Lux

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The lux (symbol: lx) is the SI unit of illuminance. It is used in photometry as a measure of the intensity of light, with wavelengths weighted according to the luminosity function, a standardized model of human brightness perception. In English, "lux" is used in both singular and plural[1].

Definition

1 lx = 1 lm/m² = 1 cd·m²·m^–4

Explanation

Lux is a derived unit based on lumen, and lumen is a derived unit based on candela.

One lux is equal to one lumen per square metre, where 4π lumens is the total luminous flux of a light source of one candela of luminous intensity.

Illuminance	Abbr.	Example
0.00005 lux	50 µlx	Starlight
<1 lux		Moonlight
0.0001 lux	100 µlx	Moonless overcast night sky
0.001 lux	1 mlx	Moonless clear night sky
0.01 lux	10 mlx	Quarter Moon
0.25 lux	250 mlx	Full Moon on a clear night
10 lux		Candle at a distance of 30 cm (1 ft)
50 lux		Family living room
80 lux		Hallway/Toilet
400 lux		A brightly lit office
400 lux		Sunrise or sunset on a clear day.
1000 lux	1 klx	Typical TV studio lighting
32000 lux	32 klx	Sunlight on an average day (min.)
100000 lux	100 klx	Sunlight on an average day (max.)

Lux versus lumen

The difference between the lux and the lumen is that the lux takes into account the area over which the luminous flux is spread. 1000 lumens, concentrated into an area of one square metre, lights up that square metre with an illuminance of 1000 lux. The same 1000 lumens, spread out over ten square metres, produces a dimmer illuminance of only 100 lux.

Achieving an illuminance of 500 lux might be possible in a home kitchen with a single fluorescent light fixture with an output of 12000 lumens. To light a factory floor with dozens of times the area of the kitchen would require dozens of such fixtures. Thus, lighting a larger area to the same level of lux requires a greater number of lumens.

Lux versus footcandle

One footcandle ≈ 10.764 lux. The footcandle (or lumen per square foot) is a non-SI unit of illuminance. Like the BTU, it is obsolete but it is still in fairly common use in the United States, particularly in construction-related engineering and in building codes. Because lux and footcandles are different units of the same quantity, it is perfectly valid to convert footcandles to lux and vice versa.

The name "footcandle" conveys "the illuminance cast on a surface by a one-candela source one foot away." As natural as this sounds, this style of name is now frowned upon, because the dimensional formula for the unit is not foot · candela, but lumen/sq ft. Some sources do however note that the "lux" can be thought of as a "metre-candle" (i.e. the illuminance cast on a surface by a one-candela source one meter away). A source that is farther away casts less illumination than one that is close, so one lux is less illuminance than one footcandle. Since illuminance follows the inverse-square law, and since one foot = 0.3048 m, one lux = 0.3048² footcandle ≈ 1/10.764 footcandle.

In practical applications, as when measuring room illumination, it is very difficult to measure illuminance more accurately than ±10%, and for many purposes it is quite sufficient to think of one footcandle as about ten lux.

Relationship between illuminance and power

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 eye 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/meter², and accordingly the corresponding radiometric unit, which has no special name, is the watt/meter². There is no single conversion factor between lux and watt/meter²; 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.

At a monochromatic light wavelength of 555 nm, the green-colored wavelength to which the eye is most sensitive, the power needed to make one lumen is minimum, at 1.464 mW/m²; that is, the peak of the luminosity function is 683.002 lumens per watt. This means that for green light of this particular wavelength, one lumen = 1/683 watt. The luminosity function falls to zero in the infrared and ultraviolet wavelengths.

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 is most sensitive, but must include a generous mixture of red and blue wavelengths to which it is much less sensitive.

This means that typical 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 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 in fact based on the measurement of eyes and is reasonably close to the sensitivity curve for most eyes.

SI photometry units

SI photometry units

Quantity	Symbol	SI unit	Abbr.	Notes
Luminous energy	Qv	lumen second	lm·s	units are sometimes called talbots
Luminous flux	F	lumen (= cd·sr)	lm	also called luminous power
Luminous intensity	Iv	candela (= lm/sr)	cd	an SI base unit
Luminance	Lv	candela per square metre	cd/m2	units are sometimes called nits
Illuminance	Ev	lux (= lm/m2)	lx	Used for light incident on a surface
Luminous emittance	Mv	lux (= lm/m2)	lx	Used for light emitted from a surface
Luminous efficacy		lumen per watt	lm/W	ratio of luminous flux to radiant flux; maximum possible is 683.002

Non-SI units of illuminance

• foot-candle (=10.76 lx)
• phot (=10 klx)
• nox (=1 mlx)

Use in consumer camera specifications

Specifications for camcorders (video cameras) often include a minimum illuminance level in lux at which the camera will record a satisfactory image. A camera with good low-light capability will have a lower lux rating. Still cameras do not use such a specification, since longer exposure times can generally be used to make pictures at very low illuminance levels, as opposed to the case in video cameras where a maximum exposure time is generally set by the frame rate.

External links

• Radiometry and photometry FAQ Professor Jim Palmer's Radiometry FAQ page (University of Arizona).