The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Hosoon Yang - One of the best experts on this subject based on the ideXlab platform.
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integration of differential wavefront sampling with Merit Function regression for efficient alignment of three mirror anastigmat optical system
Proceedings of SPIE, 2010Co-Authors: Seonghui Kim, Yunjong Kim, Hanshin Lee, Sug Whan Kim, Hosoon YangAbstract:ABSTRACT We first studied the characteristics of alignment performances of two computer-aided alignment algorithms i.e. Merit Function regression (MFR) and di fferential wavefront sampling (DWS). The initial study shows i) that, utilizing damped least square algorithm, MFR offers accurate alignment estimation to the optical systems with non-linear wavefront sensitivity to changes in alignment parameters, but at the expense of neglecting the coupling effects among multiple optical components, and ii) that DWS can estimate the alignment state while taking the inter-element coupling effects into consideration, but at the expense of increased sensitivity to measurement error associated with experiment apparatus. Following the aforementioned study, we report a new improved alignment computation technique benefitted from modified MFR computation incorporating the concept of standard DWS method. The optical system used in this study is a three-mirror anastignmat (TMA) based optical design for the next generation geostationary ocean color instrument (GOCI-II). Using an aspheric primary mirror of 210 mm in diameter, the F/7.3 TMA design offers good imaging performance such as 80% in 4 um in GEE, MTF of 0.65 at 65.02 in Nyquist frequency. The optical system is designed to be packaged into a compact dimension of 0.25m × 0.55m × 1.050m. The trial simulation runs demonstrate that this integrated alignment method show much better alignment estimation accuracies than those of standard MFR and DWS methods, especially when in presence of measurement errors. The underlying concept, computational details and trial simulation results are presented together w ith implications to potential applications. Keywords: Alignment, Merit Function regression, Differential wavefront sampling, Zernike polynomial, Three mirror anastigmat
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Merit Function regression method for efficient alignment control of two mirror optical systems
Optics Express, 2007Co-Authors: Hosoon YangAbstract:The precision alignment of high-performance, wide-field optical systems is generally a difficult and often laborious process. We report a new Merit Function regression method that has the potential to bring to such an optical alignment process higher efficiency and accuracy than the conventional sensitivity table method. The technique uses actively damped least square algorithm to minimize the Zernike coefficient-based Merit Function representing the difference between the designed and misaligned optical wave fronts. The application of this method for the alignment experiment of a Cassegrain type collimator of 900mm in diameter resulted in a reduction of the mean system rms wave-front error from 0.283λ to 0.194λ, and in the field dependent wave-front error difference from ±0.2λ to ±0.014λ in just two alignment actions. These results demonstrate a much better performance than that of the conventional sensitivity table method simulated for the same steps of experimental alignment.
Florian Bociort - One of the best experts on this subject based on the ideXlab platform.
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systematics of the design shapes in the optical Merit Function landscape
Proceedings of SPIE, 2010Co-Authors: Florian Bociort, P Van GrolAbstract:In this paper we describe new properties of the design landscape that could lead in the future to a new way to determine good starting points for subsequent local optimization. While in optimization the focus is usually only on local minima, here we show that points selected in the vicinity of other types of critical points (i.e. points where the Merit Function gradient vanishes) can be very useful starting points. We study here a problem that is simple enough to be analyzed in detail, the design landscape of triplets with variable curvatures. We show here how representatives of all triplet design shapes observed in global optimization runs can be obtained in a simple and systematic way by locally optimizing for each design shape one starting point obtained with the new method. Good approximations of these special starting points are also computed analytically with two theoretical models. We have found a one-to-one correspondence between the possible triplet design shapes and the critical points resulting from a model based on third-order spherical aberration within the framework of thin-lens theory. The same number and properties of critical points are predicted by a second model, which is even simpler and mathematically more general.
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chaotic behavior in an algorithm to escape from poor local minima in lens design
Optics Express, 2009Co-Authors: Maarten Van Turnhout, Florian BociortAbstract:In lens design, damped least-squares methods are typically used to find the nearest local minimum to a starting configuration in the Merit Function landscape. In this paper, we explore the use of such a method for a purpose that goes beyond local optimization. The Merit Function barrier, which separates an unsatisfactory solution from a neighboring one that is better, can be overcome by using low damping and by allowing the Merit Function to temporarily increase. However, such an algorithm displays chaos, chaotic transients and other types of complex behavior. A successful escape of the iteration trajectory from a poor local minimum to a better one is associated with a crisis phenomenon that transforms a chaotic attractor into a chaotic saddle. The present analysis also enables a better understanding of peculiarities encountered with damped least-squares algorithms in conventional local optimization tasks.
