Use of artificial neural networks for Hartmann-sensor lenslet centroid estimation

For adaptive optical systems to compensate for atmospheric-turbulence effects, the wave-front perturbation must be measured with a wave-front sensor (WFS). A Hartmann WFS typically divides the optical aperture into subapertures and then measures the slope of the wave front within each subaperture. Hartmann WFS slope measurements are based on estimating the location of the centroid of the image that is formed from a guide star within each subaperture. Conventional techniques for centroid estimation involve the use of a linear estimator and conversion tables. Neural networks provide nonlinear solutions to this problem. We address the use of neural networks for estimating the location of the centroid from the subaperture image. We find that neural networks provide more accurate estimates over a larger dynamic range and with less variance than do the conventional linear centroid estimator.     

Measuring the centroid gain of a Shack-Hartmann quad-cell wavefront sensor by using slope discrepancy

Shack-Hartmann wavefront sensors (SH WFS) are used by many adaptive optics (AO) systems to measure the wavefront. In this WFS, the centroid of the spots is proportional to the wavefront slope. If the detectors consist of 2 x 2 quad cells, as is the case in most astronomical AO systems, then the centroid measurement is proportional to the centroid gain. This quantity varies with the strength of the atmospheric turbulence and the angular extent of the beacon. The benefits of knowing the centroid gain and current techniques to measure it are discussed. A new method is presented, which takes advantage of the fact that, in a SH-WFS-based AO system, there are usually more measurements than actuators. Centroids in the null space of the wavefront reconstructor, called slope discrepancy measurements, contain information about the centroid gain. Tests using the W. M. Keck Observatory AO system demonstrate the accuracy of the algorithm.     

Hot-air optical turbulence generator for the testing of adaptive optics systems: principles and characterization

A statistically repeatable, hot-air optical turbulence generator, based on the forced mixing of two air flows with different temperatures, is described. Characterization results show that it is possible to generate any turbulence strength up to CN2 Dh approximately 6 x 10(-10) m1/3, allowing a ratio of beam diameter to Fried's parameter as large as D/r0 approximately 25 for one crossing through the turbulator or D/r0 approximately 38 for two crossings. The outer scale (L0 approximately 133 +/- 60 mm) is found to be compatible with the turbulator mixing chamber size (170 mm), and the inner scale (l0 approximately 7.6 +/- 3.8 mm) is compatible with the values in the literature for the free atmosphere. The temporal power spectrum analysis of the centroid of the focused image shows good agreement with Kolmogorov's theory. Therefore the device can be used with confidence to emulate realistic turbulence in a controlled manner. A calibrated CN2 profile, both in layer altitude and strength, is necessary for the testing of off-axis adaptive optics correction (multiconjugate adaptive optics). Testing was done to calibrate the CN2 profile using the slope detection and ranging technique. The first results, with only one layer, show the validity of the approach and indicate that a multiple-pass scheme is viable with a few modifications of the current setup.     

Biased estimators and object-spectrum estimation in the method of deconvolution from wave-front sensing

The method of deconvolution from wave-front sensing (DWFS), which is a method for improving the quality of astronomical images measured through atmospheric turbulence, uses simultaneous shortexposure measurements of both an image and the output of a wave-front sensor exposed to an image of the telescope pupil. The wave-front sensor measurements are used to reconstruct an estimate of the instantaneous generalized pupil function of the telescope, which is used to compute an estimate of the instantaneous optical transfer function (OTF). This estimate of the OTF is then used in a deconvolution procedure. We point out the existence and origin of an unnoticed bias in the estimator for the DWFS method. This bias leads to nonrandom errors in the estimated object spectrum beyond those expected to arise by virtue of low-pass filtering and noise, including the possibility of an overall system transfer function greater than unity at some spatial frequencies. An alternative measurement and postprocessing scheme to overco e this source of error is suggested.     

