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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 8, Iss. 7 — Jul. 1, 1991
  • pp: 1099–1105

Effect of an aperture on the spectrum of partially coherent light

John T. Foley  »View Author Affiliations


JOSA A, Vol. 8, Issue 7, pp. 1099-1105 (1991)
http://dx.doi.org/10.1364/JOSAA.8.001099


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Abstract

It is shown for a particular class of partially coherent fields that, when such a field is incident upon a circular aperture, the spectrum of the light at an observation point in the far zone of the aperture is different from the spectrum of the light in the aperture. An explicit expression for the spectrum at such observation points is obtained, and it is shown that the difference between the two spectra depends on the ratio of the radius of the aperture to the effective correlation length of the light in the aperture. Numerical examples are presented, and the relevant limiting cases are discussed.

© 1991 Optical Society of America

History
Original Manuscript: July 16, 1990
Revised Manuscript: March 5, 1991
Manuscript Accepted: March 12, 1991
Published: July 1, 1991

Citation
John T. Foley, "Effect of an aperture on the spectrum of partially coherent light," J. Opt. Soc. Am. A 8, 1099-1105 (1991)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-8-7-1099


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References

  1. E. Wolf, “Invariance of the spectrum of light on propagation,” Phys. Rev. Lett. 56, 1370–1372 (1986). [CrossRef] [PubMed]
  2. G. M. Morris, D. Faklis, “Effects of source correlation on the spectrum of light,” Opt. Commun. 62, 5–11 (1987). [CrossRef]
  3. E. Wolf, “Non-cosmological redshifts of spectral lines,” Nature (London) 326, 363–365 (1987). [CrossRef]
  4. E. Wolf, “Redshifts and blueshifts of spectral lines caused by source correlations,” Opt. Commun. 62, 12–16 (1987). [CrossRef]
  5. E. Wolf, “Redshifts and blueshifts of spectral lines emitted by two correlated sources,” Phys. Rev. Lett. 58, 2646–2648 (1987). The sources discussed in Refs. 3–5 were three-dimensional primary sources. The corresponding results for planar secondary sources are essentially the same. [CrossRef] [PubMed]
  6. D. Faklis, M. Morris, “Spectral shifts produced by source correlations,” Opt. Lett. 13, 4–6 (1988). [CrossRef] [PubMed]
  7. F. Gori, G. Guattari, C. Palma, “Observation of optical redshifts and blueshifts produced by source correlations,” Opt. Commun. 67, 1–4 (1988). [CrossRef]
  8. H. C. Kandpal, J. S. Vaishya, K. C. Joshi, “Wolf shift and its application in spectroradiometry,” Opt. Commun. 73, 169–172 (1989). [CrossRef]
  9. J. T. Foley, “The effect of an aperture on the spectrum of partially coherent light,” Opt. Commun. 75, 347–352 (1990). [CrossRef]
  10. μis sometimes also referred to as the complex degree of spectral coherence.
  11. E. W. Marchand, E. Wolf, “Radiometry with sources of any state of coherence,”J. Opt. Soc. Am. 64, 1219–1226 (1974), Eqs. (2) and (12), with the factor cos2θ omitted because of the paraxial approximation. [CrossRef]
  12. These values of ω¯ and Γ were chosen so that s(0)(ω) corresponds, roughly, to the analogous spectrum observed in Ref. 2, their SIIconv(ω). This is a broadband spectrum.
  13. To within the resolution used to plot Figs. 4–6, there is no shift of peak of the spectrum. More detailed calculations show that small shifts do occur, even for fairly large values of a/ L¯. Such shifts are discussed, for on-axis observation points, in Ref. 9.
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 119–120.

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