Abstract

We present an experimental study showing the effect of the change in the bandwidth of light on the magnitude of both the complex degree of coherence and the spectral degree of coherence at a pair of points in the cross-section of a beam. A variable bandwidth source with a Young’s interferometer is utilized to produce the interference fringes. We also report for the first time that if the field is quasi-monochromatic or sufficiently narrowband, the elements of both the beam coherence polarization matrix and the cross-spectral density matrix, normalized to intensities (spectral densities) at the two points possess identical values.

© 2010 OSA

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  1. L. Mandel and E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37(2), 231–287 (1965).
    [CrossRef]
  2. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge: Cambridge University Press, 1999), chapter 10.
  3. L. Mandel and E. Wolf, “Spectral coherence and the concept of cross-spectral purity,” J. Opt. Soc. Am. 66(6), 529–535 (1976).
    [CrossRef]
  4. 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. 72(3), 343–351 (1982).
    [CrossRef]
  5. 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(1), 76–85 (1986).
    [CrossRef]
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge: Cambridge University Press, 1995), chapters 4 and 7.
  7. E. Wolf, “Young’s interference fringes with narrow-band light,” Opt. Lett. 8(5), 250–252 (1983).
    [CrossRef] [PubMed]
  8. A. T. Friberg and E. Wolf, “Relationships between the complex degrees of coherence in the space-time and in the space-frequency domains,” Opt. Lett. 20(6), 623–625 (1995).
    [CrossRef] [PubMed]
  9. D. F. V. James and E. Wolf, “Some new aspects of Young’s interference experiment,” Phys. Lett. A 157(1), 6–10 (1991).
    [CrossRef]
  10. L. Basano, P. Ottonello, G. Rottigni, and M. Vicari, “Spatial and temporal coherence of filtered thermal light,” Appl. Opt. 42(31), 6239–6244 (2003).
    [CrossRef] [PubMed]
  11. B. Kanseri and H. C. Kandpal, “Experimental observation of invariance of spectral degree of coherence with change in bandwidth of light,” Opt. Lett. 35(1), 70–72 (2010).
    [CrossRef] [PubMed]
  12. E. Wolf, Introduction to Theory of Coherence and Polarization of Light (Cambridge: Cambridge University Press, 2007), chapters 3 and 4.
  13. J. C. Ricklin and F. M. Davidson, “Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication,” J. Opt. Soc. Am. A 19(9), 1794–1802 (2002).
    [CrossRef]
  14. F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23(4), 241–243 (1998).
    [CrossRef]
  15. F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” J. Opt. A: Pure App. Opt. 7(5), 941–951 (1998).
    [CrossRef]
  16. B. Kanseri, S. Rath, and H. C. Kandpal, “Determination of the beam coherence polarization matrix of a random electromagnetic beam,” IEEE J. Quantum Electron. 45(9), 1163–1167 (2009).
    [CrossRef]
  17. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
    [CrossRef]
  18. H. Roychowdhury and E. Wolf, “Determination of the electric cross-spectral density matrix of a random electromagnetic beam,” Opt. Commun. 226(1-6), 57–60 (2003).
    [CrossRef]
  19. B. Kanseri, S. Rath, and H. C. Kandpal, “Determination of the amplitude and the phase of the elements of electric cross-spectral density matrix by spectral measurements,” Opt. Commun. 282(15), 3059–3062 (2009).
    [CrossRef]
  20. B. Kanseri and H. C. Kandpal, “Experimental determination of electric cross-spectral density matrix and generalized Stokes parameters for a laser beam,” Opt. Lett. 33(20), 2410 (2008).
    [CrossRef] [PubMed]
  21. G. P. Agrawal and E. Wolf, “propagation-induced polarization changes in partially coherent optical beams,” J. Opt. Soc. Am. A 17(11), 2019–2023 (2000).
    [CrossRef]
  22. F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert-Zernike theorem for partially polarized sources,” Opt. Lett. 25(17), 1291–1293 (2000).
    [CrossRef]
  23. E. Wolf, “Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation,” Opt. Lett. 28(13), 1078–1080 (2003).
    [CrossRef] [PubMed]
  24. O. Korotkova, M. Salem, and E. Wolf, “The far zone behaviour of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
    [CrossRef]
  25. J. Tervo, T. Setälä, and A. T. Friberg, “Theory of partially coherent electromagnetic fields in the space–frequency domain,” J. Opt. Soc. Am. A 21(11), 2205 (2004).
    [CrossRef]
  26. O. Korotkova and E. Wolf, “Spectral degree of coherence of a random three-dimensional electromagnetic field,” J. Opt. Soc. Am. A 21(12), 2382–2385 (2004).
    [CrossRef]
  27. J. Ellis and A. Dogariu, “Complex degree of mutual polarization,” Opt. Lett. 29(6), 536–538 (2004).
    [CrossRef] [PubMed]
  28. P. Réfrégier and F. Goudail, “Invariant degrees of coherence of partially polarized light,” Opt. Express 13(16), 6051–6060 (2005).
    [CrossRef] [PubMed]
  29. H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Complex degree of coherence for partially coherent general beams in atmospheric turbulence,” J. Opt. Soc. Am. A 24(9), 2891 (2007).
    [CrossRef]
  30. Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express 16(20), 15834–15846 (2008).
    [CrossRef] [PubMed]
  31. M. Salem and E. Wolf, “Coherence-induced polarization changes in light beams,” Opt. Lett. 33(11), 1180–1182 (2008).
    [CrossRef] [PubMed]
  32. P. Réfrégier and A. Roueff, “Coherence polarization filtering and relation with intrinsic degrees of coherence,” Opt. Lett. 31(9), 1175–1177 (2006).
    [CrossRef] [PubMed]
  33. M. Salem and G. P. Agrawal, “Effects of coherence and polarization on the coupling of stochastic electromagnetic beams into optical fibers,” J. Opt. Soc. Am. A 26(11), 2452–2458 (2009).
    [CrossRef]
  34. S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A, Pure Appl. Opt. 10(5), 055001 (2008).
    [CrossRef]
  35. E. Fortin, “Direct demonstration of the Fresnel-Arago laws,” Am. J. Phys. 38(7), 917–918 (1970).
    [CrossRef]

