Abstract

When a filter is placed in front of a double slit illuminated by a primary source of finite extent, the theory of partial coherence predicts that in general the interference fringes do not acquire unit visibility even as the passband of the filter is made arbitrarily narrow. The effect of reducing the filter bandwidth is that the visibility of the fringes tends to the modulus of the spectral degree of coherence and that more interference fringes become visible. A systematic experimental verification of these theoretical predictions is lacking so far and is provided here from the use of a highly sensitive CCD camera.

© 2003 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Cambridge University, Cambridge, UK, 1999), p. 588.
  2. M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).
  3. L. Mandel, E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
    [CrossRef]
  4. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, UK, 1995), pp. 307–318.
  5. E. Wolf, “New theory of partial coherence in the space-frequency domain. Part I: Spectra and cross spectra of steady state sources,” J. Opt. Soc. Am. A 72, 343–351 (1982).
    [CrossRef]
  6. E. Wolf, “New theory of partial coherence in the space-frequency domain. Part II: Steady-state fields and higher-order correlations,” J. Opt. Soc. Am. A 3, 76–85 (1986).
    [CrossRef]
  7. E. Wolf, D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59, 771–818 (1996).
    [CrossRef]
  8. E. Wolf, “Young’s interference fringes with narrow-band light,” Opt. Lett. 8, 250–252 (1983).
    [CrossRef] [PubMed]
  9. D. F. V. James, E. Wolf, “Some new aspects of Young’s interference experiment,” Phys. Lett. A 157, 6–10 (1991).
    [CrossRef]
  10. A. T. Friberg, E. Wolf, “Relationships between the complex degrees of coherence in the space-time and in the space-frequency domains,” Opt. Lett. 20, 623–625 (1995).
    [CrossRef] [PubMed]
  11. L. Basano, S. Leporatti, P. Ottonello, V. Palestini, R. Rolandi, “Measurements of surface roughness: use of a CCD camera to correlate doubly scattered speckle patterns,” Appl. Opt. 34, 7286–7290 (1995).
    [CrossRef] [PubMed]
  12. L. Basano, P. Ottonello, G. Rottigni, M. Vicari, “Degree of spectral coherence, space-frequency plots and correlation-induced spectral changes,” Opt. Commun. 207, 77–83 (2002).
    [CrossRef]
  13. Ref. 4, pp. 174–176.

2002 (1)

L. Basano, P. Ottonello, G. Rottigni, M. Vicari, “Degree of spectral coherence, space-frequency plots and correlation-induced spectral changes,” Opt. Commun. 207, 77–83 (2002).
[CrossRef]

1996 (1)

E. Wolf, D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59, 771–818 (1996).
[CrossRef]

1995 (2)

1991 (1)

D. F. V. James, E. Wolf, “Some new aspects of Young’s interference experiment,” Phys. Lett. A 157, 6–10 (1991).
[CrossRef]

1986 (1)

1983 (1)

1982 (1)

E. Wolf, “New theory of partial coherence in the space-frequency domain. Part I: Spectra and cross spectra of steady state sources,” J. Opt. Soc. Am. A 72, 343–351 (1982).
[CrossRef]

1965 (1)

L. Mandel, E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

Basano, L.

L. Basano, P. Ottonello, G. Rottigni, M. Vicari, “Degree of spectral coherence, space-frequency plots and correlation-induced spectral changes,” Opt. Commun. 207, 77–83 (2002).
[CrossRef]

L. Basano, S. Leporatti, P. Ottonello, V. Palestini, R. Rolandi, “Measurements of surface roughness: use of a CCD camera to correlate doubly scattered speckle patterns,” Appl. Opt. 34, 7286–7290 (1995).
[CrossRef] [PubMed]

Beran, M. J.

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge University, Cambridge, UK, 1999), p. 588.

Friberg, A. T.

James, D. F. V.

E. Wolf, D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59, 771–818 (1996).
[CrossRef]

D. F. V. James, E. Wolf, “Some new aspects of Young’s interference experiment,” Phys. Lett. A 157, 6–10 (1991).
[CrossRef]

Leporatti, S.

Mandel, L.

L. Mandel, E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, UK, 1995), pp. 307–318.

Ottonello, P.

L. Basano, P. Ottonello, G. Rottigni, M. Vicari, “Degree of spectral coherence, space-frequency plots and correlation-induced spectral changes,” Opt. Commun. 207, 77–83 (2002).
[CrossRef]

L. Basano, S. Leporatti, P. Ottonello, V. Palestini, R. Rolandi, “Measurements of surface roughness: use of a CCD camera to correlate doubly scattered speckle patterns,” Appl. Opt. 34, 7286–7290 (1995).
[CrossRef] [PubMed]

Palestini, V.

Parrent, G. B.

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).

