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Radiometric or
photometric quantity
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Formula
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Definition of
radiometric quantities
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Radiant power [W]
Luminous flux [lm]
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Φe/v
= dQe/v/dt
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Radiant power Φe
is defined as the total power dQe
emitted by a light source per unit time dt.
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Radiant intensity [W/sr]
Luminous intensity
[lm/sr = cd]
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Ie/v
= dΦe/v/dΩ
dΩ = dA/r²
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Radiant intensity Ie
is defined as the radiant power dΦe
emitted per unit solid angle dΩ. The unit
solid angle dΩ is calculated from the area
dA of the surface area of a sphere and the
distance r² of this area from the center of
the sphere.
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Irradiance [W/m²]
Luminous intensity [lm/m² = lux]
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Ee/v
= dΦe/v/dA
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Irradiance Ee
is a radiometric quantity that does not
relate to a light source but to a detector
area in the space. Irradiance is calculated
from the ratio of the radiant power dΦe
and the area of the detector dA.
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Radiance [W/sr m²]
Luminance [cd/m²]
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Le/v
= dΦe/v/dA dΩ
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Radiance Le
is measured for extended, i.e. not point,
light sources and is defined as the radiant
power dΦe
emitted from an area dA per unit solid angle
dΩ.
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Note: Subscript "e" relates to "radiometric" and "v" to
"photometric"
The V(λ) curve is used in photometry to convolute the
radiometric quantity that is a function of the wavelength λ with the
sensitivity function of the human eye in the wavelength range from 380 nm to
780 nm. The photometric quantity luminous flux Φv
is then obtained by integrating radiant power Φe(λ)
as follows:
The unit of luminous flux Φv
is the lumen [lm]. Factor Km = 683 lm/W
establishes the relationship between the (physical) radiometric unit watt
and the (physiological) photometric unit lumen. All other photometric
quantities are also obtained from the integral of their corresponding
radiometric quantity weighted with the V(λ) curve.
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