The topic is the use and misuse of the term intensity. The following article appeared in a slightly different form in the letters to the editor column in Optics and Photonics News, February 1995, p 6.


Every year I get more intense on intensity, describing the use and misuse of the term in my undergraduate and graduate classes in radiometry. This seemingly innocuous word has several usages in optics. I have seen intensity used in six forms to date: (i) W/sr, (ii) W/sq-m, (iii), W/sq-m-sr, (iv) watts, (v) 1/cm/molecule/sq-cm and (vi) 1/sq-cm-amagat, the latter two used for spectral line strengths. I have industriously instructed my students to carefully inspect the meaning and dimensionality whenever they see or hear the term intensity. In classical optics, intensity is used in about half of the elementary and advanced texts in the context of W/sr. Most of the others use it for W/sq m and several actually feature both usages! A backwards look reveals that intensity was used as flux per steradian prior to the year 1800(1). My initial inclination was to abandon the obvious historical precedent and search for a new and descriptive term for the quantity (flux per steradian), leaving the confusion for the rest of the community to sort out. Others have pursued this course as well. Intensitance has been suggested by W. L. Wolfe (2), and pointance (3) is a geometrical term in the style of sterance as suggested by R. Clark Jones. I came up with emicance, an old English word meaning brilliance. This search was abandoned when it finally came to my attention that intensity is an SI base quantity, it appears in the official definition of the candela (4):

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540E12 hertz and that has a radiant intensity in that direction of (1/683) watts per steradian [16th CGPM (1979), Resolution 3].

The dimensionality of intensity is (photometric or radiometric) flux per steradian; the luminous and radiant are merely adjectives. As an SI base quantity, intensity has the same stature as the other six SI base quantities: length (meter), mass (kilogram), time (second), thermodynamic temperature (Kelvin), etc. To use intensity with units W/sq-m, W/sq-m–sr or any other units makes as much sense as measuring length in meters per second. To replace intensity would involve a fundamental change in the SI base system, not merely the substitution of some other word.

It is time that editors and reviewers for the various AIP, OSA, SPIE, etc. publications insist on proper usage of the term intensity, and consider rejection of those submissions that refuse to conform.

  1. Bouguer, M. Pierre and Nicolas Louis de la Caille, Traite d’optique sur la gradation de la lumiere, De l’imperimerie de H. L. Guerin & L. F. Delatour, Paris (1760). English translation as Optical treatise on the gradation of light; by W. E. Knowles Middleton, University of Toronto Press, Toronto (1961).
  2. Wolfe, W. L., letter in Optics and Photonics News, September 1992, p. 86.
  3. Spiro, I. J., “Radiometry and photometry,” columns in Opt. Eng.13, G183 (1974) and 15, SR-7 (1976). See also R. C. Jones, “Terminology in radiometry and photometry,” J. Opt. Soc. Amer. 53, 1314 (1963) The above are reprinted in I. J. Spiro, “Selected papers on Radiometry,” SPIE Milestone series MS14 (1990). A summary is given in C. L. Wyatt “Radiometric calibration: Theory and Methods,” Academic, NY (1978).
  4. Taylor, B. N., “The International System of Units (SI),” NIST Special Publication 330 (1991).

James M. Palmer
Associate Research Professor
Optical Sciences Center
University of Arizona
Tucson, AZ 85721

A similar article appeared in Metrologia , the official journal of the International Bureau of Weights and Measures after a poster presentation at the NEWRAD absolute radiometry conference in Baltimore in 1992. It was extremely well received in the radiometry/photometry community. The reference is: J.M. Palmer, “Getting INTENSE on intensity,” Metrologia 30, 371 (1993).

Additional notes (22 April 1995)

There has been little discussion since the above letter was published. I fear that the charlatans will just keep on being ignorant or belligerent, and we will continue to produce scientists and engineers that are not lucid when using these terms. The only argument that seems reasonable is whether or not the terms radiometric and luminous are truly adjectives when applied to intensity. If deemed not, then we have the unattractive possibility of other intensities (i.e., specific intensity, field intensity, etc.) with other root dimensionalities.


Activity is picking up on this discussion during the year 2000. Charles Poynton has referred to this page from his Gamma <> and Color <> FAQ sites. A recent radiometry/photometry FAQ was posted here last year and has received critical acclaim from researchers all over the world, including those at NIST.


Herein I have gathered a number of strange units that hint at the unusual uses of the term. Contributions are welcome!

From a manufacturer of retroreflector pavement markers comes the term specific intensity. It is defined as ( candlepower of the returned light at the chosen observation and entrance angle for each foot candle of illumination at the reflector on a plane perpendicular to the incident light.

In a bit shorter form, it is cd/fc (good ol’ British unit of length) and the units work out to ft2/sr. How weird is that? Is this a recognized standard from ASTM, ANSI or some other agency or organization?