Binary adaptive optics: atmospheric wave-front correction with a half-wave phase shifter

We describe a binary approach to adaptive wave-front correction, especially suitable for narrow band applications, which would be simpler than conventional adaptive technology. Appropriate parts of the aberrant wave front are phase retarded by half a wavelength to ensure that none of the image-forming rays add together destructively. Simulations for monochromatic light show that the residual wave-front errors, in the absence of other errors, would result in Strehl ratios of ~40% with diffraction-limited widths at visible wavelengths. We simulate the imaging performance of such a system and describe a possible implementation that uses a ferroelectric liquid-crystal spatial light modulator.     

Psychometrically appropriate assessment of afocal optics by measurement of the Strehl intensity ratio

Several different performance criteria have been proposed for assessing the quality of visual afocal sights. Earlier research by one of the authors (Haig) has shown that a high degree of correlation exists between a subjective assessment of performance and the Strehl intensity ratio of the optical system. We discuss some of the problems in choosing an objective performance criterion for visual sights and describe equipment that has been developed for measuring the line Strehl ratio of binoculars, both on and off axes. The equipment can be modified for testing other types of visual sight. It can also be used for measuring several additional performance parameters such as the modulation transfer function, transmission, and field curvature.     

Gap-to-T c ratio as a function of the Fermi level shift

Within the framework of the BCS theory, the gap-to-T_C ratioR=2‡ ₀/kT_c is evaluated numerically (‡₀ is the energy gap atT = 0 andT> _c is the critical temperature) for a superconductor with a van Hove singularity (vHs) in the density of states as a function of the shifts (δ) of the Fermi level with respect to the vHs. It is found thatR varies asymmetrically with δ and that the variations are strong near δ = 0. Our numerical calculation shows that the largest R’s occur at certain values of δ⊋0.     

Strehl ratio and modulation transfer function for segmented mirror telescopes as functions of segment phase error

We derive the Strehl ratio for a segmented mirror telescope as a function of the rms segment phase error and the observing wavelength, with and without the effects of the atmosphere. A simple analytical expression is given for the atmosphere-free case. Although our specific results are in the context of the Keck telescope, they are presented in a way that should be readily adaptable to other segmented geometries. We also derive the corresponding modulation transfer functions. These results are useful in determining how accurately a segmented mirror telescope needs to be phased for a variety of observing applications.     

Study of a MEMS-based Shack-Hartmann wavefront sensor with adjustable pupil sampling for astronomical adaptive optics

We introduce a Shack-Hartmann wavefront sensor for adaptive optics that enables dynamic control of the spatial sampling of an incoming wavefront using a segmented mirror microelectrical mechanical systems (MEMS) device. Unlike a conventional lenslet array, subapertures are defined by either segments or groups of segments of a mirror array, with the ability to change spatial pupil sampling arbitrarily by redefining the segment grouping. Control over the spatial sampling of the wavefront allows for the minimization of wavefront reconstruction error for different intensities of guide source and different atmospheric conditions, which in turn maximizes an adaptive optics system's delivered Strehl ratio. Requirements for the MEMS devices needed in this Shack-Hartmann wavefront sensor are also presented.     

Adaptive optics: wave-front correction by use of adaptive filtering and control

A class of adaptive-optics problems is described in which phase distortions caused by atmospheric turbulence are corrected by adaptive wave-front reconstruction with a deformable mirror, i.e., the control loop that drives the mirror adapts in real time to time-varying atmospheric conditions, as opposed to the linear time-invariant control loops used in conventional adaptive optics. The basic problem is posed as an adaptive disturbance-rejection problem with many channels. The solution given is an adaptive feedforward control loop built around a multichannel adaptive lattice filter. Simulation results are presented for a 1-m telescope with both one-layer and two-layer atmospheric turbulence profiles. These results demonstrate the significant improvement in imaging resolution produced by the adaptive control loop compared with a classical linear time-invariant control loop.     

Numerical simulation of an adaptive optics system with laser propagation in the atmosphere

A comprehensive model of laser propagation in the atmosphere with a complete adaptive optics (AO) system for phase compensation is presented, and a corresponding computer program is compiled. A direct wave-front gradient control method is used to reconstruct the wave-front phase. With the long-exposure Strehl ratio as the evaluation parameter, a numerical simulation of an AO system in a stationary state with the atmospheric propagation of a laser beam was conducted. It was found that for certain conditions the phase screen that describes turbulence in the atmosphere might not be isotropic. Numerical experiments show that the computational results in imaging of lenses by means of the fast Fourier transform (FFT) method agree well with those computed by means of an integration method. However, the computer time required for the FFT method is 1 order of magnitude less than that of the integration method. Phase tailoring of the calculated phase is presented as a means to solve the problem that variance of the calculated residual phase does not correspond to the correction effectiveness of an AO system. It is found for the first time to our knowledge that for a constant delay time of an AO system, when the lateral wind speed exceeds a threshold, the compensation effectiveness of an AO system is better than that of complete phase conjugation. This finding indicates that the better compensation capability of an AO system does not mean better correction effectiveness.     

