Abstract

A variety of the complex degree of spectral coherence μ is provided for investigating the correlation-induced spectral changes resulting from two-beam interference in the space-frequency domain. Primary two-point sources with variant Gaussian-like spectra illuminate the secondary source plane across which spatially, partially coherent wave fields result to produce μ. The variational aspects of μ are controllable by the primary source parameters. The spectral changes are discussed in detail in association with the μ-dependent interference term. The argument of μ plays a particularly important role in asymmetric changes in spectrum.

© 1998 Optical Society of America

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  1. E. Wolf, “Invariance of spectrum of light on propagation,” Phys. Rev. Lett. 56, 1370–1372 (1986).
    [CrossRef] [PubMed]
  2. E. Wolf, “Non-cosmological redshifts of spectral lines,” Nature (London) 326, 363–365 (1987).
    [CrossRef]
  3. E. Wolf, “Redshifts and blueshifts of spectral lines caused by source correlations,” Opt. Commun. 62, 12–16 (1987).
    [CrossRef]
  4. E. Wolf, “Red shifts and blue shifts of spectral lines emitted by two correlated sources,” Phys. Rev. Lett. 58, 2646–2648 (1987).
    [CrossRef] [PubMed]
  5. Z. Dacic, E. Wolf, “Changes in the spectrum of a partially coherent light beam propagation in free space,” J. Opt. Soc. Am. A 5, 1118–1126 (1988).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. Y. Ohtsuka, “Spectrum invariance for a particular class of optical fields propagated in far zone,” Opt. Rev. 2, 347–351 (1995).
    [CrossRef]
  9. T. Shirai, T. Asakura, “Multiple light scattering from spatially random media under the second-order Born approximation,” Opt. Commun. 105, 22 (1994).
    [CrossRef]
  10. G. M. Morris, D. Faklis, “Effects of source correlations on the spectrum of light,” Opt. Commun. 62, 5–11 (1987).
    [CrossRef]
  11. D. Faklis, G. M. Morris, “Spectral shifts produced by source correlations,” Opt. Lett. 13, 4–6 (1988).
    [CrossRef] [PubMed]
  12. F. Gori, G. Guattari, C. Palma, C. Padovani, “Observation of optical redshifts and blueshifts produced by source correlations,” Opt. Commun. 67, 1–4 (1988).
    [CrossRef]
  13. H. C. Kandpal, J. S. Vaishya, K. C. Joshi, “Spectral shift due to source correlation for paraxial rays,” Opt. Commun. 79, 270–272 (1990).
    [CrossRef]
  14. K. C. Joshi, H. C. Kandpal, J. S. Vaishya, “Spectral shift due to source correlation in conventional spectroradiometric measurements,” Appl. Opt. 30, 1471–1474 (1991).
    [CrossRef] [PubMed]
  15. J. Rai, S. Rai, S. Chopra, “Source-correlation effects in the time domain,” Phys. Rev. A 47, 4400–4403 (1993).
    [CrossRef] [PubMed]
  16. K. Saxena, D. S. Mehta, H. C. Kandpal, T. S. Vaishya, K. C. Joshi, “Experimental studies of field correlations using spectral interferometric technique,” Opt. Commun. 111, 423–426 (1994).
    [CrossRef]
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    [CrossRef]
  18. H. C. Kandpal, J. S. Vaishya, K. C. Joshi, “Correlation-induced spectral shifts in optical measurements,” Opt. Eng. 33, 1996–2012 (1994).
    [CrossRef]
  19. E. Wolf, D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59, 771–818 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  23. D. N. Rao, V. N. Kumar, “Experimental demonstration of spectral modification in a Mach-Zehnder interferometer,” J. Mod. Opt. 41, 1757–1763 (1994).
    [CrossRef]
  24. D. S. Mehta, H. C. Kandpal, K. Saxena, J. S. Vaishya, K. C. Joshi, “Displacement measurements from coherence-induced spectral changes in a Mach-Zehnder interferometer,” Opt. Commun. 119, 352–360 (1995).
    [CrossRef]
  25. D. F. V. James, E. Wolf, “Determination of field correlations from spectral measurements with application to synthetic aperture imaging,” Radio Sci. 26, 1239–1243 (1991).
    [CrossRef]
  26. H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, K. C. Joshi, “Angular separation of a pair of sources by spectral interferometric technique,” J. Mod. Opt. 42, 447–454 (1995).
    [CrossRef]
  27. Y. Ohtsuka, M. Kamada, S. Tanaka, “Correlation-induced spectral changes dependent upon spatiotemporal interference effects,” Opt. Rev. 3, 153–160 (1995).
    [CrossRef]
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  29. K. A. Nugent, “Radiometric measurements and correlation-induced spectral changes,” Metrologia 29, 319–324 (1992).
    [CrossRef]
  30. K. D. Mielenz, “ ‘Wolf shifts’ and their physical interpretation under laboratory conditions,” J. Res. Natl. Inst. Stand. Technol. 98, 231–240 (1993).
    [CrossRef]
  31. E. Wolf, T. Shirai, H. Chen, W. Wang, “Coherence filters and their uses,” J. Mod. Opt. 44, 1345–1353 (1997).
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1997 (2)

