The Luminance $L_v$ is the quantity defined by the formula: [1]
$$ \begin{equation} L_v=\cfrac{d\Phi_v}{dAcos\theta d\Omega} \end{equation} $$where $d\Phi_v$ is the luminous flux transmitted by an elementary beam passing through the given point and propagating in the solid angle, $d\Omega$, containing the given direction. $dA$ is the area of a section of that beam containing the given point. $\theta$ is the angle between the normal to that section and the direction of the beam.
$L_v$ unit is candela per square metre (or nits) $cd\cdot m^{-2}=lm\cdot m^{-2}\cdot sr^{-1}$.
Colour defines the following luminance computation methods:
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import colour
colour.utilities.filter_warnings(True, False)
sorted(colour.LUMINANCE_METHODS.keys())
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Note: 'astm2008' and 'cie1976' are convenient aliases for respectively 'ASTM D1535-08' and 'CIE 1976'.
Newhall, Nickerson, and Judd (1943) fitted a quintic-parabola function to the adjusted Munsell-Sloan-Godlove reflectances, the resulting equation computing luminance $R_Y$ as function of Munsell value $V$ is expressed as follows: [2]
$$ \begin{equation} R_Y=1.2219V-0.23111V^2+0.23951V^3-0.021009V^4+0.0008404V^5 \end{equation} $$See Also: The Munsell Renotation System notebook for in-depth information about the Munsell Renotation System.
The colour.luminance_Newhall1943 definition is used to compute luminance $R_Y$:
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colour.colorimetry.luminance_Newhall1943(3.74629715382)
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Note: Input Munsell value $V$ is in domain [0, 10], output luminance $R_Y$ is in domain [0, 100].
The colour.luminance definition is implemented as a wrapper for various luminance computation methods:
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colour.colorimetry.luminance(3.74629715382, method='Newhall 1943')
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Since 1943, the reference white used for the Munsell Renotation System has changed.
As a result the quintic-parabola function from Newhall, Nickerson, and Judd (1943) has been adjusted: Each coefficient of the function has been multiplied by 0.975, the reflectance factor of magnesium oxide with respect to the perfect reflecting diffuser and then rounded to five digits.
The updated equation for computing luminance $Y$ as function of the Munsell value $V$ is expressed as follows: [3]
$$ \begin{equation} Y=1.1914V-0.22533V^2+0.23352V^3-0.020484V^4+0.00081939V^5 \end{equation} $$See Also: The Munsell Renotation System notebook for in-depth information about the Munsell Renotation System.
The colour.luminance_ASTMD153508 definition is used to compute luminance $Y$:
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colour.colorimetry.luminance_ASTMD153508(3.74629715382)
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Note: Input Munsell value $V$ is in domain [0, 10], output luminance $Y$ is in domain [0, 100].
Using the colour.luminance wrapper definition:
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colour.luminance(3.74629715382, method='ASTM D1535-08')
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In [6]:
colour.luminance(3.74629715382, method='astm2008')
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The CIE $L^a^b^$* approximately uniform colourspace defined in 1976 computes the *luminance* $Y$ quantity as follows: [4]
$$ \begin{equation} Y=\begin{cases}Y_n*\biggl(\cfrac{L^*+16}{116}\biggr)^3 & for\ L^*>\kappa*\epsilon\\ Y_n*\biggl(\cfrac{L^*}{\kappa}\biggr) & for\ L^*<=\kappa*\epsilon \end{cases} \end{equation} $$where $Y_n$ is the reference white luminance. with $$ \begin{equation} \begin{aligned} \epsilon&\ =\begin{cases}0.008856 & Actual\ CIE\ Standard\\ 216\ /\ 24389 & Intent\ of\ the\ CIE\ Standard \end{cases}\\ \kappa&\ =\begin{cases}903.3 & Actual\ CIE\ Standard\\ 24389\ /\ 27 & Intent\ of\ the\ CIE\ Standard \end{cases} \end{aligned} \end{equation} $$
The original $\epsilon$ and $\kappa$ constants values have been shown to exhibit discontinuity at the junction point of the two functions grafted together to create the Lightness $L^*$ function. [5]
Colour uses the rational values instead of the decimal values for these constants.
See Also: The CIE $L^*a^*b^*$ Colourspace notebook for in-depth information about the CIE $L^a^b^$* colourspace.
The colour.luminance_CIE1976 definition is used to compute Luminance $Y$:
In [7]:
colour.colorimetry.luminance_CIE1976(37.9856290977)
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Note: Input Lightness $L^*$ and and $Y_n$ are in domain [0, 100], output luminance $Y$ is in domain [0, 100].
Using the colour.luminance wrapper definition:
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colour.luminance(37.9856290977, method='CIE 1976')
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colour.luminance(37.9856290977, method='cie1976')
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colour.colorimetry.luminance_Fairchild2010(24.902290269546651, 1.836)
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colour.luminance(24.902290269546651, method='Fairchild 2010', epsilon=1.836)
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colour.colorimetry.luminance_Fairchild2011(26.459509817572265, 0.710)
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In [13]:
colour.luminance(26.459509817572265, method='Fairchild 2011', epsilon=0.710)
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