Abstract

We provide measurements of Young’s double-slit experiment using a partially-coherent light source consisting of a helium-neon laser incident on a rotating piece of white paper. The data allow a quantitative comparison with both the standard theory that does not account for the width of the slits, and a full, analytic model that does. The data agree much more favorably with the full calculation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. A. A. Michelson and F. G. Pease, “Measurement of the diameter of alpha-orionis by the interferometer,” Proc. Natl. Acad. Sci. USA 7, 143–146 (1921).
    [Crossref] [PubMed]
  2. E. Wolf, “A macroscopic theory of interference and diffraction of light from finite sources. I. fields with a narrow spectral range,” Proc. Royal Soc. 225, 96–111 (1954).
    [Crossref]
  3. B. J. Thompson and E. Wolf, “Two-beam interference with partially coherent light,” J. Opt. Soc. Am. 47, 895–902 (1957).
    [Crossref]
  4. B. J. Thompson, “Illustration of the phase change in two-beam interference with partially coherent light,” J. Opt. Soc. Am. 48, 95–97 (1958).
    [Crossref]
  5. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), pp. 572–577.
  6. B. J. Thompson and R. Sudol, “Finite-aperture effects in the measurement of the degree of coherence,” J. Opt. Soc. Am. A 1, 598–604 (1984).
    [Crossref]
  7. A. S. Marathay and D. B. Pollock, “Young’s interference fringes with finite-sized sampling apertures,” J. Opt. Soc. Am. A 1, 1057–1059 (1984).
    [Crossref]
  8. D. Bloor, “Coherence and correlation—two advanced experiments in optics,” Am. J. Phys. 32, 936–941 (1967).
    [Crossref]
  9. S. Mallick, “Degree of coherence in the image of a quasi-monochromatic source,” Appl. Opt. 6, 1403–1405 (1967).
    [Crossref] [PubMed]
  10. D. N. Grimes, “Measurement of the second-order degree of coherence by means of a wavefront shearing interferometer,” Appl. Opt. 10, 1567–1570 (1971).
    [Crossref] [PubMed]
  11. B. T. King and W. Tobin, “Charge-coupled device detection of two-beam interference with partially coherent light,” Am. J. Phys. 62, 133–137 (1994).
    [Crossref]
  12. D. Ambrosini, G. S. Spagnolo, D. Paoletti, and S. Vicalvi, “High-precision digital automated measurement of degree of coherence in the Thompson and Wolf experiment,” Pure Appl. Opt. 7, 933–939 (1998).
    [Crossref]
  13. J. P. Sharpe and D. P. Collins, “Demonstration of optical spatial coherence using a variable width source,” Am. J. Phys. 79, 554–557 (2011).
    [Crossref]
  14. Often, the viewing screen is placed in the focal plane of a lens located immediately after the double-slit to ensure the viewing screen is in the far-field, as seen in Fig. 1.
  15. E. Hecht, Optics, 3rd ed. (Addison Wesley, 1998), pp. 566–571.
  16. We note that the integral can, of course, also be done numerically, and this may be a more instructive approach for students.
  17. A more pedagogical discussion of this experiment is available ; seeD. P. Jackson, N. Ferris, R. Strauss, H. Li, and B. J. Pearson, “Subtleties with Young’s double-slit experiment: investigation of spatial coherence and fringe visibility,” Am. J. Phys. 86, 683–689 (2018).
    [Crossref]

2018 (1)

A more pedagogical discussion of this experiment is available ; seeD. P. Jackson, N. Ferris, R. Strauss, H. Li, and B. J. Pearson, “Subtleties with Young’s double-slit experiment: investigation of spatial coherence and fringe visibility,” Am. J. Phys. 86, 683–689 (2018).
[Crossref]

2011 (1)

J. P. Sharpe and D. P. Collins, “Demonstration of optical spatial coherence using a variable width source,” Am. J. Phys. 79, 554–557 (2011).
[Crossref]

1998 (1)

D. Ambrosini, G. S. Spagnolo, D. Paoletti, and S. Vicalvi, “High-precision digital automated measurement of degree of coherence in the Thompson and Wolf experiment,” Pure Appl. Opt. 7, 933–939 (1998).
[Crossref]

1994 (1)

B. T. King and W. Tobin, “Charge-coupled device detection of two-beam interference with partially coherent light,” Am. J. Phys. 62, 133–137 (1994).
[Crossref]

1984 (2)

1971 (1)

1967 (2)

S. Mallick, “Degree of coherence in the image of a quasi-monochromatic source,” Appl. Opt. 6, 1403–1405 (1967).
[Crossref] [PubMed]

D. Bloor, “Coherence and correlation—two advanced experiments in optics,” Am. J. Phys. 32, 936–941 (1967).
[Crossref]

1958 (1)

1957 (1)

1954 (1)

E. Wolf, “A macroscopic theory of interference and diffraction of light from finite sources. I. fields with a narrow spectral range,” Proc. Royal Soc. 225, 96–111 (1954).
[Crossref]

1921 (1)

A. A. Michelson and F. G. Pease, “Measurement of the diameter of alpha-orionis by the interferometer,” Proc. Natl. Acad. Sci. USA 7, 143–146 (1921).
[Crossref] [PubMed]

Ambrosini, D.