Comparison of adaptive optics and phase-conjugate mirrors for correction of aberrations in double-pass amplifiers

Correction of birefringence-induced effects (depolarization and bipolar focusing) were achieved in double-pass amplifiers by use of a Faraday rotator between the laser rod and the retroreflecting optic. A necessary condition was ray retrace. Retrace was limited by imperfect conjugate-beam fidelity and by nonreciprocal refractive indices. We compared various retroreflectors: stimulated-Brillouin-scatter phase-conjugate mirrors (PCMs), PCMs with rod-to-PCM relay imaging (IPCM), IPCMs with astigmatism-correcting adaptive optics, and all-adaptive-optic imaging variable-radius mirrors. Results with flash-lamp-pumped, Nd:Cr:GSGG double-pass amplifiers showed the superiority of adaptive optics over nonlinear optic retroreflectors in terms of maximum average power, improved beam quality, and broader oscillator pulse duration/bandwidth operating range. Hybrid PCM-adaptive optics retroreflectors yielded intermediate power/beam-quality results.     

Calibration of a deformable mirror and Strehl ratio measurements by use of phase diversity

Calibration experiments with a bimorph mirror are presented. Phase-diversity wave-front sensing is used for measuring the control matrix, nulling wave-front errors in the optical setup, including the mirror, and measuring Strehl ratios and residual higher-order aberrations. The Strehl ratio of the calibrated system is measured to be 0.975, corresponding to 1/40 wave rms in the residual wave front. The conclusion is that a phase-diversity wave-front sensor is easier to install and use than interferometers and can replace them in optical setups for testing adaptive optics systems.     

Mean-square residual error of a wavefront after propagation through atmospheric turbulence and after correction with Zernike polynomials

The root-mean-square (rms) of the residual wavefront, after propagation through atmospheric turbulence and corrected from Zernike polynomials, has been derived for the von Kármán turbulence model. The rms for any location in the telescope pupil and the pupil average rms have been calculated. It is shown that the residual rms on the edge of the pupil can be up to 35% larger than the pupil average residual rms. The results are useful to estimate the required rms stroke of deformable mirror (DM) actuators when they are used as a second stage of correction either in a tip-tilt, single-DM configuration or in a tip-tilt, two-DM (woofer-tweeter) setup.     

Analysis of modes and behavior of a multiconjugate adaptive optics system

We study the so-called three-dimensional mapping of turbulence, a method solving the cone effect (or focus anisoplanatism) by using multiple laser guide stars (LGSs). This method also permits a widening of the corrected field of view much beyond the isoplanatic field. Multiple deformable mirrors, conjugated to planes at chosen altitudes among the turbulent layers, are used to correct in real time the wave fronts measured from the LGSs. We construct an interaction matrix describing the multiconjugate adaptive optics system and analyze the eigenmodes of the system. We show that the global tilt mode is singular because it cannot be localized in altitude, so that it must be corrected only once at any altitude. Furthermore, when the tilt from the LGS cannot be measured, the singularity of the global tilt yields the delocalization of particular forms of defocus and astigmatism. This imposes the use of a single natural guide star located anywhere in the corrected field to measure these modes. We show as an example that the cone effect can be corrected with a Strehl of 0.8 with four LGSs (tilt ignored) on an 8-m telescope in the visible when a single laser star provides a Strehl of 0.1. The maximum field of view of 100 arc sec in diameter can be reconstructed with an on-axis Strehl ratio of 30%. We also show that the measurement of the height of the layers can be done with current techniques and that additional layers, not accounted for, do not significantly degrade the performance in the configuration that we model.     

Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra

Adaptive optics systems provide a real-time compensation for atmospheric turbulence. However, the correction is often only partial, and a deconvolution is required for reaching the diffraction limit. The need for a regularized deconvolution is discussed, and such a deconvolution technique is presented. This technique incorporates a positivity constraint and some a priori knowledge of the object (an estimate of its local mean and a model for its power spectral density). This method is then extended to the case of an unknown point-spread function, still taking advantage of similar a priori information on the point-spread function. Deconvolution results are presented for both simulated and experimental data.     

Gas permeability of nuclear membranes as a function of effective pore diameter

We have examined experimentally and theoretically the transport of various gases in channels with a diameter comparable to that of the molecule dimensions.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 4, pp. 616–623, October, 1989.     

