Related papers: Zernike moments description of solar and astronomi…
Fresnel zone plates (FZPs), with patterns of $1\,\mu$m resolution, allow the formation of clean, diffraction-limited foci -- but have a static phase profile. Spatial light modulators (SLMs) allow dynamic control of spatial beam intensity…
Accurate modeling of geometric distortion is essential for precise astrometric calibration in wide-field imaging surveys. We present a self-calibration method based on Zernike polynomials, applied to imaging data from the Wide Field Survey…
Atmospheric processes involve both space and time. This is why human analysis of atmospheric imagery can often extract more information from animated loops of image sequences than from individual images. Automating such an analysis requires…
The kinematics of the Solar zenith passage on the Earth was shown as a simple harmonic motion. This analytical model used the uniform circular motion to describe the Earth's rotation relative to its axis and relative to the Sun, also this…
Analysis of the imaging of some simple distributions of object phase by a phase plate of Zernike type shows that sharp transitions in the object phase are well transmitted. The low-frequency components of the complete object function are…
These notes are very much work-in-progress and simply intended to showcase, in various degrees of details (and rigour), some of the cosmology calculations that class_sz can do. We describe the class_sz code in C, Python and Jax. Based on…
Context. Solar wavefront sensing has been a challenge for astrophysical instrumentalists, due to the low contrast between the Sun and the sky background compared to night-time observations, which limits the performance of adaptive optics…
A physical applicability of normed split-algebras, such as hyperbolic numbers, split-quaternions and split-octonions is considered. We argue that the observable geometry can be described by the algebra of split-octonions. In such a picture…
Solar activity is controlled by the magnetic field, which also causes the variability of the solar irradiance that in turn is thought to influence the climate on Earth. The magnetic field manifests itself in the form of structures of…
Planets are often covered with thin cracked shells. From mud films to lithospheres of rock or ice, fracture networks form two-dimensional (2D) tessellations of convex polygons whose geometry encodes their genesis. Here we chart the geometry…
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…
Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other…
We developed a Python based framework for astronomical image processing and analysis. Astronomical image loading, normalizing, stacking, and filtering processes represent visible range images from grayscale. Besides, the blending process…
Periodic space crystals are well established and widely used in physical sciences. Time crystals have been increasingly explored more recently, where time is disconnected from space. Periodic relativistic spacetime crystals on the other…
We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…
It is shown, for the first time, that the zitterbewegung of photon can appear near the Dirac point in two-dimensional photonic crystal. The superiority of such a phenomenon for photons is that it can be found in different scaling structures…
A new kind of geometric invariants is proposed in this paper, which is called affine weighted moment invariant (AWMI). By combination of local affine differential invariants and a framework of global integral, they can more effectively…
A desirable feature of models with large extra dimensions and a TeV range string scale is the possibility to understand an ultralight sterile neutrino needed for a simultaneous understanding of solar, atmospheric and LSND results as a…
In this paper, we analyze the nontrivial zeros of the Riemann zeta-function using the multidimensional scaling (MDS) algorithm and computational visualization features. The nontrivial zeros of the Riemann zeta-function as well as the…
Topological textures in magnetically ordered materials are important case studies for fundamental research with promising applications in data science. They can also serve as photonic elements to mold electromagnetic fields endowing them…