Related papers: Non-axisymmetric aberration patterns from wide-fie…
We propose and implement an aberration correction method for the creation of extended arrays of spots well beyond the isoplanatic region of any optical system. The method relies on an extensive calibration of aberrations in terms of Zernike…
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…
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…
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 differential equation proposed by Frits Zernike to obtain a basis of polynomial orthogonal solutions on the the unit disk to classify wavefront aberrations in circular pupils, is shown to have a set of new orthonormal solution bases,…
In the context of adaptive optics for astronomy, one can rely on the statistics of the turbulent phase to assess a part of the system's performance. Temporal statistics with one source and spatial statistics with two sources are well-known…
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…
Axially symmetric telescopes produce well known "Seidel" off-axis third-order aberration patterns: coma, astigmatism, curvature of field and distortion. When axial symmetry is broken by the small misalignments of optical elements,…
We present a method using Zernike moments for quantifying rotational and reflectional symmetries in scanning transmission electron microscopy (STEM) images, aimed at improving structural analysis of materials at the atomic scale. This…
We present a technique for the accurate estimation of large-scale errors in an antenna surface using astronomical sources and detectors. The technique requires several out-of-focus images of a compact source and the signal-to-noise ratio…
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…
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…
Context: Telescopes like the Extremely Large Telescope (ELT) and the Giant Magellan Telescope (GMT) will be used together with extreme adaptive optics (AO) instruments to directly image Earth-like planets. The AO systems will need to…
We describe phase-retrieval holography measurements of the 100-m diameter Green Bank Telescope using astronomical sources and an astronomical receiver operating at a wavelength of 7 mm. We use the technique with parameterization of the…
Shack Hartmann Sensor (SHS) is inflicted with significant background noise that deteriorates the wave-front reconstruction accuracy. In this paper, a simple method to remove the back ground noise with the use of Zernike polynomials is…
We investigate whether a three-mirror system, having secondary and the tertiary mirrors with surfaces warped by Zernike polynomials generated by active vase mirrors, is suitable to do the corrections of a fixed parabolic mirror observing at…
An explanation for the origin of asymmetry along the preferential axis of the PSF of an AO system is developed. When phase errors from high altitude turbulence scintillate due to Fresnel propagation, wavefront amplitude errors may be…
This paper demonstrates a method of interpreting the mechanism of aberration of optical systems based on non-Fourier transform optical transfer function (OTF). According to the parameters of object plane cosine fringe, we obtain the…
The method of geodesic deviations has been applied to derive accurate analytic approximations to geodesics in Schwarzschild space-time. The results are used to construct analytic expressions for the source terms in the Regge-Wheeler and…
Two-wavelength adaptive optics (AO) systems sense turbulence-induced wavefront distortions using an artificial beacon or natural guidestar at one wavelength, while correcting and possibly transmitting at another. Although most existing AO…