Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering

We describe modeling and simulation results for the Thirty Meter Telescope on the degradation of sodium laser guide star Shack-Hartmann wavefront sensor measurement accuracy that will occur due to the spatial structure and temporal variations of the mesospheric sodium layer. By using a contiguous set of lidar measurements of the sodium profile, the performance of a standard centroid and of a more refined noise-optimal matched filter spot position estimation algorithm is analyzed and compared for a nominal mean signal level equal to 1000 photodetected electrons per subaperture per integration time, as a function of subaperture to laser launch telescope distance and CCD pixel readout noise. Both algorithms are compared in terms of their rms spot position estimation error due to noise, their associated wavefront error when implemented on the Thirty Meter Telescope facility adaptive optics system, their linear dynamic range, and their bias when detuned from the current sodium profile.     

Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors

Noise effects induced by laser guide star (LGS) elongation have to be considered globally in a multi-LGS tomographic reconstruction analysis. This allows a fine estimation of performance and the comparison of different launching options. We present a modal analysis of the wavefront error with Shack-Hartmann wavefront sensors based on quasi-analytical matrix formalism. Including spot elongation and the Rayleigh fratricide effect, edge launching produces similar performance to central launching and avoids the risk of possible underestimation of fratricide scatter. Performance improves slightly with an optimized centroid estimator and is not affected by a slight field-of-view truncation of the subapertures. Finally we discuss detector characteristics for a LGS Shack-Hartmann wavefront sensor.     

Shack Hartmann wave-front measurement with a large F-number plastic microlens array

A new plastic microlens array, consisting of 900 lenslets, has been developed for the Shack Hartmann wave-front sensor.The individual lens is 300 μm × 300μm and has a focal length of 10 mm, which provides the same focal size, 60 μm in diameter, with a constant peak intensity. One can improve thewave-front measurement accuracy by reducing the spot centroiding error by averaging a few frame memories of an image processor. A deformable mirror for testing the wave-front sensor gives anappropriate defocus and astigmatism, and the laser wave front is measured with a Shack Hartmann wave-front sensor. The measurement accuracy and reproducibility of our wave-front sensor are better than λ/20 and λ/50 (λ = 632.8 nm),respectively, in rms.     

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.     

Return flux budget of polychromatic laser guide stars

The polychromatic laser guide star (PLGS) is one of the solutions proposed to extend the sky coverage by large telescopes to 100% by enabling a complete knowledge of all perturbation orders of the wavefront. The knowledge of the tip-tilt is deduced from the monitoring of the chromatic components of the PLGS, from 330 nm to the visible or near infrared. Here we study the original scheme to create the PLGS by resonant excitation of the mesospheric sodium by two pulsed lasers (tens of kilohertz repetition rate, tens of watts average power, tens of nanoseconds pulse duration), at 589 and 569 nm, respectively. The efficiency of this process is investigated numerically by means of both Bloch equation and rate equation models. The influence of numerous laser parameters is studied. In the best case, having optimized all laser parameters, the return flux at 330 nm should not exceed 7x10(4) photons/s/m2 for 2x18 W laser average power at the mesosphere. This maximum is obtained for a modeless laser whose spot diameter corresponds to 4 times the diffraction limit. For a diffraction-limited spot, the return flux falls down to 4x10(4)photons/s/m2.     

Microchannel plate cross-strip detectors with high spatial and temporal resolution

The cross-strip imaging readout employs charge division, and centroiding, of microchannel plate charge signals detected on two orthogonal layers of sense strips to encode event X-Y positions and times. We have developed cross-strip detectors and fully parallel channel position encoding electronics. The front-end amplifiers utilize two 32-channel pre-amplifier ASICs that send signals to a full 64-channel 60 MHz ADC circuit followed by a FPGA event-processing board. Tests with a software Finite Impulse Response filter and centroiding algorithm demonstrate <10mm resolution with a 32mm cross-strip anode detector using low microchannel plate gain (～10(6)). The self-triggered event timing accuracy is 750 ps, and the system is capable of encoding photons at >1 MHz in combination with firmware-based FPGA centroiding algorithms.     

