mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, laureate...

the number of terms that may be used by Zernike polynomials, vision scientists use the first 15 polynomials, based on the fact that they are enough to...

In mathematics, pseudo-Zernike polynomials are well known and widely used in the analysis of optical systems. They are also widely used in image analysis...

be mathematically modeled using Zernike polynomials. Developed by Frits Zernike in the 1930s, Zernike's polynomials are orthogonal over a circle of unit...

Since the 1960s, Zernike's circle polynomials are widely used in optical design, optical metrology and image analysis. Zernike's work helped awaken...

Gegenbauer polynomials, and thus also the Legendre, Zernike and Chebyshev polynomials, are special cases of the Jacobi polynomials. The Jacobi polynomials were...

In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to...

Touchard polynomials Wilkinson's polynomial Wilson polynomials Zernike polynomials Pseudo-Zernike polynomials Alexander polynomial HOMFLY polynomial Jones...

Table of spherical harmonics Vector spherical harmonics Zernike polynomials Jacobi polynomials Atomic orbital A historical account of various approaches...

{1-x^{2}}}}} or w ( x ) = 1 − x 2 {\textstyle w(x)={\sqrt {1-x^{2}}}} . Zernike polynomials are defined on the unit disk and have orthogonality of both radial...

wavelength domain, which enables correction of optical aberrations using Zernike polynomials. Some commercially available technologies include: D-ILA JVC’s Direct-drive...

defect gradually resolves as the cornea heals. Optical aberration Zernike polynomials a coma-correcting meniscus lens 4571036, Gebelein, Rolin J. & Shafer...

a spherically symmetric function F0(k) . The Hankel transform of Zernike polynomials are essentially Bessel Functions (Noll 1976): R n m ( r ) = ( − 1...

plane waves. In addition, Frits Zernike proposed still another functional decomposition based on his Zernike polynomials, defined on the unit disc. The...

orthogonal polynomials, including Jacobi polynomials P(α,β) n and their special cases Legendre polynomials, Chebyshev polynomials, Gegenbauer polynomials, Zernike...

Its main use is in curve-fitting wavefronts with Cartesian polynomials or Zernike polynomials. However, similar to a real engine piston moving up and down...

Weierstrass: Weierstrass function Louis Weisner: Weisner's method E. T. Whittaker: Whittaker function Wilson polynomial Frits Zernike: Zernike polynomials...

field, a quadrupole field, an octupole field, etc.[citation needed] Zernike polynomials: Used in optics to calculate aberrations of optical systems. Each...

defocus and other aberrations must be minimized. Defocus is modeled in Zernike polynomial format as a ( 2 ρ 2 − 1 ) {\displaystyle a(2\rho ^{2}-1)} , where...

m n ( r , θ ) {\displaystyle V_{mn}(r,\theta )} is derived from Zernike polynomials and is defined by V m n ( r , θ ) = R m n ( r ) e j n θ {\displaystyle...

conjunction with piston (the first Zernike polynomial term), X and Y tilt can be modeled using the second and third Zernike polynomials: X-Tilt: a 1 ρ cos ⁡ ( θ...

mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after Frits Zernike, the Dutch optical...

55.1427F. doi:10.1364/JOSA.55.001427. NOLL, R. J. (March 1976). "Zernike polynomials and atmospheric turbulence". Journal of the Optical Society of America...

form of Zernike polynomials. For predefined statistics of aberrations a deformable mirror with M actuators can be equivalent to an ideal Zernike corrector...

ISBN 978-0-387-90262-3. Dai, G. (1996). "Modal wave-front reconstruction with Zernike polynomials and Karhunen–Loeve functions". JOSA A. 13 (6): 1218. Bibcode:1996JOSAA...

corrections have been developed. One proceeds analytically, estimating a Zernike polynomial description of the current shape of the mirror, and from this computing...

Guild, part of Girlguiding Vertical trefoil and oblique trefoil, Zernike polynomials Trefoil knot fold, a protein fold This disambiguation page lists...

aberrations caused by scintillation (degraded seeing), to higher Zernike polynomials. AO systems at NOFS will migrate to the 1.55-m and 1.8-m telescopes...

applications of loudspeaker radiation. An extended version of the Zernike polynomials, known as ENZ, was applied to solve forward and inverse problems...

plane was studied by Zernike and Nijboer in the 1930–40s. A central role in their analysis is played by Zernike's circle polynomials that allow an efficient...