By definition, light outside the visible spectrum cannot be seen by the
standard human vision system, and therefore does not contribute to, and indeed can subtract from, luminous efficacy.
Explanation under daytime or bright conditions, as standardized by the
CIE in 1924. The horizontal axis is wavelength in nanometers. Luminous efficacy of radiation measures the fraction of electromagnetic power which is useful for lighting. It is obtained by dividing the
luminous flux by the
radiant flux. Light wavelengths outside the
visible spectrum reduce luminous efficacy, because they contribute to the radiant flux, while the luminous flux of such light is zero. Wavelengths near the peak of the eye's response contribute more strongly than those near the edges.
Wavelengths of light outside of the
visible spectrum are not useful for general illumination. Furthermore, human vision responds more to some wavelengths of light than others. This response of the eye is represented by the
luminous efficiency function. This is a standardized function representing
photopic vision, which models the response of the eye's
cone cells, that are active under typical daylight conditions. A separate curve can be defined for dark/night conditions, modeling the response of
rod cells without cones, known as
scotopic vision. (
Mesopic vision describes the transition zone in dim conditions, between photopic and scotopic, where both cones and rods are active.) Photopic luminous efficacy of radiation has a maximum possible value of , for the case of monochromatic light at a wavelength of . Scotopic luminous efficacy of radiation reaches a maximum of for monochromatic light at a wavelength of .
Mathematical definition Luminous efficacy (of radiation), denoted
K, is defined as : K = \frac{\Phi_\mathrm{v}}{\Phi_\mathrm{e}} = \frac{\int_0^\infty K(\lambda) \Phi_{\mathrm{e},\lambda}\,\mathrm{d}\lambda}{\int_0^\infty \Phi_{\mathrm{e},\lambda}\,\mathrm{d}\lambda}, where • Φv is the
luminous flux; • Φe is the
radiant flux; • Φe,λ is the
spectral radiant flux; • is the
spectral luminous efficacy.
Examples ====
Photopic vision==== ====
Scotopic vision ==== of a
black body. Wavelengths outside the
visible light band (~380–750nm, bounded within grey dotted lines) have very low luminous efficiency. == Lighting efficiency == Artificial light sources are usually evaluated in terms of luminous efficacy of the source, also sometimes called
wall-plug efficacy. This is the ratio between the total luminous flux emitted by a device and the total amount of input power (electrical, etc.) it consumes. The luminous efficacy of the source is a measure of the efficiency of the device with the output adjusted to account for the spectral response curve (the luminosity function). When expressed in dimensionless form (for example, as a fraction of the maximum possible luminous efficacy), this value may be called
luminous efficiency of a source,
overall luminous efficiency or
lighting efficiency. The main difference between the luminous efficacy of radiation and the luminous efficacy of a source is that the latter accounts for input energy that is lost as
heat or otherwise exits the source as something other than electromagnetic radiation. Luminous efficacy of radiation is a property of the radiation emitted by a source. Luminous efficacy of a source is a property of the source as a whole.
Examples The following table lists luminous efficacy of a source and efficiency for various light sources. Note that all lamps requiring
electrical/electronic ballast are unless noted (see also voltage) listed without
losses for that, reducing total efficiency. Sources that depend on thermal emission from a solid filament, such as
incandescent light bulbs, tend to have low overall efficacy because, as explained by Donald L. Klipstein, "An ideal thermal radiator produces visible light most efficiently at temperatures around 6300 °C (6600 K or 11,500 °F). Even at this high temperature, a lot of the radiation is either infrared or ultraviolet, and the theoretical luminous [efficacy] is 95 lumens per watt. No substance is solid and usable as a light bulb filament at temperatures anywhere close to this. The
surface of the sun is not quite that hot." At temperatures where the
tungsten filament of an ordinary light bulb remains solid (below 3683 kelvin), most of its emission is in the
infrared. ==SI photometry units==