1996 (1)

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

1995 (5)

H. C. Kandpal, J. S. Vaishya, K. Saxena, D. S. Mehta, K. C. Joshi, “Intensity distribution across a source from spectral measurements,” J. Mod. Opt. 42, 455–464 (1995).
[CrossRef]

D. S. Mehta, H. C. Kandpal, K. Saxena, J. S. Vaishya, K. C. Joshi, “Displacement measurements from coherence-induced spectral changes in a Mach-Zehnder interferometer,” Opt. Commun. 119, 352–360 (1995).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, K. C. Joshi, “Angular separation of a pair of sources by spectral interferometric technique,” J. Mod. Opt. 42, 447–454 (1995).
[CrossRef]

Y. Ohtsuka, M. Kamada, S. Tanaka, “Correlation-induced spectral changes dependent upon spatiotemporal interference effects,” Opt. Rev. 3, 153–160 (1995).
[CrossRef]

Y. Ohtsuka, “Spectrum invariance for a particular class of optical fields propagated in far zone,” Opt. Rev. 2, 347–351 (1995).
[CrossRef]

1994 (4)

T. Shirai, T. Asakura, “Multiple light scattering from spatially random media under the second-order Born approximation,” Opt. Commun. 105, 22 (1994).
[CrossRef]

K. Saxena, D. S. Mehta, H. C. Kandpal, T. S. Vaishya, K. C. Joshi, “Experimental studies of field correlations using spectral interferometric technique,” Opt. Commun. 111, 423–426 (1994).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, K. C. Joshi, “Correlation-induced spectral shifts in optical measurements,” Opt. Eng. 33, 1996–2012 (1994).
[CrossRef]

D. N. Rao, V. N. Kumar, “Experimental demonstration of spectral modification in a Mach-Zehnder interferometer,” J. Mod. Opt. 41, 1757–1763 (1994).
[CrossRef]

1993 (3)

K. D. Mielenz, “ ‘Wolf shifts’ and their physical interpretation under laboratory conditions,” J. Res. Natl. Inst. Stand. Technol. 98, 231–240 (1993).
[CrossRef]

G. S. Agrawal, D. F. V. James, “Spectral changes in the Mach Zehnder interferometer,” J. Mod. Opt. 40, 1431–1436 (1993).
[CrossRef]

J. Rai, S. Rai, S. Chopra, “Source-correlation effects in the time domain,” Phys. Rev. A 47, 4400–4403 (1993).
[CrossRef] [PubMed]

1992 (1)

K. A. Nugent, “Radiometric measurements and correlation-induced spectral changes,” Metrologia 29, 319–324 (1992).
[CrossRef]

1991 (3)

1990 (3)

G. Agrawal, A. Gamliel, “Spectrum of partially coherent light: transmission from near to far zone,” Opt. Commun. 78, 1–6 (1990).
[CrossRef]