2010 (1)

2009 (3)

M. Salem and G. P. Agrawal, “Effects of coherence and polarization on the coupling of stochastic electromagnetic beams into optical fibers,” J. Opt. Soc. Am. A 26(11), 2452–2458 (2009).
[CrossRef]

B. Kanseri, S. Rath, and H. C. Kandpal, “Determination of the beam coherence polarization matrix of a random electromagnetic beam,” IEEE J. Quantum Electron. 45(9), 1163–1167 (2009).
[CrossRef]

B. Kanseri, S. Rath, and H. C. Kandpal, “Determination of the amplitude and the phase of the elements of electric cross-spectral density matrix by spectral measurements,” Opt. Commun. 282(15), 3059–3062 (2009).
[CrossRef]

2008 (4)

2007 (1)

2006 (1)

2005 (1)

2004 (4)

2003 (4)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[CrossRef]

H. Roychowdhury and E. Wolf, “Determination of the electric cross-spectral density matrix of a random electromagnetic beam,” Opt. Commun. 226(1-6), 57–60 (2003).
[CrossRef]

E. Wolf, “Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation,” Opt. Lett. 28(13), 1078–1080 (2003).
[CrossRef] [PubMed]

L. Basano, P. Ottonello, G. Rottigni, and M. Vicari, “Spatial and temporal coherence of filtered thermal light,” Appl. Opt. 42(31), 6239–6244 (2003).
[CrossRef] [PubMed]

2002 (1)

2000 (2)

1998 (2)

F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23(4), 241–243 (1998).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” J. Opt. A: Pure App. Opt. 7(5), 941–951 (1998).
[CrossRef]

1995 (1)

1991 (1)

D. F. V. James and E. Wolf, “Some new aspects of Young’s interference experiment,” Phys. Lett. A 157(1), 6–10 (1991).
[CrossRef]

1986 (1)

1983 (1)

1982 (1)

1976 (1)

1970 (1)

E. Fortin, “Direct demonstration of the Fresnel-Arago laws,” Am. J. Phys. 38(7), 917–918 (1970).
[CrossRef]

1965 (1)

L. Mandel and E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37(2), 231–287 (1965).
[CrossRef]

Agrawal, G. P.

Basano, L.

Baykal, Y.

Borghi, R.

F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert-Zernike theorem for partially polarized sources,” Opt. Lett. 25(17), 1291–1293 (2000).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” J. Opt. A: Pure App. Opt. 7(5), 941–951 (1998).
[CrossRef]

Cai, Y.

