Zernike polynomials: a guide

@article{Lakshminarayanan2011ZernikePA,
  title={Zernike polynomials: a guide},
  author={Vasudevan Lakshminarayanan and Andrea Fleck},
  journal={Journal of Modern Optics},
  year={2011},
  volume={58},
  pages={545 - 561}
}
In this paper we review a special set of orthonormal functions, namely Zernike polynomials which are widely used in representing the aberrations of optical systems. We give the recurrence relations, relationship to other special functions, as well as scaling and other properties of these important polynomials. Mathematica code for certain operations are given in the Appendix. 
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