thumb|right|400px|[[Photopic vision|Photopic (black) and scotopic (green) luminous efficiency functions. and may be used to convert radiant energy into luminous (i.e., visible) energy. It also forms the central color matching function in the CIE 1931 color space.
Details
thumb|[[Fluorescence in beer. The one watt laser appears much dimmer than the fluorescence it produces, because the camera, like the human eye, is much more sensitive between 500 and 600 nm than at the laser's 450 nm wavelength.]]
There are two luminous efficiency functions in common use. For everyday light levels, the photopic luminosity function best approximates the response of the human eye. For low light levels, the response of the human eye changes, and the scotopic curve applies. The photopic curve is the CIE standard curve used in the CIE 1931 color space.
The luminous flux (or visible power) in a light source is defined by the photopic luminosity function (assuming it is bright enough to activate photopic vision in the eyes). The following equation calculates the total luminous flux in a source of light:
: <math>\Phi_\mathrm{v} = 683.002\ (\mathrm{lm/W}) \cdot \int^\infin_0 \overline{y}(\lambda) \Phi_{\mathrm{e},\lambda}(\lambda)\, \mathrm{d}\lambda,</math>
where
- Φ<sub>v</sub> is the luminous flux, in lumens;
- Φ<sub>e,λ</sub> is the spectral radiant flux, in watts per nanometre;
- (λ), also known as V(λ), is the luminosity function, dimensionless;
- λ is the wavelength, in nanometres.
Formally, the integral is the inner product of the luminosity function with the spectral power distribution. Their work in 2008 has revealed that "luminous efficiency or V(l) functions change dramatically with chromatic adaptation".
ISO standard
The ISO standard is ISO/CIE FDIS 11664–1. The standard provides an incremental table by nm of each value in the visible range for the CIE 1924 function.
Scotopic luminosity
For very low levels of intensity (scotopic vision), the sensitivity of the eye is mediated by rods, not cones, and shifts toward the violet, peaking around for young eyes; the sensitivity is equivalent to
Luminosity for mesopic vision, a wide transitioning band between scotopic and phototic vision, is more poorly standardized. The consensus is that this luminous efficiency can be written as a weighted average of scotopic and mesopic luminosities, but different organizations provide different weighting factors.
Human variation
Color blindness
right|thumb|400px|Protanopic (red, dotted) and deuteranopic (green, dashed) luminosity functions. For comparison, the standard photopic curve is shown (black, solid).
Color blindness changes the sensitivity of the eye as a function of wavelength. For people with protanopia, the peak of the eye's response is shifted toward the short-wave part of the spectrum (approximately 540 nm), while for people with deuteranopia, there is a slight shift in the peak of the spectrum, to about 560 nm. A method for estimating the transmittance of the human crystalline lens depending on age is standardized as CIE 203:2012, though further improvement has been proposed. For a few more lens transmission functions, see the Lucas (2014) Irradiance Toolbox.
Other functions
Non-vision parameters
The wavelength-dependent effect of light is seen not only with vision, but also (in humans) in the circadian rhythm via melanopsin. For reporting the effect of light on the human circadian rhythm, a value called melanopic illuminance is used, defined using a luminous efficiency function specific to the melanopsin. The unit is lux (lx) used in a non-SI-compliant fashion. With CIE S 026:2018, the system has become SI-compliant, with the melanopic equivalent daylight illuminance (M-EDI, unit lx) being derived from melanopic irradiance (unit W/m<sup>2</sup>). A human being subject to 100 lx of M-EDI of light should have the same alternation to their circadian rhythm as if they are being exposed to 100 lx of daylight.
alt=Modern Roomyou1 sensor that measures melanopic equivalent daylight illuminance (M-EDI) alongside other indoor climate parameters.|thumb|Some modern sensors, such as the Roomyou1, are designed to measure melanopic equivalent daylight illuminance (M-EDI) alongside other indoor climate parameters.
Lucas (2014) and the later CIE S 026 also define luminous efficiency function specific to four other human opsins. Lucas uses non-SI-compliant lux while CIE uses SI-compliant EDI lux. Some modern sensors, such as the Roomyou1, are designed to measure melanopic equivalent daylight illuminance (M-EDI) alongside other indoor climate parameters.
Non-human animals
Most non-primate mammals have the a similar luminous efficiency function to people with protanopia. Their insensitivity to long-wavelength red light makes it possible to use such illumination while studying the nocturnal life of animals.
Definition of melanopic illuminance and opsin-specific illuminances in the sense of Lucas (2014) are available for rodents. There is a significant difference at short wavelengths (< 420 nm) because the rodent eye filters light differently before the retina compared to the human eye.
The wavelength-dependent attractive effect on bees and moths have been quantified with a relative arbitrary unit of "attraction". These data have been used to design white LED light sources with lower arthopod attraction at night.
See also
- A-weighting and equal-loudness contour, related sound concepts
- Apparent magnitude
- Color vision
- Quantum efficiency, the image sensor equivalent
References
CIE documents
Curve data
External links
- Color and Research Vision Laboratory - luminous efficiency data tables