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Photometry

Definition: the science and technology of measuring properties of light related to its perceived brightness for human eyes

German: Photometrie

Categories: general optics, light detection and characterization

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Photometry is the science and technology of quantifying and measuring properties of light related to its perceived brightness for human eyes. It thus deals with visible light only, not with infrared and ultraviolet light, and takes into account the spectral sensitivity of the human eye.

Note that the term brightness should be used only as a qualitative indication for perceived brightness, not as a measurable quantity (although it is often used instead of radiance or luminance).

Wavelength-dependent Sensitivity of the Human Eye

The wavelength-dependent sensitivity of the human eye plays an essential role in photometry. Many photometric quantities are obtained by multiplying or integrating a radiometric quantity with a weighting factor (luminosity function). Here, one needs to distinguish between two different situations:

  • When the human eye receives sufficiently intense light from illuminated objects (with at least a couple of cd/m2), it essentially uses its cone cells, which allow for color perception (photopic vision). The eye has three different kinds of such cones (S, M and L) with different spectral sensitivities. For estimating the overall perceived brightness, one can use the CIE photopic luminosity function y(λ) (or V(λ)):
photopic response
Figure 1: The photopic response function according to CIE. Data source: Colour & Vision Research Laboratory of the University College London, page on luminous efficiency functions.
  • Under faint illumination conditions, the human eye uses the substantially more sensitive rod cells (scotopic vision). There is only one kind of those rods, and as a result one cannot perceive colors with them. The resulting visual impression is gray. The perceived brightness can be estimated with the CIE scotopic luminosity function:
photopic response
Figure 2: The scotopic response function according to CIE (1951). Data source: Colour & Vision Research Laboratory of the University College London, page on luminous efficiency functions.

Note that the peak scotopic response is at somewhat shorter wavelengths, and light with wavelength from ≈640 nm on is hardly visible at all with the rods.

The luminous flux, which is generated in a light source, for example, can be calculated using the photopic luminosity function (i.e., assuming sufficiently highlight intensities) and the spectral radiant flux:

luminous flux

The constant value of ≈683 lm/W indicates that for the peak wavelength of ≈555 nm (in the green region), where the photopic luminosity function is 1, one obtains ≈683 lumen per watt of optical power. The luminous efficacy of 683 lm/W would be that of a light source which could completely convert electrical energy into light at 555 nm. Real light sources stay well below that limiting value; for example, white light emitting diodes (LEDs) are normally between 150 lm/W and 200 lm/W; the theoretical limit is around 300 lm/W for white light, which necessarily contains a red and blue light, for which the eye is less sensitive.

Both mentioned luminosity functions apply to the typical healthy human eye. In practice, there are certain variations, e.g. a reduction in sensitivity mostly on the short-wavelength part due to aging lenses. Some individuals exhibit substantial deviations from the norm, for example in the form of color blindness. For them, the standard luminosity functions are not applicable.

Photometric Quantities

There is a wide range of photometric quantities, most of which are directly related to radiometric quantities:

QuantitySymbolUnitsRemarksRelated radiometric quantity
luminous energyQvlumen second (lm s)quantifying the visual impression of a light pulse, for exampleradiant energy
luminous fluxΦvlumen (lm)luminous energy per unit time, e.g. emitted by a light sourceradiant flux
luminous intensityIvcandela (cd = lm/sr)luminous flux per unit solid angleradiant intensity
luminanceLvcandela per square meter (cd/m2 = lm sr−1 m−2)luminous flux per unit solid angle and unit projected arearadiance
illuminanceEvlux (lx) (= lm/m2)luminous flux incident on a surface, e.g. an office deskirradiance
luminous exitanceMvlux (lx) (= lm/m2)luminous flux emitted from a surfaceradiant exitance
luminous exposureHvlux second (lx s)time-integrated illuminanceradiant exposure
luminous efficacyηlumen per watt (lm/W)luminous flux per watt of optical power or per watt of consumed electrical power of a lamp
luminous efficiencyVluminous efficacy relative to its maximum possible value for a given optical spectrum

The subscript “v” of many of those quantities indicates that they refer to vision rather than to physical energies (“e”) as in radiometry.

Some of those terms are frequently confused. For example, luminous efficiency is often used instead of luminous efficacy; this can often easily be recognized from the used units.

Measurement of Photometric Quantities

For the measurement of photometric quantities, there are various kinds of photometers. In particular, there are instruments for measuring the illuminance and for the total luminous flux. Further derived quantities can often be calculated from measured illuminance values, for example.

See also: radiometry, photometers, luminous flux, luminous efficacy and efficiency, illuminance, photometers
and other articles in the categories general optics, light detection and characterization

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