Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after Frits Zernike, they play an important role in geometrical optics.where m and n are nonnegative integers with n>=m, is the azimuthal angle in radians, and is the normalized radial distance. The radial polynomials Rmn are defined asIn 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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