A. Gamliel, G. P. Agrawal, “Wolf effect in homogeneous and inhomogeneous media,” J. Opt. Soc. Am. A 7, 2184–2192 (1990).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, K. C. Joshi, “Spectral shift due to source correlation for paraxial rays,” Opt. Commun. 79, 270–272 (1990).
[CrossRef]

1988 (3)

1987 (4)

E. Wolf, “Non-cosmological redshifts of spectral lines,” Nature (London) 326, 363–365 (1987).
[CrossRef]

E. Wolf, “Redshifts and blueshifts of spectral lines caused by source correlations,” Opt. Commun. 62, 12–16 (1987).
[CrossRef]

E. Wolf, “Red shifts and blue shifts of spectral lines emitted by two correlated sources,” Phys. Rev. Lett. 58, 2646–2648 (1987).
[CrossRef] [PubMed]

G. M. Morris, D. Faklis, “Effects of source correlations on the spectrum of light,” Opt. Commun. 62, 5–11 (1987).
[CrossRef]

1986 (1)

E. Wolf, “Invariance of spectrum of light on propagation,” Phys. Rev. Lett. 56, 1370–1372 (1986).
[CrossRef] [PubMed]

1976 (1)

Agrawal, G.

G. Agrawal, A. Gamliel, “Spectrum of partially coherent light: transmission from near to far zone,” Opt. Commun. 78, 1–6 (1990).
[CrossRef]

Agrawal, G. P.

Agrawal, G. S.

G. S. Agrawal, D. F. V. James, “Spectral changes in the Mach Zehnder interferometer,” J. Mod. Opt. 40, 1431–1436 (1993).
[CrossRef]

Arimoto, H.

Asakura, T.

T. Shirai, T. Asakura, “Multiple light scattering from spatially random media under the second-order Born approximation,” Opt. Commun. 105, 22 (1994).
[CrossRef]

Chen, H.

E. Wolf, T. Shirai, H. Chen, W. Wang, “Coherence filters and their uses,” J. Mod. Opt. 44, 1345–1353 (1997).

Chopra, S.

J. Rai, S. Rai, S. Chopra, “Source-correlation effects in the time domain,” Phys. Rev. A 47, 4400–4403 (1993).
[CrossRef] [PubMed]

Dacic, Z.

Faklis, D.

D. Faklis, G. M. Morris, “Spectral shifts produced by source correlations,” Opt. Lett. 13, 4–6 (1988).
[CrossRef] [PubMed]

G. M. Morris, D. Faklis, “Effects of source correlations on the spectrum of light,” Opt. Commun. 62, 5–11 (1987).
[CrossRef]

Foley, J. T.

Gamliel, A.

A. Gamliel, G. P. Agrawal, “Wolf effect in homogeneous and inhomogeneous media,” J. Opt. Soc. Am. A 7, 2184–2192 (1990).
[CrossRef]

G. Agrawal, A. Gamliel, “Spectrum of partially coherent light: transmission from near to far zone,” Opt. Commun. 78, 1–6 (1990).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gori, F.

F. Gori, G. Guattari, C. Palma, C. Padovani, “Observation of optical redshifts and blueshifts produced by source correlations,” Opt. Commun. 67, 1–4 (1988).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, C. Palma, C. Padovani, “Observation of optical redshifts and blueshifts produced by source correlations,” Opt. Commun. 67, 1–4 (1988).
[CrossRef]

James, D. F. V.

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

G. S. Agrawal, D. F. V. James, “Spectral changes in the Mach Zehnder interferometer,” J. Mod. Opt. 40, 1431–1436 (1993).
[CrossRef]

D. F. V. James, E. Wolf, “Determination of field correlations from spectral measurements with application to synthetic aperture imaging,” Radio Sci. 26, 1239–1243 (1991).
[CrossRef]

Joshi, K. C.