Davidson, F. M.

Dogariu, A.

Ellis, J.

Eyyuboglu, H. T.

Fortin, E.

E. Fortin, “Direct demonstration of the Fresnel-Arago laws,” Am. J. Phys. 38(7), 917–918 (1970).
[CrossRef]

Friberg, A. T.

Gori, F.

Goudail, F.

Guattari, G.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” J. Opt. A: Pure App. Opt. 7(5), 941–951 (1998).
[CrossRef]

James, D. F. V.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A, Pure Appl. Opt. 10(5), 055001 (2008).
[CrossRef]

D. F. V. James and E. Wolf, “Some new aspects of Young’s interference experiment,” Phys. Lett. A 157(1), 6–10 (1991).
[CrossRef]

Kandpal, H. C.

B. Kanseri and H. C. Kandpal, “Experimental observation of invariance of spectral degree of coherence with change in bandwidth of light,” Opt. Lett. 35(1), 70–72 (2010).
[CrossRef] [PubMed]

B. Kanseri, S. Rath, and H. C. Kandpal, “Determination of the beam coherence polarization matrix of a random electromagnetic beam,” IEEE J. Quantum Electron. 45(9), 1163–1167 (2009).
[CrossRef]

B. Kanseri, S. Rath, and H. C. Kandpal, “Determination of the amplitude and the phase of the elements of electric cross-spectral density matrix by spectral measurements,” Opt. Commun. 282(15), 3059–3062 (2009).
[CrossRef]

B. Kanseri and H. C. Kandpal, “Experimental determination of electric cross-spectral density matrix and generalized Stokes parameters for a laser beam,” Opt. Lett. 33(20), 2410 (2008).
[CrossRef] [PubMed]

Kanseri, B.

B. Kanseri and H. C. Kandpal, “Experimental observation of invariance of spectral degree of coherence with change in bandwidth of light,” Opt. Lett. 35(1), 70–72 (2010).
[CrossRef] [PubMed]

B. Kanseri, S. Rath, and H. C. Kandpal, “Determination of the beam coherence polarization matrix of a random electromagnetic beam,” IEEE J. Quantum Electron. 45(9), 1163–1167 (2009).
[CrossRef]

B. Kanseri, S. Rath, and H. C. Kandpal, “Determination of the amplitude and the phase of the elements of electric cross-spectral density matrix by spectral measurements,” Opt. Commun. 282(15), 3059–3062 (2009).
[CrossRef]

B. Kanseri and H. C. Kandpal, “Experimental determination of electric cross-spectral density matrix and generalized Stokes parameters for a laser beam,” Opt. Lett. 33(20), 2410 (2008).
[CrossRef] [PubMed]

Korotkova, O.

Mandel, L.

L. Mandel and E. Wolf, “Spectral coherence and the concept of cross-spectral purity,” J. Opt. Soc. Am. 66(6), 529–535 (1976).
[CrossRef]

L. Mandel and E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37(2), 231–287 (1965).
[CrossRef]

Ottonello, P.

Piquero, G.

Rath, S.

B. Kanseri, S. Rath, and H. C. Kandpal, “Determination of the beam coherence polarization matrix of a random electromagnetic beam,” IEEE J. Quantum Electron. 45(9), 1163–1167 (2009).
[CrossRef]

B. Kanseri, S. Rath, and H. C. Kandpal, “Determination of the amplitude and the phase of the elements of electric cross-spectral density matrix by spectral measurements,” Opt. Commun. 282(15), 3059–3062 (2009).
[CrossRef]

Réfrégier, P.

Ricklin, J. C.

Rottigni, G.

Roueff, A.

Roychowdhury, H.

H. Roychowdhury and E. Wolf, “Determination of the electric cross-spectral density matrix of a random electromagnetic beam,” Opt. Commun. 226(1-6), 57–60 (2003).
[CrossRef]

Salem, M.

Santarsiero, M.

F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert-Zernike theorem for partially polarized sources,” Opt. Lett. 25(17), 1291–1293 (2000).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” J. Opt. A: Pure App. Opt. 7(5), 941–951 (1998).
[CrossRef]

Setälä, T.

Shirai, T.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A, Pure Appl. Opt. 10(5), 055001 (2008).
[CrossRef]

Tervo, J.