Intrinsic limitations of Shack-Hartmann wavefront sensing on an extended laser guide source

In this paper we investigate the behavior of various centroiding methods (weighted center of gravity, matched filtering, and correlation) classically used in Shack-Hartmann wavefront sensing when dealing with an elongated asymmetric spot. We study the impact of model errors on these centroiding methods at high signal-to-noise ratios, and, using a one-dimensional formalism, we show that the associated estimates all suffer from a bias uncorrelated with the actual spot displacement if its shape is not known precisely. Additionally, we show that the correlation method provides an estimate with a unitary gain whatever the parameters used, while the other two methods introduce a non-unitary gain in the estimation process. Finally, we show that the sampling of the spot structures after filtering by some convolution kernels is crucial to get an unbiased estimate of the spot displacement.     

Tilt angular anisoplanatism and a full-aperture tilt-measurement technique with a laser guide star

A method is presented for sensing atmospheric wave-front tilt from a laser guide star (LGS) by observing a laser beacon with auxiliary telescopes. The analysis is performed with a LGS scatter model and Zernike polynomial expansion of wave-front distortions. It is shown that integration of the LGS image over its angular extent and the position of the auxiliary telescope in an array reduce the tilt sensing error associated with the contribution from the downward path. This allows us to single out only the wave-front tilt of the transmitted beam on the uplink path that corresponds to the tilt for the scientific object. The tilt angular correlation is analyzed in the atmosphere with a finite turbulence outer scale. The tilt correlation angle depends on the angular size of the telescope and the outer scale of turbulence. The tilt sensing error increases with the auxiliary telescope diameter, suggesting that an auxiliary telescope must be small. The Strehl ratio associated with the contribution from the downward path is in the range from 0.1 to 0.9 when the relative telescope diameter D/r(0) varies from 4 to 93 and the turbulence outer scale is in the 10-150-m range. Tilt correction increases the Strehl ratio compared with the uncorrected image for all the system parameters and seeing conditions considered. The method discussed gives a higher performance than the conventional technique, which uses an off-axis natural guide star. A scheme for measuring tilt with a beam projected from a small aperture is described. This scheme allows us to avoid phosphorescence of the main optical train for a sodium LGS.     

Turbulence-induced zernike aberrations of optical wavefronts in partial adaptive compensation

Abstract

The residual phase error after correction for turbulence-induced phase aberrations by a partially compensating adaptive optics system with a laser guide star (LGS) as reference is computed by using the phase expansion on the Zernike polynomials. To get the most from the compensation, the limitation due to the actuator spacing of a deformable mirror, temporal lag and angular separation between the object and the LGS (anisoplanatism effect) have been analysed in this paper. If Fried's parameter r₀ is 10.7 cm, the temporal lag should be less than 2ms for a sodium LGS. Also the higher the aberration radial degree is, the less the actuator spacing is required. To correct for aberration of radial degree higher than 4 (if r₀ is 10.7 cm), the actuator spacing should be less than 300mm.     

Analysis of the cornea-to-PMMA ablation efficiency rate

The relative ablation efficiency at different materials (in particular human cornea and poly(methyl methacrylate) (PMMA)) was analysed. A comprehensive model, which directly considers applied correction, including astigmatism, as well as laser beam characteristics and ablative spot properties has been developed. The model further provides a method to convert the deviations in achieved ablation observed in PMMA to equivalent deviations in the cornea. Radiant exposures from about 90?mJ/cm² to about 500?mJ/cm² correspond to cornea-to-PMMA ablation ratios of about 9 and about 1.7, respectively (about 7 and 1.3 optically). Super-Gaussian order from simple Gaussian profile to flat-top profile, and for a radiant exposure of 250?mJ/cm², correspond to cornea-to-PMMA ratios of about 2.3 and about 1.6, respectively (about 1.7 and about 1.2 optically). For a Gaussian beam of 160?mJ/cm² radiant exposure, a severe overcorrection of +50% in PMMA corresponds only to an overcorrection of +29% on corneal tissue, whereas a moderate overcorrection of +20% in PMMA corresponds to an overcorrection of +12% on corneal tissue. For a severe undercorrection of ?50% ablation observed in PMMA, the range for radiant exposures from about 90?mJ/cm² to about 500?mJ/cm² correspond to corneal undercorrections of about ?14% to about ?40%, respectively. The proposed model can be used for calibration, ablation pattern test and development, verification and validation purposes of laser systems used for ablation processes at relatively low cost and would directly improve the quality of results.     

