Abstract

A polynomial phase mask is designed and fabricated for enhancing the depth of field of a microscope by more than tenfold. A generic polynomial of degree 31 that consists of 16 odd power terms is optimized by simulated annealing with a realistic average modulation transfer function (MTF) iteratively set as the target MTF. Optical experimental results are shown.

© 2008 Optical Society of America

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References

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  1. E. R. Dowski, Jr., and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859-1866 (1995).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  4. S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335-345 (2004).
    [CrossRef]
  5. Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56-66 (2007).
    [CrossRef]
  6. A. Sauceda and J. Ojeda-Castañeda, “High focal depth with fractional-power wave fronts,” Opt. Lett. 29, 560-562 (2004).
    [CrossRef] [PubMed]
  7. S. S. Sherif, E. R. Dowski, and W. T. Cathey, “Extended depth of field in hybrid imaging systems: circular aperture,” J. Mod. Opt. 51, 1191-1209 (2004).
  8. S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
    [CrossRef] [PubMed]
  9. S. S. Sherif, W. T. Cathey, and E. R. Dowski, “Phase plate to extend the depth of field of incoherent hybrid imaging systems,” Appl. Opt. 43, 2709-2721 (2004).
    [CrossRef] [PubMed]

2007 (1)

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56-66 (2007).
[CrossRef]

2006 (1)

2004 (4)

A. Sauceda and J. Ojeda-Castañeda, “High focal depth with fractional-power wave fronts,” Opt. Lett. 29, 560-562 (2004).
[CrossRef] [PubMed]

S. S. Sherif, W. T. Cathey, and E. R. Dowski, “Phase plate to extend the depth of field of incoherent hybrid imaging systems,” Appl. Opt. 43, 2709-2721 (2004).
[CrossRef] [PubMed]

S. S. Sherif, E. R. Dowski, and W. T. Cathey, “Extended depth of field in hybrid imaging systems: circular aperture,” J. Mod. Opt. 51, 1191-1209 (2004).

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

2001 (1)

1995 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Ben-Eliezer, E.

Cathey, W. T.

Chi, W.

Dowski, E. R.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

George, N.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Konforti, N.

Liu, L.

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56-66 (2007).
[CrossRef]

Marom, E.

Ojeda-Castañeda, J.

Pauca, V. P.

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

Plemmons, R. J.

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

Prasad, S.

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

Sauceda, A.

Sherif, S. S.

S. S. Sherif, E. R. Dowski, and W. T. Cathey, “Extended depth of field in hybrid imaging systems: circular aperture,” J. Mod. Opt. 51, 1191-1209 (2004).

S. S. Sherif, W. T. Cathey, and E. R. Dowski, “Phase plate to extend the depth of field of incoherent hybrid imaging systems,” Appl. Opt. 43, 2709-2721 (2004).
[CrossRef] [PubMed]

Sun, J.

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56-66 (2007).
[CrossRef]

Torgersen, T. C.

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

van der Gracht, J.

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Yang, Q.

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56-66 (2007).
[CrossRef]

Zalevsky, Z.

Appl. Opt. (3)

J. Mod. Opt. (1)

S. S. Sherif, E. R. Dowski, and W. T. Cathey, “Extended depth of field in hybrid imaging systems: circular aperture,” J. Mod. Opt. 51, 1191-1209 (2004).

Opt. Commun. (1)

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56-66 (2007).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (1)

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

Science (1)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Target MTFs in iterations of the simulated annealing processes.

Fig. 2
Fig. 2

(a) Optimized MTFs and (b) PTFs for various defocus values after the first iteration.

Fig. 3
Fig. 3

(a) MTFs and (b) PTFs of the final solution.

Fig. 4
Fig. 4

Phase profile of the optimized mask. The linear phase term is removed.

Fig. 5
Fig. 5

Images with and without phase mask for several negative defocuses and the images restored by decovolution.

Tables (2)

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Table 1 Coefficients of the Optimized Polynomial

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Table 2 Comparison With Other Phase Masks and Their Fit to the Proposed Phase Mask

Equations (7)

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ϕ ( x o , y o ) = 2 π λ n = 0 N β n ( x o 2 n + 1 + y o 2 n + 1 ) ,
Cost = m = 1 M 0 2 | MTF ( u ; ( W 20 ) m ) MTF target ( u ) | 2 d u ,
W 20 = L 2 2 ( 1 f 1 d obj 1 d img )
PSF ( x ) | FT { rect ( x o ) exp [ j ϕ ( x o ) + j 2 π λ W 20 x o 2 ] } | 2 .
[ MTF target ( u ) ] i + 1 = 1 M m = 1 M [ MTF ( u ; ( W 20 ) m ) ] i ,
d ϕ d x o = 2 π λ n = 0 N β n ( 2 n + 1 ) x o 2 n .
F ( u , v ) = OTF diffraction limited ( u , v ) { m = 1 M MTF ( u , v ; ( W 20 ) m ) / M } × exp [ j m = 1 M PTF ( u , v ; ( W 20 ) m ) / M ] ,

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