Abstract

Based on our earlier work on Zernike annular polynomials,1 expressions for some higher-order radial polynomials are given, thus providing a complete set up to the sixth order.

© 1984 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. N. Mahajan, “Zernike annular polynomials for imaging systems with annular pupils,”J. Opt. Soc. Am. 71, 75–85 (1981); J. Opt. Soc. Am. 71, 1408 (1981).
    [Crossref]
  2. V. N. Mahajan, “Zernike annular polynomials,” (Aerospace Corporation, Los Angeles, Calif., 1984).
  3. W. H. Steel, “Etude des effets combines des aberrations et d’une obturation centrale de la pupille sur le contraste des images optiques,” Rev. Opt. (Paris) 32, 143–178 (1953).

1981 (1)

1953 (1)

W. H. Steel, “Etude des effets combines des aberrations et d’une obturation centrale de la pupille sur le contraste des images optiques,” Rev. Opt. (Paris) 32, 143–178 (1953).

Mahajan, V. N.

Steel, W. H.

W. H. Steel, “Etude des effets combines des aberrations et d’une obturation centrale de la pupille sur le contraste des images optiques,” Rev. Opt. (Paris) 32, 143–178 (1953).

J. Opt. Soc. Am. (1)

Rev. Opt. (Paris) (1)

W. H. Steel, “Etude des effets combines des aberrations et d’une obturation centrale de la pupille sur le contraste des images optiques,” Rev. Opt. (Paris) 32, 143–178 (1953).

Other (1)

V. N. Mahajan, “Zernike annular polynomials,” (Aerospace Corporation, Los Angeles, Calif., 1984).

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.


Equations (5)

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

R 5 1 ( ρ ; ) = 10 ( 1 + 4 2 + 4 ) ρ 5 - 12 ( 1 + 4 2 + 4 4 + 6 ) ρ 3 + 3 ( 1 + 4 2 + 10 4 + 4 6 + 8 ) ρ ( 1 - 2 ) 2 [ ( 1 + 4 2 + 4 ) ( 1 + 9 2 + 9 4 + 6 ) ] 1 / 2 ,
R 5 3 ( ρ ; ) = 5 ρ 5 - 4 [ ( 1 - 10 ) / ( 1 - 8 ) ] ρ 3 { ( 1 - 2 ) - 1 [ 25 ( 1 - 12 ) - 24 ( 1 - 10 ) 2 / ( 1 - 8 ) ] } 1 / 2 ,
R 6 4 ( ρ ; ) = 6 ρ 6 - 5 [ ( 1 - 12 ) / ( 1 - 10 ) ] ρ 4 { ( 1 - 2 ) - 1 [ 36 ( 1 - 14 ) - 35 ( 1 - 12 ) 2 / ( 1 - 10 ) ] } 1 / 2 ,
R 6 2 ( ρ ; ) = 15 ( 1 + 4 2 + 10 4 + 4 6 + 8 ) ρ 6 - 20 ( 1 + 4 2 + 10 4 + 10 6 + 4 8 + 10 ) ρ 4 + 6 ( 1 + 4 2 + 10 4 + 20 6 + 10 8 + 4 10 + 12 ) ρ 2 ( 1 - 2 ) 2 [ ( 1 + 4 2 + 10 4 + 4 6 + 8 ) ( 1 + 9 2 + 45 4 + 65 6 + 45 8 + 9 10 + 12 ) ] 1 / 2 .
R n n - 2 ( ρ ; ) = n ρ n - ( n - 1 ) [ ( 1 - 2 n ) / ( 1 - 2 ( n - 1 ) ) ] ρ n - 2 { ( 1 - 2 ) - 1 [ n 2 ( 1 - 2 ( n + 1 ) ) - ( n 2 - 1 ) ( 1 - 2 n ) 2 / ( 1 - 2 ( n - 1 ) ) ] } 1 / 2 .

Metrics