Generalized 3D Zernike functions for analytic construction of band-limited line-detecting wavelets

Report, Preprint English OPEN
Janssen, Augustus J. E. M.;
  • Publisher: s.n.
  • Subject: Mathematics - Classical Analysis and ODEs

We consider 3D versions of the Zernike polynomials that are commonly used in 2D in optics and lithography. We generalize the 3D Zernike polynomials to functions that vanish to a prescribed degree $\alpha\geq0$ at the rim of their supporting ball $\rho\leq1$. The analyti... View more
  • References (13)
    13 references, page 1 of 2

    [1] R. Duits, Perceptual Organization in Image Analysis, Ph.D. thesis, Eindhoven University of Technology, The Netherlands, 2005.

    [8] M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, United Kingdom,, 1999).

    [9] T.A. Brunner, \Impact of lens aberrations on optical lithography", IBM J. Res. Develop. 41, 57{67 (1997).

    [10] R.M. Aarts and A.J.E.M. Janssen, \On-axis and far- eld sound radiation from resilient at and dome-shaped radiators", J. Acoust. Soc. Am. 125, 1444{1455 (2009).

    [11] R.J. Mathar, \Zernike basis to Cartesian transformations", Serb. Astron. J. 179, 107{120 (2009).

    [12] H. Liu, B.K. Poon, A.J.E.M. Janssen and P.H. Zwart, \Computation of uctuating scattering pro les via three-dimensional Zernike polynomials", Acta Crystallographica A68, 561{567 (2012).

    [13] B.H. Shakibaei and R. Paramesran, \Recursive formula to compute Zernike radial polynomials", Optics Letters 38, 2487{2489 (2013).

    [14] F.W.J. Olver, D.W. Lozier, R.F. Boisvert and C.W. Clark, NIST Handbook of Mathematical Functions (Cambridge University Press, Cambridge, United Kingdom, 2010).

    [15] G. Szego, Orthogonal Polynomials (AMS, Providence, 4th ed., 1975).

    [16] F.G. Tricomi, Vorlesungen uber Orthogonalreihen (Springer-Verlag, Berlin, 1955).

  • Similar Research Results (3)
  • Related Organizations (1)
  • Metrics
Share - Bookmark