The Experts below are selected from a list of 2760 Experts worldwide ranked by ideXlab platform
Ronald G Hadley - One of the best experts on this subject based on the ideXlab platform.
-
the complex Jacobi iterative method for three dimensional wide angle beam propagation
Optics Express, 2008Co-Authors: R Godoyrubio, Peter Bienstman, Ronald G HadleyAbstract:A new complex Jacobi iterative technique adapted for the solution of three-dimensional (3D) wide-angle (WA) beam propagation is presented. The beam propagation equation for analysis of optical propagation in waveguide structures is based on a novel modified Pade(1,1) approximant operator, which gives evanescent waves the desired damping. The resulting approach allows more accurate approximations to the true Helmholtz equation than the standard Pade approximant operators. Furthermore, a performance comparison of the traditional direct matrix inversion and this new iterative technique for WA-beam propagation method is reported. It is shown that complex Jacobi Iteration is faster and better-suited for large problems or structures than direct matrix inversion.
-
a three dimensional non paraxial beam propagation method using complex Jacobi Iteration
Lasers and Electro-Optics Society Meeting, 2008Co-Authors: Khai Le Quang, Peter Bienstman, R Godoyrubio, Ronald G HadleyAbstract:A new complex Jacobi iterative technique adapted for the solution of three-dimensional (3D) non-paraxial beam propagation is presented. The beam propagation equation for analysis of optical propagation in waveguide structures is based on a novel modified Pade(1,1) approximant operator we recently proposed. The effectiveness of our new approach is demonstrated in comparison with the traditional direct matrix inversion. Our method is targeted towards large waveguide structures with a long path length.
-
3d wide angle beam propagation using complex Jacobi Iteration
Integrated Photonics Research and Applications Nanophotonics for Information Systems (2005) paper IME2, 2005Co-Authors: Ronald G HadleyAbstract:A new iterative technique recently developed for solution of the Helmholtz Equation is adapted for solution of 3D wide-angle beam propagation. The method is targeted towards large problems or structures with frequently-changing boundaries.
-
a complex Jacobi iterative method for the indefinite helmholtz equation
Journal of Computational Physics, 2005Co-Authors: Ronald G HadleyAbstract:An iterative procedure is described for the solution of the indefinite Helmholtz equation that is a two-step generalization of classic Jacobi Iteration using complex Iteration parameters. The method converges for well-posed problems at a rate dependent only upon the grid size, wavelength and the effective absorption seen by the field. The use of a simple Jacobi preconditioner allows the solution of 3D problems of interest in waveguide optics in reasonable runtimes on a personal computer with memory usage that scales linearly with the number of grid points. Both the iterative method and the preconditioner are fully parallelizable.
Peter Bienstman - One of the best experts on this subject based on the ideXlab platform.
-
non paraxial beam propagation in nonlinear optical waveguides using complex Jacobi Iteration
International Conference on Numerical Simulation of Optoelectronic Devices, 2009Co-Authors: Peter BienstmanAbstract:We present the recently introduced beam propagation method using complex Jacobi Iteration adapted for efficient modeling of non-paraxial beam propagation in nonlinear optical waveguides.
-
fast three dimensional generalized rectangular wide angle beam propagation method using complex Jacobi Iteration
Journal of The Optical Society of America B-optical Physics, 2009Co-Authors: Peter BienstmanAbstract:A fast and efficient three-dimensional generalized rectangular wide-angle beam propagation method (GR-WA-BPM) based on a recently proposed modified Pade (1,1) approximant is presented. In our method, at each propagation step, the beam propagation equation is recast in terms of a Helmholtz equation with a source term, which is solved quickly and accurately by a recently introduced complex Jacobi iterative (CJI) method. The efficiency of the GR-WA-BPM for the analysis of tilted optical waveguides is demonstrated in comparison with the standard wide-angle beam propagation method based on Hadley's scheme. In addition, since the utility of the CJI method depends mostly on its execution speed in comparison with the traditional direct matrix inversion, several performance comparisons are also presented.
-
fast wide angle bpms using complex Jacobi Iteration
International workshop on Optical Waveguide Theory and Numerical Modelling 18th Book of abstracts, 2009Co-Authors: Khai Le Quang, Peter Bienstman, G R HadleyAbstract:Efforts to improve the limitations of the paraxial approximation in the beam propagation method have so far made use of wide-angle formulations. Different treatments of WA-BPM based on the slowly varying envelope approximation (SVEA) have been developed. There exist real Pade approximant operators mentioned here as Hadley(m,n) [1] and complex Pade approximant operators [2]. In addition, treatments of WA-BPM without having to make the SVEAs have also been reported, including the series expansion technique of the propagator, the split-step of beam propagation equation and the rational KP(m,n) approximant we recently proposed [3]. For Hadley(1,1) and KP(1,1) approximant-based beam propagation of wave profiles within a 2D cross section, the beam propagation equation can be cast in terms of a Helmholtz equation with source term, but that equation needs to be solved efficiently since numerous propagation steps are routinely required during the course of a problem solution. For this purpose a recently introduced complex Jacobi iterative (CJI) method [4] is proposed for the solution of WA beam propagation and shown to be highly efficient. Since the utility of the CJI technique depends mostly upon its execution speed in comparison with the traditional direct matrix inversion (DMI) method, we also present several speed comparisons. Numerical implementations are carried out for 3D optical waveguide structures.
