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We explain four variants of an adaptive finite element method with cubic splines and compare their performance in simple elliptic model problems. The methods in comparison are Truncated Hierarchical B-splines with two different refinement…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
In this work, we propose a new paradigm of iterative model-based reconstruction algorithms for providing real-time solution for zooming-in and refining a region of interest in medical and clinical tomographic images. This algorithmic…
In this paper we are exploring the possibilities of 3D printing in the fabrication of mirrors for astronomy. Taking the advantages of 3D printing to solve the existing problems caused by traditional manufacturing, two proof-of-concept…
Over the past decade, reflection matrix microscopy (RMM) and advanced image reconstruction algorithms have emerged to address the fundamental imaging depth limitations of optical microscopy in thick biological tissues and complex media. In…
Document rectification in real-world scenarios poses significant challenges due to extreme variations in camera perspectives and physical distortions. Driven by the insight that complex transformations can be decomposed and resolved…
Modern video generators still struggle with complex physical dynamics, often falling short of physical realism. Existing approaches address this using external verifiers or additional training on augmented data, which is computationally…
This work develops user-friendly a posteriori error estimates of finite element methods, based on smoothers of linear iterative solvers. The proposed method employs simple smoothers, such as Jacobi or Gauss-Seidel iteration, on an auxiliary…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
In recent years, 3D Gaussian splatting (3DGS) has achieved remarkable progress in novel view synthesis. However, accurately reconstructing glossy surfaces under complex illumination remains challenging, particularly in scenes with strong…
In this paper, we present a new robotic system to perform defect inspection tasks over free-form specular surfaces. The autonomous procedure is achieved by a six-DOF manipulator, equipped with a line scan camera and a high-intensity…
Metasurfaces are an emerging technology that may supplant many of the conventional optics found in imaging devices, displays, and precision scientific instruments. Here, we develop a method for designing optical systems composed of multiple…
Optical cavities are frequently used in quantum technologies to enhance light matter interactions, with applications including single photon generation and entanglement of distant emitters. The Fabry-P\'{e}rot resonator is a popular choice…
A simple method of constructing the 3D surface of non-transparent micro-objects by extending the depth-of-field on the whole attainable surface is presented. The series of images of a sample are recorded by the sequential movement of the…
We discuss realization, properties and performance of the adaptive finite element approach to the design of nano-photonic components. Central issues are the construction of vectorial finite elements and the embedding of bounded components…
Phase is a fundamental resource for optical imaging but cannot be directly observed with intensity measurements. The existing methods to quantify a phase distribution rely on complex devices and structures. Here we experimentally…
We report on the fabrication and characterization of a micromechanical oscillator consisting only of a free-standing dielectric Bragg mirror with high optical reflectivity and high mechanical quality. The fabrication technique is a hybrid…
Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause…
As deep neural networks become the state-of-the-art approach in the field of computer vision for dense prediction tasks, many methods have been developed for automatic estimation of the target outputs given the visual inputs. Although the…
Multifocal plane microscopy (MUM) allows three dimensional objects to be imaged in a single camera frame. Our approach uses dual orthogonal diffraction phase gratings with a quadratic distortion of the lines to apply defocus to the first…