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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. 18, Iss. 4 — Apr. 1, 2001
  • pp: 902–909

Radiometry and wide-angle wave fields. I. Coherent fields in two dimensions

M. A. Alonso  »View Author Affiliations


JOSA A, Vol. 18, Issue 4, pp. 902-909 (2001)
http://dx.doi.org/10.1364/JOSAA.18.000902


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Abstract

A family of interconnected analogs of the radiance or specific intensity from classical radiometry are defined for coherent monochromatic wave fields. These generalized radiances are explicitly conserved along rays, regardless of wavelength. Unlike several previous definitions, the new forms are suitable for the description of fields propagating in all directions.

© 2001 Optical Society of America

OCIS Codes
(030.5620) Coherence and statistical optics : Radiative transfer
(030.5630) Coherence and statistical optics : Radiometry

Citation
M. A. Alonso, "Radiometry and wide-angle wave fields. I. Coherent fields in two dimensions," J. Opt. Soc. Am. A 18, 902-909 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-4-902


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References

  1. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th (expanded) ed. (Cambridge U. Press, Cambridge, UK, 1999), pp. 193–199.
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, New York, 1995), pp. 287–307.
  3. R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), pp. 13–27.
  4. A. Walther, The Ray and Wave Theory of Lenses (Cambridge U. Press, Cambridge, UK, 1995), pp. 69–78.
  5. L. S. Dolin, “Beam description of weakly-inhomogeneous wave fields,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 7, 559–563 (1964).
  6. A. Walther, “Radiometry and coherence,” J. Opt. Soc. Am. 58, 1256–1259 (1968).
  7. A. Walther, “Radiometry and coherence,” J. Opt. Soc. Am. 63, 1622–1623 (1973).
  8. Yu. N. Barabanenkov, “On the spectral theory of radiation transfer equations,” Sov. Phys. JETP 29, 679–684 (1969).
  9. E. W. Marchand and E. Wolf, “Generalized radiometry for radiation from partially coherent sources,” Opt. Commun. 6, 305–308 (1972).
  10. E. W. Marchand and E. Wolf, “Radiometry with sources of any state of coherence,” J. Opt. Soc. Am. 64, 1219–1226 (1974).
  11. M. Nieto-Vesperinas, “Classical radiometry and radiative transfer theory: a short-wavelength limit of a general mapping of cross-spectral densities in second-order coherence theory,” J. Opt. Soc. Am. A 3, 1354–1359 (1986).
  12. G. S. Agarwal, J. T. Foley, and E. Wolf, “The radiance and phase-space representations of the cross-spectral density operator,” Opt. Commun. 62, 67–72 (1987).
  13. See also Ref. 2, pp. 292–297.
  14. E. Wolf, “Coherence and radiometry,” J. Opt. Soc. Am. 68, 6–17 (1978).
  15. A. T. Friberg, “Effects of coherence in radiometry,” Opt. Eng. 21, 927–936 (1982).
  16. A. T. Friberg, “On the generalized radiance associated with radiation from a quasihomogeneous planar source,” Opt. Acta 28, 261–277 (1981).
  17. J. T. Foley and E. Wolf, “Radiometry as a short-wavelength limit of statistical wave theory with globally incoherent sources,” Opt. Commun. 55, 236–241 (1985).
  18. K. Kim and E. Wolf, “Propagation law for Walther’s first generalized radiance function and its short-wavelength limit with quasi-homogeneous sources,” J. Opt. Soc. Am. A 4, 1233–1236 (1987).
  19. A. T. Friberg, G. S. Agarwal, J. T. Foley, and E. Wolf, “Statistical wave-theoretical derivation of the free-space transport equation of radiometry,” J. Opt. Soc. Am. B 9, 1386–1393 (1992).
  20. M. J. Bastiaans, “Wigner distribution function and its application to first-order optics,” J. Opt. Soc. Am. 69, 1710–1716 (1980).
  21. E. Wolf, “Radiometric model for propagation of coherence,” Opt. Lett. 19, 2024–2026 (1994).
  22. A. T. Friberg and S. Yu. Popov, “Radiometric description of intensity and coherence in generalized holographic axicon images,” Appl. Opt. 35, 3039–3046 (1996).
