Related papers: Zernike moments description of solar and astronomi…

Over the past 30 years, numerous large-scale photometric astronomical surveys have been conducted, including SDSS, Pan-STARRS, Gaia,2MASS, WISE, and others. These surveys provide extensive photometric measurements that can be used to infer…

It is shown that the description of the solar cycle that takes into account the odd zonal harmonic of the solar magnetic field allows us to deepen our knowledge of two important aspects of the solar activity. First, to clarify and expand…

We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…

We have developed a method that maps large astronomical images onto a two-dimensional map and clusters them. A combination of various state-of-the-art machine learning (ML) algorithms is used to develop a fully unsupervised image quality…

Observations of the Sun from the Earth are always limited by the presence of the atmosphere, which strongly disturbs the images. A solution to this problem is to place the telescopes in space satellites, which produce observations without…

Understanding the reasons of the cyclic variation of the total solar irradiance is one of the most challenging targets of modern astrophysics. These studies prove to be essential also for a more climatologic issue, associated to the global…

Zernike polynomials are commonly used to represent the wavefront phase on circular optical apertures, since they form a complete and orthonormal basis on the unit circle. Here, we present a generalization of this Zernike basis for a variety…

I present a software tool for solving the astrometry of astronomical images. The code puts emphasis on robustness against failures for correctly matching the sources in the image to a reference catalog, and on the stability of the solutions…

The spatial dependence of total column ozone varies strongly with latitude, so that homogeneous models (invariant to all rotations) are clearly unsuitable. However, an assumption of axial symmetry, which means that the process model is…

The emergence of a new discipline called space weather, which aims at understanding and predicting the impact of solar activity on the terrestrial environment and on technological systems, has led to a growing need for analysing solar…

Sets of orthogonal basis functions over two-dimensional circular areas--most often representing pupils in optical applications--are known in the literature for the full circle (Zernike or Jacobi polynomials) and the annulus. This work…

Breakthroughs in our understanding of physical phenomena have traditionally followed improvements in instrumentation. Studies of the magnetic field of the Sun, and its influence on the solar dynamo and space weather events, have benefited…

We describe the statistical properties of the dynamics of the quadratic polynomials P_a(z):=e^{2\pi a i} z+z^2 on the complex plane, with a of high return times. In particular, we show that these maps are uniquely ergodic on their measure…

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…

Zhegalkin zebra motives are tilings of the plane by black and white polygons representing certain ${\mathbb F}_2$-valued functions on ${\mathbb R}^2$. They exhibit a rich geometric structure and provide easy to draw insightful…

Wavefront reconstruction is a critical component in various optical systems, including adaptive optics, interferometry, and phase contrast imaging. Traditional reconstruction methods often employ either the Cartesian (pixel) basis or the…

Optical aberrations significantly degrade image quality in microscopy, particularly when imaging deeper into samples. These aberrations arise from distortions in the optical wavefront and can be mathematically represented using Zernike…

The study of shapes of the images of objects is an important issue not only because it reveals its dynamical state but also it helps to understand the object's evolutionary history. We discuss a new technique in cosmological image analysis…

Astronomical observations already produce vast amounts of data through a new generation of telescopes that cannot be analyzed manually. Next-generation telescopes such as the Large Synoptic Survey Telescope and the Square Kilometer Array…

The large-scale magnetic fields of stars can be obtained with the Zeeman-Doppler-Imaging (ZDI) technique, but their interpretation is still challenging as the contribution of the small-scale field or the reliability of the reconstructed…