Skip to main content
SpringerLink
Log in

Theoretical Basis of Blackbody Radiometry

  • Chapter
  • First Online:
Blackbody Radiometry

Part of the book series: Springer Series in Measurement Science and Technology ((SSMST))

Abstract

The theoretical basis of blackbody radiometry includes the radiation laws of a perfect blackbody discovered at the turn of the nineteenth and twentieth centuries and the theory of the radiation heat transfer developed by the mid-1960s. To ensure uniformity of presentation throughout the book, the synopsis of fundamental ideas, definitions, and laws are given in this chapter in the modern form. The concept of a perfect blackbody and its fundamental radiation laws are introduced and explained. The nomenclature of radiative properties of surfaces are considered in connection with the reciprocity principle, Kirchhoff’s law, and the energy conservation law. The radiance temperature concept is discussed. The simplest methods for calculation of radiative heat transfer in geometrical configurations, typical for radiometric systems, are outlined. Thus, the chapter allows readers to update their knowledge to proceed to the next chapters.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Change history

  • 28 March 2021

    The original publication can be found online.

Notes

  1. 1.

    Cited in English translation [41] of the original article [40].

References

  1. J. Agassi, Radiation Theory and the Quantum Revolution (Birkhduser Verlag, Basel, Switzerland, 1993)

    Google Scholar 

  2. R.E. Alley, M. Jentoft-Nilsen, Advanced Spaceborne Thermal Emission & Reflection Radiometer. Algorithm Theoretical Basis Document for Brightness Temperature. (Jet Propulsion Laboratory, Pasadena, CA, 1999), https://trs.jpl.nasa.gov/bitstream/handle/2014/18629/99-2009.pdf?sequence=1&isAllowed=y. Accessed 02 Jan 2019

  3. Ž Andreić, Distribution temperature calculations by fitting the Planck radiation curve to a measured spectrum. Appl. Opt. 31, 126–130 (1992)

    ADS  Google Scholar 

  4. ANSI/IES RP-16–10. Nomenclature and Definitions for Illuminating Engineering. (The IES Nomenclature Committee, Illuminating Engineering Society of North America, New York, 2010)

    Google Scholar 

  5. T.M. Apostol, Zeta and related functions, in NIST Handbook of Mathematical Functions. ed. by F.W.J. Olver (NIST and Cambridge University Press, New York, 2010), pp. 601–616

    Google Scholar 

  6. G.B. Arfken, H.J. Weber, F.E. Harris, Mathematical Methods for Physicists. A Comprehensive Guide, 7th ed. (Acad. Press, Amsterdam, 2013)

    Google Scholar 

  7. K.E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind (Cambridge University Press, Cambridge, UK, 1997)

    MATH  Google Scholar 

  8. M. Badino, The Bumpy Road. Max Planck from Radiation Theory to the Quantum (1896–1906) (Springer, Cham, Switzerland, 2015)

    Google Scholar 

  9. M. Bass, (ed.). Handbook of Optics, Vol. IV. Optical Properties of Materials, Nonlinear Optics, Quantum Optics, 3rd. edn. (McGraw-Hill, New York, 2010)

    Google Scholar 

  10. R.E. Bedford, Calculation of effective emissivities of cavity sources of thermal radiation, in Theory and Practice of Radiation Thermometry. ed. by D.P. DeWitt, G.D. Nutter (Wiley, New York, 1988), pp. 653–672

    Google Scholar 

  11. A. Berk, Analytically derived conversion of spectral band radiance to brightness temperature. J. Quant. Spectrosc. Rad. Transfer 109, 1266–1276 (2008)

    ADS  Google Scholar 

  12. D.C. Bertilone, Stokes parameters and partial polarization of far-field radiation emitted by hot bodies. J. Opt. Soc. Am. 11, 2298–2304 (1994)

    ADS  Google Scholar 

  13. J.T. Bevans, D.K. Edwards, Radiation exchange in an enclosure with directional wall properties. J. Heat Transfer 87, 388–396 (1965)

