Abstract

We put forward the idea of implementing a confocal setup to suppress the large sidelobes spreading all through the field outside the central core. They are produced when an apodization film is imposed on an ordinary lens. Furthermore, this avoids the imaging quality degradation caused by nonaxial points and non-Gaussian-plane points. Also a configuration for achieving three-dimensional superresolution is depicted and discussed.

© 1997 Optical Society of America

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References

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  1. M. Born, E. Wolf, “Elements of the theory of diffraction,” in Principles of Optics (Pergamon, London, 1975), Chap. 8, pp. 370–458.
  2. B. R. Frieden, “On arbitrarily perfect imagery with a finite aperture,” Opt. Acta 16, 795–807 (1969).
    [CrossRef]
  3. B. R. Frieden, “The extrapolating pupil, image synthesis, and some thought applications,” Appl. Opt. 9, 2489–2496 (1970).
    [CrossRef] [PubMed]
  4. C. J. R. Sheppard, “Scanning optical microscopy,” in Advances in Optical and Electron Microscopy, R. Barer, V. E. Cosslett, eds. (Academic, London, 1987), Vol. 10, pp. 1–98.
  5. T. Wilson, Confocal Microscopy (Academic, London1990).

1970 (1)

1969 (1)

B. R. Frieden, “On arbitrarily perfect imagery with a finite aperture,” Opt. Acta 16, 795–807 (1969).
[CrossRef]

Born, M.

M. Born, E. Wolf, “Elements of the theory of diffraction,” in Principles of Optics (Pergamon, London, 1975), Chap. 8, pp. 370–458.

Frieden, B. R.

B. R. Frieden, “The extrapolating pupil, image synthesis, and some thought applications,” Appl. Opt. 9, 2489–2496 (1970).
[CrossRef] [PubMed]

B. R. Frieden, “On arbitrarily perfect imagery with a finite aperture,” Opt. Acta 16, 795–807 (1969).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, “Scanning optical microscopy,” in Advances in Optical and Electron Microscopy, R. Barer, V. E. Cosslett, eds. (Academic, London, 1987), Vol. 10, pp. 1–98.

Wilson, T.

T. Wilson, Confocal Microscopy (Academic, London1990).

Wolf, E.

M. Born, E. Wolf, “Elements of the theory of diffraction,” in Principles of Optics (Pergamon, London, 1975), Chap. 8, pp. 370–458.

Appl. Opt. (1)

Opt. Acta (1)

B. R. Frieden, “On arbitrarily perfect imagery with a finite aperture,” Opt. Acta 16, 795–807 (1969).
[CrossRef]

Other (3)

M. Born, E. Wolf, “Elements of the theory of diffraction,” in Principles of Optics (Pergamon, London, 1975), Chap. 8, pp. 370–458.

C. J. R. Sheppard, “Scanning optical microscopy,” in Advances in Optical and Electron Microscopy, R. Barer, V. E. Cosslett, eds. (Academic, London, 1987), Vol. 10, pp. 1–98.

T. Wilson, Confocal Microscopy (Academic, London1990).

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Figures (3)

Fig. 1
Fig. 1

Suggested experimental setup for achieving lateral superresolution. An apodization film is inserted at the back focal plane of lens 1, and lens 2 is added to form a confocal configuration so as to suppress the great sidelobes caused by the apodization film.

Fig. 2
Fig. 2

Confocal setup with a point source and a point detector based on Fig. 1. P1 represents the combination of lens 1 and its apodization film with the effective point amplitude response of h1. P2 is lens 2 with point amplitude response h2.

Fig. 3
Fig. 3

Suggested configuration for achieving three-dimensional superresolution.

Equations (41)

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UNβ=x0/2πβ11/2neven=0N-1n/2λnc1-3/2×ψnc1, 0ψnc1, βx0/β1,
c1=β1x0
Etβ=AUNβ.
Pβ=1,ββ10,otherwise.
aNx=-+EtβPβexpiβxdβ=A -β1+β1 UNβexpiβxdβ.
aNx=Aneven=0N λnc1-1ψnc1, 0ψnc1, x.
aNxsincπβ1x xx0,
β1=β1/δN,
ΔN=6x0/N.
aNx-Δ=A neven=0N λnc1-1ψnc1, Δψnc1, x.
h1x=aNx.
h2x=sincπβ2x,
U1x=h1x.
U2x=h1xOx-xs,
Ox=0 if x>x0/2.
Ox-xs=0 if x-xs>x0/2
xsx0/2.
Ox-xs=0 if x>x0.
U2x=aNxOx-xsxx00otherwise.
U3x=U2h2=-+ U2xh2x-xdx,
Ixs=-+U3x2Ddx,
D=δx.
Ixs=heffOx2,
heffx=h1x·h2x
heffx=sin cπβ1/δNxsin cπβ2xxx00otherwise.
UN,Nβ, γ=UNβUNγ
aN,Nx, y=Aneven=0N λnc1-1ψnc1, 0ψnc1, x×neven=0N λnc2-1ψnc2, 0ψnc2, y,
c1=β1x0, c2=γ1y0,
aN,Nx, ysincπβ1xsincπγ1y xx0, yy0,
β1=β1/δN, β1=γ1/δN,
WMβ=βneven=0M-1n/2λnc-3/2ψnc, 0×ψnc, z01-2β2/β22,
c=β22z0/4k,
bMz=-β2+β2WMβexpjz/2kβ2dβ.
bMz=Aneven=0Mλnc-1ψnc, 0ψnc,z.
bMz-Δ=Aneven=0M λnc-1ψnc, Δψnc, z.
bMzsincπβ2z zz0,
β2=β2/δM,
heffx, y, z=h1x, yh2z,
h1x, y=aN,Nx, yxx0, yy0,0otherwise,
h2z=bMzzz00otherwise.
heffx, y, z=sin cπβ1/δnxsin cπγ1/δnYsin cπβ2/δMz0xx0, yy0, zz0otherwise.

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