Abstract

Performance parameters for focusing, widely used to investigate the properties of pupil filters, are extended to the scalar nonparaxial regime. These measures can be used to investigate focusing properties of different types of focusing systems, including those with apodizers and superresolving masks.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. J. R. Sheppard and Z. S. Hegedus, J. Opt. Soc. Am. A 5, 643 (1988).
    [CrossRef]
  2. M. Martinez-Corral, R. Martinez-Cuenca, I. Escobar, and G. Saavedra, Appl. Phys. Lett. 85, 4319 (2004).
    [CrossRef]
  3. T. G. Jabbour and S. M. Kuebler, Opt. Express 14, 1033 (2005).
    [CrossRef]
  4. H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and T. C. Chong, Appl. Phys. Lett. 89, 171102 (2006).
    [CrossRef]
  5. J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).
  6. C. J. R. Sheppard and H. J. Matthews, J. Opt. Soc. Am. A 4, 1354 (1987).
    [CrossRef]
  7. B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
    [CrossRef]
  8. M. W. Kowarz, Opt. Commun. 110, 274 (1994).
    [CrossRef]
  9. M. A. Alonso and G. W. Forbes, J. Opt. Soc. Am. A 17, 2391 (2000).
    [CrossRef]
  10. C. W. McCutchen, J. Opt. Soc. Am. 54, 240 (1964).
    [CrossRef]
  11. C. J. R. Sheppard and K. G. Larkin, J. Mod. Opt. 41, 1495 (1994).
    [CrossRef]
  12. C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
    [CrossRef]
  13. J. J. Stamnes, Opt. Commun. 37, 311 (1981).
    [CrossRef]

2006

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and T. C. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

2005

2004

M. Martinez-Corral, R. Martinez-Cuenca, I. Escobar, and G. Saavedra, Appl. Phys. Lett. 85, 4319 (2004).
[CrossRef]

2000

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).

M. A. Alonso and G. W. Forbes, J. Opt. Soc. Am. A 17, 2391 (2000).
[CrossRef]

1994

C. J. R. Sheppard and K. G. Larkin, J. Mod. Opt. 41, 1495 (1994).
[CrossRef]

M. W. Kowarz, Opt. Commun. 110, 274 (1994).
[CrossRef]

1993

C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
[CrossRef]

1988

1987

1981

J. J. Stamnes, Opt. Commun. 37, 311 (1981).
[CrossRef]

1964

1959

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Alonso, M. A.

Campos, J.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).

Chong, T. C.

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and T. C. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Escalera, J. C.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).

Escobar, I.

M. Martinez-Corral, R. Martinez-Cuenca, I. Escobar, and G. Saavedra, Appl. Phys. Lett. 85, 4319 (2004).
[CrossRef]

Forbes, G. W.

Gu, M.

C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
[CrossRef]

Hegedus, Z. S.

Jabbour, T. G.

Kowarz, M. W.

M. W. Kowarz, Opt. Commun. 110, 274 (1994).
[CrossRef]

Kuebler, S. M.

Larkin, K. G.

C. J. R. Sheppard and K. G. Larkin, J. Mod. Opt. 41, 1495 (1994).
[CrossRef]

Martinez-Corral, M.

M. Martinez-Corral, R. Martinez-Cuenca, I. Escobar, and G. Saavedra, Appl. Phys. Lett. 85, 4319 (2004).
[CrossRef]

Martinez-Cuenca, R.

M. Martinez-Corral, R. Martinez-Cuenca, I. Escobar, and G. Saavedra, Appl. Phys. Lett. 85, 4319 (2004).
[CrossRef]

Matthews, H. J.

McCutchen, C. W.

Miao, X. S.

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and T. C. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Saavedra, G.

M. Martinez-Corral, R. Martinez-Cuenca, I. Escobar, and G. Saavedra, Appl. Phys. Lett. 85, 4319 (2004).
[CrossRef]

Sheppard, C. J. R.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).

C. J. R. Sheppard and K. G. Larkin, J. Mod. Opt. 41, 1495 (1994).
[CrossRef]

C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
[CrossRef]

C. J. R. Sheppard and Z. S. Hegedus, J. Opt. Soc. Am. A 5, 643 (1988).
[CrossRef]

C. J. R. Sheppard and H. J. Matthews, J. Opt. Soc. Am. A 4, 1354 (1987).
[CrossRef]

Shi, L. P.

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and T. C. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Stamnes, J. J.

J. J. Stamnes, Opt. Commun. 37, 311 (1981).
[CrossRef]

Tan, W. L.

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and T. C. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Wang, H. F.

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and T. C. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Yuan, G. Q.

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and T. C. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Yzuel, M. J.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).

Appl. Phys. Lett.

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and T. C. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

M. Martinez-Corral, R. Martinez-Cuenca, I. Escobar, and G. Saavedra, Appl. Phys. Lett. 85, 4319 (2004).
[CrossRef]

J. Mod. Opt.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).

C. J. R. Sheppard and K. G. Larkin, J. Mod. Opt. 41, 1495 (1994).
[CrossRef]

C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

M. W. Kowarz, Opt. Commun. 110, 274 (1994).
[CrossRef]

J. J. Stamnes, Opt. Commun. 37, 311 (1981).
[CrossRef]

Opt. Express

Proc. R. Soc. London, Ser. A

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

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 (2)

Fig. 1
Fig. 1

Behavior of (a) the parameter F, representing the fraction of the focused energy in the focal spot, and (b) the parameter F I , the intensity at the focus compared with the integrated intensity in the focal plane, both as compared with an aplanatic system for the Herschel condition and the perfect wave. The limiting numerical values α 90 ° are shown.

Fig. 2
Fig. 2

Behavior of (a) the transverse gain parameter G T , (b) the axial gain parameter G A , and (c) the 3D gain parameter G P , all as compared with an aplanatic system for the Herschel condition, the perfect wave, and the Bessel beam. The limiting numerical values for α 90 ° are shown.

Equations (15)

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

U ( ρ , z ) = i k f 0 π P ( θ ) J 0 ( k ρ sin θ ) exp ( i k z cos θ ) sin θ d θ .
U ( ρ , z ) = i k f 1 1 Q ( c ) [ 1 k 2 ρ 2 ( 1 c 2 ) 4 ] [ 1 + i k z c k 2 z 2 c 2 2 ] d c .
I ( 0 , z ) = k 2 f 2 I 0 2 { 1 k 2 z 2 [ I 2 I 0 ( I 1 I 0 ) 2 ] } ,
I ( ρ , 0 ) = k 2 f 2 I 0 2 [ 1 k 2 ρ 2 2 ( 1 I 2 I 0 ) ] .
F = I 0 2 2 1 1 Q ( c ) 2 d c
F I = 2 I 0 2 0 1 Q ( c ) 2 c d c .
G T = 3 2 ( 1 I 2 I 0 )
G A = 3 [ I 2 I 0 ( I 1 I 0 ) 2 ] .
G P = 1 3 ( 2 G T + G A ) = 1 ( I 1 I 0 ) 2 .
G T = sin 2 α 2 ( 3 2 sin 2 α 2 ) ,
G A = sin 4 α 2 ,
G P = sin 2 α 2 ( 2 sin 2 α 2 ) .
G T = 3 2 sin 2 α ,
G A = 0 ,
G P = sin 2 α .

Metrics