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, K. C. Joshi, “Angular separation of a pair of sources by spectral interferometric technique,” J. Mod. Opt. 42, 447–454 (1995).
[CrossRef]

D. S. Mehta, H. C. Kandpal, K. Saxena, J. S. Vaishya, K. C. Joshi, “Displacement measurements from coherence-induced spectral changes in a Mach-Zehnder interferometer,” Opt. Commun. 119, 352–360 (1995).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, K. Saxena, D. S. Mehta, K. C. Joshi, “Intensity distribution across a source from spectral measurements,” J. Mod. Opt. 42, 455–464 (1995).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, K. C. Joshi, “Correlation-induced spectral shifts in optical measurements,” Opt. Eng. 33, 1996–2012 (1994).
[CrossRef]

K. Saxena, D. S. Mehta, H. C. Kandpal, T. S. Vaishya, K. C. Joshi, “Experimental studies of field correlations using spectral interferometric technique,” Opt. Commun. 111, 423–426 (1994).
[CrossRef]

K. C. Joshi, H. C. Kandpal, J. S. Vaishya, “Spectral shift due to source correlation in conventional spectroradiometric measurements,” Appl. Opt. 30, 1471–1474 (1991).
[CrossRef] [PubMed]

H. C. Kandpal, J. S. Vaishya, K. C. Joshi, “Spectral shift due to source correlation for paraxial rays,” Opt. Commun. 79, 270–272 (1990).
[CrossRef]

Kamada, M.

Y. Ohtsuka, M. Kamada, S. Tanaka, “Correlation-induced spectral changes dependent upon spatiotemporal interference effects,” Opt. Rev. 3, 153–160 (1995).
[CrossRef]

Kandpal, H. C.

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, K. C. Joshi, “Angular separation of a pair of sources by spectral interferometric technique,” J. Mod. Opt. 42, 447–454 (1995).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, K. Saxena, D. S. Mehta, K. C. Joshi, “Intensity distribution across a source from spectral measurements,” J. Mod. Opt. 42, 455–464 (1995).
[CrossRef]

D. S. Mehta, H. C. Kandpal, K. Saxena, J. S. Vaishya, K. C. Joshi, “Displacement measurements from coherence-induced spectral changes in a Mach-Zehnder interferometer,” Opt. Commun. 119, 352–360 (1995).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, K. C. Joshi, “Correlation-induced spectral shifts in optical measurements,” Opt. Eng. 33, 1996–2012 (1994).
[CrossRef]

K. Saxena, D. S. Mehta, H. C. Kandpal, T. S. Vaishya, K. C. Joshi, “Experimental studies of field correlations using spectral interferometric technique,” Opt. Commun. 111, 423–426 (1994).
[CrossRef]

K. C. Joshi, H. C. Kandpal, J. S. Vaishya, “Spectral shift due to source correlation in conventional spectroradiometric measurements,” Appl. Opt. 30, 1471–1474 (1991).
[CrossRef] [PubMed]

H. C. Kandpal, J. S. Vaishya, K. C. Joshi, “Spectral shift due to source correlation for paraxial rays,” Opt. Commun. 79, 270–272 (1990).
[CrossRef]

Kumar, V. N.

D. N. Rao, V. N. Kumar, “Experimental demonstration of spectral modification in a Mach-Zehnder interferometer,” J. Mod. Opt. 41, 1757–1763 (1994).
[CrossRef]

Mandel, L.

Mehta, D. S.

D. S. Mehta, H. C. Kandpal, K. Saxena, J. S. Vaishya, K. C. Joshi, “Displacement measurements from coherence-induced spectral changes in a Mach-Zehnder interferometer,” Opt. Commun. 119, 352–360 (1995).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, K. Saxena, D. S. Mehta, K. C. Joshi, “Intensity distribution across a source from spectral measurements,” J. Mod. Opt. 42, 455–464 (1995).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, K. C. Joshi, “Angular separation of a pair of sources by spectral interferometric technique,” J. Mod. Opt. 42, 447–454 (1995).
[CrossRef]

K. Saxena, D. S. Mehta, H. C. Kandpal, T. S. Vaishya, K. C. Joshi, “Experimental studies of field correlations using spectral interferometric technique,” Opt. Commun. 111, 423–426 (1994).
[CrossRef]

Mielenz, K. D.

