Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing

Adaptive optics provides a real-time compensation for atmospheric turbulence that severely limits the resolution of ground-based observation systems. The correction quality relies on a key component, that is, the wavefront sensor (WFS). When observing extended sources, WFS precision is limited by anisoplanatism effects. Anisoplanatism induces a variation of the turbulent phase and of the collected flux in the field of view. We study the effect of this phase and scintillation anisoplanatism on wavefront analysis. An analytical expression of the error induced is given in the Rytov regime. The formalism is applied to a solar and an endoatmospheric observation. Scintillation effects are generally disregarded, especially in astronomical conditions. We shall prove that this approximation is not valid with extended objects.     

Characteristic functions of Hartmann-Shack wavefront sensors and laser-ray-tracing aberrometers

It is shown that the aberration estimated at any point of the pupil using wavefront slope aberrometers such as Hartmann-Shack wavefront sensors or laser ray tracers is a spatial average of the actual aberration weighted by a characteristic function that depends on the aberrometer design and on the estimation procedure. This characteristic function, whose explicit form is given here for wavefront slope aberrometers using either modal or zonal estimators, may be useful in analyzing some basic aspects of the aberrometer performance. It is also instrumental in establishing the links between the statistical properties of the actual and the estimated aberrations. Explicit formulas are given to show in terms of this function how the bias arises in the first- and second-order statistics of the retrieved aberrations. This approach is mathematically equivalent to the analysis of the effects of modal coupling (cross-coupling and aliasing). It may provide, however, some complementary insight.     

Semi-open queuing networks: a review of stochastic models,solution methods and new research areas

Capturing the waiting times (at an external queue) for a customer to access a movable resource is an important step towards measuring customer service and system performance in manufacturing, logistics, communication and health care systems. Such waiting time measures are typically used for sizing resource and buffer capacities, and thereby minimising customer waiting time probabilities. In this regard, semi-open queuing networks (SOQNs), which decouple the arriving customers/transactions from the network resources using a synchronisation station (also known as a semaphore queue), can potentially capture the customer/transaction waiting times/costs more precisely and provide a rich network modelling construct. Hence, modelling manufacturing or service systems using SOQNs is an important step towards measuring customer flow times (sojourn times) wherein the customer waiting times at an external queue are a critical component. In this paper, we present several stochastic models for manufacturing and service systems using SOQNs and also discuss the potential applications of SOQNs. We then review the solution methods for SOQNs and also compare the numerical accuracies for three promising methods. Finally, we include the potential research areas in SOQNs.     

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.     

Optimization of sensing parameters for a confocal signal-based wavefront corrector in microscopy

The accuracy of a confocal signal-based wavefront corrector depends on several parameters such as spatial variation of optical properties within the specimen, aberration magnitude and composition, time required for the correction, etc. Here, a numerical analysis has been performed with the aim to improve system performance. The goal of the search algorithm in a confocal signal-based wavefront corrector is to estimate the Zernike coefficients of the aberrations. High-magnitude aberrations show low Strehl ratios. Repeating the correction process results in higher Strehl ratios, but at the cost of increased time. An in-focus on-axis specimen results in higher Strehl ratio compared to an out-of-focus and off-optical-axis specimen. For all cases, the wavefront correction accuracy is better, when the diameter of the pinhole is chosen to be equal to that of the Airy disk. The lower limit on the pinhole size for detecting small magnitude aberrations is set by noise.     

Wavelet penalized likelihood estimation in generalized functional models

The paper deals with generalized functional regression. The aim is to estimate the influence of covariates on observations, drawn from an exponential distribution. The link considered has a semiparametric expression: if we are interested in a functional influence of some covariates, we authorize others to be modeled linearly. We thus consider a generalized partially linear regression model with unknown regression coefficients and an unknown nonparametric function. We present a maximum penalized likelihood procedure to estimate the components of the model introducing penalty based wavelet estimators. Asymptotic rates of the estimates of both the parametric and the nonparametric part of the model are given and quasi-minimax optimality is obtained under usual conditions in literature. We establish in particular that the ? ¹-penalty leads to an adaptive estimation with respect to the regularity of the estimated function. An algorithm based on backfitting and Fisher-scoring is also proposed for implementation. Simulations are used to illustrate the finite sample behavior, including a comparison with kernel- and spline-based methods.     

Optimization of star-oriented and layer-oriented wavefront sensing concepts for ground layer adaptive optics

Multiconjugate adaptive optics is one of the major challenges in adaptive optics. It requires the measurement of the volumic distribution of the turbulence. Two wavefront sensing (WFS) concepts have been proposed to perform the wavefront analysis for such systems: the star-oriented and layer-oriented approaches. We give a performance analysis and a comparison of these two concepts in the framework of the simplest of the multi-guide-star adaptive optics systems, that is, ground layer adaptive optics. A phase-related criterion is proposed to assess analytically the performance of both concepts. This study highlights the main advantages and drawbacks of each WFS concept and shows how it is possible to optimize the concepts with respect to the signal to noise ratio on the phase measurement. A comparison of their optimized versions is provided and shows that one can expect very similar performance with the two optimized concepts.     