Vicalvi, S.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” J. Opt. A: Pure App. Opt. 7(5), 941–951 (1998).
[CrossRef]

Vicari, M.

Volkov, S. N.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A, Pure Appl. Opt. 10(5), 055001 (2008).
[CrossRef]

Wolf, E.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A, Pure Appl. Opt. 10(5), 055001 (2008).
[CrossRef]

M. Salem and E. Wolf, “Coherence-induced polarization changes in light beams,” Opt. Lett. 33(11), 1180–1182 (2008).
[CrossRef] [PubMed]

O. Korotkova and E. Wolf, “Spectral degree of coherence of a random three-dimensional electromagnetic field,” J. Opt. Soc. Am. A 21(12), 2382–2385 (2004).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, “The far zone behaviour of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
[CrossRef]

E. Wolf, “Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation,” Opt. Lett. 28(13), 1078–1080 (2003).
[CrossRef] [PubMed]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[CrossRef]

H. Roychowdhury and E. Wolf, “Determination of the electric cross-spectral density matrix of a random electromagnetic beam,” Opt. Commun. 226(1-6), 57–60 (2003).
[CrossRef]

G. P. Agrawal and E. Wolf, “propagation-induced polarization changes in partially coherent optical beams,” J. Opt. Soc. Am. A 17(11), 2019–2023 (2000).
[CrossRef]

A. T. Friberg and E. Wolf, “Relationships between the complex degrees of coherence in the space-time and in the space-frequency domains,” Opt. Lett. 20(6), 623–625 (1995).
[CrossRef] [PubMed]

D. F. V. James and E. Wolf, “Some new aspects of Young’s interference experiment,” Phys. Lett. A 157(1), 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(1), 76–85 (1986).
[CrossRef]

E. Wolf, “Young’s interference fringes with narrow-band light,” Opt. Lett. 8(5), 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. 72(3), 343–351 (1982).
[CrossRef]

L. Mandel and E. Wolf, “Spectral coherence and the concept of cross-spectral purity,” J. Opt. Soc. Am. 66(6), 529–535 (1976).
[CrossRef]

L. Mandel and E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37(2), 231–287 (1965).
[CrossRef]

Am. J. Phys. (1)

E. Fortin, “Direct demonstration of the Fresnel-Arago laws,” Am. J. Phys. 38(7), 917–918 (1970).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

B. Kanseri, S. Rath, and H. C. Kandpal, “Determination of the beam coherence polarization matrix of a random electromagnetic beam,” IEEE J. Quantum Electron. 45(9), 1163–1167 (2009).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, “Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams,” J. Opt. A, Pure Appl. Opt. 10(5), 055001 (2008).
[CrossRef]

J. Opt. A: Pure App. Opt. (1)

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix,” J. Opt. A: Pure App. Opt. 7(5), 941–951 (1998).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (7)

Opt. Commun. (3)

H. Roychowdhury and E. Wolf, “Determination of the electric cross-spectral density matrix of a random electromagnetic beam,” Opt. Commun. 226(1-6), 57–60 (2003).
[CrossRef]

B. Kanseri, S. Rath, and H. C. Kandpal, “Determination of the amplitude and the phase of the elements of electric cross-spectral density matrix by spectral measurements,” Opt. Commun. 282(15), 3059–3062 (2009).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, “The far zone behaviour of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (10)

P. Réfrégier and A. Roueff, “Coherence polarization filtering and relation with intrinsic degrees of coherence,” Opt. Lett. 31(9), 1175–1177 (2006).
[CrossRef] [PubMed]

E. Wolf, “Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation,” Opt. Lett. 28(13), 1078–1080 (2003).
[CrossRef] [PubMed]

B. Kanseri and H. C. Kandpal, “Experimental determination of electric cross-spectral density matrix and generalized Stokes parameters for a laser beam,” Opt. Lett. 33(20), 2410 (2008).
[CrossRef] [PubMed]

B. Kanseri and H. C. Kandpal, “Experimental observation of invariance of spectral degree of coherence with change in bandwidth of light,” Opt. Lett. 35(1), 70–72 (2010).
[CrossRef] [PubMed]

M. Salem and E. Wolf, “Coherence-induced polarization changes in light beams,” Opt. Lett. 33(11), 1180–1182 (2008).
[CrossRef] [PubMed]

