration in this telescope and compares this with the results from using filled circular Zernike polynomials.

Feedback interferometry with membrane mirror for adaptive optics

Feedback interferometers can be used for many optical measurements as well as aberration correction. The choice of the phase modulator in the interferometer has major influence on the operation of the feedback system. Conventional wisdom is that independent actuator movement is a basic requirement for the modulator in order to allow the feedback system to operate in stable fashion and that membrane mirrors are not suitable. We demonstrate the operation of a feedback interferometer which uses a membrane mirror as the phase modulator. We show that even with the strong coupling introduced by the influence function of the membrane mirror, the feedback system can still operate normally. Our interferometer is based on a radial shearing polarizing Sagnac interferometer. The current system is able to correct static aberration with significant improvement on Strehl ratio.

Calibration of NAOS and CONICA static aberrations

We describe and evaluate the performance of a phase diversity wavefront sensor used to measure the static aberrations of the VLT instrument NAOS–CONICA. The main limitations of this phase diversity technique are compiled. We investigate the systematic errors due to the experimental implementation and the design restrictions. Further error sources stem from the imperfect knowledge of the system, and from limitations of the algorithm. The influence of these errors on the wavefront estimation is evaluated on numerical and experimental data. This study highlights the essential verifications and calibrations needed to obtain accurate results and gives a practical guideline for the application of a phase diversity wavefront sensor. The comprehensive calibration results and the final gain in optical performance are presented and discussed in a complementary paper ([CITE]).

Calibration of NAOS and CONICA static aberrations

NAOS is the first adaptive optics (AO) system of the Very Large Telescope and will provide CONICA with diffraction-limited images. CONICA is a near infrared camera that offers a variety of imaging and spectroscopic observing modes. A technique will be described to benefit of the AO system to correct not only for atmospheric turbulence but also for the internal optical aberrations of the high-resolution camera and the beam splitters of NAOS. The aberrant optical components in the light path of CONICA as well as the beam splitters are outside of the AO loop and therefore no self-acting correction is possible. Independently of the AO wavefront sensor, a separate measurement of these aberrations using a method called phase diversity allows one to predict for a certain instrument configuration the corresponding aberrations. They are quantified by sets of Zernike coefficients that are rendered to the adaptive optics. This technique turns out to be very flexible and results in a further improvement of the optical overall performance. The application of phase diversity to the instrument is investigated in a preceding paper (Blanc et al. 2003). In the present paper we present in detail the instrumental implementation of phase diversity, the obtained calibration results, and the achieved gain in optical performance.

Practical Considerations in Restoring Images from Phase‐Diverse Speckle Data

ABSTRACTWe discuss practical problems and solutions associated with the “phase‐diverse” speckle (PDS) imaging technique for reconstruction of high‐resolution images from ground‐based telescope data. The PDS method uses an ensemble of short‐exposure images obtained simultaneously from multiple cameras to jointly estimate the object and the sequence of instantaneous phase distortions observed by each camera. Different known static phase aberrations are imposed on each optical channel; the known aberrations then function as constraints in the estimation problem. In this paper, we extend a previously derived model and present new data calibration techniques to compensate for various undesirable effects present in real‐world PDS data. These effects include relative tip‐tilt and image magnification changes between the diversity channels. The extended model and its associated (modified) objective functions lead to a new nonlinear optimization problem. Solution methods, software, and results using real telescope data are discussed.

Novel micromachined membrane mirror characterization and closed-loop demonstration

Micromachined electrostatic membrane mirrors have been in use for several years in active and adaptive optics applications. We introduce a deformable mirror with small static aberrations and resistant to damage during electrostatic snap-down in an architecture designed so that a multi-layer dielectric coating that can be applied before the mirror is released. We also make laboratory performance measurements and produce a closed-loop control algorithm.

Behavior of Remnant Speckles in an Adaptively Corrected Imaging System

Adaptive correction on large ground-based telescopes is enabling a variety of novel studies that would be impossible at the limits of spatial and spectral resolution imposed by the Earth's turbulent atmosphere. Even relatively high-order systems, however, do not yield a perfect correction and as a result are compromised by a low-intensity halo of remnant light that is removed from the core of the point-spread function (PSF) and dispersed in the focal plane. Worse still, this halo is neither constant in time nor uniform in position but is concentrated in transient spots that move about as mutually coherent patches of phase over the telescope aperture happen to combine constructively in the image plane. These in the PSF set limits on ground-based searches for faint companions to bright stars. We describe here simple properties of the physics of formation that will affect the statistics of residual speckles in a fundamental way: at high correction, the secondary maxima of the static PSF will coherently amplify or pin the time-varying speckles, influencing their effective characteristic lifetimes and dramatically changing their spatial distribution. Furthermore, as a result of pinning, temporal variations in the noncommon path errors that occur in practical adaptive optics systems will cause an additional gradual drift in the spatial distribution of speckles, as Airy rings shift. Speckle pinning may be exploited to suppress noise by tailoring the PSF with static aberrations artificially injected via the deformable mirror so as to clear a region of the PSF of Airy rings and hence of pinned speckles, a technique that we term speckle sweeping.

Closed-loop adaptive optics in the human eye

We have developed a prototype apparatus for real-time closed-loop measurement and correction of aberrations in the human eye. The apparatus uses infrared light to measure the wave-front aberration at 25 Hz with a Hartmann-Shack sensor. Defocus is removed by a motorized optometer, and higher-order aberrations are corrected by a membrane deformable mirror. The device was first tested with an artificial eye. Correction of static aberrations takes approximately five iterations, making the system capable of following aberration changes at 5 Hz. This capability allows one to track most of the aberration dynamics in the eye. Results in living eyes showed effective closed-loop correction of aberrations, with a residual uncorrected wave front of 0.1microm for a 4.3-mm pupil diameter. Retinal images of a point source in different subjects with and without adaptive correction of aberrations were estimated in real time. The results demonstrate real-time closed-loop correction of aberration in the living eye. An application of this device is as electro-optic "spectacles" to improve vision.

