Abstract

Some consequences of using partially coherent fields in the recently proposed method of power-extinction diffraction tomography are analyzed. It is found that the method is very tolerant of short spectral coherence lengths. The spectral coherence length of the field is shown to set the scale of a low-pass filter that acts on the subject. The implications of these results for implementation of the method are discussed.

© 2001 Optical Society of America

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References

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  1. P. S. Carney, E. Wolf, and G. S. Agarwal, J. Opt. Soc. Am. A 16, 2643 (1999).
    [CrossRef]
  2. W. H. Carter, J. Opt. Soc. Am. 60, 306 (1970).
    [CrossRef]
  3. E. Wolf, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 83–110.
    [CrossRef]
  4. M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University Press, Cambridge, 1999), Sec.  13.2.
    [CrossRef]
  5. P. Hariharan, Optical Holography (Cambridge University Press, Cambridge, 1996).
    [CrossRef]
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
    [CrossRef]

1999 (1)

1970 (1)

Agarwal, G. S.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University Press, Cambridge, 1999), Sec.  13.2.
[CrossRef]

Carney, P. S.

Carter, W. H.

Hariharan, P.

P. Hariharan, Optical Holography (Cambridge University Press, Cambridge, 1996).
[CrossRef]

Mandel, L.

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

Wolf, E.

P. S. Carney, E. Wolf, and G. S. Agarwal, J. Opt. Soc. Am. A 16, 2643 (1999).
[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), Sec.  13.2.
[CrossRef]

E. Wolf, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 83–110.
[CrossRef]

J. Opt. Soc. Am. (1)

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

Other (4)

E. Wolf, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 83–110.
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University Press, Cambridge, 1999), Sec.  13.2.
[CrossRef]

P. Hariharan, Optical Holography (Cambridge University Press, Cambridge, 1996).
[CrossRef]

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

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Figures (2)

Fig. 1
Fig. 1

Scheme for generating two mutually coherent beams needed to determine the data function. Two identical beams are generated at the beam splitter (BS). The final direction of propagation of the second beam and path-length difference between the beams is controlled by the mirror (M). The beams are finally incident on the object with directions given by s1 and s2.

Fig. 2
Fig. 2

Demonstrating the effects of partial coherence on the reconstruction of an absorbing sphere. In all cases the susceptibility is η=0.01i/2π. In (a) ka=3π, kΔ=10π (dashed curve), and kΔ=3π (solid curve). In (b) ka=10π, kΔ=10π (solid curve), and kΔ=100π (dashed curve). In (c) ka=20π, kΔ=10π (solid curve), and kΔ=100π (dashed curve).

Equations (13)

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Ds1,s2=fs1,s2-f*s2,s1,
Ds1,s2k8πA02Peπ2k-Pe-π2k+iPe0-Peπk.
Ds1,s2=2ik2d3rαrexp-ikr·s1-s2,
A0s,s=k2A02π2Δ2σs2exp18-4k2σs2s+s2-k2Δ2s-s2,
1Δ2=14σs2+1σg2.
Pel=P1e+P2e+P12el,
P12el=4πkImA0s,sexpikls1·Ss×fs,Ssd2sd2s+A0*s,s×exp-ikls1·SsfSs,sd2sd2s,
P12el=8πkImA0s,scosktz^·s×Fs·Ssd2sd2s.
Fs·SsFcosθ+sy+sy-sx-sx2sinθ-sy-sy-sx+sx24cosθ-sx-sx+sy-sy24Fcosθ,
1-sj21-12sj2.
P12el=8πkA02ReeiL1+iL/δ2Im Fcosθ+1+cosθ2ReeiLδ21+iL/δ22Im Fcosθ,
Ds1,s2=i1+ξIm Fs1·s2+1+s1·s22δ2×1+1-π2/δ4ξ2Im Fs1·s2,
αPCr=1+ξ2αLPr+k1+1-π2/δ4ξ264δ2π3×s22-s2/2expikr·sIm F1-s2/2d3s,

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