Image sharpness and beam focus VLSI sensors for adaptive optics

High-resolution wavefront control for adaptive optics requires accurate sensing of a measure of optical quality. We present two analog very-large-scale-integration (VLSI) image-plane sensors that supply real-time metrics of image and beam quality, for applications in imaging and line-of-sight laser communication. The image metric VLSI sensor quantifies sharpness of the received image in terms of average rectified spatial gradients. The beam metric VLSI sensor returns first and second order spatial moments of the received laser beam to quantify centroid and width. Closed-loop wavefront control of a laser beam through turbulence is demonstrated using a spatial phase modulator and analog VLSI controller that performs stochastic parallel gradient descent of the beam width metric.     

Characterization of trabecular bone using the backscattered spectral centroid shift

Ultrasonic attenuation in bone in vivo is generally measured using a through-transmission method at the calcaneus. Although attenuation in calcaneus has been demonstrated to be a useful predictor for osteoporotic fracture risk, measurements at other clinically important sites, such as hip and spine, could potentially contain additional useful diagnostic information. Through-transmission measurements may not be feasible at these sites due to complex bone shapes and the increased amount of intervening soft tissue. Centroid shift from the backscattered signal is an index of attenuation slope and has been used previously to characterize soft tissues. In this paper, centroid shift from signals backscattered from 30 trabecular bone samples in vitro were measured. Attenuation slope also was measured using a through-transmission method. The correlation coefficient between centroid shift and attenuation slope was -0.71. The 95% confidence interval was (-0.86, -0.47). These results suggest that the backscattered spectral centroid shift may contain useful diagnostic information potentially applicable to hip and spine.     

Estimation of laser beam pointing parameters in the presence of atmospheric turbulence

The problem of estimating mechanical boresight and jitter performance of a laser pointing system in the presence of atmospheric turbulence is considered. A novel estimator based on maximizing an average probability density function (pdf) of the received signal is presented. The proposed estimator uses a Gaussian far-field mean irradiance profile, and the irradiance pdf is assumed to be lognormal. The estimates are obtained using a sequence of return signal values from the intended target. Alternatively, one can think of the estimates being made by a cooperative target using the received signal samples directly. The estimator does not require sample-to-sample atmospheric turbulence parameter information. The approach is evaluated using wave optics simulation for both weak and strong turbulence conditions. Our results show that very good boresight and jitter estimation performance can be obtained under the weak turbulence regime. We also propose a novel technique to include the effect of very low received intensity values that cannot be measured well by the receiving device. The proposed technique provides significant improvement over a conventional approach where such samples are simply ignored. Since our method is derived from the lognormal irradiance pdf, the performance under strong turbulence is degraded. However, the ideas can be extended with appropriate pdf models to obtain more accurate results under strong turbulence conditions.     

低信噪比下扩展目标质心的高精度计算方法

分析了扩展目标在Shack-Hartmann传感器中的成像特点。针对成像特点,提出了一种提取子光斑位置的质心计算方法。该方法应用多阈值分割和多结构元形态学去噪预处理后再进行质心计算。在信噪比低、扩展度大的情况下,能够有效地抑制噪声,减小噪声对质心计算精度的影响。在不同信噪比和扩展度下,相对于一般质心方法,该方法能够显著地提高探测精度。当信噪比为0.5,扩展度达13时,该方法的平均绝对误差不到1个像素。     

高精度星敏感器星点光斑质心算法

高精度星敏感器星点光斑的质心精度是星敏感器整体精度的基础,它需要达到角秒级的量级。因此,提出了一种基于亚像元相关法的星像质心算法。这种算法是利用互相关匹配实现图像定位的原理,将星像质心定位到亚像素上来提高质心精度。它可以克服由于系统误差和图像采集所带来的误差。根据系统的光学参数设计以及星像的光谱、亮度及其在视场中的位置特征,仿真得到点列图模型,针对视场内与光轴的不同夹角仿真制作一系列亚像元理想模板,然后对星像加高斯随机噪声,把有随机噪声的星像与理想星像进行相关运算来求星像质心精度。通过仿真实验,得到相关法具有较高的星像质心精度,定位精度可以优于1/12个像素的量级。     

