Abstract

A new method for handling Zernike polynomials is presented. Owing to its efficiency, this method enables the use of Zernike polynomials as a basis for wave-front fitting in shearography systems. An excerpt of a C++ class is presented to show how the polynomials are calculated and represented in computer memory.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Swantner, W. W. Chow, “Gram–Schmidt orthonormalization of Zernike polynomials for general aperture shapes,” Appl. Opt. 33, 1832–1837 (1994).
    [Crossref] [PubMed]
  2. M. P. Rimmer, J. C. Wyant, “Evaluation of large aberrations using a lateral-shear interferometer having variable shear,” Appl. Opt. 14, 142–150 (1975).
    [Crossref] [PubMed]
  3. M. Carpio, D. Malacara, “Closed Cartesian representation of the Zernike polynomials,” Opt. Commun. 110, 514–516 (1994).
    [Crossref]
  4. D. Malacara, ed., Optical Shop Testing, 2nd ed., Wiley Series in Pure and Applied Optics (Wiley, New York, 1992), Eqs. (13.26)–(13.27), p. 466.
  5. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1995), Secs. 2.6, 15.4.
  6. A full listing of the CZernike class plus a listing of a sample program can be obtained from the author.

1994 (2)

W. Swantner, W. W. Chow, “Gram–Schmidt orthonormalization of Zernike polynomials for general aperture shapes,” Appl. Opt. 33, 1832–1837 (1994).
[Crossref] [PubMed]

M. Carpio, D. Malacara, “Closed Cartesian representation of the Zernike polynomials,” Opt. Commun. 110, 514–516 (1994).
[Crossref]

1975 (1)

Carpio, M.

M. Carpio, D. Malacara, “Closed Cartesian representation of the Zernike polynomials,” Opt. Commun. 110, 514–516 (1994).
[Crossref]

Chow, W. W.

Flannery, B. P.

W.H. Press, S.A. Teukolsky, W.T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1995), Secs. 2.6, 15.4.

Malacara, D.

M. Carpio, D. Malacara, “Closed Cartesian representation of the Zernike polynomials,” Opt. Commun. 110, 514–516 (1994).
[Crossref]

Press, W.H.

W.H. Press, S.A. Teukolsky, W.T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1995), Secs. 2.6, 15.4.

Rimmer, M. P.

Swantner, W.

Teukolsky, S.A.

W.H. Press, S.A. Teukolsky, W.T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1995), Secs. 2.6, 15.4.

Vetterling, W.T.

W.H. Press, S.A. Teukolsky, W.T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1995), Secs. 2.6, 15.4.

Wyant, J. C.

Appl. Opt. (2)

Opt. Commun. (1)

M. Carpio, D. Malacara, “Closed Cartesian representation of the Zernike polynomials,” Opt. Commun. 110, 514–516 (1994).
[Crossref]

Other (3)

D. Malacara, ed., Optical Shop Testing, 2nd ed., Wiley Series in Pure and Applied Optics (Wiley, New York, 1992), Eqs. (13.26)–(13.27), p. 466.

W.H. Press, S.A. Teukolsky, W.T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1995), Secs. 2.6, 15.4.

A full listing of the CZernike class plus a listing of a sample program can be obtained from the author.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Partial listing of CZernike.cp, a C++ class for calculating Zernike polynomials.6

Tables (1)

Tables Icon

Table 1 First 10 Zernike Polynomials

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

x differencex, y=Fx-S2, y-Fx+S2, y,
y differencex, y=Fx, y-S2-Fx, y+S2,
Fx, y=i=1N aiZix, y,
n=intceil-1.5+0.5×sqrt1+i×8,
m=n-i+n+1×n/2,
Binomx, y=xy,
Factx=x!.
ap,q=fMatpq,

Metrics