For example, Zernike polynomials are orthogonal on the unit disk.
2.
In mathematics, the Zernike polynomials are a orthogonal on the unit disk.
3.
The third-order ( and lower ) Zernike polynomials correspond to the normal lens aberrations.
4.
In addition, Frits Zernike proposed still another functional decomposition based on his Zernike polynomials, defined on the unit disc.
5.
The Zernike polynomials satisfy the following recurrence relation which depends neither on the degree nor on the azimuthal order of the radial polynomials:
6.
In optometry and ophthalmology, Zernike polynomials are used to describe lens from an ideal spherical shape, which result in refraction errors.
7.
The phase function is retrieved by the unknown-coefficient weighted product with ( known values ) of Zernike polynomial across the unit grid.
8.
The above relation is especially useful since the derivative of R _ n ^ m can be calculated from two radial Zernike polynomials of adjacent degree:
9.
Zernike polynomials are usually expressed in terms of polar coordinates ( ?, ? ), where ? is radial coordinate and ? is the angle.
10.
In precision optical manufacturing, Zernike polynomials are used to characterize higher-order errors observed in interferometric analyses, in order to achieve desired system performance.
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