基于Radon变换的合成孔径声纳多普勒中心估计

不准确的多普勒中心估计会显著降低合成孔径声纳图像质量。基于多普勒中心与斜视角直接相关的事实，提出了一种使用Radon变换估计多普勒中心的方法。仿真结果说明，此方法是有效的，可用于低信噪比、大斜视角情况下的多普勒中心估计。     

PSF dedicated to estimation of displacement vectors for tissue elasticity imaging with ultrasound

This paper investigates a new approach devoted to displacement vector estimation in ultrasound imaging. The main idea is to adapt the image formation to a given displacement estimation method to increase the precision of the estimation. The displacement is identified as the zero crossing of the phase of the complex cross-correlation between signals extracted from the lateral direction of the ultrasound RF image. For precise displacement estimation, a linearity of the phase slope is needed as well as a high phase slope. Consequently, a particular point spread function (PSF) dedicated to this estimator is designed. This PSF, showing oscillations in the lateral direction, leads to synthesis of lateral RF signals. The estimation is included in a 2-D displacement vector estimation method. The improvement of this approach is evaluated quantitatively by simulation studies. A comparison with a speckle tracking technique is also presented. The lateral oscillations improve both the speckle tracking estimation and our 2-D estimation method. Using our dedicated images, the precision of the estimation is improved by reducing the standard deviation of the lateral displacement error by a factor of 2 for speckle tracking and more than 3 with our method compared to using conventional images. Our method performs 7 times better than speckle tracking. Experimentally, the improvement in the case of a pure lateral translation reaches a factor of 7. Finally, the experimental feasibility of the 2-D displacement vector estimation is demonstrated on data acquired from a Cryogel phantom.     

High-resolution lidar observations of mesospheric sodium and implications for adaptive optics

Observations of sodium density variability in the upper mesosphere/lower thermosphere, obtained using a high-resolution lidar system, show rapid fluctuations in the sodium centroid altitude. The temporal power spectrum extends above 1 Hz and is well-fit by a power law having a slope that is -1.95±0.12. These fluctuations produce focus errors in adaptive optics systems employing continuous-wave sodium laser guide stars, which can be significant for large-aperture telescopes. For a 30 m aperture diameter, the associated rms wavefront error is approximately 4 nm per meter of altitude change and increases as the square of the aperture diameter. The vertical velocity of the sodium centroid altitude is found to be ~23 ms(-1) on a 1 s time scale. If these high-frequency fluctuations arise primarily from advection of horizontal structure by the mesospheric wind, our data imply that variations in the sodium centroid altitude on the order of tens of meters occur over the horizontal scales spanned by proposed laser guide star asterisms. This leads to substantial differential focus errors (~107 nm over a 1 arc min separation with a 30 m aperture diameter) that may impact the performance of wide-field adaptive optics systems. Short-lasting and narrow sodium density enhancements, more than 1 order of magnitude above the local sodium density, occur due to advection of meteor trails. These have the ability to change the sodium centroid altitude by as much as 1 km in less than 1 s, which could result in temporary disruption of adaptive optics systems.     

Wavefront error caused by centroid position random error

The wavefront error caused by centroid position random error is derived in detail, and an exact formula, which evaluates the wavefront error associated with the centroid position random error, is obtained when the Zernike modes are used as the basis for wavefront reconstruction. The formula is proved by two Shack–Hartmann wavefront sensors with different wavefront reconstruction matrices, and it can precisely describe the wavefront measuring error caused by centroid position random error.     

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.     

Processing wave-front-sensor slope measurements using artificial neural networks

For adaptive-optics systems to compensate for atmospheric turbulence effects, the wave-front perturbation must be measured with a wave front sensor (WPS), and key parameters of the atmosphere and the adaptive-optics system must be known. Two parameters of particular interest include the Fried coherence length r(0) and the WPS slope measurement error. Statistics-based optimal techniques, such as the minimum variance phase reconstructor, have been developed to improve the imaging performance of adaptive-optics systems. However, these statistics-based models rely on knowledge of the current state of the key parameters. Neural networks provide nonlinear solutions to adaptive-optics problems while offering the possibility of adapting to changing seeing conditions. We address the use of neural networks for three tasks: (l) to reduce the WPS slope measurement error, (2) to estimate the Fried coherence length r(0), and (3) to estimate the variance of the WPS slope measurement error. All of these tasks are accomplished by using only the noisy WPS measurements as input. Where appropriate, we compare our method with classical statistics-based methods to determine if neural networks offer true benefits in performance. Although a statistics-based method is found to perform better than a neural network in reducing WPS slope measurement error, neural networks perform better in estimating the variance of the WPS slope measurement error, and both methods perform well in estimating r(0).     

