Related papers: Analytical decomposition of Zernike and hexagonal …

The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating…

The decomposition of an image into a linear combination of digitised basis functions is an everyday task in astronomy. A general method is presented for performing such a decomposition optimally into an arbitrary set of digitised basis…

We consider and provide an accurate study for the fractional Zernike functions on the punctured unit disc, generalizing the classical Zernike polynomials and their associated $\beta$-restricted Zernike functions. Mainly, we give the…

Context: Telescopes like the Extremely Large Telescope (ELT) and the Giant Magellan Telescope (GMT) will be used together with extreme adaptive optics (AO) instruments to directly image Earth-like planets. The AO systems will need to…

The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data…

In this paper we present a simple and effective method, based on appropriate superpositions of Bessel-Gauss beams, which in the Fresnel regime is able to describe in analytic form the 3D evolution of important waves as Bessel beams, plane…

To directly image Earth-like planets, contrast levels of 10^-8 - 10^-10 are required. The next generation of instruments will need wavefront control below the nanometer level to achieve these goals. The Zernike wavefront sensor (ZWFS) is a…

Recent studies have shown convolutional neural networks (CNNs) can be trained to perform modal decomposition using intensity images of optical fields. A fundamental limitation of these techniques is that the modal phases can not be uniquely…

Future space telescopes with coronagraph instruments will use a wavefront sensor (WFS) to measure and correct for phase errors and stabilize the stellar intensity in high-contrast images. The HabEx and LUVOIR mission concepts baseline a…

Wavefront sensing is a widely-used non-interferometric, single-shot, and quantitative technique providing the spatial-phase of a beam. The phase is obtained by integrating the measured wavefront gradient. Complex and random wavefields…

Wave propagation through random continuous media remains an important fundamental problem with applications ranging from remote sensing to quantum communication. Typically, such media are characterized by smooth refractive index…

The Zernike wavefront sensor (ZWFS) is a concept belonging to the wide class Fourier-filtering wavefront sensor (FFWFS). The ZWFS is known for its extremely high sensitivity while having a low dynamic range, which makes it a unique sensor…

In wavefront characterization, often the combination of a Shack-Hartmann sensor and a reconstruction method utilizing the Cartesian derivatives of Zernike circle polynomials (the least-squares method, to be called here Method A) is used,…

In this paper, we develop a numerical method for the computation of (quasi-)resonances in spherical symmetric, heterogeneous Helmholtz problems with piecewise smooth refractive index. Our focus lies in resonances very close to the real…

The next generation of large telescopes for direct imaging of exoplanets will require segmented primary mirrors. Over both long and short timescales, these telescopes experience segment misalignments which degrade the final science image.…

Adaptive optics (AO) is critical in astronomy, optical communications and remote sensing to deal with the rapid blurring caused by the Earth's turbulent atmosphere. But current AO systems are limited by their wavefront sensors, which need…

Semantic segmentation, which aims to classify every pixel in an image, is a key task in machine perception, with many applications across robotics and autonomous driving. Due to the high dimensionality of this task, most existing approaches…

A method for the analytical evaluation of layer potentials arising in the collocation boundary element method for the Laplace and Helmholtz equation is developed for piecewise flat boundary elements with polynomial shape functions. The…

We consider the numerical solution of high-frequency scattering problems modeled by the Helmholtz equation with a bounded obstacle. Although the analysis of this problem dates back at least 50 years, over the past decade or so, tools and…

We present a single-image numerical phase retrieval method for Zernike phase-contrast microscopy (ZPM) that addresses halo and shade-off artifacts, as well as the weak phase condition, without requiring hardware modifications. By employing…