Abstract

A modified form of diffraction tomography is presented in which measurements of the phase of the scattered field are replaced with measurements of the intensity on two planes beyond the scatterer. The new method is illustrated by an example.

© 2002 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, Cambridge, 1999).
    [CrossRef]
  2. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).
  3. G. Gbur and E. Wolf, J. Opt. Soc. Am. A 18, 2132 (2001).
    [CrossRef]
  4. M. R. Teague, J. Opt. Soc. Am. 73, 1434 (1983).
    [CrossRef]
  5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
    [CrossRef]
  6. G. Gbur and E. Wolf, J. Opt. Soc. Am. A 19, 2194 (2002).
    [CrossRef]

2002

2001

1983

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, Cambridge, 1999).
[CrossRef]

Gbur, G.

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
[CrossRef]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

Teague, M. R.

Wolf, E.

G. Gbur and E. Wolf, J. Opt. Soc. Am. A 19, 2194 (2002).
[CrossRef]

G. Gbur and E. Wolf, J. Opt. Soc. Am. A 18, 2132 (2001).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, Cambridge, 1999).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, Cambridge, 1999).
[CrossRef]

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

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Figures (2)

Fig. 1
Fig. 1

Illustrating the notation for tomographic reconstruction of a scattering object.

Fig. 2
Fig. 2

Reconstruction of a complex scattering potential by use of the new tomographic method. The dashed curve indicates the actual scattering potential. It can be seen that there is good agreement between the actual and the reconstructed potentials.

Equations (14)

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UrUirexpψr,
ψr=1UirVFrexpikr-rr-rUird3r,
Fr=k24πn2r-1.
ψx,y,z=i2π21wF˜us1+vs2+w-ks0×expiw-kzexpiux+vydudv,
w=k2-u2-v2whenu2+v2k2,iu2+v2-k2whenu2+v2>k2,F˜K=12π3VFrexp-iK·rd3r.
Ix,y,z=Ux,y,z2=expψx,y,z+ψ*x,y,z.
DIx,y,z=logIx,y,z=ψx,y,z+ψ*x,y,z.
DˆIu,v;z=12π2DIx,y,z×exp-iux+vydxdy.
DˆIu,v;z=i2π2w2(w*F˜us1+vs2+w-ks0×expiw-kz-wF˜-us1-vs2+w-ks0*×exp-iw*-kz).
DˆΔu,v;dDˆIu,v;d-DˆIu,v;d+Δexpiw-kΔΔ,
DˆΔu,v;d=2π2iwΔF˜us1+vs2+w-ks0×expiw-kd1-exp2iw-kΔ.
ψˆu,v;d=2π2iwF˜us1+vs2+w-ks0×expiw-kd,
2k-k2-u2-v2Δ=2nπ,
u2+v22πk/Δ.

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