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saddle points in the Merit Function landscape of lithographic objectives
Proceedings of SPIE 2005 vol. 5962, 2005Co-Authors: Oana Marinescu, Florian BociortAbstract:The multidimensional Merit Function space of complex optical systems contains a large number of local minima that are connected via links that contain saddle points. In this work, we illustrate a method to construct such saddle points with examples of deep UV objectives and extreme UV mirror systems for lithography. The central idea of our method is that, at certain positions in a system with N surfaces that is a local minimum, a thin meniscus lens or two mirror surfaces can be introduced to construct a system with N+2 surfaces that is a saddle point. When the optimization goes down on the two sides of the saddle point, two minima are obtained. We show that often one of these two minima can be reached from several other saddle points constructed in the same way. The practical advantage of saddle-point construction is that we can produce new designs from the existing ones in a simple, efficient and systematic manner.
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generating saddle points in the Merit Function landscape of optical systems
Proceedings of SPIE 2005 vol. 5962, 2005Co-Authors: Florian Bociort, Maarten Van TurnhoutAbstract:Finding multiple local minima in the Merit Function landscape of optical system optimization is a difficult task, especially for complex designs that have a large number of variables. We discuss here a method that enables a rapid generation of new local minima for optical systems of arbitrary complexity. We have recently shown that saddle points known in mathematics as Morse index 1 saddle points can be useful for global optical system optimization. In this work we show that by inserting a thin meniscus lens (or two mirror surfaces) into an optical design with N surfaces that is a local minimum, we obtain a system with N+2 surfaces that is a Morse index 1 saddle point. A simple method to compute the required meniscus curvatures will be discussed. Then, letting the optimization roll down on both sides of the saddle leads to two different local minima. Often, one of them has interesting special properties.
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the network structure of the Merit Function space of euv mirror systems
Proceedings of SPIE 2005 vol. 5874, 2005Co-Authors: Oana Marinescu, Florian BociortAbstract:The Merit Function space of mirror systems for EUV lithography is studied. Local minima situated in a multidimensional Merit Function space are connected via links that contain saddle points and form a network. In this work we present the first networks for EUV lithographic objectives and discuss how these networks change when control parameters, such as aperture and field are varied and constraints are used to limit the variation domain of the variables. A good solution in a network obtained with a limited number of variables has been locally optimized with all variables to meet practical requirements.
Wolfgang Birkfellner - One of the best experts on this subject based on the ideXlab platform.
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efficient implementation of the rank correlation Merit Function for 2d 3d registration
Physics in Medicine and Biology, 2010Co-Authors: Michael Figl, Helmar Bergmann, Christoph Bloch, Christelle Gendrin, Christoph Weber, S A Pawiro, Johann Hummel, Primož Markelj, Franjo Pernus, Wolfgang BirkfellnerAbstract:A growing number of clinical applications using 2D/3D registration have been presented recently. Usually, a digitally reconstructed radiograph is compared iteratively to an x-ray image of the known projection geometry until a match is achieved, thus providing six degrees of freedom of rigid motion which can be used for patient setup in image-guided radiation therapy or computer-assisted interventions. Recently, stochastic rank correlation, a Merit Function based on Spearman's rank correlation coefficient, was presented as a Merit Function especially suitable for 2D/3D registration. The advantage of this measure is its robustness against variations in image histogram content and its wide convergence range. The considerable computational expense of computing an ordered rank list is avoided here by comparing randomly chosen subsets of the DRR and reference x-ray. In this work, we show that it is possible to omit the sorting step and to compute the rank correlation coefficient of the full image content as fast as conventional Merit Functions. Our evaluation of a well-calibrated cadaver phantom also confirms that rank correlation-type Merit Functions give the most accurate results if large differences in the histogram content for the DRR and the x-ray image are present.
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a comment on the rank correlation Merit Function for 2d 3d registration
Proceedings of SPIE, 2010Co-Authors: Michael Figl, Christoph Bloch, Wolfgang BirkfellnerAbstract:Lots of procedures in computer assisted interventions register pre-interventionally generated 3D data sets to the intraoperative situation using fast and simply generated 2D images, e.g. from a C-Arm, a B-mode Ultrasound, etc. Registration is typically done by generating a 2D image out of the 3D data set, comparison to the original 2D image using a planar similarity measure and subsequent optimisation. As these two images can be very different, a lot of different comparison Functions are in use. In a recent article Stochastic Rank Correlation, a Merit Function based on Spearman's rank correlation coefficient was presented. By comparing randomly chosen subsets of the images, the authors wanted to avoid the computational expense of sorting all the points in the image. In the current paper we show that, because of the limited grey level range in medical images, full image rank correlation can be computed almost as fast as Pearson's correlation coefficient. A run time estimation is illustrated with numerical results using a 2D Shepp-Logan phantom at different sizes, and a sample data set of a pig.