Rolandi, R.

Rottigni, G.

L. Basano, P. Ottonello, G. Rottigni, M. Vicari, “Degree of spectral coherence, space-frequency plots and correlation-induced spectral changes,” Opt. Commun. 207, 77–83 (2002).
[CrossRef]

Vicari, M.

L. Basano, P. Ottonello, G. Rottigni, M. Vicari, “Degree of spectral coherence, space-frequency plots and correlation-induced spectral changes,” Opt. Commun. 207, 77–83 (2002).
[CrossRef]

Wolf, E.

E. Wolf, D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59, 771–818 (1996).
[CrossRef]

A. T. Friberg, E. Wolf, “Relationships between the complex degrees of coherence in the space-time and in the space-frequency domains,” Opt. Lett. 20, 623–625 (1995).
[CrossRef] [PubMed]

D. F. V. James, E. Wolf, “Some new aspects of Young’s interference experiment,” Phys. Lett. A 157, 6–10 (1991).
[CrossRef]

E. Wolf, “New theory of partial coherence in the space-frequency domain. Part II: Steady-state fields and higher-order correlations,” J. Opt. Soc. Am. A 3, 76–85 (1986).
[CrossRef]

E. Wolf, “Young’s interference fringes with narrow-band light,” Opt. Lett. 8, 250–252 (1983).
[CrossRef] [PubMed]

E. Wolf, “New theory of partial coherence in the space-frequency domain. Part I: Spectra and cross spectra of steady state sources,” J. Opt. Soc. Am. A 72, 343–351 (1982).
[CrossRef]

L. Mandel, E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, UK, 1995), pp. 307–318.

M. Born, E. Wolf, Principles of Optics (Cambridge University, Cambridge, UK, 1999), p. 588.

Appl. Opt. (1)

J. Opt. Soc. Am. A (2)

E. Wolf, “New theory of partial coherence in the space-frequency domain. Part II: Steady-state fields and higher-order correlations,” J. Opt. Soc. Am. A 3, 76–85 (1986).
[CrossRef]

E. Wolf, “New theory of partial coherence in the space-frequency domain. Part I: Spectra and cross spectra of steady state sources,” J. Opt. Soc. Am. A 72, 343–351 (1982).
[CrossRef]

Opt. Commun. (1)

L. Basano, P. Ottonello, G. Rottigni, M. Vicari, “Degree of spectral coherence, space-frequency plots and correlation-induced spectral changes,” Opt. Commun. 207, 77–83 (2002).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (1)

D. F. V. James, E. Wolf, “Some new aspects of Young’s interference experiment,” Phys. Lett. A 157, 6–10 (1991).
[CrossRef]

Rep. Prog. Phys. (1)

E. Wolf, D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59, 771–818 (1996).
[CrossRef]

Rev. Mod. Phys. (1)

L. Mandel, E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

Other (4)

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, UK, 1995), pp. 307–318.

M. Born, E. Wolf, Principles of Optics (Cambridge University, Cambridge, UK, 1999), p. 588.

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).

Ref. 4, pp. 174–176.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup: L, halogen lamp; SS, primary slit; DS, double slit; F, filter; T, fiber taper glued to the CCD surface (see text).

Fig. 2
Fig. 2

(a) Image of the fringe pattern detected by the CCD camera (at a 633-nm wavelength and a 1-nm bandwidth). (b) Curve A, intensity profile obtained from (a); curve B, overall systematic error (shifted downward to avoid overlapping curve A); curve C, intensity profile after correction of the systematic error. In curves A, B, and C the vertical scales are in arbitrary units.

Fig. 3
Fig. 3

Experimental measurement of fringe visibility vs log 10 of the bandwidth (nanometers) for two sequences of filters centered at wavelengths of circles, 633 nm and, squares, 488 nm. The open circle marks the result for the unfiltered lamp. The points of each sequence are joined by dotted lines only for clarity.

Fig. 4
Fig. 4

Normalized experimental records of the interference fringes: (a) unfiltered lamp, (b) 130-nm bandwidth, (c) 10-nm bandwidth, (d) 1-nm bandwidth. Plots (b), (c), and (d) are for a central wavelength of 633 nm.

Fig. 5
Fig. 5

(a) Numerical simulation for a 1-nm passband centered on a wavelength of 633 nm. (b) Experimental results for the same conditions used in the simulation. In both figures the vertical scales refer to normalized values.

Tables (1)

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Table 1 Filters Employed in the Experiment

Equations (6)

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Γ12τ=V*P1, tVP2, t+τ.
γ12τ=Γ12τΓ110Γ2201/2.
μ12ω=W12ωW11ωW22ω1/2,
Wjkω= exp-iωτΓjkτdτ.
γ12+0=μ12ω0,
μ=sinxx, where x=πadλr.

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