    Google Scholar 

  14. R.P. Bobco, A script-F Matrix formulation for enclosures with arbitrary surface emission and reflection characteristics. J. Heat Transfer 93, 33–40 (1971)

    Google Scholar 

  15. L. Boltzmann, Über eine von Hrn. Bartoli entdeckte Beziehung der Wärmestrahlung zum zweiten Hauptsatz. Wiedernannsche Annalen der Physik. 22, 31–39 (1884)

    Google Scholar 

  16. S.B. Bopche, A. Sridharan, Determination of view factors by contour integral technique. Ann. Nucl. Energy 36, 1681–1688 (2009)

    Google Scholar 

  17. M.A. Bramson, Infrared Radiation. A Handbook for Applications (Springer, New York, 1968)

    Google Scholar 

  18. S.L. Chang, K.T. Rhee, Blackbody radiation functions. Int. Commun. Heat Mass Transf. 11, 451–455 (1984)

    Google Scholar 

  19. P.E. Ciddor, Refractive index of air: new equations for the visible and near infrared. Appl. Optics 35, 1566–1573 (1996)

    ADS  Google Scholar 

  20. M.F. Cohen, J.R. Wallace, The form factor, in Radiosity and Realistic Image Synthesis. ed. by M.F. Cohen, J.R. Wallace (Acad. Press, Boston, MA, 1995), pp. 65–107

    MATH  Google Scholar 

  21. R.C. Corlett, Direct numerical simulation of thermal radiation in vacuum. J. Heat Transfer 88, 376–382 (1966)

    Google Scholar 

  22. E.R.G. Eckert, E.M. Sparrow, Radiative heat exchange between surfaces with specular reflection. Int. J. Heat Mass Transfer 3, 42–54 (1961)

    Google Scholar 

  23. B. Edlén, The refractive index of air. Metrologia 2, 71–80 (1966)

    ADS  Google Scholar 

  24. J.L. Gardner, Uncertainties in source distribution temperature and correlated colour temperature. Metrologia 43, 403–408 (2006)

    ADS  Google Scholar 

  25. T.A. Germer, J.C. Zwinkels, B.K. Tsai, et al. (eds.) Theoretical concepts in spectrophotometric measurements. in Spectrophotometry: Accurate Measurement of Optical Properties of Materials, ed. by T.A. Germer, J.C. Zwinkels, B.K. Tsai (Acad. Press, Amsterdam, 2014), pp. 11–66

    Google Scholar 

  26. M.A. Heald, Where is the “Wien peak”? Amer. J. Phys. 71, 1322–1323 (2003)

    ADS  Google Scholar 

  27. D. Hoffmann, On the experimental context of Planck’s foundation of quantum theory. Centaurus 43, 240–259 (2001)

    MathSciNet  MATH  Google Scholar 

  28. J. Hollandt, J. Hartmann, O. Struß, et al. Industrial applications of radiation thermometry. in eds. by Z.M. Zhang, B K. Tsai, G. Machin, Radiometric Temperature Measurements. II. Applications, (Academic Press, Amsterdam, 2010), pp. 1–56

    Google Scholar 

  29. J.R. Howell, Application of Monte Carlo to heat transfer problems, in Advances in Heat Transfer, vol. 5, ed. by T.F. Irvine, J.P. Hartnett (Academic Press, New York, 1968), pp. 1–54

    Google Scholar 

  30. J.R. Howell, M.P. Mengüç, R. Siegel, Thermal Radiation Heat Transfer, 6th edn. (CRC Press, Boca Raton, FL, 2016)

    Google Scholar 

  31. J.R. Howell, A Catalog of Radiation Heat Transfer Configuration Factors, 3rd edn. (University of Texas at Austin, 2018), https://www.thermalradiation.net/indexCat.html. Accessed 17 Oct 2019

  32. J.R. Howell, The Monte Carlo method in radiative heat transfer. J. Heat Transfer 120, 547–560 (1998)

    Google Scholar 

  33. J.F. Hughes, A. Van Dam, M. Mcguire et al. Computer Graphics. Principles and Practice, 3rd edn. (Addison-Wesley, Upper Saddle River, NJ, 2014)