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stochastic rank correlation a robust Merit Function for 2d 3d registration of image data obtained at different energies
Medical Physics, 2009Co-Authors: Wolfgang Birkfellner, Shuo Dong, Joachim Kettenbach, Michael Figl, Christelle Gendrin, Johann Hummel, M Stock, Dietmar Georg, Helmar BergmannAbstract:In this article, the authors evaluate a Merit Function for 2D/3D registration called stochastic rank correlation (SRC). SRC is characterized by the fact that differences in image intensity do not influence the registration result; it therefore combines the numerical advantages of cross correlation (CC)-type Merit Functions with the flexibility of mutual-information-type Merit Functions. The basic idea is that registration is achieved on a random subset of the image, which allows for an efficient computation of Spearman's rank correlation coefficient. This measure is, by nature, invariant to monotonic intensity transforms in the images under comparison, which renders it an ideal solution for intramodal images acquired at different energy levels as encountered in intrafractional kV imaging in image-guided radiotherapy. Initial evaluation was undertaken using a 2D/3D registration reference image dataset of a cadaver spine. Even with no radiometric calibration, SRC shows a significant improvement in robustness and stability compared to CC. Pattern intensity, another Merit Function that was evaluated for comparison, gave rather poor results due to its limited convergence range. The time required for SRC with 5% image content compares well to the other Merit Functions; increasing the image content does not significantly influence the algorithm accuracy. The authors conclude that SRC is a promising measure for 2D/3D registration in IGRT and image-guided therapy in general.
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the zernike expansion an example of a Merit Function for 2d 3d registration based on orthogonal Functions
Medical Image Computing and Computer-Assisted Intervention, 2008Co-Authors: Shuo Dong, Joachim Kettenbach, Isabella Hinterleitner, Helmar Bergmann, Wolfgang BirkfellnerAbstract:Current Merit Functions for 2D/3D registration usually rely on comparing pixels or small regions of images using some sort of statistical measure. Problems connected to this paradigm the sometimes problematic behaviour of the method if noise or artefacts (for instance a guide wire) are present on the projective image. We present a Merit Function for 2D/3D registration which utilizes the decomposition of the X-ray and the DRR under comparison into orthogonal Zernike moments; the quality of the match is assessed by an iterative comparison of expansion coefficients. Results in a imaging study on a physical phantom show that --- compared to standard cross-correlation --- the Zernike moment based Merit Function shows better robustness if histogram content in images under comparison is different, and that time expenses are comparable if the Merit Function is constructed out of a few significant moments only.
Masao Fukushima - One of the best experts on this subject based on the ideXlab platform.
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a new Merit Function and a descent method for semidefinite complementarity problems
1998Co-Authors: Nobuo Yamashita, Masao FukushimaAbstract:Recently, Tseng extended several Merit Functions for the nonlinear complementarity problem to the semidefinite complementarity problem (SDCP) and investigated various properties of those Functions. In this paper, we propose a new Merit Function for the SDCP based on the squared Fischer-Burmeister Function and show that it has some favorable properties. Particularly, we give conditions under which the Function provides a global error bound for the SDCP and conditions under which it has bounded level sets. We also present a derivative-free method for solving the SDCP and prove its global convergence under suitable assumptions.
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unconstrained optimization reformulations of variational inequality problems
Journal of Optimization Theory and Applications, 1997Co-Authors: Nobuo Yamashita, Kouichi Taji, Masao FukushimaAbstract:Recently, Peng considered a Merit Function for the variational inequality problem (VIP), which constitutes an unconstrained differentiable optimization reformulation of VIP. In this paper, we generalize the Merit Function proposed by Peng and study various properties of the generalized Function. We call this Function the D-gap Function. We give conditions under which any stationary point of the D-gap Function is a solution of VIP and conditions under which it provides a global error bound for VIP. We also present a descent method for solving VIP based on the D-gap Function.
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equivalence of the generalized complementarity problem to differentiable unconstrained minimization
Journal of Optimization Theory and Applications, 1996Co-Authors: Christian Kanzow, Masao FukushimaAbstract:We consider an unconstrained minimization reformulation of the generalized complementarity problem (GCP). The Merit Function introduced here is differentiable and has the property that its global minimizers coincide with the solutions of GCP. Conditions for its stationary points to be global minimizers are given. Moreover, it is shown that the level sets of the Merit Function are bounded under suitable assumptions. We also show that the Merit Function provides global error bounds for GCP. These results are based on a condition which reduces to the condition of the uniform P-Function when GCP is specialized to the nonlinear complementarity problem. This condition also turns out to be useful in proving the existence and uniqueness of a solution for GCP itself. Finally, we obtain as a byproduct an error bound result with the natural residual for GCP.
