Related papers: Transformation of Zernike coefficients: A Fourier …
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…
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…
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…
We increase the scope of previous work on change of basis between finite bases of polynomials by defining ascending and descending bases and introducing three techniques for defining them from known ones. The minimum degrees of polynomials…
Wavefront aberrations can reflect the imaging quality of high-performance optical systems better than geometric aberrations. Although laser interferometers have emerged as the main tool for measurement of transmitted wavefronts, their…
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…
Several quantities related to the Zernike circle polynomials admit an expression as an infinite integral involving the product of two or three Bessel functions. In this paper these integrals are identified and evaluated explicitly for the…
The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based…
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…
Zernike polynomials are widely used to describe the wavefront phase as they are well suited to the circular geometry of various optical apertures. Non-conventional optical systems, such as future large optical telescopes with highly…
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…
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…
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…
Zernike polynomials are one of the most widely used mathematical descriptors of optical aberrations in the fields of imaging and adaptive optics. Their mathematical orthogonality as well as isomorphisms with experimentally observable…
The influence of low-spatial frequency errors of an optical component of an imaging system on the point spread function can be quantified using Zernike polynomials. High-spatial frequency errors cause strong scattering due to which the…
We consider 3D versions of the Zernike polynomials that are commonly used in 2D in optics and lithography. We generalize the 3D Zernike polynomials to functions that vanish to a prescribed degree $\alpha\geq0$ at the rim of their supporting…
The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction…
Optical imaging quality can be severely degraded by system and sample induced aberrations. Existing adaptive optics systems typically rely on iterative search algorithm to correct for aberrations and improve images. This study demonstrates…
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…