zernike polynomial sentence in Hindi
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- For example, Zernike polynomials are orthogonal on the unit disk.
- In mathematics, the Zernike polynomials are a orthogonal on the unit disk.
- The third-order ( and lower ) Zernike polynomials correspond to the normal lens aberrations.
- In addition, Frits Zernike proposed still another functional decomposition based on his Zernike polynomials, defined on the unit disc.
- The Zernike polynomials satisfy the following recurrence relation which depends neither on the degree nor on the azimuthal order of the radial polynomials:
- In optometry and ophthalmology, Zernike polynomials are used to describe lens from an ideal spherical shape, which result in refraction errors.
- The phase function is retrieved by the unknown-coefficient weighted product with ( known values ) of Zernike polynomial across the unit grid.
- The above relation is especially useful since the derivative of R _ n ^ m can be calculated from two radial Zernike polynomials of adjacent degree:
- Zernike polynomials are usually expressed in terms of polar coordinates ( ?, ? ), where ? is radial coordinate and ? is the angle.
- In precision optical manufacturing, Zernike polynomials are used to characterize higher-order errors observed in interferometric analyses, in order to achieve desired system performance.
- Defocus is modeled in Zernike polynomial format as a ( 2 \ rho ^ 2-1 ), where a is the defocus coefficient in wavelengths of light.
- The telescope is still in operation after a half century of astronomy at NOFS . It performs key quasar-based degraded seeing ), to higher Zernike polynomials.
- Fast algorithms to calculate the forward and inverse Zernike transform use symmetry properties of trigonometric functions, separability of radial and azimuthal parts of Zernike polynomials, and their rotational symmetries.
- In each Zernike polynomial Z ^ m _ n, the subscript n is the "'order of aberration "', all the Zernike polynomials in which n = 3 are called third-order aberrations and all the polynomials with n = 4, fourth order aberrations and so on.
- In each Zernike polynomial Z ^ m _ n, the subscript n is the "'order of aberration "', all the Zernike polynomials in which n = 3 are called third-order aberrations and all the polynomials with n = 4, fourth order aberrations and so on.
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