    Google Scholar 

  34. R.W.G. Hunt, M.R. Pointer, Measuring Colour, 4th edn. (Wiley, Chichester, UK, 2011)

    Google Scholar 

  35. ILV: International Lighting Vocabulary/Vocabulaire International de l’Eclairage/ Internationales Wörterbuch der Lichttechnik. CIE S 017/E:2011. (CIE Central Bureau, Vienna, 2011)

    Google Scholar 

  36. J. Jablonski, C. Durell, J. LaVeigne, et al. A turn-key calibration roadmap for temperature and radiance from 0.3–14 µm. Proc. SPIE. 10178, 1017804 (2017)

    Google Scholar 

  37. J.H. Jeans, Temperature-radiation and the partition of energy in continuous media. Phil. Mag. Series 6(17), 229–254 (1909)

    MATH  Google Scholar 

  38. H. Kangro, Early History of Planck’s Radiation Law (Taylor and Francis, London, 1976)

    Google Scholar 

  39. G.R. Kirchhoff, Über den Zusammenhang zwischen Emmission und Absorption von Licht und Wärme. Monatsberichte der Königlichen Preuß. Akademie der Wissenschaften zu Berlin aus dem Jahre. 1859, 783–787 (1860)

    Google Scholar 

  40. G.R. Kirchhoff, Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht. Annalen der Physik. 185, 275–301 (1860)

    Google Scholar 

  41. G. Kirchhoff, On the relation between the radiating and absorbing powers of different bodies for light and heat. The London, Edinburgh, and Dublin Phil. Mag. J. Sci. 20(130), 1–21 (1860)

    Google Scholar 

  42. T.S. Kuhn, Black-Body Theory and the Quantum Discontinuity. 1894–1912 (The University of Chicago Press, Chicago, 1978)

    Google Scholar 

  43. J.H. Lambert, Photometry, or, on the Measure and Gradations of Light, Colors and Shade (English translation of 1760 Latin edn.) (Illuminating Engineering, New York, 2001)

    Google Scholar 

  44. S.H. Lin, E.M. Sparrow, Radiant interchange among curved specularly reflecting surfaces—application to cylindrical and conical cavities. J. Heat Transfer 87, 299–307 (1965)

    Google Scholar 

  45. S. Marschner, P. Shirley, Fundamentals of Computer Graphics, 4th edn. (CRC Press, Boca Raton, FL, 2016)

    MATH  Google Scholar 

  46. S. Maruyama, Radiation heat transfer between arbitrary three-dimensional bodies with specular and diffuse surfaces. Num. Heat Transfer, Part a 24, 181–196 (1993)

    ADS  Google Scholar 

  47. H. Masuda, Radiation heat transfer between specularly and diffusely reflecting surfaces. J. Quant. Spectrosc. Radiat. Transfer 16, 997–1009 (1976)

    ADS  Google Scholar 

  48. R.J. Mathar, Refractive index of humid air in the infrared: model fits. J. Opt. A: Pure Appl. Opt. 9, 470–476 (2007)

    ADS  Google Scholar 

  49. M.F. Modest, Radiative Heat Transfer, 3rd edn. (Acad. Press, New York, 2013)

    Google Scholar 

  50. J. Muelaner, Ciddor Equation for Refractive Index of Air (2015), https://www.mathworks.com/matlabcentral/fileexchange/52204-ciddor-equation-for-refractive-index-of-air. Accessed 21 Dec 2018

  51. M.H.N. Naraghi, B.T.F. Chung, A stochastic approach for radiative exchange in enclosures with nonparticipating medium. J. Heat Transfer. 106, 690–698 (1984)

    ADS  Google Scholar 

  52. F.E. Nicodemus, J.C. Richmond, J.J. Hsia, et al. Geometrical Considerations and Nomenclature for Reflectance. NBS Monograph 160. (Natl. Bureau of Standards, U.S. Dept. of Commerce, Washington, DC, 1977)