J. Ellis and A. Dogariu, “Complex degree of mutual polarization,” Opt. Lett. 29(6), 536–538 (2004).
[CrossRef] [PubMed]

E. Wolf, “Young’s interference fringes with narrow-band light,” Opt. Lett. 8(5), 250–252 (1983).
[CrossRef] [PubMed]

A. T. Friberg and E. Wolf, “Relationships between the complex degrees of coherence in the space-time and in the space-frequency domains,” Opt. Lett. 20(6), 623–625 (1995).
[CrossRef] [PubMed]

F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23(4), 241–243 (1998).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert-Zernike theorem for partially polarized sources,” Opt. Lett. 25(17), 1291–1293 (2000).
[CrossRef]

Phys. Lett. A (2)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[CrossRef]

D. F. V. James and E. Wolf, “Some new aspects of Young’s interference experiment,” Phys. Lett. A 157(1), 6–10 (1991).
[CrossRef]

Rev. Mod. Phys. (1)

L. Mandel and E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37(2), 231–287 (1965).
[CrossRef]

Other (3)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge: Cambridge University Press, 1999), chapter 10.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge: Cambridge University Press, 1995), chapters 4 and 7.

E. Wolf, Introduction to Theory of Coherence and Polarization of Light (Cambridge: Cambridge University Press, 2007), chapters 3 and 4.

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Figures (3)

Fig. 1
Fig. 1

Schematics of the experimental setup. S Tungsten halogen lamp, D diffuser, M monochromator with microprocessor (MP) control (1, 2 are the entrance and exit slits of the monochromator, respectively), SS single slit, P polarizer, DS double slit, H half wave plate, R observation plane, PD photodiode, DMM digital multimeter, F fiber, SM spectrometer and DP data processor.

Fig. 2
Fig. 2

Photograph of the interference fringes obtained at plane R. The entrance and the exit slits of the monochromator were opened for (a) 2, (b) 1.6, (c) 1.2, (d) 0.8, (e) 0.4 and (f) 0.1 mm.

Fig. 3
Fig. 3

(a) Behaviour of the magnitude of the spectral degree of coherence (spectral visibility) with the change in the bandwidth of the light. (b) The change in the absolute value of the degree of coherence (visibility) with bandwidth of light, measured for the central fringe (shown by dots) and for either side of the central fringe (shown by triangles). The dotted line in (a) and (b) shows the trend line plotted as linear fit. The error bars show the uncertainty in the measurements calculated at 95% confidence interval.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

μ ( r 1 , r 2 , ω ) = W ( r 1 , r 2 , ω ) [ W ( r 1 , r 1 , ω ) W ( r 2 , r 2 , ω ) ] 1 2 ,
γ ( r 1 , r 2 , τ ) = Γ ( r 1 , r 2 , τ ) [ Γ ( r 1 , r 1 , 0 ) Γ ( r 2 , r 2 , 0 ) ] 1 2 ,
γ ( r 1 , r 2 , τ ) = 0 [ s ( r 1 , ω ) ] 1 2 [ s ( r 2 , ω ) ] 1 2 μ ( r 1 , r 2 , ω ) exp ( i ω τ ) d ω ,
s ( r i , ω ) = S ( r i , ω ) S ( r i , ω ) d ω , for   i = 1 , 2.
γ ( r 1 , r 2 , 0 ) = μ ( r 1 , r 2 , ω ) ,
| γ ( r 1 , r 2 , 0 ) | = | μ ( r 1 , r 2 , ω ) | .
| μ ( r 1 , r 2 , ω ) | = S max ( r , ω ) S min ( r , ω ) S max ( r , ω ) + S min ( r , ω ) ,
J i j ( r 1 , r 2 , z ) = I i ( r 1 , z ) I j ( r 2 , z ) γ i j ( r 1 , r 2 , z ) ,
J i j ( r 1 , r 2 , 0 ) I i ( r 1 ) I j ( r 2 ) = γ i j ( r 1 , r 2 , 0 ) .
W i j ( r 1 , r 2 , ω ) S i ( r 1 , ω ) S j ( r 2 , ω ) = μ i j ( r 1 , r 2 , ω ) ,
| ρ 2 ρ 1 | c < < 1 Δ ν ,
J i j ( r 1 , r 2 , 0 ) I i ( r 1 ) I j ( r 2 ) = W i j ( r 1 , r 2 , ω ) S i ( r 1 , ω ) S j ( r 2 , ω ) , f o r ( i , j ) = ( x , y ) ;

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