Candela

The candela [ kande ː la ] (Latin for candle) is the SI base unit of luminous intensity, that is the one object emitted in a given direction luminous flux per unit solid angle ( steradian, sr ) measured at a large distance from the light source.

The candela is a photometric unit, that measures the strength of the human eye caused by the radiation received light sensation. Earlier definitions of luminous intensity unit based on reference light sources with which a source to be measured could be compared as a bright or less bright. The modern definition of the light intensity for a given wavelength of light to the beam intensity and thus to the unit watt is attached. Of the standard curve of the spectral speed of the human eye, the definition can be adapted to other wavelengths.

The choice of light intensity as a photometric base size at first appears difficult to understand, since it would look from a modern perspective about the luminous flux or luminance as more fundamental quantities. At the initial time of photometry, however, as the visual comparison of light sources stood in the foreground, the light intensity was the one property of the sources was the most accessible, one comparison and was therefore introduced as the fundamental photometric quantity.

An ordinary household candle has a luminous intensity of about 1 cd.

Definition

The 16th General Conference on Weights and Measures ( 1979) decided in Resolution 3, the following redefinition of Candela:

" The candela is the luminous intensity in a given direction of a source that emits monochromatic radiation of frequency 540.1012 hertz and has a radiant intensity in that direction of 1/683 watt per steradian. "

The definition specifies the frequency of the reference radiation, not its wavelength. In this way there is no need to specify an index of refraction of the surrounding medium.

In air under normal conditions of said frequency of 540.1012 Hz, the wavelength corresponds to 555 nm on this wavelength the human eye for photopic vision the highest sensitivity. At the same time cut chance in the immediate vicinity of this wavelength ( ie at about 555.80 nm), the sensitivity curves of the eye for day and night vision, K ( λ ) and K ' ( λ ). The definition is therefore valid for both day as well as dusk and night vision according to DIN.

By choosing the said frequency and the numeric value 683 lm / W for the maximum value of the photometric radiation equivalent the new definition is immediately adjacent the previous definition ( see below). However, new definition is not dependent on the difficult realization of a black body radiator at a high temperature. Carries you through the restriction to monochromatic radiation the modern ways to measure the optical radiation power bill and also performs the measurement task on the much more fundamental case of monochromatic radiation back. The new definition is too general ( they allowed now, for example, the sensitivity curves of the eye to be measured directly, while implicitly in their entire course element of the definition was earlier). The previous definition, however, provided an exact photometric value only for a special case with a complex broadband wavelength distribution.

Related to the luminous flux ( lumens)

An isotropic light source of luminous intensity I = 1 candela radiates in every direction a luminous flux of 1 lumen = per solid angle = 1 steradian.

The luminous flux is defined by

The light is distributed - idealized - isotropically in all directions, ie on the unit sphere surface. Therefore, a ( detached ) Household candle emits a luminous flux of about 12 lumens. Neglecting the shading of the flame through the plug body towards the bottom reflector and its effect according to the above, as well as the intensity of the flickering.

See intensity for further conversion examples.

Earlier definition and photometric radiation equivalent

The candela was defined before the introduction of the current definition as follows:

" The base unit 1 candela is the luminous intensity, with the 1/600000 square meter of the surface of a black body at the temperature of the pressure 101325 Newton by freezing platinum square perpendicular to its surface is lit. "

This definition establishes a relationship between the radiometric beam intensity and the corresponding photometric luminous intensity of a black body radiator.

The spectral radiance of a blackbody is given by Planck's radiation formula:

With

The radiation power of the surface element dA d.lambda in the wavelength range between λ and λ is emitted into the solid angle d Ⓜ whose direction β to the surface normal forms an angle. Here is perpendicular to the surface emitted radiation is considered, therefore, cos ( β ) = 1

The solidification temperature of platinum is about 2045 K ( this value was the temperature scale IPTS -68 for their corresponding secondary reference point ). The spectral radiance of a blackbody that temperature has a maximum at about 1.4 microns.

For the transition to photometric quantities these radiometric spectral curve is wavelength by wavelength with the spectral photometric radiation equivalent K ( λ ) to multiply, which in turn from the relative luminous efficiency function V ( λ ) and a conversion constant Km ( the "Maximum value of the photometric radiation equivalent " ) composed. This results in the spectral luminance

The transition from the spectral luminance of the luminance is done by integration over all wavelengths:

The integral (which can be evaluated by numerical integration ), in this example is 89.124 mW / (cm sr).

The transition from the luminance to the light intensity is done by integrating over the emission:

Since a surface homogeneous luminance is provided this is done simply by multiplying the luminance of the emitting surface, in the example, 1/60 cm ². With the numerical values ​​of the example results in:

Since the light intensity is by definition a Candela, follows for Km:

The exact result of this theoretical calculation depends on which numerical values ​​of the solidification temperature of platinum and the depth in the Planck formula fundamental constants can be chosen.

The experimental realization of the definition is difficult. Measurements of Km yielded values ​​between about 676 and 687 lm / W. The reference value is set:

Overview photometric quantities