Abstract

We present an annularly distributed phase-only mask that generates an axial irradiance distribution identical to the point spread function of the Dowski–Cathey lens [Appl. Opt. 34, 1859 (1995) ]. This apodizer has an ambiguity function with a bow-tie effect, and consequently its axial modulation transfer function varies slowly with spherical aberration.

© 2005 Optical Society of America

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References

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  1. E. R. Dowski and T. W. Cathey, Appl. Opt. 34, 1859 (1995).
    [CrossRef] [PubMed]
  2. S. Mezouari and A. A. Harvey, Opt. Lett. 28, 771 (2003).
    [CrossRef] [PubMed]
  3. N. George and W. Chi, J. Opt. Pure Appl. 5, S157 (2003).
    [CrossRef]
  4. A. Sauceda and J. Ojeda-Castaneda, Opt. Lett. 29, 560 (2004).
    [CrossRef] [PubMed]
  5. A. Castro and J. Ojeda-Castaneda, Appl. Opt. 43, 3474 (2004).
    [CrossRef] [PubMed]
  6. J. Ojeda-Castaneda, P. Andres, and E. Montes, J. Opt. Soc. Am. A 4, 313 (1987).
    [CrossRef]
  7. K.-H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, Opt. Commun. 44, 323 (1983).
    [CrossRef]

2004

2003

S. Mezouari and A. A. Harvey, Opt. Lett. 28, 771 (2003).
[CrossRef] [PubMed]

N. George and W. Chi, J. Opt. Pure Appl. 5, S157 (2003).
[CrossRef]

1995

1987

1983

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

Andres, P.

Brenner, K.-H.

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

Castro, A.

Cathey, T. W.

Chi, W.

N. George and W. Chi, J. Opt. Pure Appl. 5, S157 (2003).
[CrossRef]

Dowski, E. R.

George, N.

N. George and W. Chi, J. Opt. Pure Appl. 5, S157 (2003).
[CrossRef]

Harvey, A. A.

Lohmann, A. W.

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

Mezouari, S.

Montes, E.

Ojeda-Castaneda, J.

Sauceda, A.

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Figures (4)

Fig. 1
Fig. 1

Wave-front aberration as a function of normalized spatial frequency.

Fig. 2
Fig. 2

Axial irradiance as a function of defocus coefficient ( W 20 λ ) for phase delay ( α λ ) = 500 .

Fig. 3
Fig. 3

Modulus of the ambiguity function for ( α λ ) = 500 : (a) three-dimensional plot, (b) contour plot.

Fig. 4
Fig. 4

Contour plot of the MTF as a function of ζ and W 40 for ( α λ ) = 500 .

Equations (17)

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s ( r , W 20 ) = 2 π 0 S ( ρ ) J 0 ( 2 π r ρ ) exp [ i 2 π ( W 20 λ ) ( ρ Ω ) 2 ] ρ d ρ .
s ( 0 , W 20 ) = 2 π 0 S ( ρ ) exp [ i 2 π ( W 20 λ ) ( ρ Ω ) 2 ] ρ d ρ .
ζ = ( ρ 2 Ω 2 ) 1 2 , R ( ζ ) = S ( ρ ) ,
s ( 0 , W 20 ) = π Ω 2 exp ( i π W 20 λ ) R ( ζ ) exp [ i 2 π ( W 20 λ ) ζ ] d ζ .
h ( W 20 λ ) = R ( ζ ) exp [ i 2 π ( W 20 λ ) ζ ] d ζ 2 .
H ( ζ ) = h ( W 20 λ ) exp [ i 2 π ζ ( W 20 λ ) ] d ( W 20 λ ) .
H ( ζ ) = R ( ζ + ζ 2 ) R * ( ζ ζ 2 ) d ζ .
S ( ρ ) = P ( ρ ) exp [ i 2 π ( W 40 λ ) ( ρ Ω ) 4 ] .
S ( ρ ) = R ( ζ ) = Q ( ζ ) exp [ i 2 π ( W 40 λ ) ( ζ 2 + ζ + 1 4 ) ] , Q ( ζ ) = P ( ρ ) .
H ( ζ ; W 40 ) = exp [ i 2 π ( W 40 4 λ ) ζ ] Q ( ζ + ζ 2 ) Q * ( ζ ζ 2 ) exp [ i 2 π ( 2 W 40 ζ λ ) ζ ] d ζ .
A ( y , ζ ) = Q ( ζ + ζ 2 ) Q * ( ζ ζ 2 ) exp ( i 2 π y ζ ) d ζ .
H ( ζ ; W 40 ) = A ( y = 2 W 40 ζ λ , ζ ) .
P ( ρ ) = exp { i 2 π ( α λ ) [ ( ρ 2 Ω 2 ) 1 2 ] 3 } circ ( ρ Ω ) .
Q ( ζ ) = exp [ i 2 π ( α λ ) ζ 3 ] rect ( ζ ) .
h ( W 20 ; α λ ) = 1 2 1 2 exp [ i 2 π ( α λ ) ζ 3 ] exp [ i 2 π ( W 20 λ ) ζ ] d ζ 2 .
H ( ζ ; α λ ) = ( 1 ζ ) 2 ( 1 ζ ) 2 exp [ i 6 π ( α λ ) ζ ζ 2 + i 2 π ( 2 W 40 ζ λ ) ζ ] d ζ ,
A ( y ; ζ ) = ( 1 ζ ) 2 ( 1 ζ ) 2 exp [ i 6 π ( α λ ) ζ ζ 2 + i 2 π y ζ ] d ζ ,

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