Abstract

A simple approach based on the use of a properly designed pupil-phase profile can yield a 3D point-spread function (PSF) that rotates with changing defocus, while keeping its transverse shape approximately invariant over ±34 waves of defocus. Unlike Gauss–Laguerre mode-based approaches, it generalizes readily for encoding spherical aberration too via PSF rotation.

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References

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2008

Q. Xie and D. Zhao, Opt. Commun. 281, 7 (2008).
[CrossRef]

J. Barreiro, T.-C. Wei, and P. Kwiat, Nat. Phys. 4, 282 (2008).
[CrossRef]

S. Pavani and R. Piestun, Opt. Express 16, 3484 (2008).
[CrossRef]

2006

2004

2002

A. Vaziri, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 89, 240401 (2002).
[CrossRef]

2000

1995

1994

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

1992

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Allen, L.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Barnett, S.

Barreiro, J.

J. Barreiro, T.-C. Wei, and P. Kwiat, Nat. Phys. 4, 282 (2008).
[CrossRef]

Beijersbergen, M.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Cathey, W.

Coerwinkel, R.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Courtial, J.

DeLuca, J.

DeLuca, K.

Dowski, E.

Franke-Arnold, S.

Gibson, G.

Greengard, A.

Grover, G.

Kristensen, M.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Kwiat, P.

J. Barreiro, T.-C. Wei, and P. Kwiat, Nat. Phys. 4, 282 (2008).
[CrossRef]

Padgett, M.

Pas’ko, V.

Pavani, S.

Piestun, R.

Quirin, S.

Schechner, Y.

Shamir, J.

Spreeuw, R.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Vasnetsov, M.

Vaziri, A.

A. Vaziri, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 89, 240401 (2002).
[CrossRef]

Wei, T.-C.

J. Barreiro, T.-C. Wei, and P. Kwiat, Nat. Phys. 4, 282 (2008).
[CrossRef]

Weihs, G.

A. Vaziri, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 89, 240401 (2002).
[CrossRef]

Woerdman, J.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Xie, Q.

Q. Xie and D. Zhao, Opt. Commun. 281, 7 (2008).
[CrossRef]

Zeilinger, A.

A. Vaziri, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 89, 240401 (2002).
[CrossRef]

Zhao, D.

Q. Xie and D. Zhao, Opt. Commun. 281, 7 (2008).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Nat. Phys.

J. Barreiro, T.-C. Wei, and P. Kwiat, Nat. Phys. 4, 282 (2008).
[CrossRef]

Opt. Commun.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Q. Xie and D. Zhao, Opt. Commun. 281, 7 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Phys. Rev. Lett.

A. Vaziri, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 89, 240401 (2002).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Surface plots of the incoherent PE-PSF, with L=7 (top row) and 10 terms (middle row) in the Fresnel-zone partitioning of the pupil. The IDL-PSF is shown in the bottom row of plots. The plots from left to right are for increasing values of defocus, namely 24, 16, 8, 0, 8, 16, and 24 rad at the pupil edge.

Fig. 2.
Fig. 2.

Plots of PE-MTF and IDL-MTF versus spatial frequency along the x axis, for 0, 8, and 16 rad of defocus at the pupil edge.

Equations (8)

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

K(s,ϕ;ζ)=1πu1d2uexp[i2πu⃗·s⃗+iζu2iψ(u⃗)],
s⃗=r⃗r0,r0=defλl0R,
ζ=πδzR2λl0(l0+δz).
ψ(u,ϕu)={lϕu|l1Lu<lL,l=1,,L}.
K(s,ϕ;ζ)=2ππl=1Lilexp(ilϕ)×(l1)/Ll/LduuJl(2πus)exp(iζu2),
dϕuexp[ixcos(ϕuϕ)il(ϕuϕ)]=2πilJl(x),
l1LlLduuexp(iζu2)=exp[iζ(l1/2)/L]sin[ζ/(2L)]ζ,
K(s,ϕ;ζ)2πexp[iζ/(2L)]sin[ζ/(2L)]ζ×l=1Lilexp[il(ϕζ/L)]Jl(2πl/Ls).

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