Discrete Orthogonality of Zernike Functions and Its Application to Corneal Measurements

  • A. SoumelidisEmail author
  • Z. Fazekas
  • M. Pap
  • F. Schipp
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 60)


The optical aberrations of human eyes – as well as, those of other optical systems – are often characterized with the Zernike coefficients. Although, these coefficients are normally obtained from discrete measurement data via discrete computations, the developers and programmers of these computer programs could not rely on the discrete orthogonality of the Zernike functions despite the orthogonality of the continuous Zernike functions. Recently, meshes of points over the unit disk were found and reported that ensure this property. In the present paper, such meshes of points are used for computing Zernike coefficients in respect of cornea-like test surfaces. Test results are presented concerning the precision of the surface reconstruction from the aforementioned coefficients. The meshes proposed, however, are not exactly like what the developers hoped for. Further work is necessary in two respects, firstly, how to tune the conventional measurements so that the advantages of the proposed meshes can be exploited, secondly, how to design optical sensors that are based on such meshes.


Corneal topography discrete orthogonal systems Zernike functions 


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Computer and Automation Reserch InstituteBudapestHungary
  2. 2.University of PecsPecsHungary
  3. 3.Eotvos Lorand UniversityBudapestHungary

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