Abstract

We propose a novel phase mask called the rational phase mask (RPM) to extend the depth of field in optical-digital hybrid imaging systems. Using the invariance to defocus of the modulation transfer function as the merit function, we adopt the simulated annealing algorithm to optimize the RPM together with the other three existing phase masks. Numerical comparisons prove the RPM’s superiority.

© 2009 Optical Society of America

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References

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  1. E. R. Dowski and W. T. Cathey, Appl. Opt. 34, 1859 (1995).
    [CrossRef] [PubMed]
  2. S. S. Sherif, W. T. Cathey, and E. R. Dowski, Appl. Opt. 43, 2709 (2004).
    [CrossRef] [PubMed]
  3. H. Zhao, Q. Li, and H. Feng, Opt. Lett. 33, 11, 1171 (2008).
    [CrossRef] [PubMed]
  4. Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
    [CrossRef]
  5. J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, 4th ed. (Prentice Hall, 2004).
  6. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).
  7. H. H. Hopkins, Opt. Acta 31, 3, 345 (1984).
    [CrossRef]
  8. S. Bagheri, P. Silveira, and D. Farias, J. Opt. Soc. Am. A 25, 5, 1064 (2008).
    [CrossRef]
  9. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
    [CrossRef] [PubMed]

2008 (2)

2007 (1)

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
[CrossRef]

2005 (1)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

2004 (2)

J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, 4th ed. (Prentice Hall, 2004).

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

1995 (1)

1984 (1)

H. H. Hopkins, Opt. Acta 31, 3, 345 (1984).
[CrossRef]

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Bagheri, S.

Cathey, W. T.

Dowski, E. R.

Farias, D.

Feng, H.

Fink, K. D.

J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, 4th ed. (Prentice Hall, 2004).

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

Hopkins, H. H.

H. H. Hopkins, Opt. Acta 31, 3, 345 (1984).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Li, Q.

Liu, L.

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
[CrossRef]

Mathews, J. H.

J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, 4th ed. (Prentice Hall, 2004).

Sherif, S. S.

Silveira, P.

Sun, J.

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Yang, Q.

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
[CrossRef]

Zhao, H.

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

H. H. Hopkins, Opt. Acta 31, 3, 345 (1984).
[CrossRef]

Opt. Commun. (1)

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
[CrossRef]

Opt. Lett. (1)

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Other (2)

J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, 4th ed. (Prentice Hall, 2004).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

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Figures (4)

Fig. 1
Fig. 1

Phase profiles of the optimized phase masks.

Fig. 2
Fig. 2

Normalized MTF curves with various defocus parameters.

Fig. 3
Fig. 3

Hilbert space angles between the defocus MTF and the infocus version.

Fig. 4
Fig. 4

Simulated images of a spoke target. Rows 1–3: ψ = 0 , 10, and 30, respectively.

Tables (1)

Tables Icon

Table 1 Values of the Merit Function after Optimization

Equations (11)

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ϕ CPM ( x ) = α x 3 ,
ϕ LPM ( x ) = sign ( x ) A x 2 ( log x + B ) ,
ϕ EPM ( x ) = β x exp ( γ x 2 ) ,
ϕ RPM ( x ) = n = 0 N a n x n m = 0 M b m x m ,
ϕ RPM ( x ) = n = 1 N sign ( x ) a n x n ( 1 + m = 1 M b m x m ) ,
P ( x ) = 1 2 exp [ j ϕ ( x ) ] for x 1 .
H ( u , ψ ) = P ( x + u 2 ) P * ( x u 2 ) exp ( j 2 u ψ x ) d x ,
ψ = π L 2 4 λ ( 1 f 1 d o 1 d i ) ,
min a k l [ H ( u l , ψ k ) H ( u l , 0 ) ] 2
subject to l H ( u l , 0 ) I 0 ,
cos [ θ ( ψ ) ] = l H ( u l , 0 ) H ( u l , ψ ) [ l H ( u l , 0 ) 2 ] 1 2 [ l H ( u l , ψ ) 2 ] 1 2 .

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