Abstract

To achieve a further extension of the depth of field in wavefront-coded imaging by reducing the impact of focus error in the optical transfer function, we propose the use of a free-form phase mask (FPM) instead of a conventional cubic phase mask (CPM). We optimized the shape of the FPM using the simulated annealing algorithm and confirmed that the optimized FPM provides a much larger focal tolerance and better final images than the CPM in the noise-free case.

© 2008 Optical Society of America

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References

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1983

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

K. Brenner, A. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 44, 323 (1983).
[CrossRef]

Berriel-Valdos, L. R.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Brenner, K.

K. Brenner, A. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 44, 323 (1983).
[CrossRef]

Castro, A.

Cathey, W. T.

Christensen, M. P.

Dowski, E. R.

Gelatte, C. D.

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

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, (McGrraw-Hill, 1968).

Jaroszewicz, Z.

Kirkpatrick, S.

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

Kolodziejczyk, A.

Kubala, K.

Lohmann, A.

K. Brenner, A. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 44, 323 (1983).
[CrossRef]

Mikula, G.

Montes, Emma

Ojeda-Castaneda, J.

Petelczyc, K.

Sherif, S. S.

Somayaji, M.

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Adam Hilger, 1986).

Sypek, M.

Vecchi, M. P.

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

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

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Figures (5)

Fig. 1
Fig. 1

Bird’s-eye view of the surface of the optimized FPM.

Fig. 2
Fig. 2

Contour map of the surface of (a) the optimized FPM and (b) a conventional CPM ( α = 53.5 ) drawn with contours with an interval of 2 π rad.

Fig. 3
Fig. 3

Modulus of the ambiguity function calculated for the WFC system with (a) the optimized FPM and (b) a conventional CPM ( α = 53.5 ) .

Fig. 4
Fig. 4

Value of E as a function of defocus parameter Ψ calculated for WFC imaging systems with CPMs (solid curve, α = 53.5 ; dashed curve, α = 30 ; dotted curve, α = 90 ) and the optimized FPM.

Fig. 5
Fig. 5

Simulated images of a spoke target for an ordinary imaging system with a clear rectangular aperture (left column), simulated final images of the WFC system with the CPM ( α = 53.5 ) (middle column), and those of the WFC system with the optimized FPM (right column). (a)–(c), Ψ = 0 ; (d)–(f), Ψ = 15 ; (g)–(i), Ψ = 30 ; (j)–(l), Ψ = 45 .

Tables (1)

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Table 1 Some of the Dominant Coefficients C n m

Equations (5)

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φ ( x , y ) = α ( x 3 + y 3 ) ,
φ ( x , y ) = n = 0 K ( m = 0 n C n m x n y n m ) ,
P ( x , y ) = exp { j [ φ ( x , y ) + ψ ( x 2 + y 2 ) ] } for x , y 1 ,
ψ = π L 2 4 λ ( 1 f 1 d o 1 d c ) ,
E = k = 1 L i = 1 N j = 1 M H ( u i , v j ; ψ k ) H ( u i , v j ; 0 ) 2 i = 1 N j = 1 M H ( u i , v j ; 0 ) 2

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