## Radiometry and wide-angle wave fields. II. Coherent fields in three dimensions

JOSA A, Vol. 18, Issue 4, pp. 910-918 (2001)

http://dx.doi.org/10.1364/JOSAA.18.000910

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### Abstract

The wave-based generalized radiance definitions presented in a previous manuscript [J. Opt. Soc. A 18, 902 (2001)] for two-dimensional coherent monochromatic fields in free space are extended here to the three-dimensional case. These new definitions preserve all the properties of their two-dimensional analogs. Notably, they are exactly conserved along rays and well suited for the description of fields traveling in all directions. The different members of this set of functions are seen to correspond to weighted radial projections in momentum of the Wigner function of the field.

© 2001 Optical Society of America

**OCIS Codes**

(030.5620) Coherence and statistical optics : Radiative transfer

(030.5630) Coherence and statistical optics : Radiometry

**History**

Original Manuscript: July 6, 2000

Revised Manuscript: September 25, 2000

Manuscript Accepted: October 18, 2000

Published: April 1, 2001

**Citation**

M. A. Alonso, "Radiometry and wide-angle wave fields. II. Coherent fields in three dimensions," J. Opt. Soc. Am. A **18**, 910-918 (2001)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-4-910

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### References

- M. Born, 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.
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- See also Ref. 2, pp. 292–297.
- M. A. Alonso, “Radiometry and wide-angle wave fields. I. Coherent fields in two dimensions,” J. Opt. Soc. Am. A 18, 902–909 (2000). [CrossRef]
- K. B. Wolf, M. A. Alonso, G. W. Forbes, “Wigner functions for Helmholtz wave fields,” J. Opt. Soc. Am. A 16, 2476–2487 (1999). [CrossRef]
- E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 740–759 (1932). [CrossRef]
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- H. M. Pedersen, 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). See Eq. (5.17). [CrossRef]
- G. I. Ovchinnikov, V. I. Tatarskii, “On the problem of the relationship between coherence theory and the radiation-transfer equation,” Radiophys. Quantum Electron. 15, 1087–1089 (1972). See Eq. (2). [CrossRef]
- 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, E. Wolf, eds. (Plenum, New York, 1990), pp. 883–887. See Eq. (12).
- H. M. Pedersen, “Exact theory of free-space radiative energy transfer,” J. Opt. Soc. Am. A 8, 176–185 (1991); errata J. Opt. Soc. Am. A 8, 1518 (1991). See Eq. (6.4). [CrossRef]
- R. G. Littlejohn, R. Winston, “Corrections to classical radiometry,” J. Opt. Soc. Am. A 10, 2024–2037 (1993). The missing obliquity factor can be seen from the comparison of Eq. (5.11) of this reference with Eq. (2.9) of the present paper. Whereas the latter involves integration over a solid angle, the former is an integral over the transverse Cartesian coordinates of the direction vector. [CrossRef]

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