Abstract

A method is presented to reconstruct three-dimensional tomographic images of weakly scattering objects with subwavelength resolution. The method may be applied to data available in phase-sensitive, total-internal-reflection microscopy. The results follow from an analysis of the near-field inverse scattering problem with evanescent waves.

© 2003 Optical Society of America

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References

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  1. C. W. McCutchen, “Optical systems for observing surface topography by frustrated total internal reflection and interference,” Rev. Sci. Instrum. 35, 1340–1345 (1964).
    [CrossRef]
  2. P. A. Temple, “Total internal reflection microscopy: a surface inspection technique,” Appl. Opt. 20, 2656–2664 (1981).
    [CrossRef] [PubMed]
  3. P. J. Sides, J. Lo, “Measurement of linear nanometric distances between smooth plane parallel bodies by total internal reflection,” Appl. Phys. Lett. 69, 141–142 (1996).
    [CrossRef]
  4. P. T. C. So, H.-S. Kwon, C. Dong, “Resolution enhancement in standing-wave total internal reflection microscopy: a point-spread-function engineering approach,” J. Opt. Soc. Am. A 18, 2833–2845 (2001).
    [CrossRef]
  5. P. S. Carney, J. C. Schotland, “Three-dimensional total internal reflection microscopy,” Opt. Lett. 26, 1072–1074 (2001).
    [CrossRef]
  6. D. G. Fischer, “Subwavelength depth resolution in near-field microscopy,” Opt. Lett. 25, 1529–1531 (2000).
    [CrossRef]
  7. D. G. Fischer, “The information content of weakly scattered fields: implications for near-field imaging of three-dimensional structures,” J. Mod. Opt. 47, 1359–1374 (2000).
    [CrossRef]
  8. A. Lewis, M. Isaacson, A. Harootunian, A. Muray, “Development of a 500 Å spatial resolution light microscope. I. Light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13, 227–231 (1984).
    [CrossRef]
  9. D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
    [CrossRef]
  10. E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
    [CrossRef] [PubMed]
  11. R. Dickson, D. Norris, Y.-L. Tzeng, W. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
    [CrossRef] [PubMed]
  12. J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
    [CrossRef]
  13. P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, Oxford, UK, 1996).
  14. A. A. Maradudin, D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
    [CrossRef]
  15. F. Natterer, The Mathematics of Computerized Tomography (Wiley, New York, 1986).

2001 (2)

2000 (2)

D. G. Fischer, “Subwavelength depth resolution in near-field microscopy,” Opt. Lett. 25, 1529–1531 (2000).
[CrossRef]

D. G. Fischer, “The information content of weakly scattered fields: implications for near-field imaging of three-dimensional structures,” J. Mod. Opt. 47, 1359–1374 (2000).
[CrossRef]

1996 (2)

P. J. Sides, J. Lo, “Measurement of linear nanometric distances between smooth plane parallel bodies by total internal reflection,” Appl. Phys. Lett. 69, 141–142 (1996).
[CrossRef]

R. Dickson, D. Norris, Y.-L. Tzeng, W. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
[CrossRef] [PubMed]

1995 (1)

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

1992 (1)

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

1984 (2)

A. Lewis, M. Isaacson, A. Harootunian, A. Muray, “Development of a 500 Å spatial resolution light microscope. I. Light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13, 227–231 (1984).
[CrossRef]

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

1981 (1)

1975 (1)

A. A. Maradudin, D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
[CrossRef]

1964 (1)

C. W. McCutchen, “Optical systems for observing surface topography by frustrated total internal reflection and interference,” Rev. Sci. Instrum. 35, 1340–1345 (1964).
[CrossRef]

Betzig, E.

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

Carminati, R.

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

Carney, P. S.

Clemmow, P. C.

P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, Oxford, UK, 1996).

Denk, W.

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

Dickson, R.

R. Dickson, D. Norris, Y.-L. Tzeng, W. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
[CrossRef] [PubMed]

Dong, C.

Fischer, D. G.

D. G. Fischer, “Subwavelength depth resolution in near-field microscopy,” Opt. Lett. 25, 1529–1531 (2000).
[CrossRef]

D. G. Fischer, “The information content of weakly scattered fields: implications for near-field imaging of three-dimensional structures,” J. Mod. Opt. 47, 1359–1374 (2000).
[CrossRef]

Greffet, J.-J.

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

Harootunian, A.

A. Lewis, M. Isaacson, A. Harootunian, A. Muray, “Development of a 500 Å spatial resolution light microscope. I. Light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13, 227–231 (1984).
[CrossRef]

Isaacson, M.

A. Lewis, M. Isaacson, A. Harootunian, A. Muray, “Development of a 500 Å spatial resolution light microscope. I. Light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13, 227–231 (1984).
[CrossRef]

Kwon, H.-S.

Lanz, M.

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

Lewis, A.