Particle image velocimetry: image labeling by use of adaptive optics to modify the point-spread function

A simple method of labeling the first- and second-exposure images of a particle-image-velocimetry recording is discussed. One achieves this method by changing the transfer characteristics of the recording optics between exposures by inserting a rotating optic into the iris plane of the camera objective. Spatial filtering can then be used to address the images recorded by each exposure independently, permitting cross-correlation analysis to be implemented. Two practical systems using either an aperture plate or a phase plate are demonstrated, and we show that the phase plate is significantly more light efficient. Finally, the feasibility of image labeling high-speed flows using electro-optic devices is discussed.     

Comparison of curvature-based and Shack-Hartmann-based adaptive optics for the Gemini telescope

We present the results of independent numerical simulations of adaptive optics systems for 8-m astronomical telescopes that use both Shack-Hartmann and wave-front curvature sensors. Four differents codes provided consistency checks and redundancy. All four simulate a complete system and model noise and servo-lag effects. A common atmospheric turbulence generator was used for consistency. We present the main characteristics of the codes, and we report the system performance in term of Strehl ratio and full width at half-maximum versus the magnitude of the (on-axis) guide star. We show that a Shack-Hartmann plus stacked actuator mirror system with 10 x 10 subapertures or a curvature plus bimorph mirror system with 56 subapertures yields a 50% Strehl ratio at 1.6 mum for a m(R) = 14.7 magnitude star, with almost equivalent performance at both brighter and dimmer light levels.     

Influence of stress ratio on the threshold level for fatigue crack propagation in high strength steels

Centrally cracked specimens of JIS SM58Q and HT80 steels were fatigued. The fatigue crack growth rates, da/dn, and the stress intensity threshold levels, ΔK_th were measured over the range of stress ratio, R, from ?1 to 0.8 by the use of an automatic method of continuously decreasing stress intensity factor with crack extension. The measured ΔK_th was well represented as |ΔK_th/2|_R=(1?R)γ|ΔK_th/2|_R=0; and the propagation rate, as da/dn = A(1?R)^γm[(ΔK/2)^m ? {(1 ? R)^γ|ΔK_th/2|R=0}^m] for ?1≦R≦0.33 or da/dn = A(1 ? 0.33)^?γm [(ΔK/2)^m {(1 ? R)^γ |ΔK_th/2|R=0}^m] for 0.33 < ≦ 0.8.     

Properties of MoNxOy thin films as a function of the N/O ratio

The main purpose of this work is the preparation of single layer films of molybdenum oxynitride, MoN_xO_y. The films were deposited on steel substrates by dc reactive magnetron sputtering. The depositions were carried out from a pure Mo target and varying the flow rate of reactive gases. This allowed tuning of the crystallographic structure between insulating oxides and metallic nitrides and consequently changes in the electronic, mechanical and optical properties of the material. X-ray diffraction (XRD) results revealed the presence of molybdenum nitride for the films with low oxygen fraction: face-centered cubic phases (γ-Mo₂N) for low nitrogen flow rate or cubic MoN_x and hexagonal phase (δ-MoN) for high nitrogen flow rate. The increase of oxygen content induces an amorphization of the nitride phases and the appearance of MoO₃ phases. The increase of the oxygen fraction in the films induces also a high decrease in the film's hardness. Residual stresses were compressive, in the range of very few tenths of GPa to − 2 GPa. These results will be presented as a function of the deposition parameters, the chemical composition and the structure of the films.     

Monte Carlo simulation of the atmospheric point-spread function with an application to correction for the adjacency effect

Monte Carlo techniques are used to simulate atmospheric point-spread functions (PSF's) that are appropriate for the viewing geometries typical of the Airborne Visible-Infrared Imaging Spectrometer (AVIRIS). A model sensor is located at an altitude of 20 km and views a Lambertian surface through a horizontally homogeneous and vertically stratified atmosphere. Simulations show the effects on the PSF of variation of the aerosol phase function, the aerosol optical thickness, the sensor viewing angle, and the wavelength. An algorithm that uses the PSF to correct high-contrast images for adjacency effects is developed and applied to an AVIRIS image of Big Pine Key in the Florida Keys. A method to approximate the atmospheric PSF's without the need to resort to a Monte Carlo simulation is described. Correction of the AVIRIS image through the use of the approximated PSF is consistent with a previous correction. Error analysis is difficult and scene dependent; however, the correction algorithm is shown to be capable of indicating regions of high-contrast images in which conventional estimates of surface-leaving radiance are likely to be unreliable due to adjacency effects.