Which luminous efficacy function does BIPM reference?

Question

The definition of candela given by BIPM is as follows:

The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency $540\times10^{12}\,\mathrm{Hz}$, $K_{\mathrm{cd}}$, to be $683$ when expressed in the unit $\mathrm{lm\,W^{–1}}$, which is equal to $\mathrm{cd\,sr\,W^{–1}}$, or $\mathrm{cd\,sr\,kg^{–1}\,m^{–2}\,s^3}$, where the kilogram, metre and second are defined in terms of $h$, $c$ and $\Delta \nu_{\mathrm{Cs}}$.

So, from this definition we can only directly characterize luminous intensity of 540 THz light. To find luminous intensity of light with any other spectrum we need the normalized luminous efficacy function (to be scaled by $K_{\mathrm{cd}}$). But this one is not so definite: there're at least three versions of it, shown below in black: CIE 1931 (solid), Judd-Vos modified (dashed), and Sharpe, Stockman, Jagla & Jägle 2005 (dotted).

(source)

So which of these, if any, does BIPM reference with its definition of candela?

Answer 1

The BIPM booklet on photometry [MEP 2019. p 6] states: "The above definition of the candela applies to photopic, scotopic and mesopic vision."

In essence, this means that for any spectral luminosity function whatever, the value for 540 THz is by definition 683 lm/W. In other words, the graphs of these functions, when using SI units, all go through the same point (540 THz, 683 lm/W). The SI system does not depend on any specific luminosity function; it can be applied to all of them.

For current realizations of the SI units lm, cd, lx with various luminosity functions, see [REAL 2019]; for an introduction into concepts of photometry, see [MEP 2019].

References:

    [REAL 2019] "Mise en pratique for the definition of the candela
                 and associated derived units for photometric and
                 radiometric quantities in the SI".
                 Part of Appendix 2 to the SI Brochure 9, 2019.
     <https://www.bipm.org/utils/en/pdf/si-mep/SI-App2-candela>

   [MEP 2019] "BUREAU INTERNATIONAL DES POIDS ET MESURES.
               PRINCIPLES GOVERNING PHOTOMETRY".
               2nd Edition. 2019.
     <https://www.bipm.org/utils/common/pdf/rapportBIPM/RapportB IPM-2019-05.pdf>

Answer 2

The answer by Michael Deckers provides some useful references, but is not completely correct.

The Rapport BIPM-2019/05 linked in that answer does give

1. Spectral luminous efficiency functions in sections 4.1 through 4.3 and tables 1 and 2 — for all of photopic (2° and 10° FOV versions), scotopic and mesopic vision, the latter for varying levels of adaptation.
2. The conditions when to use each of these functions in section 4.5. In particular, there's the following rule for the 2° FOV photopic luminous efficiency function $V(\lambda)$:

... the $V(\lambda)$ function applies at all luminance levels for foveal view, i.e. for all on-axis visual tasks (where objects seen by the eye are in a narrow field of view in central vision).

And also

If the luminous efficiency function used is not specified, it is assumed to be the $V(\lambda)$ function.

3. The names of the quantities for each adaptation mode, corresponding to the different luminous efficiency functions.

Moreover, some rules are given in section 5.5 to avoid confusion with the alternative CIE-defined observers, although the names and symbols of the units (candela, lumen etc.), as said by Michael Deckers, remain the same.