Railway track allocation: models and methods

Efficiently coordinating the movement of trains on a railway network is a central part of the planning process for a railway company. This paper reviews models and methods that have been proposed in the literature to assist planners in finding train routes. Since the problem of routing trains on a railway network entails allocating the track capacity of the network (or part thereof) over time in a conflict-free manner, all studies that model railway track allocation in some capacity are considered relevant. We hence survey work on the train timetabling, train dispatching, train platforming, and train routing problems, group them by railway network type, and discuss track allocation from a strategic, tactical, and operational level.     

Random phase plate for wavefront sensing via phase retrieval and a volume speckle field

A random phase plate is prepared by illuminating a photoresist plate with a fully developed speckle field and using the developed phase plate (DPP) as a diffuser. Wavefront sensing is implemented using phase retrieval based on the recording of speckle intensity patterns at various distances from the DPP and the wave propagation equation. The effects of the roughness height of the DPP on the phase retrieval are investigated. From simulations a roughness height of lambda/10 results in a speckle field that yields good phase reconstruction for the spherical test wavefront incident on the DPP. From the experiments different portions of the DPP that received varying exposures are examined. A section of the phase plate with a characteristic roughness height facilitated the generation of a speckle field that is optimum for the phase retrieval algorithm. Thus a random phase plate with varying roughness height allows optimized measurements of wavefronts with different curvatures. Analytical expressions describing the second-order intensity statistics (fourth-order field statistics) for a field traversing a specific diffuser are presented. This DPP will not give rise to a fully developed speckle field, but knowing the statistics of the depth of the DPP will facilitate a rigorous treatment of the problem.     

On the efficacy of stochastic collocation,stochastic Galerkin,and stochastic reduced order models for solving stochastic problems

The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method. Rather, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.     

Strain and stress computations in stochastic finite element methods

This paper focuses on the computation of statistical moments of strains and stresses in a random system model where uncertainty is modeled by a stochastic finite element method based on the polynomial chaos expansion. It identifies the cases where this objective can be achieved by analytical means using the orthogonality property of the chaos polynomials and those where it requires a numerical integration technique. To this effect, the applicability and efficiency of several numerical integration schemes are considered. These include the Gauss–Hermite quadrature with the direct tensor product—also known as the Kronecker product—Smolyak's approximation of such a tensor product, Monte Carlo sampling, and the Latin Hypercube sampling method. An algorithm for reducing the dimensionality of integration under a direct tensor product is also explored for optimizing the computational cost and complexity. The convergence rate and algorithmic complexity of all of these methods are discussed and illustrated with the non‐deterministic linear stress analysis of a plate. Copyright © 2007 John Wiley & Sons, Ltd.     

Detection of distortions in models of stochastic systems

Objects described by stochastic differential equations and the associated control systems under the conditions of possible distortions in models generating these systems are considered. A solution of problems of detecting and diagnostics of distortions which utilizes sequential decision rules and the maximum of posterior probability criterion is validated. As an application, and efficient algorithm of the fastest detection of a maneuver of a moving object which assesses the given probabilities of the type I and type II errors is developed. The necessary programming system is established and positive results of computational experiments are obtained. Translated from Izmeritel'naya Tekhnika, No. 3, pp. 9–11, March, 1996.     

On estimating Weibull modulus by moments and maximum likelihood methods

The effect of true Weibull modulus and sample size on Weibull modulus estimated by moments and maximum likelihood methods was investigated. Results indicated that the value of true Weibull modulus had no effect on estimated modulus for the maximum likelihood method, and a strong effect for the moments method, especially when sample size was less than 30. In addition, the distribution of Weibull modulus estimated by both methods was investigated using the modified Anderson–Darling statistics for goodness of fit. It was found that the distribution was not normal, lognormal, 3-parameter Weibull, or 3-parameter log-Weibull for the maximum likelihood method, as reported in previous studies. For the moments method however, the distribution of normalized Weibull moduli was found to be lognormal for sample sizes of 40 and above. The other three distributions showed a significant level of lack-of-fit at all sample sizes. An erratum to this article can be found at     

Image field distribution model of wavefront aberration and models of distortion and field curvature

The distribution model of wavefront aberrations, which takes on a significant role in the designs and alignments of imaging optical systems without vignetting, is newly presented. This model decomposes the complicated distributions into the characteristic components, which clarifies the alignment criteria. For the actual alignments, only small displacements (decentering, tilt, and surface distance) of rotationally symmetric surfaces in the system are assumed. Then, the model, which regards the aberration distributions of the system as the sum of the contributions of each surface, is extended for the system with surface displacements. As a result of the derivation, it is concluded that the aberration distributions in the rotationally nonsymmetric systems can be expressed as the sum of several folds of rotationally symmetric components. In addition, it is presented that, based on this model, suitable distribution models, even of the arbitrary higher order, can be constructed for any aberration coefficients in various optical systems.     

The berth allocation problem: models and solution methods

In this paper, we consider the problem of allocating space at berth for vessels with the objective of minimizing total weighted flow time. Two mathematical formulations are considered where one is used to develop a tree search procedure while the other is used to develop a lower bound that can speed up the tree search procedure. Furthermore, a composite heuristic combining the tree search procedure and pair-wise exchange heuristic is proposed for large size problems. Finally, computational experiments are reported to evaluate the efficiency of the methods. Correspondence to: Raymond K. CheungThe authors would like to thank the helpful comments of two anonymous referees and the editors. The research was supported in part by Grant HKUST6039/01E of the Research Grant Council of Hong Kong