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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 16 — Jun. 1, 1998
  • pp: 3464–3470

Thermodynamic constraints on reflectance reciprocity and Kirchhoff’s law

William C. Snyder, Zhengming Wan, and Xiaowen Li  »View Author Affiliations


Applied Optics, Vol. 37, Issue 16, pp. 3464-3470 (1998)
http://dx.doi.org/10.1364/AO.37.003464


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Abstract

Contrary to common belief, neither reciprocity of the bidirectional reflectance distribution function (BRDF) nor the directional form of Kirchhoff’s electromagnetic radiation law can be demonstrated on the basis of energy conservation. The BRDF is generally considered reciprocal as an extension of Helmholtz reciprocity, but Helmholtz reciprocity does not always hold. We describe the flaw in a thermodynamic demonstration of reciprocity that uses an enclosure calculation. Some conclusions can be drawn from the enclosure calculation, but reciprocity requires more restrictive conditions. We conclude that, although they can be violated, reciprocity and the directional form of Kirchhoff’s law generally hold because of the quantum-mechanical principle of time-reversal invariance, which applies to most materials.

© 1998 Optical Society of America

OCIS Codes
(000.6850) General : Thermodynamics
(120.5630) Instrumentation, measurement, and metrology : Radiometry

History
Original Manuscript: July 21, 1997
Revised Manuscript: January 20, 1998
Published: June 1, 1998

Citation
William C. Snyder, Zhengming Wan, and Xiaowen Li, "Thermodynamic constraints on reflectance reciprocity and Kirchhoff’s law," Appl. Opt. 37, 3464-3470 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-16-3464


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References

  1. R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 2nd ed. (Hemisphere, Washington, D.C., 1981), pp. 65–66.
  2. W. C. Snyder, Z. Wan, “Surface temperature correction for active infrared reflectance measurements of natural materials,” Appl. Opt. 35, 2216–2220 (1996). [CrossRef] [PubMed]
  3. W. C. Snyder, Z. Wan, “BRDF models to predict spectral reflectance and emissivity in the thermal infrared,” IEEE Trans. Geosci. Remote Sens. 36, 214–225 (1998). [CrossRef]
  4. F. Nicodemus, J. Richmond, J. Hsia, I. Ginsberg, T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, NBS Monograph 160 (National Bureau of Standards, Washington, D.C., 1977), pp. 3–6.
  5. C. von Fragstein, “Über die Formulierung des Kirchhoffschen Gesetzes und ihre Bedeutung für eine zweckmässige Definition von Remissionszahlen,” Optik 12, 60–68 (1955).
  6. F. Clarke, D. Parry, “Helmholtz reciprocity: its validity and application to reflectometry,” Ltg. Res. Technol. 17, 1–11 (1985). [CrossRef]
  7. L. Levi, Applied Optics (Wiley, New York, 1968), p. 84.
  8. F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965), pp. 382–384.
  9. A. Shelankov, G. Pikus, “Reciprocity in reflection and transmission of light,” Phys. Rev. B 46, 3326–3336 (1992). [CrossRef]
  10. W. C. Snyder, “Reciprocity of the bidirectional reflectance distribution function (BRDF) in measurements and models of structured surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 685–691 (1998). [CrossRef]
  11. C. von Fragstein, “Ist eine Lichtbewegung stets umkehrbar?” Opt. Acta 2, 16–22 (1955). [CrossRef]
  12. H. Okayama, I. Ogura, “Experimental verification of nonreciprocal response in light scattering from rough surfaces,” Appl. Opt. 23, 3349–3352 (1984). [CrossRef] [PubMed]
  13. W. H. Venable, “Comments on reciprocity failure,” Appl. Opt. 24, 3943 (1985). [CrossRef] [PubMed]
  14. M.-J. Kim, “Verification of the reciprocity theorem,” Appl. Opt. 27, 2645–2646 (1988). [CrossRef] [PubMed]
  15. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), pp. 380–381.
  16. A. T. DeHoop, “Reciprocity theorem for the electromagnetic field scattered by an obstacle,” Appl. Sci. Res. Sec. B 8, 135–140 (1960). [CrossRef]
  17. F. E. Nicodemus, “Directional reflectance and emissivity of an opaque surface,” Appl. Opt. 4, 767–773 (1965). [CrossRef]
  18. F. Nicodemus, Radiometry, Vol. 4 of Applied Optics and Optical Engineering (Academic, New York, 1967), Chap. 8, p. 284.
  19. G. Bauer, “Reflexionsmessungen an offenen Hohlräumen,” Optik 18, 603–622 (1961).
  20. K. Frank, Principles of Heat Transfer (Intext, New York, 1973), p. 244.
  21. A. Baltes, “On the validity of Kirchhoff’s law of heat radiation for a body in a nonequilibrium environment,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1976), Vol. 13, pp. 3–25. [CrossRef]
  22. J. Salisbury, A. Wald, D. D’Aria, “Thermal-infrared remote sensing and Kirchhoff’s law. 1. Laboratory measurements,” J. Geophys. Res. 99, 11897–11911 (1994). [CrossRef]
  23. F. Grum, R. Becherer, “Radiometry,” in Optical Radiation Measurements, F. Grum, ed. (Academic, New York, 1979), Vol. 1, p. 115.
  24. A. Springsteen, Labsphere, Inc., North Sutton, N.H. 03260-0070 (personal communication, 1996).
  25. D. S. Kimes, W. W. Newcomb, R. F. Nelson, J. B. Schutt, “Directional reflectance distributions of a hardwood and pine forest canopy,” IEEE Trans. Geosci. Remote Sens. GE-24, 281–293 (1986). [CrossRef]
  26. D. W. Deering, S. P. Ahmad, T. F. Eck, B. P. Banerjee, “Temporal attributes of the bidirectional reflectance for three Boreal forest canopies,” Proc. IGARSS’95 1, 1239–1241 (1995).
  27. K.-T. Kriebel, “On the limited validity of reciprocity in measured BRDFs,” Remote Sens. Environ. 58, 52–62 (1996). [CrossRef]

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