K. D. Mielenz, “ ‘Wolf shifts’ and their physical interpretation under laboratory conditions,” J. Res. Natl. Inst. Stand. Technol. 98, 231–240 (1993).
[CrossRef]

Morris, G. M.

D. Faklis, G. M. Morris, “Spectral shifts produced by source correlations,” Opt. Lett. 13, 4–6 (1988).
[CrossRef] [PubMed]

G. M. Morris, D. Faklis, “Effects of source correlations on the spectrum of light,” Opt. Commun. 62, 5–11 (1987).
[CrossRef]

Nugent, K. A.

K. A. Nugent, “Radiometric measurements and correlation-induced spectral changes,” Metrologia 29, 319–324 (1992).
[CrossRef]

Ohtsuka, Y.

H. Arimoto, Y. Ohtsuka, “Measurements of the complex degree of spectral coherence by use of a wave-front-folded interferometer,” Opt. Lett. 22, 958–960 (1997).
[CrossRef] [PubMed]

Y. Ohtsuka, M. Kamada, S. Tanaka, “Correlation-induced spectral changes dependent upon spatiotemporal interference effects,” Opt. Rev. 3, 153–160 (1995).
[CrossRef]

Y. Ohtsuka, “Spectrum invariance for a particular class of optical fields propagated in far zone,” Opt. Rev. 2, 347–351 (1995).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, C. Palma, C. Padovani, “Observation of optical redshifts and blueshifts produced by source correlations,” Opt. Commun. 67, 1–4 (1988).
[CrossRef]

Palma, C.

F. Gori, G. Guattari, C. Palma, C. Padovani, “Observation of optical redshifts and blueshifts produced by source correlations,” Opt. Commun. 67, 1–4 (1988).
[CrossRef]

Rai, J.

J. Rai, S. Rai, S. Chopra, “Source-correlation effects in the time domain,” Phys. Rev. A 47, 4400–4403 (1993).
[CrossRef] [PubMed]

Rai, S.

J. Rai, S. Rai, S. Chopra, “Source-correlation effects in the time domain,” Phys. Rev. A 47, 4400–4403 (1993).
[CrossRef] [PubMed]

Rao, D. N.

D. N. Rao, V. N. Kumar, “Experimental demonstration of spectral modification in a Mach-Zehnder interferometer,” J. Mod. Opt. 41, 1757–1763 (1994).
[CrossRef]

Saxena, K.

D. S. Mehta, H. C. Kandpal, K. Saxena, J. S. Vaishya, K. C. Joshi, “Displacement measurements from coherence-induced spectral changes in a Mach-Zehnder interferometer,” Opt. Commun. 119, 352–360 (1995).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, K. Saxena, D. S. Mehta, K. C. Joshi, “Intensity distribution across a source from spectral measurements,” J. Mod. Opt. 42, 455–464 (1995).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, K. C. Joshi, “Angular separation of a pair of sources by spectral interferometric technique,” J. Mod. Opt. 42, 447–454 (1995).
[CrossRef]

K. Saxena, D. S. Mehta, H. C. Kandpal, T. S. Vaishya, K. C. Joshi, “Experimental studies of field correlations using spectral interferometric technique,” Opt. Commun. 111, 423–426 (1994).
[CrossRef]

Shirai, T.

E. Wolf, T. Shirai, H. Chen, W. Wang, “Coherence filters and their uses,” J. Mod. Opt. 44, 1345–1353 (1997).

T. Shirai, T. Asakura, “Multiple light scattering from spatially random media under the second-order Born approximation,” Opt. Commun. 105, 22 (1994).
[CrossRef]

Tanaka, S.

Y. Ohtsuka, M. Kamada, S. Tanaka, “Correlation-induced spectral changes dependent upon spatiotemporal interference effects,” Opt. Rev. 3, 153–160 (1995).
[CrossRef]

Vaishya, J. S.