Homogenization of Carbides in Ni60/WC Composite Coatings Made by Fiber Laser Remelting

In the current study, the effect of laser remelting on homogenization of carbides in WC-reinforced Ni60 composite coatings was investigated. Ni60 + 50 wt% WC composite coatings were fabricated on the surface of Q550 steel by LDF4000-100 fiber laser device. First cladding layer was made by rectangle laser spot and then circular laser spot was utilized to remelt the coatings. Microstructure characteristics were investigated by optical microscope and scanning electron microscopy. Elemental distribution and phase constitution were analyzed by energy disperse spectroscopy and X-ray diffraction. The results showed that accumulation of residual WC particles was sufficiently eliminated under the effect of laser remelting. The irregularly shaped carbides in first cladding layer were transformed into well-distributed polygonal carbides by laser remelting. Statistical analysis indicated median size of reinforcement particles decreased from 35.40 to 5.62 µm. Microhardness of remelted region had a smooth profile and decreased by ?50 HV_0.1 than that of first cladding region. Homogenization of carbides in nickel composite coating was well realized by laser remelting.     

Impact of sodium laser guide star fratricide on multi-conjugate adaptive optics systems

Laser beams projected from the ground to form sodium layer laser guide stars (LGSs) for adaptive optics (AO) systems experience scattering and absorption that reduce their intensity as they propagate upward through the atmosphere. Some fraction of the scattered light will be collected by the other wavefront sensors and causes additional background in parts of the pupil. This cross-talk between different LGS wavefront sensors is referred to as the fratricide effect. In this paper we quantify the magnitude of four different sources of scattering/absorption and backscattering, and we evaluate their impact on performance with various zenith angles and turbulence profiles for one particular AO system. The resulting wavefront error for the Thirty Meter Telescope (TMT) multi-conjugate AO (MCAO) system, NFIRAOS, is on the order of 5 to 20 nm RMS, provided that the mean background from the fratricide effect can be calibrated and subtracted with an accuracy of 80%. We also present the impact on system performance of momentary variations in LGS signal levels due to variations in cirrus absorption or laser power, and we show that this affects the performance more than does an equal variation in the level of the fratricide.     

Methods for correcting tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics

Multiconjugate adaptive optics (MCAO) is a technique for correcting turbulence-induced phase distortions in three dimensions instead of two, thereby greatly expanding the corrected field of view of an adaptive optics system. This is accomplished with use of multiple deformable mirrors conjugate to distinct ranges in the atmosphere, with actuator commands computed from wave-front sensor (WFS) measurements from multiple guide stars. Laser guide stars (LGSs) must be used (at least for the forseeable future) to achieve a useful degree of sky coverage in an astronomical MCAO system. Much as a single LGS cannot be used to measure overall wave-front tilt, a constellation of multiple LGSs at a common range cannot detect tilt anisoplanatism. This error alone will significantly degrade the performance of a MCAO system based on a single tilt-only natural guide star (NGS) and multiple tilt-removed LGSs at a common altitude. We present a heuristic, low-order model for the principal source of tilt anisoplanatism that suggests four possible approaches to eliminating this defect in LGS MCAO: (i) tip/tilt measurements from multiple NGS, (ii) a solution to the LGS tilt uncertainty problem, (iii) additional higher-order WFS measurements from a single NGS, or (iv) higher-order WFS measurements from both sodium and Rayleigh LGSs at different ranges. Sample numerical results for one particular MCAO system configuration indicate that approach (ii), if feasible, would provide the highest degree of tilt anisoplanatism compensation. Approaches (i) and (iv) also provide very useful levels of performance and do not require unrealistically low levels of WFS measurement noise. For a representative set of parameters for an 8-m telescope, the additional laser power required for approach (iv) is on the order of 2 W per Rayleigh LGS.     

Refractive-index patterning of tellurite glass surfaces by laser spot heating

A dot pattern of a refractive-index change was formed by spot heating with laser-beam irradiation on sodium tellurite glasses. The 15Na(2)O . 85TeO(2) (mol. %) glass doped with 2 mol. % of CoO was irradiated by a green light-beam spot (532 nm) ~800 mum in diameter from the second-harmonic generator of a Q-switched pulsed YAG laser. The map of the refractive index of the glass was determined with an He-Ne laser beam by a scanning ellipsometric technique at a resolution of 100 mum x 50 mum, indicating that the spots possessing a refractive index lower by ~0.05 were formed at the region irradiated by the laser beam.     

