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This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…

Numerical Analysis · Mathematics 2024-04-30 Ying Cai , Hailong Guo , Zhimin Zhang

We present a description of our method to process a set of autocollimator-based deflectometer 1-dimensional line-scans taken over a large optical surface and reconstruct them to a best-fit conic-section surface. The challenge with our task…

Optics · Physics 2016-04-28 Samantha J. Thompson , Richard Lang , Paul Rees , Gareth W. Roberts

It is shown that the problem of designing a two-reflector system transforming a plane wave front with given intensity into an output plane front with prescribed output intensity can be formulated and solved as the Monge-Kantorovich mass…

Analysis of PDEs · Mathematics 2007-05-23 Tilmann Glimm , Vladimir Oliker

This paper addresses the problem of reconstructing the surface shape of transparent objects. The difficulty of this problem originates from the viewpoint dependent appearance of a transparent object, which quickly makes reconstruction…

Image and Video Processing · Electrical Eng. & Systems 2021-05-24 Kai Han , Kwan-Yee K. Wong , Miaomiao Liu

In this paper, we propose an efficient joint precoding design method to maximize the weighted sum-rate in wideband intelligent reflecting surface (IRS)-assisted cell-free networks by jointly optimizing the active beamforming of base…

Signal Processing · Electrical Eng. & Systems 2024-12-10 Yajun Wang , Jinghan Jiang , Xin Du , Zhuxian Lian , Qingqing Wu , Wen Chen

In this paper we broadly consider techniques which utilize projections on rays for data collection, with particular emphasis on optical techniques. We formulate a variety of imaging techniques as either special cases or extensions of…

Computer Vision and Pattern Recognition · Computer Science 2014-02-12 Keith Dillon , Yeshaiahu Fainman

Conventional method for Gaussian beam collimation is to expand the beam waist to achieve a smaller divergence angle. Recent transformation optics offers an unconventional path to control the electromagnetic field. In this paper we show that…

Optics · Physics 2013-03-29 Yuancheng Fan , Jin Han , Hongqiang Li

We present an inverse method for transforming a given parallel light emittance to two light distributions at different parallel target planes using two freeform reflectors. The reflectors control both the spatial and directional target…

Slender beam-like structures frequently occur in engineering applications and often interact at discrete locations through joints or connectors. Accurate modeling of such interactions is particularly challenging when different numerical…

Computational Engineering, Finance, and Science · Computer Science 2026-04-13 Ivo Steinbrecher , Nora Hagmeyer , Christoph Meier , Alexander Popp

It remains an open problem to find the optimal configuration of phase shifts under the discrete constraint for intelligent reflecting surface (IRS) in polynomial time. The above problem is widely believed to be difficult because it is not…

Information Theory · Computer Science 2023-09-08 Shuyi Ren , Kaiming Shen , Xin Li , Xin Chen , Zhi-Quan Luo

The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…

Numerical Analysis · Mathematics 2022-04-21 Oded Stein , Eitan Grinspun , Alec Jacobson , Max Wardetzky

Filterless optical transport networks relies on passive optical interconnections between nodes, i.e., on splitters/couplers and amplifiers. While different studies have investigated their design, none of them offer a solution for an optimal…

Networking and Internet Architecture · Computer Science 2021-01-05 Brigitte Jaumard , Yan Wang

The knowledge of receiver beam shapes is essential for accurate radio interferometric imaging. Traditionally, this information is obtained by holographic techniques or by numerical simulation. However, such methods are not feasible for an…

Instrumentation and Methods for Astrophysics · Physics 2013-07-19 Sarod Yatawatta

We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…

Mathematical Physics · Physics 2015-06-19 Stuart Kent , Shankar C. Venkataramani

We propose an efficient inverse design approach for multifunctional optical elements based on adaptive deep diffractive neural networks (a-D$^2$NNs). Specifically, we introduce a-D$^2$NNs and design two-layer diffractive devices that can…

Optics · Physics 2022-06-08 Yuyao Chen , Yilin Zhu , Wesley A. Britton , Luca Dal Negro

For more than 150 years, scientists have advanced aberration theory to describe, analyse, and eliminate imperfections that disturb the imaging quality of optical components and systems. Simultaneously, they have developed optical design…

Optics · Physics 2021-06-01 Fabian Duerr , Hugo Thienpont

We worked out a new group of collimated plasmon beams by the means of in-plane diffraction with symmetric phase modulation. As the phase type changes from 1.8 to 1.0, the beam undergoes an interesting evolution from focusing to a straight…

Optics · Physics 2015-06-12 L. Li , T. Li , S. M. Wang , S. N. Zhu

In this paper, colocated MIMO radar waveform design is considered by minimizing the integrated side-lobe level to obtain beam patterns with lower side-lobe levels than competing methods. First, a quadratic programming problem is formulated…

Information Theory · Computer Science 2018-07-24 Haisheng Xu , Rick S. Blum , Jian Wang , Jian Yuan

In this article, we propose a new dimensionality-independent and gradient-free sampler, called Geometric Optics Approximation Sampling, which is based on the reflector antenna system. The core idea is to construct a reflecting surface that…

Numerical Analysis · Mathematics 2024-11-18 Zejun Sun , Guang-Hui Zheng

We combine two-dimensional freeform reflector design with a scattering surface modelled using microfacets, i.e., small specular surfaces representing surface roughness. The model results in a convolution integral for the scattered light…