D. Ambrosini, G. S. Spagnolo, D. Paoletti, and S. Vicalvi, “High-precision digital automated measurement of degree of coherence in the Thompson and Wolf experiment,” Pure Appl. Opt. 7, 933–939 (1998).
[Crossref]

Bloor, D.

D. Bloor, “Coherence and correlation—two advanced experiments in optics,” Am. J. Phys. 32, 936–941 (1967).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), pp. 572–577.

Collins, D. P.

J. P. Sharpe and D. P. Collins, “Demonstration of optical spatial coherence using a variable width source,” Am. J. Phys. 79, 554–557 (2011).
[Crossref]

Ferris, N.

A more pedagogical discussion of this experiment is available ; seeD. P. Jackson, N. Ferris, R. Strauss, H. Li, and B. J. Pearson, “Subtleties with Young’s double-slit experiment: investigation of spatial coherence and fringe visibility,” Am. J. Phys. 86, 683–689 (2018).
[Crossref]

Grimes, D. N.

Hecht, E.

E. Hecht, Optics, 3rd ed. (Addison Wesley, 1998), pp. 566–571.

Jackson, D. P.

A more pedagogical discussion of this experiment is available ; seeD. P. Jackson, N. Ferris, R. Strauss, H. Li, and B. J. Pearson, “Subtleties with Young’s double-slit experiment: investigation of spatial coherence and fringe visibility,” Am. J. Phys. 86, 683–689 (2018).
[Crossref]

King, B. T.

B. T. King and W. Tobin, “Charge-coupled device detection of two-beam interference with partially coherent light,” Am. J. Phys. 62, 133–137 (1994).
[Crossref]

Li, H.

A more pedagogical discussion of this experiment is available ; seeD. P. Jackson, N. Ferris, R. Strauss, H. Li, and B. J. Pearson, “Subtleties with Young’s double-slit experiment: investigation of spatial coherence and fringe visibility,” Am. J. Phys. 86, 683–689 (2018).
[Crossref]

Mallick, S.

Marathay, A. S.

Michelson, A. A.

A. A. Michelson and F. G. Pease, “Measurement of the diameter of alpha-orionis by the interferometer,” Proc. Natl. Acad. Sci. USA 7, 143–146 (1921).
[Crossref] [PubMed]

Paoletti, D.

D. Ambrosini, G. S. Spagnolo, D. Paoletti, and S. Vicalvi, “High-precision digital automated measurement of degree of coherence in the Thompson and Wolf experiment,” Pure Appl. Opt. 7, 933–939 (1998).
[Crossref]

Pearson, B. J.

A more pedagogical discussion of this experiment is available ; seeD. P. Jackson, N. Ferris, R. Strauss, H. Li, and B. J. Pearson, “Subtleties with Young’s double-slit experiment: investigation of spatial coherence and fringe visibility,” Am. J. Phys. 86, 683–689 (2018).
[Crossref]

Pease, F. G.

A. A. Michelson and F. G. Pease, “Measurement of the diameter of alpha-orionis by the interferometer,” Proc. Natl. Acad. Sci. USA 7, 143–146 (1921).
[Crossref] [PubMed]

Pollock, D. B.

Sharpe, J. P.

J. P. Sharpe and D. P. Collins, “Demonstration of optical spatial coherence using a variable width source,” Am. J. Phys. 79, 554–557 (2011).
[Crossref]

Spagnolo, G. S.

D. Ambrosini, G. S. Spagnolo, D. Paoletti, and S. Vicalvi, “High-precision digital automated measurement of degree of coherence in the Thompson and Wolf experiment,” Pure Appl. Opt. 7, 933–939 (1998).
[Crossref]

Strauss, R.

A more pedagogical discussion of this experiment is available ; seeD. P. Jackson, N. Ferris, R. Strauss, H. Li, and B. J. Pearson, “Subtleties with Young’s double-slit experiment: investigation of spatial coherence and fringe visibility,” Am. J. Phys. 86, 683–689 (2018).
[Crossref]

Sudol, R.

Thompson, B. J.

Tobin, W.

B. T. King and W. Tobin, “Charge-coupled device detection of two-beam interference with partially coherent light,” Am. J. Phys. 62, 133–137 (1994).
[Crossref]

Vicalvi, S.

D. Ambrosini, G. S. Spagnolo, D. Paoletti, and S. Vicalvi, “High-precision digital automated measurement of degree of coherence in the Thompson and Wolf experiment,” Pure Appl. Opt. 7, 933–939 (1998).
[Crossref]

Wolf, E.

B. J. Thompson and E. Wolf, “Two-beam interference with partially coherent light,” J. Opt. Soc. Am. 47, 895–902 (1957).
[Crossref]

E. Wolf, “A macroscopic theory of interference and diffraction of light from finite sources. I. fields with a narrow spectral range,” Proc. Royal Soc. 225, 96–111 (1954).
[Crossref]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), pp. 572–577.