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, K. C. Joshi, “Angular separation of a pair of sources by spectral interferometric technique,” J. Mod. Opt. 42, 447–454 (1995).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, K. Saxena, D. S. Mehta, K. C. Joshi, “Intensity distribution across a source from spectral measurements,” J. Mod. Opt. 42, 455–464 (1995).
[CrossRef]

D. S. Mehta, H. C. Kandpal, K. Saxena, J. S. Vaishya, K. C. Joshi, “Displacement measurements from coherence-induced spectral changes in a Mach-Zehnder interferometer,” Opt. Commun. 119, 352–360 (1995).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, K. C. Joshi, “Correlation-induced spectral shifts in optical measurements,” Opt. Eng. 33, 1996–2012 (1994).
[CrossRef]

K. C. Joshi, H. C. Kandpal, J. S. Vaishya, “Spectral shift due to source correlation in conventional spectroradiometric measurements,” Appl. Opt. 30, 1471–1474 (1991).
[CrossRef] [PubMed]

H. C. Kandpal, J. S. Vaishya, K. C. Joshi, “Spectral shift due to source correlation for paraxial rays,” Opt. Commun. 79, 270–272 (1990).
[CrossRef]

Vaishya, T. S.

K. Saxena, D. S. Mehta, H. C. Kandpal, T. S. Vaishya, K. C. Joshi, “Experimental studies of field correlations using spectral interferometric technique,” Opt. Commun. 111, 423–426 (1994).
[CrossRef]

Wang, W.

E. Wolf, T. Shirai, H. Chen, W. Wang, “Coherence filters and their uses,” J. Mod. Opt. 44, 1345–1353 (1997).

Wolf, E.

E. Wolf, T. Shirai, H. Chen, W. Wang, “Coherence filters and their uses,” J. Mod. Opt. 44, 1345–1353 (1997).

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

D. F. V. James, E. Wolf, “Determination of field correlations from spectral measurements with application to synthetic aperture imaging,” Radio Sci. 26, 1239–1243 (1991).
[CrossRef]

Z. Dacic, E. Wolf, “Changes in the spectrum of a partially coherent light beam propagation in free space,” J. Opt. Soc. Am. A 5, 1118–1126 (1988).
[CrossRef]

E. Wolf, “Non-cosmological redshifts of spectral lines,” Nature (London) 326, 363–365 (1987).
[CrossRef]

E. Wolf, “Redshifts and blueshifts of spectral lines caused by source correlations,” Opt. Commun. 62, 12–16 (1987).
[CrossRef]

E. Wolf, “Red shifts and blue shifts of spectral lines emitted by two correlated sources,” Phys. Rev. Lett. 58, 2646–2648 (1987).
[CrossRef] [PubMed]

E. Wolf, “Invariance of spectrum of light on propagation,” Phys. Rev. Lett. 56, 1370–1372 (1986).
[CrossRef] [PubMed]

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

Appl. Opt. (1)

J. Mod. Opt. (5)

E. Wolf, T. Shirai, H. Chen, W. Wang, “Coherence filters and their uses,” J. Mod. Opt. 44, 1345–1353 (1997).

G. S. Agrawal, D. F. V. James, “Spectral changes in the Mach Zehnder interferometer,” J. Mod. Opt. 40, 1431–1436 (1993).
[CrossRef]

D. N. Rao, V. N. Kumar, “Experimental demonstration of spectral modification in a Mach-Zehnder interferometer,” J. Mod. Opt. 41, 1757–1763 (1994).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, K. Saxena, D. S. Mehta, K. C. Joshi, “Intensity distribution across a source from spectral measurements,” J. Mod. Opt. 42, 455–464 (1995).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, K. C. Joshi, “Angular separation of a pair of sources by spectral interferometric technique,” J. Mod. Opt. 42, 447–454 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Res. Natl. Inst. Stand. Technol. (1)

K. D. Mielenz, “ ‘Wolf shifts’ and their physical interpretation under laboratory conditions,” J. Res. Natl. Inst. Stand. Technol. 98, 231–240 (1993).
[CrossRef]

Metrologia (1)

K. A. Nugent, “Radiometric measurements and correlation-induced spectral changes,” Metrologia 29, 319–324 (1992).
[CrossRef]

Nature (London) (1)

E. Wolf, “Non-cosmological redshifts of spectral lines,” Nature (London) 326, 363–365 (1987).
[CrossRef]

Opt. Commun. (8)

