The Unit of Luminous Intensity: Candela (cd)

Light is that part of the spectrum of electromagnetic radiation that the human eye can see. It lies between about 400 and 700 nanometers. All the units for measuring and defining light are based on the candela, which is the unit defining the luminous intensity from a small source, in a particular direction. This unit was originally based on the light emission from a flame.

The standard later came to be defined as the glow from molten platinum. The current definition is a radical departure from the previous formulations, because it defines light intensity in terms of the unit for radiated power in general, the watt, or joule per second. The candela is therefore no longer strictly necessary as a fundamental unit, because it is now defined in terms of a fundamental SI unit.

Historically, the engineers' unit of power, the watt, has been separated from the unit of luminous intensity, which is also a form of power, because the eye has a varying sensitivity over the visual spectrum, being relatively insensitive to blue and to red light. This radiation may make a deep impression on the viewer but, relative to yellow-green light, more watts of radiation are needed to cause a signal to reach the brain. Because of this the candela has to be defined for radiation at a single frequency. This makes the definition rather abstract, because no such light exists as something you can buy in a lamp store. The comforting symbolism of the candle has disappeared in the merciless striving for scientific precision.

Definition:
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 chosen is that to which the eye is most sensitive. This frequency is normally referred to as the corresponding wavelength: 555 nanometer. The wavelength varies with the medium through which the light passes, so, in the interest of precision, our relatively familiar wavelength description of light is not used in the standard.

The strange choice of the number 683 is to make the value identical to that obtained with the previous version of the unit: the emission from 1 square centimeter of glowing, solidifying platinum.

The steradian is the cone of light spreading out from the source which would illuminate one square meter of the inner surface of a sphere of 1 m radius around the source.

The light intensity coming towards the observer is assumed to be reaching all angles within the enclosing steradian at the same intensity. It doesn't have to in practice: one can perfectly well measure the luminous intensity from a lighthouse beam, knowing that it actually only covers less than a hundredth of a steradian. One measures the light received by a small sensor of known area and multiplies this to give the corresponding value for one steradian.

Luminous emission is not the same as the perceived brightness of the source when you look at it. The definition implies a small source, because the energy stream from it is defined as energy within a given solid angle, independent of distance to the measuring instrument. If the source is very small, a tiny quartz halogen torch bulb for example, the brightness will appear to be intense even if its emission is one candela. If the source is, like a candle, small but not really a point, you will get an impression of a small area of light of moderate brightness, even though the light intensity is also one candela. The apparent brightness of a source when you look directly at it must not be confused with its luminous emission. The brightness of a source is measured in candela per square meter. Everything that is visible can be regarded as a light source.

V-lambda Curve

The measurement of luminous intensity from a useful light source requires extra information: the relative sensitivity of the eye to different wavelengths. The luminous intensity of a "white" light source is defined by multiplying the watts emitted at each wavelength by the efficiency of that wavelength in exciting the eye, relative to the efficiency at 555 nm. This efficiency factor is referred to as the V-lambda curve.

This curve, obtained by averaging results from experiments with many people, has long been standardized as an essential component in the quantitative description of light. The curve defines the relationship between the human sensation of light and the physical concept of energy, which is the quantity to which measuring instruments react. The Photopic curve is the typical day light response curve and Scotopic is the typical night adjusted response curve.

The watts emitted by a light source can be measured by absorbing all the light in a perfectly black surface and measuring the heat produced. A filter corresponding to the V-lambda curve can be placed in front of the black absorber to convert the result to what the human eye and brain regard as 'brightness'. Practical measuring instruments contain filtered sensors which convert the absorbed light under the V-Lambda curve into electric current.  

The lumen and the lux

A light source emits with an intensity in a given direction that is measured in candela. Manufacturers of lamps and lamp fittings issue diagrams that show the distribution of light intensity in all directions. 

The pale green ray shows that this particular wide angle spot light emits 300 cd in a direction 30 degrees from its axis. The luminous intensity directly forward is 460 cd.

The candela value is independent of distance. One can think of it as the emission from the lamp, which then loses interest in what happens to the photons it has ejected. We need a new unit for the light energy moving through space in the direction of our object.

This unit of invisible light in transit is the lumen.

The official definition of the lumen, the unit of luminous flux, is:

The luminous flux dF of a source of luminous intensity I (cd) in an element of solid angle dR is given by dF = IdR

In plain English: The flux from a light source is equal to the intensity in candela multiplied by the solid angle over which the light is emitted, taking account of the varying intensity in different directions.

The candela is a unit of intensity: a light source can be emitting with an intensity of one candela in all directions, or one candela in just a narrow beam. The intensity is the same but the total energy flux from the lamp, in lumens, is not the same. The output from a lamp is usually quoted in lumens, summed over all directions, together with the distribution diagram in candela, shown above.

Another quantity that is often quoted in catalogues is lumens per watt. The lumen is formally derived from the candela, which is based on light of a single wavelength. A practical lamp of many wavelengths has the lumen output calculated from the wattage emitted as radiation multiplied by the luminous efficiency at each wavelength, as described in the section on the candela.

The diagram gives just the candela values emitted from the lamp. The designer needs to translate this into light energy falling on an object at any distance from the lamp. The energy density striking an object is given in lumens per square meter, generally known as lux.

This value can easily be calculated from the diagram for a point source. The candela value given for 60 degrees, 300, corresponds to 300 lumens streaming out into a cone of one steradian, according to the definition given above. One steradian covers one square meter on the surface of a globe of 1 meter radius. If an object were at this distance it would receive 300 lumens per square meter. To deduce the value for any other distance, just use the inverse square law. At 3 meters away from the lamp the flux on a square meter has fallen to one ninth of 300 lumens = 33. The lux value is therefore 33.

The lumen flux from a practical light source is the sum of the energy in each wavelength band, multiplied by the luminous efficiency of that wavelength. The lumen value contains no information about whether the light flux is dominated by energy in the luminously inefficient blue wavelength or, as with a tungsten lamp, is largely provided by luminously inefficient radiation at the red end of the spectrum.

Illuminance Units & Conversions
( basic units, lumens / unit area )

Use the Conversion Calculator

Luminance Units & Conversions
( basic units, lumens/ steradian X unit area )

Use the Conversion Calculator

Typical levels of Luminance and Illuminance

( For a luminance factor of 20%, average reflectance of a typical scene )

At the threshold of vision the dark adapted observer can see a flash if it contains on average 90
photons at the cornea or 9 at the retina. This is equivalent to a candle at 30 miles on a clear night.