Am. J. Phys. (4)

D. Bloor, “Coherence and correlation—two advanced experiments in optics,” Am. J. Phys. 32, 936–941 (1967).
[Crossref]

J. P. Sharpe and D. P. Collins, “Demonstration of optical spatial coherence using a variable width source,” Am. J. Phys. 79, 554–557 (2011).
[Crossref]

B. T. King and W. Tobin, “Charge-coupled device detection of two-beam interference with partially coherent light,” Am. J. Phys. 62, 133–137 (1994).
[Crossref]

A more pedagogical discussion of this experiment is available ; seeD. P. Jackson, N. Ferris, R. Strauss, H. Li, and B. J. Pearson, “Subtleties with Young’s double-slit experiment: investigation of spatial coherence and fringe visibility,” Am. J. Phys. 86, 683–689 (2018).
[Crossref]

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

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

Proc. Natl. Acad. Sci. USA (1)

A. A. Michelson and F. G. Pease, “Measurement of the diameter of alpha-orionis by the interferometer,” Proc. Natl. Acad. Sci. USA 7, 143–146 (1921).
[Crossref] [PubMed]

Proc. Royal Soc. (1)

E. Wolf, “A macroscopic theory of interference and diffraction of light from finite sources. I. fields with a narrow spectral range,” Proc. Royal Soc. 225, 96–111 (1954).
[Crossref]

Pure Appl. Opt. (1)

D. Ambrosini, G. S. Spagnolo, D. Paoletti, and S. Vicalvi, “High-precision digital automated measurement of degree of coherence in the Thompson and Wolf experiment,” Pure Appl. Opt. 7, 933–939 (1998).
[Crossref]

Other (4)

Often, the viewing screen is placed in the focal plane of a lens located immediately after the double-slit to ensure the viewing screen is in the far-field, as seen in Fig. 1.

E. Hecht, Optics, 3rd ed. (Addison Wesley, 1998), pp. 566–571.

We note that the integral can, of course, also be done numerically, and this may be a more instructive approach for students.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), pp. 572–577.

Supplementary Material (1)

NameDescription
» Visualization 1       This video shows the intensity distributions for the standard model and the more complete model as the size of the source increases.

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Figures (5)

Fig. 1
Fig. 1 Experimental set-up (top view). An expanded HeNe laser incident on a rotating white card, together with a variable slit, produces an extended, incoherent light source of width b. After passing through a double-slit aperture, a scanning fiber optic coupler collects the light and sends it to a single-photon, avalanche photodiode (APD).
Fig. 2
Fig. 2 Experimental data (circles) and theoretical predictions (curves) using the standard model of Eq. (3) for six different source sizes. Note the disagreement that occurs in fringe spacing [panels (b) and (e)] and fringe depth [panels (c) and (f)].
Fig. 3
Fig. 3 Experimental data (circles) and theoretical predictions (curves) using the full model of Eq. (6) for six difference source sizes. Compared to Fig. 2, the agreement is significantly better.
Fig. 4
Fig. 4 An image from the supplemental video highlights the fact that the standard model (blue) and the full model (red) predict different fringe positions depending on the source size ϕ (see Visualization 1).
Fig. 5
Fig. 5 Sample data and predictions for a circular source of angular size ϕ = 1.25 mrad. The full model (red) matches the data much more closely than the standard model (blue).

Equations (11)

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I ( y ) = sinc 2 ( k a 2 s y ) cos 2 ( k d 2 s y ) = 1 2 sinc 2 ( k a 2 s y ) [ 1 + cos ( k d s y ) ] ,
I ( y ) = 2 I ( 0 ) ( y ) [ 1 + | γ 12 | cos ( k d s y + β 12 ) ] ,
I ( y ) = 1 2 sinc 2 ( k a y 2 s ) [ 1 + sinc ( k ϕ d 2 ) cos ( k d s y ) ] .
V I max I min I max + I min = | sinc ( k ϕ d 2 ) | ,
I ( y ) = A b / 2 b / 2 d w sinc 2 [ k a 2 s ( y + s w ) ] cos 2 [ k d 2 s ( y + s w ) ] ,
I ( y ) = s 2 k a 2 [ I c ( k y ) + I s ( k y ) I c ( k y + ) I s ( k y + ) ] ,
I c ( x ) 1 x { 1 + cos ( d ˜ x ) cos ( a ˜ x ) 1 2 cos [ ( d ˜ a ˜ ) x ] 1 2 cos [ ( d ˜ + a ˜ ) x ] }
I s ( x ) d ˜ Si ( d ˜ x ) a ˜ Si ( a ˜ x ) ( d ˜ a ˜ ) Si [ ( d ˜ a ˜ ) x ] ( d ˜ + a ˜ ) Si [ ( d ˜ + a ˜ ) x ] ,
Si ( x ) 0 x sin t t d t
I ( y ) = 1 2 sinc 2 ( k a y 2 s ) [ 1 + Bessinc ( k ϕ d 2 ) cos ( k d s y ) ] ,
I ( y ) = C b / 2 b / 2 d w b 2 ( 2 w ) 2 sinc 2 [ k a 2 s ( y + s w ) ] cos 2 [ k d 2 s ( y + s w ) ] ,

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