    Google Scholar 

  53. N. Ohta, A.R. Robertson, Colorimetry Fundamentals and Applications (Wiley, Chichester, UK, 2005)

    Google Scholar 

  54. C. Oleari, Standard Colorimetry. Definitions Algorithms and Software (Wiley, Chichester, UK, 2016)

    Google Scholar 

  55. J.C. Owens, Optical refractive index of air: dependence on pressure, temperature and composition. Appl. Opt. 6, 51–59 (1967)

    ADS  Google Scholar 

  56. M. Pharr, W. Jakob, G. Humphreys, Physically Based Rendering. From Theory to Implementation, 3rd edn. (Morgan Kaufmann, Cambridge, MA, 2017)

    Google Scholar 

  57. M. Planck, The Theory of Heat Radiation (P. Blakiston’s Son & Co., Philadelphia, PA, 1914)

    MATH  Google Scholar 

  58. M. Planck, Über eine Verbesserung der Wienschen Spektralgleichung. Verh. Dtsch. Phys. Ges. 2, 202–204 (1900)

    Google Scholar 

  59. M. Planck, Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum. Verh. Dtsch. Phys. Ges. 2, 237–245 (1900)

    MATH  Google Scholar 

  60. M. Polyanskiy, Refractive Index Database (2018), https://refractiveindex.info/?shelf=other&book=air&page=Ciddor. Accessed 17 Oct 2019

  61. A.V. Prokhorov, L.M. Hanssen, S.N. Mekhontsev, Calculation of the radiation characteristics of blackbody radiation sources. in eds. by Z.M. Zhang, B. Tsai, G. Machin, (eds.) Radiometric Temperature Measurements. I. Fundamental, (Acad. Press, Amsterdam, 2010), pp. 181–240

    Google Scholar 

  62. Rayleigh, Lord: Remarks upon the law of complete radiation. Phil. Mag. 49, 539–540 (1900)

    Google Scholar 

  63. A. Resnick, C. Persons, G. Lindquist, Polarized emissivity and Kirchhoff’s law. Appl. Opt. 38, 1384–1387 (1999)

    ADS  Google Scholar 

  64. J.C. Richmond, F.E. Nicodemus, Blackbodies, blackbody radiation, and temperature scales, in ed. by F.E. Nicodemus, Self-study Manual on Optical Radiation Measurements: Part 1—Concepts, Chapter 12 (U.S. Dept. of Commerce, NBS, 1985)

    Google Scholar 

  65. J. Roberts, Black Body Radiation Functions (The University of Newcastle 1971), https://ia902303.us.archive.org/25/items/Roberts1971/Roberts-1971.pdf. Accessed 17 Oct 2019

  66. P. Rosenkranz, M. Matus, M.L. Rastello. On estimation of distribution temperature. Metrologia 43, S130–S134 (2006)

    Google Scholar 

  67. W.D. Ross, Methods of representing radiation formulas. J. Opt. Soc. Amer. 44, 770–771 (1954)

    ADS  Google Scholar 

  68. O. Sandus, A review of emission polarization. Appl. Opt. 4, 1634–1642 (1965)

    ADS  Google Scholar 

  69. A.F. Sarofim, H.C. Hottel, Radiative exchange among non-Lambert surfaces. J. Heat Transfer. 88, 37–43 (1966)

    Google Scholar 

  70. P. Saunders, E. Woolliams, H. Yoon, et al. Uncertainty Estimation in Primary Radiometric Temperature Measurement (CCT, BIPM, 2018), https://www.bipm.org/utils/en/pdf/si-mep/MeP-K-2018_Absolute_Primary_Radiometry_Uncertainty.pdf. Accessed 17 Oct 2019

  71. G. Schaepman-Strub, M.E. Schaepman, T.H. Painter et al., Reflectance quantities in optical remote sensing—definitions and case studies. Remote Sens. Environ. 103, 27–42 (2006)

    ADS  Google Scholar 

  72. J. Smith, Air Refractive Index (2011), https://www.mathworks.com/matlabcentral/fileexchange/31240-air-refractive-index. Accessed 17 Oct 2019

  73. E.M. Sparrow, Heat radiation between simply-arranged surfaces having different temperatures and emissivities. AIChE J. 8, 12–18 (1962)

