Iterative wave-front reconstruction for open-loop metrology applications: Shack-Hartmann and shearing interferometer wave-front sensing using Fourier or Multigrid reconstructors

Numerous techniques exist to reconstruct the wave-front in Shack-Hartmann and shearing interferometer wave-front sensors. Two of these techniques involve solving the least-squares wave-front reconstruction via Fourier transform or Multigrid methods. These two techniques operate on a square grid and are sensitive to both nonlinearities and to the methods used to extend the gradients beyond the aperture to the edges of the square grid. Both of these sensitivities can lead to large residual wave-front errors when reconstructing large aberrations. In this article we introduce an iterative computational loop in the reconstruction process which is designed to improve the reconstruction variances introduced by these parameters. This technique allows for accurate reconstruction of large phases which can arise in applications such as open-loop compensation of atmospheric turbulence, aberrometers and metrology. In this article, it is demonstrated that large aberrations can be accurately reconstructed utilizing this iterative method with Fourier or Multigrid reconstructors.     

平行光管气流扰动的液晶自适应光学校正

利用液晶自适应光学技术,建立了一套验证系统.使用哈特曼传感器为波前探测器件,反射式的LCOS液晶器件为波前校正器件,以闭环控制校正方式工作.初步实现了波前PV值从1.02λ下降到0.37λ（λ＝633 nm）的校正准确度,成像质量明显提高.系统的调制传递函数由校正前的不到10 lp/mm提高到了校正后的超过50 lp/mm.     

Pyramid sensor for segmented mirror alignment

We report what is to our knowledge the first laboratory experiment that shows the use of a pyramid wavefront sensor to cophase and align segmented mirrors having three degrees of freedom per segment, i.e., piston, tip, and tilt. In the laboratory the iterative alignment procedure reached a wavefront residual error of about 10 nm. The residual error was equally distributed between piston, tip, and tilt. These results demonstrate that the pyramid can successfully simultaneously sense the piston, tip, and tilt of a segmented mirror. This last feature makes this technique very attractive in phasing and aligning astronomical segmented telescopes such as extremely large telescopes currently under extensive studies.     

Adaptive wave-front correction by means of all-optical feedback interferometry

A novel adaptive wave-front correction system based on an all-optical feedback interferometer is described. In this system the two-dimensional output fringe intensity from a Mach-Zehnder interferometer with large radial shear is optically fed back to an optically addressed phase-only liquid-crystal spatial light modulator. Consequently, without a separate aberration-free reference wave, the modulator phase approximates the conjugate of the interferometer phase that is directly related to the phase of the input aberrated wave front, so this system is applicable in adaptive optics. We successfully achieved real-time correction of aberrated wave fronts: A diffraction pattern that was seriously distorted because of aberrations was transformed into a diffraction-limited spot immediately after the feedback loop was closed.     

High-speed horizontal-path atmospheric turbulence correction with a large-actuator-number microelectromechanical system spatial light modulator in an interferometric phase-conjugation engine

Results of atmospheric propagation for a high-speed, large-actuator-number adaptive optics system are presented. The system uses a microelectromechanical system- (MEMS-) based spatial light modulator correction device with 1024 actuators. Tests over a 1.35-km path achieved correction speeds in excess of 800 Hz and Strehl ratios close to 0.5. The wave-front sensor was based on a quadrature interferometer that directly measures phase. This technique does not require global wave-front reconstruction, making it relatively insensitive to scintillation and phase residues. The results demonstrate the potential of large-actuator-number MEMS-based spatial light modulators to replace conventional deformable mirrors.     

Electron density characterization by use of a broadband x-ray-compatible wave-front sensor

The use of a Hartmann wave-front sensor to accurately measure the line-integrated electron density gradients formed in laser-produced and z-pinch plasma experiments is examined. This wave-front sensor may be used with a soft-x-ray laser as well as with incoherent line emission at multikilovolt x-ray energies. This diagnostic is significantly easier to use than interferometery and moiré deflectometry, both of which have been demonstrated with soft-x-ray lasers. This scheme is experimentally demonstrated in the visible region by use of a Shack-Hartmann wave-front sensor and a liquid-crystal spatial light modulator to simulate a phase profile that could occur when an x-ray probe passes through a plasma. The merits of using a Hartmann sensor include a wide dynamic range, broadband or low-coherence-length light capability, high x-ray efficiency, two-dimensional gradient determination, multiplexing capability, and experimental simplicity. Hartmann sensors could also be utilized for wavelength testing of extreme-ultraviolet lithography components and x-ray phase imaging of biological specimens.     