E. Wolf, “Redshifts and blueshifts of spectral lines caused by source correlations,” Opt. Commun. 62, 12–16 (1987).
[CrossRef]

G. Agrawal, A. Gamliel, “Spectrum of partially coherent light: transmission from near to far zone,” Opt. Commun. 78, 1–6 (1990).
[CrossRef]

T. Shirai, T. Asakura, “Multiple light scattering from spatially random media under the second-order Born approximation,” Opt. Commun. 105, 22 (1994).
[CrossRef]

G. M. Morris, D. Faklis, “Effects of source correlations on the spectrum of light,” Opt. Commun. 62, 5–11 (1987).
[CrossRef]

K. Saxena, D. S. Mehta, H. C. Kandpal, T. S. Vaishya, K. C. Joshi, “Experimental studies of field correlations using spectral interferometric technique,” Opt. Commun. 111, 423–426 (1994).
[CrossRef]

D. S. Mehta, H. C. Kandpal, K. Saxena, J. S. Vaishya, K. C. Joshi, “Displacement measurements from coherence-induced spectral changes in a Mach-Zehnder interferometer,” Opt. Commun. 119, 352–360 (1995).
[CrossRef]

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Opt. Eng. (1)

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[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

(a) Optical system for illustration, (b) two Gaussian-like spectra S(ζ1;ω) and S(ζ2;ω).

Fig. 2
Fig. 2

Numerically computed results of |μξ;ω)| and arg μ(Δξ;ω). The numerical values for the parameters ζ0, Δζ, Δω, and R(ω1, ω2) are denoted in each figure. A set of three parameters fixed for computing is given in each of the left-hand figures.

Fig. 3
Fig. 3

Schematic of the measurement system of μ.

Fig. 4
Fig. 4

Two SLD’s spectra show S1(ω) and S2(ω) used in the primary source. Their profiles are almost Gaussian.

Fig. 5
Fig. 5

Three spectra S(x;ω), S+(x;ω) and S-(x;ω) measured at P(x).

Fig. 6
Fig. 6

V(x;ω) obtained from three measured S(x;ω), S+(x;ω) and S-(x;ω).

Fig. 7
Fig. 7

(a) Measured and computed |μξ;ω)| for three values of Δζ, (b) measured and computed arg μ(Δξ;ω) for the same values of Δζ’s as in (a).

Fig. 8
Fig. 8

Dependence of μ on Δξ. |μ| and arg μ are plotted in (a) and (b), respectively, for ω=352 and 356 THz with fixed parameters ζ0=0 mm, Δζ=0.04 mm, Δω=3.0 THz, and R(ω1, ω2)=0.5.

Fig. 9
Fig. 9

Observed spectra Ss(ω) and S(x;ω). The solid curves represent Ss(ω), and the three kinds of dotted curves represent S(x;ω). The fixed parameters for the measurements are (a) Δζ=0.04 mm, Δω=3.0 THz, and R(ω1, ω2)=0.5; (b) ζ0=0 mm, Δω=3.0 THz, and R(ω1, ω2)=0.5; (c) ζ0=0 mm, Δζ=0.04 mm, and R(ω1, ω2)=0.5; (d) ζ0=0 mm, Δζ=0.04 mm, and Δω=3.0 THz.

Fig. 10
Fig. 10

Spectral modulation factors M(x, Δξ;ω) with the same parameters as in Fig. 9.

Equations (36)