    Google Scholar 

  74. E.M. Sparrow, A new and simpler formulation for radiative angle factors. J. Heat Transfer. 85, 81–87 (1963)

    Google Scholar 

  75. E.M. Sparrow, V.K. Jonsson, Absorption and emission characteristics of diffuse spherical enclosures. J. Heat Transfer. 84, 188–189 (1962)

    Google Scholar 

  76. E.M. Sparrow, S.L. Lin, Radiation heat transfer at a surface having both specular and diffuse reflectance components. Int. J. Heat Mass Transfer. 8, 769–779 (1965)

    Google Scholar 

  77. E.M. Sparrow, R.D. Cess, Radiation Heat Transfer, Augmented edn. (Hemisphere Publ., Washington, DC, 1978)

    Google Scholar 

  78. E.M. Sparrow, E.R.G. Eckert, V.K. Jonsson, An enclosure theory for radiative exchange between specularly and diffusely reflecting surfaces. J. Heat Transfer. 84, 294–299 (1962)

    Google Scholar 

  79. J. Stefan, Über die Beziehung zwischen der Wärmestrahlung und der Temperatur. Sitzungsberichte der kaiserlichen Akademie der Wissenschaften: Mathematisch-Naturwissenschaftliche Classe 79, 391–428 (1879)

    Google Scholar 

  80. S.M. Stewart, R.B. Johnson, Blackbody Radiation. A History of Thermal Radiation Computational Aids and Numerical Methods (CRC Press, Boca Raton, FL, 2017)

    Google Scholar 

  81. J.A. Stone, J.H. Zimmerman, Index of refraction of air, in Engineering Metrology Toolbox. Refractive Index of Air Calculator (2011), https://emtoolbox.nist.gov/Wavelength/Documentation.asp. Accessed 17 Oct. 2019

  82. A.S. Tenney, Radiation ratio thermometry, in Theory and Practice of Radiation Thermometry. ed. by D.P. DeWitt, G.D. Nutter (Wiley, New York, 1988), pp. 459–494

    Google Scholar 

  83. D. Ter Haar, The Old Quantum Theory (Pergamon Press, Oxford, 1967)

    MATH  Google Scholar 

  84. J.S. Toor, R.A. Viskanta, Numerical experiment of radiant heat interchange by the Monte Carlo method. Int. J. Heat Mass Transfer 11, 883–897 (1968)

    MATH  Google Scholar 

  85. W. Wien, O. Lummer, Methode zur Prüfung des Strahlungsgesetzes absolut schwarzer Körper. Ann. Phys. 292, 451–456 (1895)

    Google Scholar 

  86. W. Wien, Eine neue Beziehung der Strahlung schwarzer Körper zum zweiten Hauptsatz der Wärmetheorie. Sitzungsbericht Der Koniglich Preußischen Akademie Der Wissenschaften Zu Berlin 1, 55–62 (1893)

    MATH  Google Scholar 

  87. W. Wien, Ueber die Energievertheilung im Emissionsspectrum eines schwarzen Körpers. Ann. Phys. 58, 662–669 (1896)

    MATH  Google Scholar 

  88. E.R. Woolliams, N.P. Fox, M.G. Cox et al., Final report on CCPR K1-a: Spectral irradiance from 250 nm to 2500 nm. Metrologia. 43, 02003 (2006). https://doi.org/10.1088/0026-1394/43/1A/02003

    Article  ADS  Google Scholar 

  89. W. Zhigang, An accurate equation to determine the temperature for optimum efficiency of blackbody radiation. Infrared Phys. 33, 313–316 (1992)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. All-Russian Institute of Optical and Physical Measurements, Moscow, Russia

    Victor Sapritsky

  2. Virial International, LLC, Gaithersburg, MD, USA

    Alexander Prokhorov

Authors
  1. Victor Sapritsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander Prokhorov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Victor Sapritsky .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Sapritsky, V., Prokhorov, A. (2020). Theoretical Basis of Blackbody Radiometry. In: Blackbody Radiometry. Springer Series in Measurement Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-57789-6_3

Download citation

Publish with us

Policies and ethics

Search

Navigation