  23. A. S. Marathay, “Radiometry of partially coherent fields. I,” Opt. Acta 23, 785–794 (1976).
  24. H. M. Pedersen, “Radiometry and coherence for quasi-homogeneous scalar wavefields,” Opt. Acta 29, 877–892 (1982).
  25. R. Martinez-Herrero and P. M. Mejias, “Radiometric definitions for partially coherent sources,” J. Opt. Soc. Am. A 1, 556–558 (1984).
  26. R. Martinez-Herrero and P. M. Mejias, “Radiometric definitions from second-order coherence characteristics of planar sources,” J. Opt. Soc. Am. A 3, 1055–1058 (1986).
  27. G. I. Ovchinnikov and V. I. Tatarskii, “On the problem of the relationship between coherence theory and the radiation-transfer equation,” Radiophys. Quantum Electron. 15, 1087–1089 (1972).
  28. H. M. Pedersen, “Exact geometrical description of free space radiative energy transfer for scalar wavefields,” in Coherence and Quantum Optics VI, J. H. Eberly, L. Mandel, and E. Wolf, eds. (Plenum, New York, 1990), pp. 883–887.
  29. H. M. Pedersen, “Exact theory of free-space radiative energy transfer,” J. Opt. Soc. Am. A 8, 176–185 (1991); errata, 8, 1518 (1991).
  30. H. M. Pedersen and O. J. Løkberg, “Coherence and radiative energy transfer for linear surface gravity waves in water of constant depth,” J. Phys. A Math. Gen. 25, 5263–5278 (1992).
  31. H. M. Pedersen, “Propagation of generalized specific intensity in refracting media,” J. Opt. Soc. Am. A 9, 1623–1625 (1992).
  32. H. M. Pedersen, “Geometric theory of fields radiated from three-dimensional, quasi-homogeneous sources,” J. Opt. Soc. Am. A 9, 1626–1632 (1992).
  33. R. G. Littlejohn and R. Winston, “Corrections to classical radiometry,” J. Opt. Soc. Am. A 10, 2024–2037 (1993).
  34. H.-W. Lee, “Theory and application of the quantum phase-space distribution functions,” Phys. Rep. 259, 147–211 (1995).
  35. E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 740–759 (1932).
  36. N. L. Balasz and B. K. Jennings, “Wigner’s function and other distribution functions in mock phase spaces,” Phys. Rep. 104, 347–391 (1984).
  37. A. T. Friberg, “On the existence of a radiance function for finite planar sources of arbitrary states of coherence,” J. Opt. Soc. Am. 69, 192–198 (1979).
  38. E. P. Wigner, “Quantum mechanical distribution functions revisited,” in Perspectives in Quantum Theory, W. Yourgrau and A. van der Merwe, eds. (MIT Press, Cambridge, Mass., 1971), pp. 25–36.
  39. The existence of such a plane for all directions u imposes some extra restrictions on the region of interest. For Eq. (2.6) to be valid for at least one plane normal to each direction u, the region must contain the minimum sphere that intersects all rays that carry some amount of light.
  40. This result was obtained during a discussion with Greg W. Forbes.
  41. S. Steinberg and K. B. Wolf, “Invariant inner products on spaces of solutions of the Klein–Gordon and Helmholtz equations,” J. Math. Phys. 22, 1660–1663 (1981).
  42. M. A. Alonso, “Measurement of Helmholtz wave fields,” J. Opt. Soc. Am. A 17, 1256–1264 (2000).
  43. See Ref. 2, p. 289.
  44. K. B. Wolf, M. A. Alonso, and G. W. Forbes, “Wigner functions for Helmholtz wave fields,” J. Opt. Soc. Am. A 16, 2476–2487 (1999).
  45. M. A. Alonso and G. W. Forbes, “Uncertainty products for nonparaxial wave fields,” J. Opt. Soc. Am. A 17, 2391–2402 (2000).
  46. The only reference given here where I is identified with H is Ref. 2, page 302.
  47. A similar result was presented in R. G. Littlejohn and R. Winston, “Generalized radiance and measurement,” J. Opt. Soc. Am. A 12, 2736–2743 (1995). The treatment presented there, however, was based on Walther’s first generalized radiance. It is therefore limited to forward-propagating fields and leads to results that are not invariant under rotations of the reference frame.
  48. This function is the Helmholtz analog of the Husimi function from quantum theory. See Ref. 34.
  49. The localization properties of this function are studied in Ref. 45.

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