Real-time optical path difference compensation at the Plateau de Calern I2T interferometer

The fringe tracker system of the ASSI (Active Stabilization in Stellar Interferometry) beam combining table at the I2T interferometer is described and its performance evaluated. A new real{time algorithm for the optical path dierence (OPD) measurement is derived and validated. It is based on a sinusoidal phase modulation whose amplitude is optimized. It also allows automatic fringe detection at the beginning of an observation when scanning the OPD. The fringe tracker servo{loop bandwidth is adjusted by a numerical gain and ranges between 20 and 50 Hz in the reported experiments. On stars, fringe{locked sequences are limited to 20 s due to fringe jumps. However, the fringe tracker is able to recover the coherence area after a few seconds. Such a fringe tracker operation can last more than one hour. A fringe tracking accuracy of 85 nm is achieved for visibility ranging between 7 and 24%, a turbulence coherence time of approximately 9 ms at 0.85 m, a Fried parameter of around 14 cm at 0.5 m and an average light level of 100 000 photoevents/s, (typically visual magnitude 2 in the conditions of the experiment). Visibility losses are evaluated and are found to be mainly due to turbulent wavefront fluctuations on the two telescopes and to the static aberrations of the optical train. The measurements of OPD and angle of arrival are reduced to derive turbulence parameters: the coherence time, the average wind speed, the Fried parameter and the outer scale. Our estimations for the outer scale range between 20 and 120 m, with an average value of the order of 40 m. Both OPD and angle of arrival data, obtained on 15 m baseline and a 26 cm telescope diameter respectively, are fully compatible with the same modied Kolmogorov spectrum of the turbulence, taking into account a nite outer scale.

Cryogenic wavefront correction using membrane deformable mirrors

Micro-machined membrane deformable mirrors (MMDMs) are being evaluated for their suitability as wavefront correctors at cryogenic temperatures. Presented here are experimental results for the change in the initial mirror figure of 37-channel MMDMs from OKO Technologies upon cooling to T=78K. The changes in the influence functions are also explored. Of the sample of 3 mirrors tested, one was found to have sufficiently small initial static aberrations to be useful as a wavefront corrector at this temperature. The influence functions at T=78K were found to be similar in shape to both those at room temperature and theoretical predictions of the MMDMs surface shape. The magnitude of the surface deflection at T=78K was reduced by around 20% compared with room temperature values.

Centroid gain compensation in Shack–Hartmann adaptive optics systems with natural or laser guide star

In an adaptive optics system with an undersampled Shack-Hartmann wave-front sensor (WFS), variations in seeing, laser guide star quality, and sodium layer thickness and range distance all combine to vary WFS centroid gain across the pupil during an exposure. While using the minimum of 4 pixels per WFS subaperture improves frame rate and read noise, the WFS centroid gain uncertainty may introduce static aberrations and degrade servo loop phase margin. We present a novel method to estimate and compensate WFS gains of each subaperture individually in real time for both natural and laser guide stars.

Modeling the combined effect of static and varying phase distortions on the performance of adaptive optical systems

The end-to-end performance achieved by an adaptive optical (AO) imaging system is determined by a combination of the residual time-varying phase distortions associated with atmospheric turbulence and the quasi-static unsensed and uncorrectable aberrations in the optical system itself. Although the effects of these two errors on the time-averaged Strehl ratio and the time-averaged optical transfer function (OTF) of the AO system are not formally separable, such an approximation is found to be accurate to within a few percent for a range of representative residual wave-front errors. In these calculations, we combined static optical system aberrations and time-varying residual phase distortion characteristics of a deformable mirror fitting error, wave-front sensor noise, and anisoplanatism. The static aberrations consist of focus errors of varying magnitudes as well as a combination of unsensed and uncorrectable mirror figure errors derived from modeling by the Gemini 8-Meter Telescopes Project. The overall Strehl ratios and OTF's that are due to the combined effect of these error sources are well approximated as products of separate factors for the static and time-varying aberrations, as long as the overall Strehl ratio that is due to both errors is greater than approximately 0.1. For lower Strehl ratios, the products provide lower bounds on the actual values of the Strehl ratio and the OTF. The speckle transfer function is also well approximated by a product of two functions, but only where AO compensation is sufficiently good that speckle imaging techniques are usually not required.

Imaging performance of the liquid-crystal-adaptive lens with conductive ladder meshing

The liquid-crystal-adaptive lens (LCAL) is an electro-optical device that utilizes a graded index of refraction to bring light to focus. A set of electrodes controls the index variation in a liquid-crystal thin film. One can vary the focal length of the LCAL by changing the voltages applied to the device. The discrete nature of the electrodes causes phase aberrations. We introduce a novel electrode architecture, called conductive ladder meshing (CLM), that we developed to greatly reduce the static phase aberration (caused by the electrode structure). To reduce the dynamic phase aberration (associated with inaccurate voltages), we used a simulated-annealing voltage-dithering technique. The coherent transfer function of the LCAL was derived so that the performance of the CLM LCAL could be predicted theoretically. Theoretical analysis indicates that the CLM LCAL scatters less than 30% of incident light compared with scattering of 65% in the previous version. The focal-spot performance of the spherical LCAL was measured under coherent illumination for plane-wave illumination. Because of the improved quality of the spherical LCAL, true imaging experiments are demonstrated for a single incoming polarization under white-light illumination. Images formed by the spherical LCAL are comparable with those formed by a fixed lens in terms of resolution, although the contrast is worse.