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Future high-contrast imagers on ground-based extremely large telescopes will have to deal with the segmentation of the primary mirrors. Residual phase errors coming from the phase steps at the edges of the segments will have to be minimized…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
The regularity of refinable functions has been investigated deeply in the past 25 years using Fourier analysis, wavelet analysis, restricted and joint spectral radii techniques. However the shift-invariance of the underlying regular setting…
Numerical simulation of atmospheric turbulence is one of the biggest bottlenecks in developing computational techniques for solving the inverse problem in long-range imaging. The classical split-step method is based upon numerical wave…
We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…
Glass-like objects such as windows, bottles, and mirrors exist widely in the real world. Sensing these objects has many applications, including robot navigation and grasping. However, this task is very challenging due to the arbitrary…
We extend our previous demonstration of the first on-sky primary mirror segment closed-loop control on Keck using a vector-Zernike wavefront sensor (vZWFS), which improved the Strehl ratio on the NIRC2 science camera by up to 10 percentage…
Continuous wavefront sensing on future space telescopes allows relaxation of stability requirements while still allowing on-orbit diffraction-limited optical performance. We consider the suitability of phase retrieval to continuously…
This study investigates high-order face and edge elements in finite element methods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrange…
We consider the mathematical background of the wavefront sensor type that is widely used in Adaptive Optics systems for astronomy, microscopy, and ophthalmology. The theoretical analysis of the pyramid sensor forward operators presented in…
Active optics is defined as the control of the shape and the alignment of the components of an optical system at low temporal frequencies. For modern large telescopes with flexible monolithic or segmented primary mirrors and also flexible…
Automated segmentation of the optic cup and disk on retinal fundus images is fundamental for the automated detection / analysis of glaucoma. Traditional segmentation approaches depend heavily upon hand-crafted features and a priori…
From a structural point of view, plasmonic nanoparticles are always at least two-layer structures with a dielectric layer of stabilizing, targeting, fluorescent, Raman, or other functional molecules. To optimize the optical properties of…
The weak measurement wavefront sensor detects the phase gradient of light like the Shack-Hartmann sensor does. However, the use of one thin birefringent crystal to displace light beams results in a wavelength-dependent phase difference…
Decomposition of tomographic reconstructions has many different practical application. We propose two new reconstruction methods that combines the task of tomographic reconstruction with object decomposition. We demonstrate these…
Some metrological means, such as Shack-Hartmann, deflectometry sensors or fringe projection profilometry, measure the shape of an optical surface indirectly from slope measurements. Zonal shape reconstruction, a method to reconstruct shape…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
One of the time-consuming routine work for a radiologist is to discern anatomical structures from tomographic images. For assisting radiologists, this paper develops an automatic segmentation method for pelvic magnetic resonance (MR)…
Our work expands the use of capsule networks to the task of object segmentation for the first time in the literature. This is made possible via the introduction of locally-constrained routing and transformation matrix sharing, which reduces…
The paper presents a versatile library of quasi-analytic complex-valued wavelet packets (WPs) which originate from polynomial splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based orthonormal WPs…