A. Lewis, M. Isaacson, A. Harootunian, A. Muray, “Development of a 500 Å spatial resolution light microscope. I. Light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13, 227–231 (1984).
[CrossRef]

Lo, J.

P. J. Sides, J. Lo, “Measurement of linear nanometric distances between smooth plane parallel bodies by total internal reflection,” Appl. Phys. Lett. 69, 141–142 (1996).
[CrossRef]

Maradudin, A. A.

A. A. Maradudin, D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
[CrossRef]

McCutchen, C. W.

C. W. McCutchen, “Optical systems for observing surface topography by frustrated total internal reflection and interference,” Rev. Sci. Instrum. 35, 1340–1345 (1964).
[CrossRef]

Mills, D. L.

A. A. Maradudin, D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
[CrossRef]

Moerner, W.

R. Dickson, D. Norris, Y.-L. Tzeng, W. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
[CrossRef] [PubMed]

Muray, A.

A. Lewis, M. Isaacson, A. Harootunian, A. Muray, “Development of a 500 Å spatial resolution light microscope. I. Light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13, 227–231 (1984).
[CrossRef]

Natterer, F.

F. Natterer, The Mathematics of Computerized Tomography (Wiley, New York, 1986).

Norris, D.

R. Dickson, D. Norris, Y.-L. Tzeng, W. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
[CrossRef] [PubMed]

Pohl, D. W.

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

Schotland, J. C.

Sentenac, A.

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

Sides, P. J.

P. J. Sides, J. Lo, “Measurement of linear nanometric distances between smooth plane parallel bodies by total internal reflection,” Appl. Phys. Lett. 69, 141–142 (1996).
[CrossRef]

So, P. T. C.

Temple, P. A.

Trautman, J. K.

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

Tzeng, Y.-L.

R. Dickson, D. Norris, Y.-L. Tzeng, W. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

P. J. Sides, J. Lo, “Measurement of linear nanometric distances between smooth plane parallel bodies by total internal reflection,” Appl. Phys. Lett. 69, 141–142 (1996).
[CrossRef]

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

J. Mod. Opt. (1)

D. G. Fischer, “The information content of weakly scattered fields: implications for near-field imaging of three-dimensional structures,” J. Mod. Opt. 47, 1359–1374 (2000).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (1)

A. A. Maradudin, D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
[CrossRef]

Rev. Sci. Instrum. (1)

C. W. McCutchen, “Optical systems for observing surface topography by frustrated total internal reflection and interference,” Rev. Sci. Instrum. 35, 1340–1345 (1964).
[CrossRef]

Science (2)

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

R. Dickson, D. Norris, Y.-L. Tzeng, W. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
[CrossRef] [PubMed]

Ultramicroscopy (1)

A. Lewis, M. Isaacson, A. Harootunian, A. Muray, “Development of a 500 Å spatial resolution light microscope. I. Light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13, 227–231 (1984).
[CrossRef]

Other (2)

F. Natterer, The Mathematics of Computerized Tomography (Wiley, New York, 1986).

P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, Oxford, UK, 1996).

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Figures (1)

Fig. 1
Fig. 1

Illustration of the measurement scenario: Evanescent waves are generated at the prism face by total internal reflection (TIR); the TIR is then partly frustrated by the presence of the scatterer, which scatters evanescent modes to homogeneous modes that propagate to the far zone.

Equations (73)