Signal spatial filtering for co-phasing in seeing-limited conditions

We present the results of the co-phasing closed loop performed with a pyramid wavefront sensor for what we believe to be the first time in the presence of emulated atmospheric disturbance. The performance of the co-phasing loop is significantly improved by applying two spatial filters in the sensor signal space. The first is a zonal filter applied to the interaction matrix before the computation of the reconstructor; the second is a modal filter applied to the sensor signals before the correction command computation. The presented laboratory results demonstrate that, applying both filters, the time requested to average out the atmospheric disturbance in each loop step is reduced by 2 orders of magnitude, improving the loop stability and accuracy.     

Frequency-resolving spatiotemporal wave-front sensor

We report on a high-resolution wave-front sensor that measures the complete spatial profile of any frequency component of a laser field containing multiple frequencies. This probe technique was developed to address the necessity of measuring the spatial overlap of the carrier field with each sideband component of the field exiting the output port of a gravitational-wave interferometer. We present the results of an experimental test of the probe, where we were able to construct the spatial profile of a single radio-frequency sideband at the level of -50 dBc.     

Wideband linear-to-circular polarization conversion realized by a transmissive anisotropic metasurface

We propose a metasurface which consists of three conductive layers separated by two dielectric layers. Each conductive layer consists of a square array of square loop apertures, however, a pair of corners of each square metal patch surrounded by the square loop apertures have been truncated, so it becomes an orthotropic structure with a pair of mutually perpendicular symmetric axes u and v. The simulated results show that the metasurface can be used as a wideband transmission-type polarization converter to realize linear-to-circular polarization conversion in the frequency range from12.21 GHz to 18.39 GHz, which is corresponding to a 40.4% fractional bandwidth. Moreover, its transmission coefficients at x-and y-polarized incidences are completely equal. We have analyzed the cause of the polarization conversion, and derived several formulas which can be used to calculate the magnitudes of cross-and co-polarization transmission coefficients at y-polarized incidence, together with the phase difference between them, based on the two independent transmission coefficients at u-and v-polarized incidences. Finally, one experiment was carried out, and the experiment and simulated results are in good agreement with each other.     

Demonstration for a two-axis interferometric tilt sensor in KAGRA

Recently, a folded Mach–Zehnder interferometer with homodyne in- and quadrature-phase detection was proposed as a high-precision, wide-dynamic range tilt sensor. By way of a practical application and to validate actual performance, two-axis tilt sensors were developed and installed for one mirror of the input mode cleaner cavity in KAGRA, the large-scale cryogenic gravitational-wave telescope in Kamioka, Gifu, Japan. Building on previous work, we have demonstrated that the two-axis tilt sensor has properly sensed the tilt angle changes of the mirror motion with high precision and without calibration. Compared with our initial angular sensor, an optical lever, which is calibrated by using the interferometer tilt sensor, we found that both sensors showed actual tilt motions of the mirror at low frequencies, and the two-axis interferometer sensor has a better sensitivity at higher frequencies.     

Refractive microlens array for wave-front analysis in the medium to hard x-ray range

We report an alternative approach to x-ray wave-front analysis that uses a refractive microlens array as a Shack-Hartmann sensor. The sensor was manufactured by self-assembly and electroplating techniques and is suitable for high-resolution wave-front analysis of medium to hard x rays. We demonstrate its effectiveness at an x-ray energy of 3 keV for analysis of x-ray wave-front perturbations caused by microscopic objects. The sensor has potential advantages over other methods for x-ray phase imaging and will also be useful for the characterization of x-ray beams and optics.     

Soft-x-ray laser interferometry of a pinch discharge using a tabletop laser

We have used a tabletop soft-x-ray laser and a wave-front division interferometer to probe the plasma of a pinch discharge. A very compact capillary discharge-pumped Ne-like Ar laser emitting at 46.9 nm was combined with a wave division interferometer based on Lloyd's mirror and Sc-Si multilayer-coated optics to map the electron density in the cathode region of the discharge. This demonstration of the use of tabletop soft-x-ray laser in plasma interferometry could lead to the widespread use of these lasers in the diagnostics of dense plasmas.     

