Abstract

A generalized Radon transform is presented that relates, for the case of an evanescent wave that is incident upon a weakly scattering medium, the homogeneous components of the scattered field to the three-dimensional Fourier transform of the dielectric susceptibility. This relationship is used within the context of total internal reflection microscopy to reconstruct the depth structure of the dielectric susceptibility from simulated scattered field data.

© 2000 Optical Society of America

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References

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  1. U. Durig, D. W. Pohl, and F. Rohrer, J. Appl. Phys. 59, 3318 (1986).
    [CrossRef]
  2. E. Betzig and J. Trautman, Science 257, 189 (1992).
    [CrossRef] [PubMed]
  3. D. Courjon and C. Bainer, Rep. Prog. Phys. 57, 989 (1994).
    [CrossRef]
  4. C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
    [CrossRef]
  5. P. A. Temple, Appl. Opt. 20, 2656 (1981).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. D. G. Fischer, J. Mod. Opt. 47, 1359 (2000).
    [CrossRef]
  9. M. Bertero and P. Boccacci, An Introduction to Inverse Problems in Imaging (Institute of Physics, Bristol, England, 1998).
    [CrossRef]

2000 (1)

D. G. Fischer, J. Mod. Opt. 47, 1359 (2000).
[CrossRef]

1996 (1)

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

1994 (1)

D. Courjon and C. Bainer, Rep. Prog. Phys. 57, 989 (1994).
[CrossRef]

1992 (1)

E. Betzig and J. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

1990 (1)

1986 (1)

U. Durig, D. W. Pohl, and F. Rohrer, J. Appl. Phys. 59, 3318 (1986).
[CrossRef]

1981 (1)

1969 (1)

E. Wolf, Opt. Commun. 1, 153 (1969).
[CrossRef]

Bainer, C.

D. Courjon and C. Bainer, Rep. Prog. Phys. 57, 989 (1994).
[CrossRef]

Bertero, M.

M. Bertero and P. Boccacci, An Introduction to Inverse Problems in Imaging (Institute of Physics, Bristol, England, 1998).
[CrossRef]

Betzig, E.

E. Betzig and J. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Boccacci, P.

M. Bertero and P. Boccacci, An Introduction to Inverse Problems in Imaging (Institute of Physics, Bristol, England, 1998).
[CrossRef]

Courjon, D.

Dereux, A.

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

Durig, U.

U. Durig, D. W. Pohl, and F. Rohrer, J. Appl. Phys. 59, 3318 (1986).
[CrossRef]

Fischer, D. G.

D. G. Fischer, J. Mod. Opt. 47, 1359 (2000).
[CrossRef]

Girard, C.

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

Leblanc, S.

Pohl, D. W.

U. Durig, D. W. Pohl, and F. Rohrer, J. Appl. Phys. 59, 3318 (1986).
[CrossRef]

Rohrer, F.

U. Durig, D. W. Pohl, and F. Rohrer, J. Appl. Phys. 59, 3318 (1986).
[CrossRef]

Sarayeddine, K.

Spajer, M.

Temple, P. A.

Trautman, J.

E. Betzig and J. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Vigoureux, J.

Wolf, E.

E. Wolf, Opt. Commun. 1, 153 (1969).
[CrossRef]

Appl. Opt. (2)

J. Appl. Phys. (1)

U. Durig, D. W. Pohl, and F. Rohrer, J. Appl. Phys. 59, 3318 (1986).
[CrossRef]

J. Mod. Opt. (1)

D. G. Fischer, J. Mod. Opt. 47, 1359 (2000).
[CrossRef]

Opt. Commun. (1)

E. Wolf, Opt. Commun. 1, 153 (1969).
[CrossRef]

Rep. Prog. Phys. (2)

D. Courjon and C. Bainer, Rep. Prog. Phys. 57, 989 (1994).
[CrossRef]

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

Science (1)

E. Betzig and J. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Other (1)

M. Bertero and P. Boccacci, An Introduction to Inverse Problems in Imaging (Institute of Physics, Bristol, England, 1998).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Measurement geometry.

Fig. 2
Fig. 2

Behavior of the modulus of the normalized weighting function for s0z=1.5i and sz=1.

Fig. 3
Fig. 3

Reconstructed depth structure γrecz for Δz=λ0/10 and SNR values of (a) 20, (b) 30, and (c) 40 dB.

Equations (9)

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Usr,s0=--as;s0×expik0s·ρ±szzd2s,
s=sx,sy,0,sz=1-s21/2s21is2-11/2s2>1,
ahs;s0=k03 exp-k0s0zΔz2sz×-η˜k0s-s0,Kz×IhKz;sz,s0zdKz,
IhKz;sz,s0z=expk0s0z+ik0sz-Kzdk0s0z+ik0sz-Kz.
NDF=exp-k0s0zmaxΔz+d.
Kmax=k0s0max+s=lnNDFΔz+d2+k02+k0s1/2.
ahs;s0=k03 exp-k0s0zΔzszβ˜k0s-s0×-γ˜KzIhKz;sz,s0zdKz,
ahsi,s0i=A exp-k0s0ziΔzszi×-γ˜KzIhKz;szi,s0zidKz,i=1,,N,
ηρ,z=circρ/ρ00.05 rectz-Δz-d0/2d0+0.1 rectz-Δz-3d0/2d0.

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