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V(ζ;t)=12π0U(ζ;ω)exp(-iωt)dω,
U(ζ;ω)=-V(ζ;t)exp(iωt)dt.
V(ξ;t)=12π0U(ξ;ω)exp(-iωt)dω,
U(ξ;ω)=-V(ξ;t)exp(iωt)dt.
V(ζ;t)=V(ζ;t)[δ(ζ-ζ1)+δ(ζ-ζ2)],
U(ζ;ω)=U(ζ;ω)δ(ζ-ζ1)+U(ζ;ω)δ(ζ-ζ2),
U(ζ;ω)=-V(ζ;t)exp(iωt)dt.
V(ξ;t)=--h(ζ, ξ;t-t)V(ζ;t)dζdt,
H(ζ, ξ;ω)=iω exp(-iωr/c)2πcr,
H(ζ, ξ;ω)=-h(ζ, ξ;t)exp(-iωt)dt.
U(ξ;ω)=-H(ζ, ξ;ω)U(ζ;ω)dζ=iω2πcz-U(ζ;ω)exp-iωcz-ζξzdζ,
W(ξ1, ξ2;ω)=U*(ξ1;ω)U(ξ2;ω),
W(ξ1, ξ2;ω)=ω24π2c2z2expi ωζcz(ξ1-ξ2)×--U*(ζ;ω)U(ζ;ω)dζdζ.
U*(α2;ω)U(ζ1;ω)=U*(ζ1;ω)U(ζ2;ω)=0(ζ1ζ2),
U*(ζ1;ω)U(ζ1;ω)=U*(ζ2;ω)U(ζ2;ω)=0(ωω).
--U*(ζ;ω)U(ζ;ω)dζdζ=-dζ10U*(ζ1;ω)U(ζ1;ω)δ(ω-ω)×δ(ζ1-ζ1)dω+-dζ20U*(ζ2;ω)×U(ζ2;ω)δ(ω-ω)δ(ζ2-ζ2)dω=S(ζ1;ω)+S(ζ2;ω),
S(ζ1;ω)=|U(ζ1;ω)|2,
S(ζ2;ω)=|U(ζ2;ω)|2
W(ξ1, ξ2;ω)=ω24π2c2z2S(ζ1;ω)expi ωczζ1Δξ+S(ζ2;ω)expi ωczζ2Δξ,
μ(ξ1, ξ2;ω)=μ(Δξ;ω)=W(ξ1, ξ2;ω)[W(ξ1, ξ1;ω)W(ξ2, ξ2;ω)]1/2=S1(ω)S1(ω)+S2(ω)expi ωczζ1Δξ+S2(ω)S1(ω)+S2(ω)expi ωczζ2Δξ,
μ(Δξ;ω)=|μ|exp(i arg μ),
|μ(Δξ;ω)|=1S1(ω)+S2(ω)S1(ω)2+S2(ω)2+2S1(ω)S2(ω)cosωΔξcz(ζ1-ζ2)1/2,
arg μ(Δξ;ω)=tan-1S1(ω)sinωΔξζ1cz+S2(ω)sinωΔξζ2czS1(ω)cosωΔξζ1cz+S2(ω)cosωΔξζ2cz.
ζ0ζ1+ζ22,
Δζζ1-ζ2,
Δωω1-ω2,
R(ω1, ω2)=S1(ω1)/S2(ω2),
S(x;ω)=S+(x;ω)+S-(x;ω)+2|μ(Δξ;ω)||μT(Δξ;ω)|{S+(x;ω)S-(x;ω)}1/2×cos[ωτ+arg μ(Δξ;ω)+arg μT(Δξ;ω)],
|μ(Δξ;ω)|=env[V(x;ω)],
arg μ(Δξ;ω)=cos-1[V(x;ω)/|μ|]-cos-1[VT(x;ω)/|μT|],
V(x;ω)=S(x;ω)-[S+(x;ω)+S-(x;ω)]2|μT(Δξ;ω)|[S+(x;ω)S-(x;ω)]1/2,
VT(x;ω)=S(x;ω)-[S+(x;ω)+S-(x;ω)]2[S+(x;ω)S-(x;ω)]1/2.
W(Δξ=0;ω)=SS(ω)=ω24π2c2z2[S1(ω)+S2(ω)].
S(x;ω)=S+(x;ω)+S-(x;ω)+2|μ(Δξ;ω)|[S+(x;ω)S-(x;ω)]1/2×cos[arg μ(Δξ;ω)].
S(x;ω)=SS(ω){1+M(x, Δξ;ω)},
M(x, Δξ;ω)=2[S+(x;ω)S-(x;ω)]1/2SS(ω)|μ(Δξ;ω)|×cos{arg μ(Δξ;ω)}

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