Wikipedia and plenty of other sources give values for the luminance of the sky, of e.g. $\mathrm{2\ kcd/m^2}$. What area is the denominator representing here? How can something like the sky, that doesn't have an area, have a luminance at all?
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$\begingroup$ But to give a hint: The detector or surface being illuminated by the sky has area. As does a cross section of the sky at any chosen distance above the ground. $\endgroup$– The PhotonCommented Jul 18, 2020 at 5:49
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$\begingroup$ If a detector or surface is being illuminated, it's measured in lux = lumens per square metre, and the area is that denominator. But I'm asking about luminance, not illuminance. Luminance, as that Wikipedia article points out, is a measure of "the amount of light that passes through, is emitted from, or is reflected from a particular area". I'm asking what that area is when a figure is given for the sky as a whole. Any arbitrary cross-section of the sky has an area, but how can luminance be constant if I could choose a cross-section at any distance and thus any area? $\endgroup$– synecdocheCommented Jul 18, 2020 at 12:57
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$\begingroup$ You left out "and subtends a given solid angle" in your quote from Wikipedia. It's equivalent to consider the surface area of the source and the solid angle into which it emits, or the surface area of the detector and the solid angle subtended by the source when seen from the detector. In either case, the solid angle term depends on the area of the other surface (detector seen from the source or source seen from the detector) and the distance between source and detector. $\endgroup$– The PhotonCommented Jul 18, 2020 at 14:02
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1 Answer
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As you say in comments, in Wikipedia, the luminance is described as,
the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls within a given solid angle. [emphasis added]
in which you omitted the portion of the description which I have emphasized.
We can calculate the luminance either as the luminous flux emitted from an element of the surface into a given solid angle, or, equivalently, as the luminous flux falling on an element of a surface from a given solid angle.
In one case we consider the surface area of the source, in the other we consider the surface area of the detector. In either case, the solid angle term encompasses the surface area of the other object (the detector as seen from the source, or the source as seen from the detector) and the distance between them, being defined as $$\Omega = \frac{A}{r^2}$$ where $A$ is the area of the other object and $r$ being the distance.
answered Jul 18, 2020 at 14:08
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$\begingroup$ Okay, that makes sense, thanks. So the main reason we would want to give luminance rather than illuminance, if talking about a lit surface, is when we want to specify the solid angle that the light is coming from? $\endgroup$ Commented Jul 19, 2020 at 8:13
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$\begingroup$ @synecdoche, the key reason is probably where it says in the Wiki article, "luminance is an invariant in geometric optics". That means you can measure the luminance of a source at the source, and then quickly predict how it will illuminate surfaces at various distances. $\endgroup$ Commented Jul 19, 2020 at 13:45