## Saturday, 6 August 2011

### Relationship between illuminance and irradiance

Like all photometric units, the lux has a corresponding "radiometric" unit. The difference between any photometric unit and its corresponding radiometric unit is that radiometric units are based on physical power, with all wavelengths being weighted equally, while photometric units take into account the fact that the human eye's visua
l system is more sensitive to some wavelengths than others, and accordingly every wavelength is given a different weight. The weighting factor is known as the luminosity function.
The lux is one lumen/metre2, and the corresponding radiometric unit, which measures irradiance, is the watt/metre2. There is no single conversion factor between lux and watt/metre2; there is a different conversion factor for every wavelength, and it is not possible to make a conversion unless one knows the spectral composition of the light.
The peak of the luminosity function is at 555 nm (green); the eye's visual system is more sensitive to light of this wavelength than any other. For monochromatic light of this wavelength, the irradiance needed to make one lux is minimum, at 1.464 mW/m2. That is, one obtains 683.002 lux per W/m2 (or lumens per watt) at this wavelength. Other wavelengths of visible light produce fewer lumens per watt. The luminosity function falls to zero for wavelengths outside the visible spectrum.
For a light source with mixed wavelengths, the number of lumens per watt can be calculated by means of the luminosity function. In order to appear reasonably "white," a light source cannot consist solely of the green light to which the eye's visual photoreceptors are most sensitive, but must include a generous mixture of red and blue wavelengths to which they are much less sensitive.
This means that white (or whitish) light sources produce far fewer lumens per watt than the theoretical maximum of 683 lumens per watt. The ratio between the actual number of lumens per watt and the theoretical maximum is expressed as a percentage known as the luminous efficiency. For example, a typical incandescent light bulb has a luminous efficiency of only about 2%.
In reality, individual eyes vary slightly in their luminosity functions. However, photometric units are precisely defined and precisely measurable. They are based on an agreed-upon standard luminosity function which is based on measurements of the spectral characteristics of visual photoreception in many individual human eyes