Electron emission and acoustic emission from the fracture of graphite/epoxy composites

In past studies it has been shown that the fracture of materials leads to the emission of a variety of species, including electrons, ions, neutral molecules, and photons, all encompassed by the term fracto-emission (FE). In this paper we examine electron emission (EE) from the fracture of single graphite fibres and neat epoxy resin. We also combine measurements of EE with the detection of acoustic emission (AE) during the testing of graphite-epoxy composite specimens with various fibre orientation. The characteristics of these signals are related to known failure mechanisms in fibre-reinforced plastics. This study suggests that by comparing data from AE and FE meausrements, one can detect and distinguish the onset of internal and external failure in composites. EE measurements are also shown to be sensitive to the locus of fracture in a composite material.     

一种无需乘法器的光斑质心定位方法

光斑质心定位在光学精密跟踪和精密测量中是一项关键技术,其精度和速度直接影响了光学测量的精度和响应速度.在实际应用中,往往把灰度重心法与图像预处理方法结合起来,以提高光斑质心计算的可靠性.运用图像预处理技术有效地抑制了噪声的影响,同时也会消耗大量的逻辑资源.针对在资源受限的条件下采用灰度重心法计算光斑质心的问题,本文提出了一种无需乘法器的光斑质心计算方法,用加法运算代替乘法运算,使用递推方法完成质心计算所需的低阶矩的运算.该方法的硬件仅为5个累加器,结构简单,能够以更低的资源消耗实现光斑质心定位.通过并行技术和流水线技术,其工作频率达到515 MHz.实验证明:本文的结构在FPGA内实现,在100 MHz的工作频率下,完成一帧质心计算的延时为0.35μs,误差与传统质心方法一致,占用214个Slices,其资源消耗仅为常规灰度重心法的50%.     

Sampling error analysis of Shack–Hartmann wavefront sensor with variable subaperture pixels

Abstract

The sampling error of a Shack–Hartmann wavefront sensor with variable subaperture pixels is analysed under the consideration of various threshold values and detecting dynamic ranges. A generalized expression, which is used for fitting the sampling error of a Shack-Hartmann wavefront sensor with variable subaperture pixels, is presented. The computational results of the sampling error of a Shack–Hartmann wavefront sensor with different pixel numbers per subaperture, different detecting dynamic ranges, different atmospheric coherence length, different extended degree of the object and the different threshold values are also given. The results indicate that the sampling error of the Shack–Hartmann wavefront sensor is sensitive to the dynamic range of the subaperture, the pixel numbers per subaperture, the extended degree of the object and the coherent length of atmosphere, but not sensitive to the threshold value.     

Self-calibrated subaperture stitching test of hyper-hemispheres using latitude and longitude coordinates

Limited by the f-number of the transmission sphere, it is impossible to test the whole surface of a hyper-hemisphere using a standard interferometer directly. This paper presents an extension of the subaperture stitching test method to hyper hemispheres. The stitching algorithm is based on the coordinate mapping from local measurement frame to a global frame, and overlapping correspondence is calculated by virtue of coordinates of latitude and longitude. The reference surface error is represented by Zernike polynomials and self-calibrated during the stitching to achieve higher accuracy. Then the stitched surface error distribution is presented by map projection. To realize accessibility to the whole surface of a hyper-hemisphere, we also propose a design for the subaperture test platform, according to the subaperture lattice design. Finally, a hemisphere and a full sphere are tested and figured, respectively, to validate the method and the experimental setup.     

A Large-Area PVDF Pyroelectric Sensor for CO 2 Laser Beam Alignment

We present the design of a large-area (50 mm times 50 mm) polyvynilidene fluoride (PVDF) pyroelectric sensor array for industrial CO₂ (lambda = 10.6 mum) laser beam positioning. The array dimensions were chosen to match the area typically monitored in the alignment procedure of external optics (beam steering moving arm system, for example) used to redirect the laser beam from the laser output window to a remote working station. The instrument is provided with a tilted, high reflection, ZnSe plate which partially transmits the laser beam onto the sensor array. From positioning simulations with a Gaussian laser intensity profile with a sigma = 3.2 mm standard deviation (equivalent spot size 3sigma cong 20 mm), the positional accuracy along the two orthogonal array dimensions was found to be better than 0.02 mm for an 8 times 8 array and one order of magnitude higher for a 16 times 16 array. The centroid position of a CO₂ industrial laser beam was evaluated by integrating the pyroelectric current for a time comparable to the time duration (100-200 ms) of the laser pulses used in the alignment procedure.