-
the complex Jacobi iterative method for three dimensional wide angle beam propagation
Optics Express, 2008Co-Authors: R Godoyrubio, Peter Bienstman, Ronald G HadleyAbstract:A new complex Jacobi iterative technique adapted for the solution of three-dimensional (3D) wide-angle (WA) beam propagation is presented. The beam propagation equation for analysis of optical propagation in waveguide structures is based on a novel modified Pade(1,1) approximant operator, which gives evanescent waves the desired damping. The resulting approach allows more accurate approximations to the true Helmholtz equation than the standard Pade approximant operators. Furthermore, a performance comparison of the traditional direct matrix inversion and this new iterative technique for WA-beam propagation method is reported. It is shown that complex Jacobi Iteration is faster and better-suited for large problems or structures than direct matrix inversion.
-
a three dimensional non paraxial beam propagation method using complex Jacobi Iteration
Lasers and Electro-Optics Society Meeting, 2008Co-Authors: Khai Le Quang, Peter Bienstman, R Godoyrubio, Ronald G HadleyAbstract:A new complex Jacobi iterative technique adapted for the solution of three-dimensional (3D) non-paraxial beam propagation is presented. The beam propagation equation for analysis of optical propagation in waveguide structures is based on a novel modified Pade(1,1) approximant operator we recently proposed. The effectiveness of our new approach is demonstrated in comparison with the traditional direct matrix inversion. Our method is targeted towards large waveguide structures with a long path length.
Steve B Jiang - One of the best experts on this subject based on the ideXlab platform.
-
four dimensional cone beam ct reconstruction and enhancement using a temporal nonlocal means method
Medical Physics, 2012Co-Authors: Xun Jia, Zhen Tian, Yifei Lou, Janjakob Sonke, Steve B JiangAbstract:Purpose: Four-dimensional cone beam computed tomography (4D-CBCT) has been developed to provide respiratory phase-resolved volumetric imaging in image guided radiation therapy. Conventionally, it is reconstructed by first sorting the x-ray projections into multiple respiratory phase bins according to a breathing signal extracted either from the projection images or some external surrogates, and then reconstructing a 3D CBCT image in each phase bin independently using FDK algorithm. This method requires adequate number of projections for each phase, which can be achieved using a low gantry rotation or multiple gantry rotations. Inadequate number of projections in each phase bin results in low quality 4D-CBCT images with obvious streaking artifacts. 4D-CBCT images at different breathing phases share a lot of redundant information, because they represent the same anatomy captured at slightly different temporal points. Taking this redundancy along the temporal dimension into account can in principle facilitate the reconstruction in the situation of inadequate number of projection images. In this work, the authors propose two novel 4D-CBCT algorithms: an iterative reconstruction algorithm and an enhancement algorithm, utilizing a temporal nonlocal means (TNLM) method. Methods: The authors define a TNLM energy term for a given set of 4D-CBCT images. Minimization of this term favors those 4D-CBCT images such that any anatomical features at one spatial point at one phase can be found in a nearby spatial point at neighboring phases. 4D-CBCT reconstruction is achieved by minimizing a total energy containing a data fidelity term and the TNLM energy term. As for the image enhancement, 4D-CBCT images generated by the FDK algorithm are enhanced by minimizing the TNLM function while keeping the enhanced images close to the FDK results. A forward–backward splitting algorithm and a Gauss–Jacobi Iteration method are employed to solve the problems. The algorithms implementation on GPU is designed to avoid redundant and uncoalesced memory access, in order to ensure a high computational efficiency. Our algorithms have been tested on a digital NURBS-based cardiac-torso phantom and a clinical patient case. Results: The reconstruction algorithm and the enhancement algorithm generate visually similar 4D-CBCT images, both better than the FDK results. Quantitative evaluations indicate that, compared with the FDK results, our reconstruction method improves contrast-to-noise-ratio (CNR) by a factor of 2.56–3.13 and our enhancement method increases the CNR by 2.75–3.33 times. The enhancement method also removes over 80% of the streak artifacts from the FDK results. The total computation time is 509–683 s for the reconstruction algorithm and 524–540 s for the enhancement algorithm on an NVIDIA Tesla C1060 GPU card. Conclusions: By innovatively taking the temporal redundancy among 4D-CBCT images into consideration, the proposed algorithms can produce high quality 4D-CBCT images with much less streak artifacts than the FDK results, in the situation of inadequate number of projections.
