Applied physics

, Volume 13, Issue 4, pp 327–332 | Cite as

The circle polynomials of Zernike and their application in optics

  • William J. Tango
Contributed Papers


The Zernike polynomials are orthogonal functions defined on the unit circle, which have been used primarily in the diffraction theory of optical aberrations. A summary of their principal properties is given. It is shown that the polynomials, which are closely related to the general spherical harmonics, are especially useful in numerical calculations. In particular, by using the polynomials as a basis to represent the commonly encountered functions of optical theory, it is often possible to avoid numerical quadrature and computations are reduced to the simple manipulation of expansion coefficients.

PACS Codes

02 42.30 


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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • William J. Tango
    • 1
  1. 1.School of PhysicsUniversity of SydneyAustralia

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