Radiometry and Photometry: Units and Conversion Factors

Jurgen R. Meyer-Arendt

Although often colorful and of historical interest, some radiometric and photometric units are redundantand illogical. The essential units are few in number. These, together with their definitions and conver-sion factors, are presented here.

The following outline is concerned with definitions,symbols, units, and conversion factors as they occur,and are helpful, in radiometry and photometry. Thesituation here is more complex than in other areas ofoptics; this is for several reasons. Sometimes,different terms are used for identical quantities. Cer-tain terms such as candlepower are ill-conceived.Others like nox, phot, glim, skot or scot (identical),bril and brill (different), helios, lumerg, pharos, stilb,talbot, and blondel may merely delight the historian.The impending-we hope-general conversion to themks system, which should more properly now be re-ferred to as SI, presents us with a unique opportunityfor simplifying some of the basic definitions and units,although a solution fully satisfying to all may never befound. The term SI stands for Systbme Interna-tional-International System of Units-adopted by theEleventh General Conference on Weights and Mea-sures held 11-20 October 1960 in Paris, France, towhich the United States has been a party. In thispaper, only SI units are used, but their relationship toother units is also shown.

Close cooperation of committees of the InternationalCommission on Illumination, the International Organi-zation for Standardization, the International Electro-technical Commission, and the SUN Commission ofthe International Union of Pure and Applied Physicshas resulted in the development of a set of terms andsymbols that is receiving acceptance throughout theentire world. The symbols in the U. S. A. StandardLetter Symbols for Illuminating Engineering (USAS

The author is with Pacific University, Forest Grove, Oregon97116.

Received 26 October 1967.This paper was written at the request of the Editor after three or

four shorter papers on units and nomenclature had been submittedfor publication. The author was asked to consolidate these otherpapers and try to summarize the preferred units. This paper doesnot constitute an official report of a nomenclature committee, butnevertheless it was widely circulated in draft form and represents areasonable consensus.

Y10.18-1967) are consistent with the internationalagreements that have been reached to date. Thesesymbols have been used throughout this paper andalso are summarized in Table I. The symbols,terms, and notations are also consistent with USAS Z7.1-1967. Any difference in wording between the def-initions in this paper and those in Y10.18-1967 andZ7.1-1967 does not imply any difference in meaning.

The outstanding features of the symbols used inStandard Y10.18-1967 are (1) the use of the same set ofsymbols for radiometric and photometric quantities,with the proviso that when there is need to differen-tiate these quantities subscripts e and v, respectively,will be used, and (2) the use of a subscript X to desig-nate a spectral concentration and (X) in parentheses todesignate a function of wavelength. In some of thefollowing equations, and when otherwise obvious, sub-scripts e and v have been omitted.

Radiant Energy Qe is energy traveling in the form ofelectromagnetic waves. The term radiation, althoughwidely in use, is deprecated because words that end in-ion should be reserved for processes rather than quan-tities.

The unit of radiant energy is the joule, J.Radiant Energy Density we is radiant energy per unit

volume,W = bQ/v.

Unit: joule/meter3 , J m-3 .Radiant Power ke, also called radiant flux, is the ra-

diant energy transferred per unit time, i.e., the timerate of flow of radiant energy:

0 = Qlbt.Radiant power is measured in the same units as powerin general. Since power = work/time, and work ( =potential energy) = force X distance, the unit of poweris

1 joule_1 soe= 1 watt, W = J s-

1 second

October 1968 / Vol. 7, No. 10 / APPLIED OPTICS 2081

Table I. Radiometric and Photometric Symbols and Units

Symbol Name of unit Abbreviation of unitRadiant energy Qe joule JLuminous energy Q" talbotRadiant energy density we joule/meter3 J m-