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2U(r)+k02n2(z)U(r)=-4πk02η(r)U(r),
U=Ui+Us,
2Ui(r)+k02n2(z)Ui(r)=0.
2Us(r)+k02n2(z)Us(r)=-4πk02η(r)U(r).
Us(r)=k02d3rG(r, r)U(r)η(r),
2G(r, r)+n2(z)k02G(r, r)=-4πδ(r-r),
G(r, r)|z=0+=G(r, r)|z=0-;
zˆ·G(r, r)|z=0+=zˆ·G(r, r)|z=0-.
G(r, r)=i2πd2qkz(q){1+R(q)exp[2ikz(q)z]}×exp[ik(q)·(r-r)],
R(q)=kz(q)-kz(q)kz(q)+kz(q),
kz(q)=(k02-q2)1/2,
kz(q)=(n2k02-q2)1/2,
Ui(r)=exp[ik(q)·r],
Us(r)=k02d3rG(r, r)Ui(r)η(r).
G(r, r){1+R(q)exp[2ikz(q)z]}×exp(ik0r)rexp[-ik(q)·r],
Us(r)exp(ik0r)rA(q1, q2),
A(q1, q2)=k02d3r{1+R(q2)exp[2ikz(q2)z]}×exp{i[k(q1)-k(q2)]·r}η(r).
××E(r)-k02n2(z)E(r)=4πk02η(r)E(r),
E=Ei+Es.
××Ei(r)-k02n2(z)Ei(r)=0.
××Es(r)-k02n2(z)Es(r)=4πk02η(r)E(r).
Eαs(r)=k02d3rGαβ(r, r)Eβ(r)η(r),
××G(r, r)-k02n2(z)G(r, r)=4πδ(r-r)I,
zˆ×G(r, r)|z=0+=zˆ×G(r, r)|z=0-,
zˆ××G(r, r)|z=0+=zˆ××G(r, r)|z=0-.
Gαβ(r, r)=i2πd2qkz(q)gαβ(q, z)exp[ik(q)·(r-r)].
Eαi(r)=Eα(0)exp[ik(q)·r],
Eαs(r)=k02d3rGαβ(r, r)Eβ(0)exp[ik(q)·r]η(r).
Gαβ(r, r)gαβ(q, z)exp(ik0r)rexp[-ik(q)·r],
Eαs(r)Aαβ(q1, q2)Eβ(0)exp(ik0r)r,
Aαβ(q1, q2)=d3rwαβ(q2, z)×exp{i[k(q1)-k(q2)]·r}η(r),
wαβ(q, z)=k02gαβ(q, z).
A(x, y)=nσngn(x)fn*(y),
A*Afn=σn2fn,
AA*gn=σn2gn.
Afn=σngn,
A*gn=σnfn.
A+(x, y)=n1σnfn(x)gn*(y).
A(q1, q2)=d3rK(q1, q2;r)η(r),
K(q1, q2;r)=exp[i(q1-q2)·ρ]κ(q1, q2;z),
κ(q1, q2;z)=k02{1+R1(q2)exp[2ikz(q2)z]}×exp{i[kz(q1)-kz(q2)]z}.
η(ρ, z)=qΛcq(z)exp(iq·ρ),
K(q1, q2;r)=QΛexp(iQ·ρ)δ(Q+q2-q1)×κ(Q+q2, q2;z),
KK*(q1, q2;q1, q2)=QΛM(q2, q2;Q)δ(Q+q2-q1)δ(Q+q2-q1),
M(q2, q2;Q)=0Ldzκ(Q+q2, q2;z)×κ*(Q+q2, q2;z),
KK*gQQ=σQQ2gQQ,
gQQ(q1, q2)=CQ(q2;Q)δ(Q+q2-q1),
qΛM(q, q;Q)CQ(q;Q)=σQQ2CQ(q;Q).
fQQ(r)=1σQQqΛexp(-iQ·ρ)κ*(Q+q, q;z)CQ*(q;Q).
K(q1, q2;r)=Q,QσQQfQQ*(r)gQQ(q1, q2).
η+(r)=q1,q2K+(r; q1, q2)A(q1, q2),
K+(r; q1, q2)=Q,Q1σQQfQQ(r)gQQ*(q1, q2).
Q1σQQ2CQ(q; Q)CQ*(q; Q)=M-1(q, q; Q),
η+(r)=q1,q2,q2Qexp(-iQ·ρ)×δ(Q+q2-q1)M-1(q2, q2; Q)×κ*(Q+q2, q2; z)A(q1, q2),
Aαβ(q1, q2)=d3rKαβ(q1, q2; r)η(r),
Kαβ(q1, q2; r)=exp[i(q1-q2)·ρ]καβ(q1, q2; z),
καβ(q1, q2; z)=wαβ(q2, z)exp{i[kz(q1)-kz(q2)]z}×χ(q1, q2).
Kαβ(q1, q2; r)=Q,QσQQfQQ*(r)gQQαβ(q1, q2).
gQQαβ(q1, q2)=CQαβ(q2; Q)δ(Q+q2-q1),
fQQ(r)=1σQQqΛexp(-iQ·ρ)×κ*(Q+q, q; z)CQ*(q; Q).
qΛMαβαβ(q, q; Q)CQαβ(q; Q)=σQQ2CQαβ(q; Q),
Mαβαβ(q2, q2; Q)=0Ldzκαβ(Q+q2, q2; z)×καβ*(Q+q2, q2; z).
η+(r)=q1,q2Kαβ+(r; q1, q2)Aαβ(q1, q2),
Kαβ+(r; q1, q2)=Q,Q1σQQfQQ(r)gQQαβ*(q1, q2).
η+(r)=q1,q2,q2Qexp(-iQ·ρ)δ(Q+q2-q1)×[M-1(Q)]αβαβ(q2, q2)καβ*(Q+q2, q2; z)Aαβ(q1, q2),
g(q, z)=S-1(q)g˜(q, z)S(q),
S(q)=|q|-1qxqy0-qyqx000|q|.
g˜xx=kz(q)k02{1+R(q)exp[2ikz(q)z]},
g˜yy=1+R(q)exp[2ikz(q)z],
g˜zz=|q|k02{1-R(q)exp[2ikz(q)z]},
g˜zx=-|q|kz(q)k02{1+R(q)exp[2ikz(q)z]},
g˜xz=-|q|kz(q)k02{1-R(q)exp[2ikz(q)z]},
R(q)=kz(q)-nkz(q)kz(q)+nkz(q).

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