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A New Merit Function and A Successive Quadratic Programming Algorithm for Variational Inequality Problems
SIAM Journal on Optimization, 1996Co-Authors: Kouichi Taji, Masao FukushimaAbstract:Recently, various Merit Functions for variational inequality problems have been proposed and their properties have been studied. Unfortunately, these Functions may not be easy to evaluate unless the constraints of the problem have a relatively simple structure. In this paper, a new Merit Function for variational inequality problems with general convex constraints is proposed. At each point, the proposed Function is defined as an optimal value of a quadratic programming problem whose constraints consist of a linear approximation of the given nonlinear constraints. It is shown that the set of constrained minima of the proposed Merit Function coincides with the set of solutions to the original variational inequality problem. It is also shown that this Function is directionally differentiable in all directions and, under suitable assumptions, any stationary point of the Function over the constraint set actually solves the original variational inequality problem. Finally, a descent method for solving the variational inequality problem is proposed and its convergence is proved. The method is closely related to a successive quadratic programming method for solving nonlinear programming problems.
Jein Shan Chen - One of the best experts on this subject based on the ideXlab platform.
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geometric views of the generalized fischer burmeister Function and its induced Merit Function
Applied Mathematics and Computation, 2014Co-Authors: Huai Yin Tsai, Jein Shan ChenAbstract:Abstract In this paper, we study geometric properties of surfaces of the generalized Fischer–Burmeister Function and its induced Merit Function. Then, a visualization is proposed to explain how the convergent behaviors are influenced by two descent directions in Merit Function approach. Based on the geometric properties and visualization, we have more intuitive ideas about how the convergent behavior is affected by changing parameter. Furthermore, geometric view indicates how to improve the algorithm to achieve our goal by setting proper value of the parameter in Merit Function approach.
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on the generalized fischer burmeister Merit Function for the second order cone complementarity problem
Mathematics of Computation, 2013Co-Authors: Shaohua Pan, Sangho Kum, Yongdo Lim, Jein Shan ChenAbstract:It has been an open question whether the family of Merit Functions ψp (p > 1), the generalized Fischer-Burmeister (FB) Merit Function, associated to the second-order cone is smooth or not. In this paper we answer it partly, and show that ψp is smooth for p ∈ (1, 4), and we provide the condition for its coerciveness. Numerical results are reported to illustrate the influence of p on the performance of the Merit Function method based on ψp.
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proximal point algorithm for nonlinear complementarity problem based on the generalized fischer burmeister Merit Function
Journal of Industrial and Management Optimization, 2012Co-Authors: Yu Lin Chang, Jein Shan ChenAbstract:This paper is devoted to the study of the proximal point algorithm for solving monotone and nonmonotone nonlinear complementarity problems. The proximal point algorithm is to generate a sequence by solving subproblems that are regularizations of the original problem. After given an appropriate criterion for approximate solutions of subproblems by adopting a Merit Function, the proximal point algorithm is verified to have global and superlinear convergence properties. For the purpose of solving the subproblems efficiently, we introduce a generalized Newton method and show that only one Newton step is eventually needed to obtain a desired approximate solution that approximately satisfies the appropriate criterion under mild conditions. The motivations of this paper are twofold. One is analyzing the proximal point algorithm based on the generalized Fischer-Burmeister Function which includes the Fischer-Burmeister Function as special case, another one is trying to see if there are relativistic change on numerical performance when we adjust the parameter in the generalized Fischer-Burmeister.
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a Merit Function method for infinite dimensional soccps
Journal of Mathematical Analysis and Applications, 2011Co-Authors: Y Chiang, Shaohua Pan, Jein Shan ChenAbstract:Abstract We introduce the Jordan product associated with the second-order cone K into the real Hilbert space H , and then define a one-parametric class of complementarity Functions Φ t on H × H with the parameter t ∈ [ 0 , 2 ) . We show that the squared norm of Φ t with t ∈ ( 0 , 2 ) is a continuously F(rechet)-differentiable Merit Function. By this, the second-order cone complementarity problem (SOCCP) in H can be converted into an unconstrained smooth minimization problem involving this class of Merit Functions, and furthermore, under the monotonicity assumption, every stationary point of this minimization problem is shown to be a solution of the SOCCP.
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on the lorentz cone complementarity problems in infinite dimensional real hilbert space
Numerical Functional Analysis and Optimization, 2011Co-Authors: Xin He Miao, Jein Shan ChenAbstract:In this article, we consider the Lorentz cone complementarity problems in infinite-dimensional real Hilbert space. We establish several results that are standard and important when dealing with complementarity problems. These include proving the same growth of the Fishcher–Burmeister Merit Function and the natural residual Merit Function, investigating property of bounded level sets under mild conditions via different Merit Functions, and providing global error bounds through the proposed Merit Functions. Such results are helpful for further designing solution methods for the Lorentz cone complementarity problems in Hilbert space.
