Related papers: Sampling patterns for Zernike-like bases in non-st…
Polynomial functions are a usual choice to model the nonlinearity of lenses. Typically, these models are obtained through physical analysis of the lens system or on purely empirical grounds. The aim of this work is to facilitate an…
We investigate the aspherization of an active mirror for correcting third and fifth-order aberrations. We use a stainless steel AISI 420 mirror with a controlled pressure load, two series of 12-punctual radial positions of force application…
Zernike circular polynomials (ZCP) play a significant role in optics engineering. The symbolic expressions for ZCP are valuable for theoretic analysis and engineering designs. However, there are still two problems which remain open:…
We establish a connection between (degenerate) nonsymmetric Macdonald polynomials and standard bases and dual standard bases of maximal parabolic modules of affine Hecke algebras. Along the way we prove a (weak) polynomiality result for…
In theory of optical aberrations, an aberrated wavefront is represented by its coefficients in some orthogonal basis, for instance by Zernike polynomials. However, many wavefront measurement techniques implicitly approximate the gradient of…
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…
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the…
We consider orthogonal polynomials on the surface of a double cone or a hyperboloid of revolution, either finite or infinite in axis direction, and on the solid domain bounded by such a surface and, when the surface is finite, by…
Segmented aperture telescopes require an alignment procedure with successive steps from coarse alignment to monitoring process in order to provide very high optical quality images for stringent science operations such as exoplanet imaging.…
The Hankel determinant representations for the partition function and boundary correlation functions of the six-vertex model with domain wall boundary conditions are investigated by the methods of orthogonal polynomial theory. For specific…
We present and analyze an approximation scheme for a class of highly oscillatory kernel functions, taking the 2D and 3D Helmholtz kernels as examples. The scheme is based on polynomial interpolation combined with suitable pre- and…
Frequency domain spectroscopy allows an experimenter to establish optical properties of solids in a wide frequency band including the technically challenging 10 THz region, and in other bands enables metrological comparison between…
We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…
We compute the pointwise asymptotics of orthogonal polynomials with respect to a general class of pure point measures supported on finite sets as both the number of nodes of the measure and also the degree of the orthogonal polynomials…
Recent progress in neuroscience to image and investigate brain function has been made possible by impressive developments in optogenetic and opto-molecular tools. Such research requires advances in optical techniques for the delivery of…
In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…
We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of Jacobi elliptic functions. We find explicit expression for these polynomials in terms of a…
We construct interpolation operators for functions taking values in a symmetric space -- a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized…
High contrast imaging (HCI) is fundamentally limited by wavefront aberrations, and the ability to perform wavefront sensing from focal plane images is key to reach the full potential of ground and space-based instruments. Vortex focal plane…
Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from…