-
four dimensional cone beam ct reconstruction and enhancement using a temporal non local means method
arXiv: Medical Physics, 2012Co-Authors: Xun Jia, Zhen Tian, Yifei Lou, Janjakob Sonke, Steve B JiangAbstract:Four-dimensional Cone Beam Computed Tomography (4D-CBCT) has been developed to provide respiratory phase resolved volumetric imaging in image guided radiation therapy (IGRT). Inadequate number of projections in each phase bin results in low quality 4D-CBCT images with obvious streaking artifacts. In this work, we propose two novel 4D-CBCT algorithms: an iterative reconstruction algorithm and an enhancement algorithm, utilizing a temporal nonlocal means (TNLM) method. We define a TNLM energy term for a given set of 4D-CBCT images. Minimization of this term favors those 4D-CBCT images such that any anatomical features at one spatial point at one phase can be found in a nearby spatial point at neighboring phases. 4D-CBCT reconstruction is achieved by minimizing a total energy containing a data fidelity term and the TNLM energy term. As for the image enhancement, 4D-CBCT images generated by the FDK algorithm are enhanced by minimizing the TNLM function while keeping the enhanced images close to the FDK results. A forward-backward splitting algorithm and a Gauss-Jacobi Iteration method are employed to solve the problems. The algorithms are implemented on GPU to achieve a high computational efficiency. The reconstruction algorithm and the enhancement algorithm generate visually similar 4D-CBCT images, both better than the FDK results. Quantitative evaluations indicate that, compared with the FDK results, our reconstruction method improves contrast-to-noise-ratio (CNR) by a factor of 2.56~3.13 and our enhancement method increases the CNR by 2.75~3.33 times. The enhancement method also removes over 80% of the streak artifacts from the FDK results. The total computation time is ~460 sec for the reconstruction algorithm and ~610 sec for the enhancement algorithm on an NVIDIA Tesla C1060 GPU card.
R Godoyrubio - One of the best experts on this subject based on the ideXlab platform.
-
nonlinear wide angle beam propagation method using complex Jacobi Iteration in the fourier domain
Journal of The Optical Society of America B-optical Physics, 2011Co-Authors: R Godoyrubio, Sebastian Romerogarcia, Alejandro Ortegamonux, Gonzalo J WanguemertperezAbstract:An alternative wide-angle beam propagation method (WA-BPM) using a reformulated Fourier-based complex Jacobi iterative (CJI) technique for modeling nonlinear Kerr-type optical devices is presented. Making use of basic concepts of relaxation iterative methods, the CJI approach is modified to be incorporated as longitudinal solving strategy in WA-BPMs with transverse discretization schemes based on Fourier decomposition. After explaining the fundamentals of the resultant CJI-WA-BPM in the domain of Fourier coefficients, examples are given to show the significant improvements that are obtained, in terms of convergence rate and runtime, with respect to previous finite difference approaches.
-
the complex Jacobi iterative method for three dimensional wide angle beam propagation
Optics Express, 2008Co-Authors: R Godoyrubio, Peter Bienstman, Ronald G HadleyAbstract:A new complex Jacobi iterative technique adapted for the solution of three-dimensional (3D) wide-angle (WA) beam propagation is presented. The beam propagation equation for analysis of optical propagation in waveguide structures is based on a novel modified Pade(1,1) approximant operator, which gives evanescent waves the desired damping. The resulting approach allows more accurate approximations to the true Helmholtz equation than the standard Pade approximant operators. Furthermore, a performance comparison of the traditional direct matrix inversion and this new iterative technique for WA-beam propagation method is reported. It is shown that complex Jacobi Iteration is faster and better-suited for large problems or structures than direct matrix inversion.
-
a three dimensional non paraxial beam propagation method using complex Jacobi Iteration
Lasers and Electro-Optics Society Meeting, 2008Co-Authors: Khai Le Quang, Peter Bienstman, R Godoyrubio, Ronald G HadleyAbstract:A new complex Jacobi iterative technique adapted for the solution of three-dimensional (3D) non-paraxial beam propagation is presented. The beam propagation equation for analysis of optical propagation in waveguide structures is based on a novel modified Pade(1,1) approximant operator we recently proposed. The effectiveness of our new approach is demonstrated in comparison with the traditional direct matrix inversion. Our method is targeted towards large waveguide structures with a long path length.
Xun Jia - One of the best experts on this subject based on the ideXlab platform.
