Related papers: Analytical decomposition of Zernike and hexagonal …
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 disk. In [Diaz et all, 2014] we introduced a new Zernike basis for elliptic…
Zernike polynomials are widely used in optics and ophthalmology due to their direct connection to classical optical aberrations. While orthogonal on the unit disk, their application to discrete data or non-circular domains--such as…
Zernike polynomials are widely used mathematical models of experimentally observed optical aberrations. Their useful mathematical properties, in particular their orthogonality, make them a ubiquitous basis set for solving various problems…
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…
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…
The increasing use of freeform optical surfaces raises the demand for optical design tools developed for generalized systems. In the design process surface-by-surface aberration contributions are of special interest. The expansion of the…
Spatial mode sorting has come to prominence as an optical processing modality capable of saturating fundamental limits to numerous sensing tasks including wavefront sensing, coronagraphy, and superresolution imaging. But despite their…
A set of orthogonal polynomials on the unit disk $B(0,1)$ known as Zernike polynomials are commonly used in the analysis and evaluation of optical systems. Here Zernike polynomials are used to construct wavelets for polynomial subspaces of…
Zernike polynomials are a basis of orthogonal polynomials on the unit disk that are a natural basis for representing smooth functions. They arise in a number of applications including optics and atmospheric sciences. In this paper, we…
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.…
If the optical system of a telescope is perturbed from rotational symmetry, the Zernike wavefront aberration coefficients describing that system can be expressed as a function of position in the focal plane using spin-weighted Zernike…
The Zernike wavefront sensor (ZWFS) stands out as one of the most sensitive optical systems for measuring the phase of an incoming wavefront, reaching photon efficiencies close to the fundamental limit. This quality, combined with the fact…
This paper studies the effects on Zernike coefficients of aperture scaling, translation and rotation, when a given aberrated wavefront is described on the Zernike polynomial basis. It proposes a new analytical method for computing the…
Integration operational matrix methods based on Zernike polynomials are used to determine approximate solutions of a class of non-homogeneous partial differential equations (PDEs) of first and second order. Due to the nature of the Zernike…
The Zernike radial polynomials are a system of orthogonal polynomials over the unit interval with weight x. They are used as basis functions in optics to expand fields over the cross section of circular pupils. To calculate the roots of…
The major sources causing deterioration of optical quality in extremely large optical telescopes are misadjustments of the mirrors, deformations of monolithic mirrors, and misalignments of segments in segmented mirrors. For active optics…
Pupil mapping is a promising and unconventional new method for high contrast imaging being considered for terrestrial exoplanet searches. It employs two (or more) specially designed aspheric mirrors to create a high-contrast amplitude…
Pupil mapping is a promising and unconventional new method for high contrast imaging being considered for terrestrial exoplanet searches. It employs two (or more) specially designed aspheric mirrors to create a high-contrast amplitude…
The image degradation produced by atmospheric turbulence and optical aberrations is usually alleviated using post-facto image reconstruction techniques, even when observing with adaptive optics systems. These techniques rely on the…
Future Extremely Large Telescopes will adopt segmented primary mirrors with several hundreds of segments. Cophasing of the segments together is essential to reach high wavefront quality. The phasing sensor must be able to maintain very high…