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2.5.3 Photometry

The results of photometric matching experiments show that radiation may be evaluated in terms of visual effect by means of a quantity known as luminous flux, _γ, which is related to _{e, λ}(λ), the spectral power distribution of the radiation, by an equation of the form

where K_m is a constant, and V(λ) a function representing the wavelength-dependent sensitivity of the eye. The exact shape of V(λ) depends on the observer, but in order to provide a precise quantitative basis for photometry, an agreed set of values was recommended for adoption by the Commission International de l’Éclairage (CIE) in 1924, and accepted by the Comité International des Poids et Mesures (CIPM) in 1970 (see section 1.1.2).

The following table gives the values of this function at 10 nm intervals. For the complete tabulation at 1 nm interval refer to ISO/CIE 10527 (1991).

Photopic spectral luminous efficiency function V(λ)

The magnitude of the unit of luminous flux, the lumen, is determined by assigning a value to K_m of equation (1). However, for historical reasons the SI base unit for photometry is the unit of luminous intensity, the candela or lumen per steradian; the formal definition (16th CGPM, 1979) appears in section 1.1.1. The rounded frequency 540 × 10¹² Hz corresponds to a wavelength of 555.016 nm in standard air, whereas K_m occurs at 555 nm exactly. Thus K_m is precisely 683.002 lmW⁻¹, although the value 683 lm W⁻¹ is sufficient for all practical purposes.

The spatial properties of light are described in photometry by quantities analogous to those used in radiometry (see section 2.5.2), with luminous flux replacing radiant power. The same symbols are used for corresponding quantities, distinguished where necessary by the suffixes e (radiation) and v (photometric). These quantities are listed in the following table, together with their radiometric equivalents to indicate the relation between the two systems of measurement.

Photometric quantities

Quantity	Radiometric equivalent	Symbol	Definition	Unit name and symbol
Luminous flux	Radiant power			lumen         lm
Luminous intensity	Radiant intensity	I	∂/∂Ω	candela      cd ≡ lm sr−1
Luminance	Radiance	L	∂2/∂A ∂Ω	(nit)            cd m−2
Illuminance	Irradiance	E M	∂/∂A	lux              lm m−2
Luminous exitance	Radiant exitance			lm m−2

Luminance and colour temperature of selected light sources

Scotopic system of photometry

At low levels of luminance the relative luminous effects of radiations of different wavelength are in general no longer represented even approximately by the values of V(λ) given in the above table. This is because a different visual mechanism known as the scotopic or dark-adapted mechanism, as opposed to the photopic or light-adapted mechanism, is dominant. To evaluate electromagnetic radiation with respect to the effect it produces on the scotopic mechanism, an alternative set of weighting factors—the scotopic spectral luminous efficiency function V'(λ)—must be used, the values of which were agreed by the CIE in 1951 and accepted by the CIPM in 1976.

Scotopic spectral luminous efficiency function V'(λ)

In the alternative system of photometry obtained by taking V′(λ) as basis instead of V(λ), all the formal definitions of the previous section are retained, with terms modified by the adjective ‘scotopic’ and symbols by the addition of a prime. The calculated value for the scotopic maximum luminous efficacy K'_m is 1700.06 lmW⁻¹, which may safely be rounded to 1700 lm W⁻¹.

In the so-called mesopic region between the photopic and the scotopic, the concept of luminous flux as an additive quantity does not apply and there is at present no agreed method of spectral weighting for mesopic vision.

Reference

ISO/CIE 10527 (1991) CIE Standard Colorimetric Observers.

O.C.Jones / T.M.Goodman

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