Abstract

We describe measurement of the degree of coherence induced by a random light source distributed along the longitudinal z axis. If this degree of coherence is measured only between all the in-plane pairs of points placed along the radial lines it is proportional to the Fourier transform of the source’s three-dimensional intensity distribution as seen from the paraxial far zone. A reconstruction of the source shape from the measured degree of coherence is also demonstrated.

© 1996 Optical Society of America

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References

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  1. J. T. Armstrong, D. J. Hutter, K. J. Johnston, D. Mozurkewich, Phys. Today 48(5), 42 (1995).
    [CrossRef]
  2. J. Rosen, A. Yariv, J. Opt. Soc. Am. A 13, 2091 (1996).
    [CrossRef]
  3. J. Rosen, A. Yariv, Opt. Lett. 21, 1011 (1996).
    [CrossRef] [PubMed]
  4. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), Chap. 4, p. 150.
  5. J. W. Goodman, Statistical Optics, 1st ed. (Wiley, New York, 1985), Chap. 5, p. 208.
  6. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Chap. 10, p. 509.

1996 (2)

1995 (1)

J. T. Armstrong, D. J. Hutter, K. J. Johnston, D. Mozurkewich, Phys. Today 48(5), 42 (1995).
[CrossRef]

Armstrong, J. T.

J. T. Armstrong, D. J. Hutter, K. J. Johnston, D. Mozurkewich, Phys. Today 48(5), 42 (1995).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Chap. 10, p. 509.

Goodman, J. W.

J. W. Goodman, Statistical Optics, 1st ed. (Wiley, New York, 1985), Chap. 5, p. 208.

Hutter, D. J.

J. T. Armstrong, D. J. Hutter, K. J. Johnston, D. Mozurkewich, Phys. Today 48(5), 42 (1995).
[CrossRef]

Johnston, K. J.

J. T. Armstrong, D. J. Hutter, K. J. Johnston, D. Mozurkewich, Phys. Today 48(5), 42 (1995).
[CrossRef]

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), Chap. 4, p. 150.

Mozurkewich, D.

J. T. Armstrong, D. J. Hutter, K. J. Johnston, D. Mozurkewich, Phys. Today 48(5), 42 (1995).
[CrossRef]

Rosen, J.

Wolf, E.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), Chap. 4, p. 150.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Chap. 10, p. 509.

Yariv, A.

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

Opt. Lett. (1)

Phys. Today (1)

J. T. Armstrong, D. J. Hutter, K. J. Johnston, D. Mozurkewich, Phys. Today 48(5), 42 (1995).
[CrossRef]

Other (3)

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), Chap. 4, p. 150.

J. W. Goodman, Statistical Optics, 1st ed. (Wiley, New York, 1985), Chap. 5, p. 208.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Chap. 10, p. 509.

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Figures (4)

Fig. 1
Fig. 1

Schematic illustration for calculation of the degree of coherence between P1 and P2.

Fig. 2
Fig. 2

Experimental setup: BS, beam splitter; M’s, mirrors.

Fig. 3
Fig. 3

(a) Magnitude and (b) phase of the degree of coherence as a function of (Δx, ). (c), (d) Same as (a) and (b) after transformation of the coordinates to (Δx, Δxxmax).

Fig. 4
Fig. 4

Reconstruction of the source by an inverse Fourier transform of the complex function shown in Figs. 3(c) and 3(d). (a) Gray-level image, (b) 3-D plot.

Equations (7)

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J ( x 1 , y 1 , x 2 , y 2 ) = C I s ( r s ) exp [ - j k ( R 1 - R 2 ) ] d 3 r s ,
J ( x 1 , y 1 , x 2 , y 2 ) = C exp [ j k ( x ^ Δ x + y ^ Δ y ) R ] I s ( r s ) × exp { - j k [ x s Δ x + y s Δ y R + z s ( x ^ Δ x + y ^ Δ y ) R 2 ] } d 3 r s ,
I ( x , y ) = J ( Δ x = 0 , Δ y = 0 ) = C I s ( r s ) d 3 r s I 0 .
J ( x 1 , y 1 , x 2 , y 2 ) = J ( Δ x , Δ y , x ^ Δ x , y ^ Δ y ) .
μ ( Δ x , Δ y , q ) J ( Δ x , Δ y , r ^ Δ r ) I ( x , y ) = C 0 I s ( r s ) exp [ - j 2 π λ ( x s Δ x + y s Δ y R + z s q Δ r min R 2 ] d 3 r s ,
μ ( Δ x , p ) = I 0 - 1 exp ( j K p Δ k min / R ) × I s ( x s , z s ) exp [ - j 2 π λ ( x s Δ x R + z s p Δ x min R 2 ) ] d x s d z s ,
I s ( x s , z s ) IFT 2 - D [ μ ( Δ x λ R , p Δ x min λ R 2 ) ] ,

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