Luminosity_function

For the luminosity function in astronomy, see Luminosity function (astronomy).

Photopic (black) and scotopic [1] (green) luminosity functions. The photopic includes the CIE 1931 standard [2] (solid), the Judd-Vos 1978 modified data [3] (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data [4] (dotted). The horizontal axis is wavelength in nm.

The luminosity function describes the average sensitivity of the human eye to light of different wavelengths. It should not be considered perfectly accurate in every case, but it is a very good representation of human eye sensitivity and it is valuable as a baseline for experimental purposes. It is a standard function established by the Commission Internationale de l\'Éclairage (CIE) 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.

There are actually two luminosity 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 energy) in a light source is defined by the photopic luminosity function. The following equation calculates the total luminous flux in a source of light.

$F=683.002\backslash \; \backslash mathrm\{lm/W\}\backslash cdot\; \backslash int^\backslash infin\_0\; \backslash overline\{y\}(\backslash lambda)\; J(\backslash lambda)\; d\backslash lambda$

where

$F\backslash ,$ is the luminous flux in lumens,

$J(\backslash lambda)\backslash ,$ is the power spectral density of the radiation, in watts per unit wavelength.

$\backslash overline\{y\}(\backslash lambda)$ (also known as $V(\backslash lambda)\backslash ,$) is the standard luminosity function (which is dimensionless).

Formally, the integral is the inner product of the luminosity function with the light spectrum.Charles A. Poynton (2003). Digital Video and HDTV: Algorithms and Interfaces. Morgan Kaufmann. ISBN 1558607927.  In practice, the functions of wavelength are discretized, and the inner product is computed as an ordinary vector dot product; the CIE distributes standard tables discretized at 5 nm increments from 380 nm to 780 nm.CIE Free Documents for Download.

The standard luminosity function is normalized to a peak value of unity at 555 nm (see luminous coefficient). The value of the constant in front of the integral is usually rounded off to 683 lumens/watt. The small excess fractional value comes from the slight mismatch between the definition of the lumen and the peak of the luminosity function. The lumen is defined to be unity for a radiant energy of 1/683 watt at a frequency of 540x10¹² Hz, which corresponds to a standard air wavelength of 555.016 nm rather than 555 nm, which is the peak of the luminosity curve. The value of $\backslash overline\{y\}(\backslash lambda)$ is 0.999997 at 555.016 nm, so that a value of 683/0.999997=683.002 is the multiplicative constant.Wyszecki, Günter and Stiles, W.S. (2000). Color Science - Concepts and Methods, Quantitative Data and Formulae, 2nd edition, Wiley-Interscience. ISBN 0-471-39918-3.  The number 683 is connected to the modern (1979) definition of the candela, the unit of luminous intensity.16th Conférence générale des poids et mesures Resolution 3, CR, 100 (1979), and Metrologia, 16, 56 (1980). This arbitrary number made the new definition give numbers equivalent to those from the old definition of the candela.

Contents 1 Improvements to the standard 2 Scotopic luminosity 3 See also 4 References 5 External links

Improvements to the standard

The CIE 1931 color-matching functions, which include the CIE 1924 photopic $V(\backslash lambda)$ luminosity function as the y function, have long been acknowledged to underestimate the contribution of the blue end of the spectrum to perceived luminance. There have been numerous attempts to improve the standard function, to make it more representative of human vision[5]. Judd in 1951, improved by Vos in 1978, resulted in a function known as CIE $V\_M(\backslash lambda)$. More recently, Sharpe, Stockman, Jagla & Jägle (2005) developed a function consistent with the Stockman & Sharpe cone fundamentals.[6] These curves are plotted in the figure above.

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 507 nm for young eyes; the sensitivity is equivalent to 1699Kohei Narisada and Duco Schreuder (2004). Light Pollution Handbook. Springer. ISBN 140202665X.  or 1700Casimer DeCusatis (1998). Handbook of Applied Photometry. Springer. ISBN 1563964163.  lm/W at this peak.

The standard scotopic luminosity function or $V^\backslash prime(\backslash lambda)$ was adopted by the CIE in 1951, based on measurements by Wald (1945) and by Crawford (1949).[7]

See also

• Color vision
• A-weighting, the sound equivalent
• Quantum efficiency, the image sensor equivalent

References

External links

• UCSD Color Vision — tables of luminosity functions

This article is licensed under the GNU Free Documentation License. It uses material from Wikipedia