-
four dimensional cone beam ct reconstruction and enhancement using a temporal nonlocal means method
Medical Physics, 2012Co-Authors: Xun Jia, Zhen Tian, Yifei Lou, Janjakob Sonke, Steve B JiangAbstract:Purpose: Four-dimensional cone beam computed tomography (4D-CBCT) has been developed to provide respiratory phase-resolved volumetric imaging in image guided radiation therapy. Conventionally, it is reconstructed by first sorting the x-ray projections into multiple respiratory phase bins according to a breathing signal extracted either from the projection images or some external surrogates, and then reconstructing a 3D CBCT image in each phase bin independently using FDK algorithm. This method requires adequate number of projections for each phase, which can be achieved using a low gantry rotation or multiple gantry rotations. Inadequate number of projections in each phase bin results in low quality 4D-CBCT images with obvious streaking artifacts. 4D-CBCT images at different breathing phases share a lot of redundant information, because they represent the same anatomy captured at slightly different temporal points. Taking this redundancy along the temporal dimension into account can in principle facilitate the reconstruction in the situation of inadequate number of projection images. In this work, the authors propose two novel 4D-CBCT algorithms: an iterative reconstruction algorithm and an enhancement algorithm, utilizing a temporal nonlocal means (TNLM) method. Methods: The authors define a TNLM energy term for a given set of 4D-CBCT images. Minimization of this term favors those 4D-CBCT images such that any anatomical features at one spatial point at one phase can be found in a nearby spatial point at neighboring phases. 4D-CBCT reconstruction is achieved by minimizing a total energy containing a data fidelity term and the TNLM energy term. As for the image enhancement, 4D-CBCT images generated by the FDK algorithm are enhanced by minimizing the TNLM function while keeping the enhanced images close to the FDK results. A forward–backward splitting algorithm and a Gauss–Jacobi Iteration method are employed to solve the problems. The algorithms implementation on GPU is designed to avoid redundant and uncoalesced memory access, in order to ensure a high computational efficiency. Our algorithms have been tested on a digital NURBS-based cardiac-torso phantom and a clinical patient case. Results: The reconstruction algorithm and the enhancement algorithm generate visually similar 4D-CBCT images, both better than the FDK results. Quantitative evaluations indicate that, compared with the FDK results, our reconstruction method improves contrast-to-noise-ratio (CNR) by a factor of 2.56–3.13 and our enhancement method increases the CNR by 2.75–3.33 times. The enhancement method also removes over 80% of the streak artifacts from the FDK results. The total computation time is 509–683 s for the reconstruction algorithm and 524–540 s for the enhancement algorithm on an NVIDIA Tesla C1060 GPU card. Conclusions: By innovatively taking the temporal redundancy among 4D-CBCT images into consideration, the proposed algorithms can produce high quality 4D-CBCT images with much less streak artifacts than the FDK results, in the situation of inadequate number of projections.
-
four dimensional cone beam ct reconstruction and enhancement using a temporal non local means method
arXiv: Medical Physics, 2012Co-Authors: Xun Jia, Zhen Tian, Yifei Lou, Janjakob Sonke, Steve B JiangAbstract:Four-dimensional Cone Beam Computed Tomography (4D-CBCT) has been developed to provide respiratory phase resolved volumetric imaging in image guided radiation therapy (IGRT). Inadequate number of projections in each phase bin results in low quality 4D-CBCT images with obvious streaking artifacts. In this work, we propose two novel 4D-CBCT algorithms: an iterative reconstruction algorithm and an enhancement algorithm, utilizing a temporal nonlocal means (TNLM) method. We define a TNLM energy term for a given set of 4D-CBCT images. Minimization of this term favors those 4D-CBCT images such that any anatomical features at one spatial point at one phase can be found in a nearby spatial point at neighboring phases. 4D-CBCT reconstruction is achieved by minimizing a total energy containing a data fidelity term and the TNLM energy term. As for the image enhancement, 4D-CBCT images generated by the FDK algorithm are enhanced by minimizing the TNLM function while keeping the enhanced images close to the FDK results. A forward-backward splitting algorithm and a Gauss-Jacobi Iteration method are employed to solve the problems. The algorithms are implemented on GPU to achieve a high computational efficiency. The reconstruction algorithm and the enhancement algorithm generate visually similar 4D-CBCT images, both better than the FDK results. Quantitative evaluations indicate that, compared with the FDK results, our reconstruction method improves contrast-to-noise-ratio (CNR) by a factor of 2.56~3.13 and our enhancement method increases the CNR by 2.75~3.33 times. The enhancement method also removes over 80% of the streak artifacts from the FDK results. The total computation time is ~460 sec for the reconstruction algorithm and ~610 sec for the enhancement algorithm on an NVIDIA Tesla C1060 GPU card.