Abstract

A logarithmic phase mask was proposed in 2001, and the depth extension effect was proved at the same time. Three years later, in 2004, further research on that kind of mask obtained more results. This valuable work can be found in two papers [Proc. SPIE 4471, 272 (2001) and Appl. Opt. 43, 2709 (2004) ]. We reviewed the papers carefully and made simple modifications to that mask. The modified phase mask still had the logarithmic form, but the simulation results demonstrated that it was superior to the original one.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. R. Dowski, Jr. and W. T. Cathey, Appl. Opt. 341859 (1995).
    [CrossRef] [PubMed]
  2. S. S. Sherif, E. R. Dowski, and W. T. Cathey, Proc. SPIE 4471, 272 (2001).
    [CrossRef]
  3. S. S. Sherif, W. T. Cathey, and E. R. Dowski, Appl. Opt. 43, 2709 (2004).
    [CrossRef] [PubMed]
  4. Q. Yang, L. Liu, and J. Sun, Opt. Commun. 27256 (2007).
    [CrossRef]
  5. S. Mezouari and A. R. Harvey, Proc. SPIE 4442, 34 (2001).
    [CrossRef]
  6. A. Castro and J. Ojeda-Castañeda, Appl. Opt. 43, 3474 (2004).
    [CrossRef] [PubMed]
  7. A. Sauceda and J. Ojeda-Castañeda, Opt. Lett. 29, 560 (2004).
    [CrossRef] [PubMed]

2007 (1)

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 27256 (2007).
[CrossRef]

2004 (3)

2001 (2)

S. Mezouari and A. R. Harvey, Proc. SPIE 4442, 34 (2001).
[CrossRef]

S. S. Sherif, E. R. Dowski, and W. T. Cathey, Proc. SPIE 4471, 272 (2001).
[CrossRef]

1995 (1)

Castro, A.

Cathey, W. T.

Dowski, E. R.

Harvey, A. R.

S. Mezouari and A. R. Harvey, Proc. SPIE 4442, 34 (2001).
[CrossRef]

Liu, L.

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 27256 (2007).
[CrossRef]

Mezouari, S.

S. Mezouari and A. R. Harvey, Proc. SPIE 4442, 34 (2001).
[CrossRef]

Ojeda-Castañeda, J.

Sauceda, A.

Sherif, S. S.

S. S. Sherif, W. T. Cathey, and E. R. Dowski, Appl. Opt. 43, 2709 (2004).
[CrossRef] [PubMed]

S. S. Sherif, E. R. Dowski, and W. T. Cathey, Proc. SPIE 4471, 272 (2001).
[CrossRef]

Sun, J.

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 27256 (2007).
[CrossRef]

Yang, Q.

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 27256 (2007).
[CrossRef]

Appl. Opt. (3)

Opt. Commun. (1)

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 27256 (2007).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

S. Mezouari and A. R. Harvey, Proc. SPIE 4442, 34 (2001).
[CrossRef]

S. S. Sherif, E. R. Dowski, and W. T. Cathey, Proc. SPIE 4471, 272 (2001).
[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 (5)

Fig. 1
Fig. 1

Defocused MTF with different focus error corresponding to the logarithmic phase mask.

Fig. 2
Fig. 2

Defocused MTF with different degree of defocus corresponding to modified phase mask.

Fig. 3
Fig. 3

Phase profiles of three phase masks.

Fig. 4
Fig. 4

Fisher information as a function of defocus parameter.

Fig. 5
Fig. 5

Comparison between two phase masks.

Equations (4)

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

f ( x , y ) = sgn ( x ) α x max 2 x 2 ( log x + β ) + sgn ( y ) α y max 2 y 2 ( log y + β ) ,
ψ ( x , y ) = 2 π λ f ( x , y ) = 2 π λ [ sgn ( x ) α x max 2 x 2 ( log x + β ) + sgn ( y ) α y max 2 y 2 ( log y + β ) ] .
ψ ( x , y ) = C 1 sgn ( x ) x 2 ( log x + β ) + C 2 sgn ( y ) y 2 ( log y + β ) ,
ψ ( x , y ) = sgn ( x ) C 3 x 2 ( log x + β ) + sgn ( y ) C 4 y 2 ( log y + β ) ,

Metrics