Candela and Kcd

Light is life, not only for human, it also for animals and plants. Since the dawn of humanity, from fire of burning branches to glowing flame of candles and lanterns, from incandescent bulbs to fluorescent lamps and LED luminaires, artificial lighting has been essential to human survival and safety, it not only enables us to see, it also affects our mood and sense of well-being.

In technological society, scientists keep continuous research to define standard measurement units of artificial lighting. The practical value of measuring lighting first became apparent at the start of the 19th century, while flame was only artificial light source. Those measurements were grouped under the name photometry, and the unit of “luminous intensity” was adopted as a base unit. These references were initially founded on flame standards, their stability was weak.

Based on the approach of the radiation from a Planckian radiator (a black body), the definition of the “new candle” was promulgated as the unit of luminous intensity in 1946, it was then ratified in 1948 by the 9th CGPM which also adopted a new international name for this unit: the “candela” (the Latin word for candle), symbol cd. This new name candela was established as a SI base unit in 1954 at the 10th CGPM, and the  definition was modified in 1967 by the 13th CGPM, express as: “The candela is the luminous intensity, in the perpendicular direction, of a surface of 1/600 000 square meter of a black body at the temperature of freezing platinum under a pressure of 101 325 newtons per square meter.” The pressure in this definition is important because it affects the temperature at which platinum melts, and then affects the uncertainty.

Based on the rapidly developing of radiometric techniques, the values of the spectral luminous efficacy K(λ) for photopic vision adopted by CIE in 1924 was recommended by CIPM in 1972. The value 683lm/W for the spectral luminous efficacy of monochromatic radiation of frequency 540 × 10¹² hertz (Figure 1) has been adopted by the CIPM in 1977. This value is sufficiently accurate for the system of luminous photopic quantities and has been accepted by the 16th CGPM in 1979, then a completely new definition of the candela was adopted as: “The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 10¹² hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.” The frequency 540 × 10¹² hertz is equivalent to wavelength 555 nm. This definition acknowledges a particularity of human vision, connects the photometric quantities associated with visual sensation, to purely physical radiometric quantities of energy intensity.

The previous definition of the SI was based on seven base units and progress in science. It was revised in 2018 by the 26th CGPM, the new definition of the SI system is established in terms of a set of seven defining constants with exactly specified numerical values, the complete system of units can be derived from the fixed values of these defining constants, expressed in the units of the SI. The luminous efficacy K_cd is the creation of one of the seven SI defining constants, it is defined as: “the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² Hz, K_cd, is 683 lm/W”. And a new approach of the candela has been adopted as: “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 × 10¹² Hz, K_cd, to be 683 when expressed in the unit lm W⁻¹, which is equal to cd sr W⁻¹, or cd sr kg⁻¹ m⁻² s³, where the kilogram, meter and second are defined in terms of h, c and Δν_Cs.” This new definition of the candela has changed to a complicated wording than the 1979 definition, but the actual value of the candela is not appreciably change. These new SI definitions effected from May 20th 2019.

The nature of the seven SI defining constants ranges from fundamental constants of nature to technical constants. The luminous efficacy K_cd is a technical constant, arguably one of the most artificial and human-centered, refers to a special application for perceptions and sensations which are peculiar to the human visual system. On the basis of experimental studies, the response of human vision is different to different radiation wavelengths, K(λ) is the luminous efficacy at a given wavelength λ for express the visual response to radiation. In a well lighting environment – photopic visual condition, the human vision is maximally sensitive to wavelength 555nm [λ_m = 555nm], the total amount of visible light perceived by human vision (luminous flux) from 1Watt radiant flux of monochromatic radiation of λ_555nm is 683lm [K_m = K(λ_555nm) = 683lm/W]. For other wavelength e.g. 490nm, its K(λ_490nm) = 142lm/W, that is to say, the total amount of visible light perceived by human vision (luminous flux) from 1Watt radiant flux of monochromatic radiation of λ_490nm is 142lm, a much less luminous flux than that of λ_555nm from same radiant flux.

So, the nature of the SI constant K_cd is originally from the luminous efficacy K_m for photopic vision with a 2° field, using the standard photometric observer. The new definition of the SI base unit candela is established by the fixed numerical value of the constant K_cd. In illuminating engineering, the SI base unit candela acts as a weight for the scales，applies in photometry measurements not only to photopic (daytime vison), but also to scotopic (night vision) and mesopic (twilight vision). But it is important to note that the different states of human visual adaptation: photopic, scotopic and mesopic and the different size and position of the source in the visual field have different luminous efficacy from K(λ). More details about photometry measurements and luminous efficacy for different states of human visual adaptation are described in other articles.

Beside the photometry associated with human vision to visible light, for the generalized concept of light, or optical radiation, including also invisible light and non-image-forming light, the nonvisual effects by photochemical and photobiological are also important fields of practice illuminating engineering, such as melanopsin (human circadian rhythms) action of “blue light”, erythemal (human skin-reddening) action of UV radiation, vitamin D (in the skin for calcium metabolism) action of UV radiation, germicidal (bactericidal) action of UV radiation, poultry (chick growth and egg production) action of radiation, photosynthesis (plants) action of radiation, and so on. Each of the effects is characterized by an action spectrum (efficacy) linking the photochemical or the photobiological response to the radiation, but these have not been given within the SI. More details about practice illuminating engineering for these effects are described in other articles.

Last Update: August 31, 2020