# Luminance and illuminance of multiple point light sources

1. Dec 6, 2012

### Barry_G

Since there was some confusion previously where this post was mistaken for "homework" let me underline now *** THIS IS NOT HOMEWORK *** I've finished university 20 years ago, so this has nothing to do with any schoolwork or anything like that. I'm simply trying to understand some papers I'm reading.

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http://en.wikipedia.org/wiki/Luminance : luminance is measure of the luminous intensity per unit area... describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle.

http://en.wikipedia.org/wiki/Illuminance : illuminance is the luminous flux incident on a surface per unit area.

Having three (equally bright) point light sources at some distance from an eye we want to know what is their collective luminance and illuminance as seen by that eye. More specifically:

a.) For luminance, what is the area of the three point sources considering emitted light?

b.) For luminance, what is the area of the three point sources considering light that passes through an eye?

c.) For luminance, what is the area of the three point sources considering the image of that light as seen by an eye?

d.) For illuminance, what is the area of the three point sources considering light that passes through an eye?

e.) For illuminance, what is the area of the three point sources considering the image of that light as seen by an eye?

f.) Is luminance of the three light sources proportionally the same as illuminance considering light that passes through an eye?

g.) Is luminance of the three light sources proportionally the same as illuminance considering the image of that light as seen by an eye?

2. Dec 6, 2012

### sophiecentaur

Is there some confusion about the effect on the eye - which will be to see three sources, each with its own image on your retina and will produce an output from a small group of sensors, independent of the other two sources - or the effect on a matt surface, which will have a luminosity which has contributions from all three sources.
I think the answer to a general question about light flux depends upon the particular question that is being asked. Flux density is defined as power per unit area flowing from a source. Fluxes from different sources can add up. How they add up will depend on the actual setup - focussing or non focussing, for instance.

3. Dec 6, 2012

### Barry_G

At the end I want to be able to calculate both illuminance and luminance in order to understand the difference between them, all that in relation to point light sources and human perception of them.

So my problem is how to calculate it, I mean what is the "area" of three points? Do I take into account the whole area covered by the solid angle, which I think is defined by the field of view, and include the space between the points, or is it just about area where the light is emitted from and/or projected to?

The only area I could work out is across the lens where the light is passing into an eye, but after that light again get focused into points, more or less I think, so I have no idea how to put that into equation.

Maybe it's not even important, I guess I could just work out total intensity and then divide that with some "unit area", but because those are points sources with no actual area to begin with, then I am not sure if 'unit area' would be meter squared or the area of a single photoreceptor perhaps.

Last edited: Dec 6, 2012
4. Dec 6, 2012

### the_emi_guy

Depends entirely on the physical arrangement. Imagine the three sources are 100W light bulbs and one of them is 1 inch from your eye and the other two are both 100 meters away. You can ignore the distant ones right?. However if all three of them are right next to each other (say within the same light fixture) and all 100meters away, then their effects are additive as far as you eye is concerned.

5. Dec 6, 2012

### Barry_G

Since I want to be able to calculate their collective luminance/illuminance then we shall suppose they are all at about the same distance away, but they are not bunched up close together, so that they project as three separate dots.

As for 'additive effect', when does it start to work that way? Is there some formula for that? I guess that would be when all tree point light sources are so close that they end up being projected over the same photoreceptor(s)?

6. Dec 7, 2012

### Barry_G

After some thinking I've come to following conclusion. If we take 'unit area' to be a point or a single photoreceptor, then illuminance does not vary with the number of point light sources, so that illuminance of a single point light source is the same as illuminance of any number of point light sources (as long as they do not overlap and project over the same photoreceptor, I guess). In other words that would mean illuminance is independent of size. Can someone confirm, or dispute, this?