Shack-Hartmann波前传感器在光学检验中的应用

介绍用于光学检测的Shack-Hartmann(S-H)波前传感器,以及相应的检测实验结果。在实验室内,通过与Zygo干涉仪的测量结果对比,得出传感器的测量精度优于/50 RMS(=632.8 nm)。在外场利用星光作为光源,对口径1 m、焦距11 m的望远镜进行了系统波像差检验,测量结果为0.39~0.46RMS之间,并随着俯仰角的增加而增大,主要像差形式为三阶像散。     

Measuring the power-law exponent of an atmospheric turbulence phase power spectrum with a Shack Hartmann wave-front sensor

For non-Kolmogorov turbulence we develop a differential angle-of-arrival fluctuation coefficient, which is the ratio between the transverse and longitudinal differential angle-of-arrival variances, and a slope structure-correlation coefficient, which is the ratio between the transverse and longitudinal differences of the slope correlation function and the slope structure function, to measure the power-law exponent of a phase power spectrum with a Shack-Hartmann wave-front sensor: The differential arrival-of-angle fluctuation coefficient and the slope structure-correlation coefficient are both related to power-law exponent beta and are independent of strength parameter rho(0) of the turbulence. We compare the methods developed and use them to evaluate beta in recently completed horizontal atmospheric experiments for 1000-m laser beam propagation.     

Laser optical fibre heterodyne interferometer with frequency indicating of the phase shift of a light signal in an optical waveguide

Self-sustained oscillations in a laser optical fibre heterodyne interferometer are discussed; oscillations were produced by closing into a loop the single-mode optical fibres of the interferometer. Such oscillatory systems are shown to feature high-frequency stability. It is proposed to use this oscillating interferometer as a high-sensitivity sensor of external factors affecting the optical waveguide.     

Robust one-beam interferometer with phase-delay control

A robust one-beam interferometer with external phase-delay control is described. The device resembles a Mach-Zehnder interferometer in which the two arms are together in one collimated beam. However, the proposed device is not an amplitude-division interferometer but a wave-front division one. The phase-delay control occurs at the interferometer output with the help of two polarizing beam splitters, a quarter-wave plate, a Faraday rotator, and a polarizer. An additional phase delay is introduced by application of an electrical current to the Faraday rotator or by rotation of the polarizer (the latter is of topological origin), which permits the use of techniques of phase-stepping interferometry.     

Closed-loop aberration correction by use of a modal Zernike wave-front sensor

We describe the practical implementation of a closed-loop adaptive-optics system incorporating a novel modal wave-front sensor. The sensor consists of a static binary-phase computer-generated holographic element, which generates a pattern of spots in a detector plane. Intensity differences between symmetric pairs of these spots give a direct measure of the Zernike mode amplitudes that are present in the input wave front. We use a ferroelectric liquid-crystal spatial light modulator in conjunction with a 4-f system and a spatial filter as a wave-front correction element. We present results showing a rapid increase in Strehl ratio and focal spot quality as the system corrects for deliberately introduced aberrations.     

Interrogation technique for a fiber Bragg grating sensing array based on a Sagnac interferometer and an acousto-optic modulator

We propose and experimentally demonstrate a novel real-time interrogation technique for a fiber Bragg grating (FBG) sensing system that is based on a frequency-shifted asymmetric Sagnac interferometer. FBG sensors are connected to the Sagnac loop by an optical coupler, and an acousto-optic modulator (AOM) is asymmetrically placed in the Sagnac loop. By linearly sweeping the driving frequency of the AOM, the environmental variation around each FBG sensor can be determined by measuring the spectrum of the interference signals of the two counterpropagating light beams reflected by the corresponding FBG. The system has the advantages of low cost and real-time sensing.     

Nearly diffraction-limited laser focal spot obtained by use of an optically addressed light valve in an adaptive-optics loop

We demonstrate correction of laser wave-front distortions by use of an adaptive-optical technique based on a light valve. The setup consists of an achromatic and adjustable-sensitivity wave-front sensor and a wave-front corrector relying on an optically addressed liquid-crystal spatial light modulator. Experimental results with strongly aberrated beams focused close to the diffraction limit are presented for the cw regime. Additional experiments with pulses and measurement of damage thresholds show that this approach is relevant for spatial phase correction of ultraintense laser pulses.     

光子计数剪切干涉仪波前探测自适应光学系统噪声分析

在自适应光学系统中，波前探测器的噪声是主要误差源。针对我们建立的２．１６ｍ望远镜红外自适应光学系统，从伺服控制系统的角度分析了光子计数噪声及其在系统闭环过程中的传递，从理论上推导了系统的噪声功率谱、伺服传递函数以及开环和闭环噪声公式。另外，还给出了在系统中实测的开环和闭环噪声