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Luminance – a Term which is Worth Some Thoughts

Posted on 2021-03-08 as a part of the Photonics Spotlight (available as e-mail newsletter!)

Permanent link: https://www.rp-photonics.com/spotlight_2021_03_08.html

Author: , RP Photonics Consulting GmbH

Abstract: Luminance is an interesting term in optics, which is worth some thoughts. Here, it is discussed to which extent luminance is a measure for perceived brightness of light sources or objects, and how the term is related to some others.

Dr. Rüdiger Paschotta

Luminance is an interesting term in optics – an important measure for how bright an object can be perceived by the eye (but with various limitations, see below). If you get a definition of luminance like “luminous flux per unit solid angle and unit projected area”, that doesn't actually tell you much; it requires quite some thinking to get acquainted with that term and its importance in optics.

I authored an encyclopedia article on that term in December 2019, but use this blog article for a further discussion. It may also make more people aware of these interesting things.

Relation to Radiance and Brightness

Luminance is a term of photometry, and the corresponding term in radiometry is radiance. As a reminder, while radiometry treats purely physical quantities, photometry takes into account the perception by the human eye – more precisely, the wavelength-dependent photopic response of the eye, which applies to cases with sufficiently bright illumination for color perception. So a 1064-nm beam from a YAG laser would have some radiance, but zero luminance, since it is essentially invisible – except at extremely high intensity levels, which would rapidly damage the eye.

Brightness should never be used as a quantitative term, although it is unfortunately common to use it in laser technology instead of radiance. It is best used for qualitative statements on as how bright we perceive some visible light.

Conservation of Luminance During Propagation

Interestingly, the luminance of an illuminated or radiating object – say, the Sun – is (with some limitations, see below) independent of the observation distance. So if you travel to Mars and observe the Sun from there (of course, always through an appropriate optical attenuator in order not to damage the eye), it will appear with about the same brightness despite the substantially larger observation distance.

How can that be despite the fact that the diverging radiation from the Sun of course loses in optical intensity with increasing distance?

If you would just expose a simple photodetector (e.g. a photodiode) to the sunlight, you would indeed get a weaker signal on Mars. Your eye, however, contains a lens, and it does not simply produce a signal which is proportional to the amount of radiation hitting the lens through the pupil. Rather, the lens focuses the radiation to the retina (the light-sensitive part), and for observation from Mars the image of the sun on the retina will be smaller. Therefore, despite the smaller amount of collected light, the optical intensity occurring on the retina will be about the same as on Earth – actually even somewhat higher because on Mars there is not much of an atmosphere to attenuate the light. As a result of that, the Sun will appear even a little brighter on Mars, although smaller.

You may still have some doubts, since it is well known that distant stars appear less bright than closer ones of the same type. Shouldn't the same as above apply to that case? In principle yes, but one important detail is different. All stars except our Sun are so far away that our eye is not able to resolve their apparent sizes. (This holds even if you use a pretty good telescope.) Therefore, the diameter of the spot which is illuminated on your retina when observing such a star will not depend on its distance, but only on the quality of your eye. As a result, the optical intensity on your retina will get lower for more distant stars, and they will accordingly appear as less bright rather than just as having a reduced apparent size.

So we have seen that what is relevant for the perceived brightness is normally the luminance rather than the optical intensity impinging our eyes – except in cases where the light source is so small that it cannot be resolved.

Of course, even for large enough objects there is not a precise relation between luminance and perceived brightness. One aspect is that the eye is subject to additional influences, such as the adaptation to different brightness levels of observed scenes via changes of the pupil diameter. For very low brightness levels, we get a transition into scotopic vision, where we cannot distinguish colors anymore, but can see with substantially less light. (Cats are particularly good in that discipline, at the cost of much reduced color vision.) Also, the neurological basis of our perceptions is notoriously nonlinear, unstable and influenced by all sorts of other things. Besides, we usually do not have any analog or digital output for measuring the perceived brightness.

This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the RP Photonics Encyclopedia.

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