New a posteriori error estimator and adaptive mesh refinement strategy for 2-D crack problems

A posteriori error estimation and adaptive refinement technique for fracture analysis of 2-D/3-D crack problems is the state-of-the-art. The objective of the present paper is to propose a new a posteriori error estimator based on strain energy release rate (SERR) or stress intensity factor (SIF) at the crack tip region and to use this along with the stress based error estimator available in the literature for the region away from the crack tip. The proposed a posteriori error estimator is called the K-S error estimator. Further, an adaptive mesh refinement (h-) strategy which can be used with K-S error estimator has been proposed for fracture analysis of 2-D crack problems. The performance of the proposed a posteriori error estimator and the h-adaptive refinement strategy have been demonstrated by employing the 4-noded, 8-noded and 9-noded plane stress finite elements. The proposed error estimator together with the h-adaptive refinement strategy will facilitate automation of fracture analysis process to provide reliable solutions.     

光斑质心亚像素定位误差的实验研究

根据误差的来源将光斑质心亚像素定位误差归类为随机误差和系统误差,提出一种简单有效的实验方法对光斑质心定位误差进行定量测试.利用高精度一维电动平移台、POINT GREY Flea2-14S3 CCD相机和LED光源构建了测试系统,对测试结果进行研究和讨论,发现了测试系统LED光斑质心定位系统误差的周期性变化规律,计算得到了基于Flea2-14S3 CCD相机的光斑质心定位随机误差为0.018 pixels,系统误差为0.06 pixels,总体误差为0.063 pixels(约1/15 pixels),能够应用于以光斑质心检测为手段的测量系统中.实验表明,该测试系统可以作为估算光斑质心定位误差大小的一种有效的手段.     

Computed tomography postacquisition data correction for systemalignment errors

A critical issue in obtaining high-quality images from a computed tomography system is the mechanical alignment of the data acquisition system. This paper will compare two methods of measuring and correcting errors introduced into second-generation computed tomography data sets from misalignment of the system. Both of these methods use a projection data set from a complete scan of an object as a starting point. One method is an iterative method that looks at residual errors in selected portions of the reconstructed image. The other method requires that the centroids of the projection data coincide with the centroid of the object. It will be shown that the centroid registration algorithm can be used to accurately measure a number of important computed tomography system alignment parameters and is mathematically efficient. The residual error algorithm will be shown to give less satisfactory results     

Application of new error estimators based on gradient recovery and external domain approaches to 2D elastostatics problems

Two new error estimators for the BEM in 2D potential problems were recently presented by the authors. This work extends these two error estimators for 2D elastostatics problems. The first approach involves a local error estimator based on a gradient recovery procedure in which the error function is based on differences between smoothed and non-smoothed rates of change of boundary variables in the local tangential direction. The second approach is associated with the external problem formulation and gives both local and global measures of the error, depending on a choice of the external evaluation point. These approaches are post-processing procedures. Both estimators show consistency with mesh refinement and give similar qualitative results. The error estimator using the gradient recovery approach presents a more general characteristic as its formulation does not rely on an ‘optimal’ choice of an external parameter, such as in the case of the external domain error estimator. Also, the external domain error estimator can be used only for domains in which an exterior region exists. For example, the external domain error estimator cannot be used for an infinite domain with a crack, because a point in the exterior region (inside the crack) will not be at a finite distance to the crack surface.     

Determination of the optimal form and dimension of the marker of a digital autocollimator

The dependence of the error of an estimator of the center of gravity of a marker’s light spot in a digital image on the form and dimension of the marker is studied. The optimal parameters of the marker from the point of view of minimization of the error of measurements performed by means of a digital autocollimator are determined.