# Nits, lumen, lux and candela

Hi all,

I'm trying to understand the difference between nits, candela, lumen and lux.

Just to make sure I've got this right, I'll paste in four concise descriptions for each of the units, and if anyone can alter/adjust them, that would be great. I imagine nothing could be clearer than stating what variables need to be taken into account for each unit.

"matters" below means to "take into account" as variables. Also, "object area" could be translated as the 'viewer', or the surface that the light is shining on.

Candela/m^2 or Nit ::: light-source-intensity matters
Candela ::: light-source-intensity matters AND light-source-size matters
Lumen/m^2 or Lux ::: light-source-intensity matters AND light-source-size matters AND light-source-distance-from-object matters
Lumen ::: light-source-intensity matters AND light-source-size matters AND light-source-distance-from-object matters AND size-of-object-area matters

For the last two, the terms light-source-distance-from-object and size-of-object-area can be combined to form the translation: "angle of the light source's cone".

Is everything present and correct?

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Claude Bile
Lumen (radiometrically; Watt) - Depends on source power.
Lux (radiometrically; W/m^2) - Depends on power and source size.
Candela (radiometrically; W/sr) - Depends on power, object size and distance.
Nit (radiometrically; W/sr/m^2) - Depends on power, source size, distance and object size.

(I think by "light-source-intensity" you simply mean "power", and I think you have your list backwards)

Essentially, if a quantity is /m^2 the source size "matters" and if a quantity is /sr the distance and object size "matter". The only other thing missing is perhaps the relationship between these photometric quantities and their radiometric equivalents, only for completeness reasons do I suggest this.

Also, I like this link on photometric units - http://www.optics.arizona.edu/Palmer/rpfaq/rpfaq.htm [Broken]

Claude.

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Hi Claude,
Thanks for this very useful answer!

Actually, power, I equated with light-source-size multiplied by light-source-intensity. That is, if you were to have one LED, under my definition (which I admit, could be ambiguous), that would have the same amount of "light-source-intensity" (call it 'point brightness' if you prefer) as 100 of the same LEDs clumped together to make one macro light bulb. However, 100 LEDs have increased the light-source-size, and therefore, the overall power has increased too.

Under this definition, I've done some editing and swapping:

Lux (radiometrically; W/m^2) - Depends on light-source-intensity.
Lumen (radiometrically; Watt) - Depends on light-source-intensity and light-source-size.
Nit (radiometrically; W/sr/m^2) - Depends on light-source-intensity, distance and object size.
Candela (radiometrically; W/sr) - Depends on light-source-intensity, light-source-size, object size and distance.

Does that make sense?
Also am I right in saying that the Talbot takes all the variables of Candela, and adds the time variable to account for "luminous energy"?

Finally, why does Wikipedia say on the Lux page "10 lux - Candle at a distance of 30 cm (1 ft)", when the amount of lux coming from that candle should be independent from the observer, no matter how far they are away?

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Claude Bile
Yes, I think you have it right.

The Talbot is the Photometric equivalent of the radiometric unit Energy. In other words where energy is W.s, the Talbot is lm.s. The Talbot shares the same relationship with Candela that Energy shares with Intensity (the proper radiometric definition of intensity, W/sr).

With regard to the wikipedia definition - there are two ways you can define a lux - as a unit of Illuminance, which is a measure of light incident on a surface, or Luminous emittance, which is a measure of light emitted by a surface. If we speak of Luminous emittance, then yes, the lux emitted by a source is independent of the observer - but if we speak of Illuminance, the amount of light per unit area striking the observer, it most certainly does depend on the position of the observer.

In short, the definition from wikipedia is strictly for Illuminance and not Luminous Emittance.

Claude.

Wow, no wonder everybody's so confused about the subject, what with two definitions for one term. Which is the more correct one as defined by the SI group? Should Wikipedia mention that it has two definitions, (or maybe pick only the preferred one, with a smaller mention of the other) ? Can you edit Wikipedia if you have time to correct this?

And does the nit, lumen or candela have two (or more(!)) definitions like lux?

By the way, when we agreed upon:
Nit (radiometrically; W/sr/m^2) - Depends on light-source-intensity, distance and object size.

Shouldn't that be changed to include light-source-size instead of object-size?

To make sure we have this clear, is it true that lux can be defined as follows:
Lux definition 1 (Illuminance): Depends on Light source size, light source intensity, distance from object (or observer).
Lux defintion 2 (Luminous emittance): Depends on Light source size, and light source intensity.

I'm assuming Lux def 1 doesn't also depend on object (observer) size.

*** EDIT - I suppose no definition of lux is more 'correct' than the other - they are both used for measuring the same thing really. I suppose even the luminous emittance could depend on a 2nd light source to determine how much this 1st light source gives off ***

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Claude Bile
I will make one sweeping statement - after much thought, it has become apparent to me that the following is very important, the distinction between source and observer. For example;

I can define luminousity emitted by a source - that's pretty easy, it only depends on the source.

I can also define the luminousity incident onto an observer - This depends on the distance from the source, the luminousity of the source and the candelas emitted by the source for the particular chunk of solid angle the observer occupies as well as the size of the observer.

If one keeps everything in terms of the source then everything is much less confusing.

So - lm depends on the power spectrum emitted by the source (and nothing else).
lux depends on luminousity and surface area of the source.
candela depends on luminousity of the source and the solid angle it radiates into.
nit depends on luminousity of the source, solid angle it radiates into and the surface area of the source.

When we introduce the observer, we must account for all these things (to get the luminousity incident on the observer) and then start adding characteristics of the observer into the picture.

Claude.

I respect the idea of the kind of simplification you're making. And thanks again for the insightful post - this thread is finally beginning to clear things for me.

I suppose one thing I might say though is that I find it easier to envisage "size and distance of object" rather than the exact equivalent "solid angle it radiates into". This is why I brought the observer/object into the picture to help clarify things.

By the way, are you using "luminosity" for what Wikipedia refers to as "Luminous emittance" (or "watt per square metre"), and for what I referred to in my earlier posts as "light-source-intensity" ?

I would rather each type be split into its component units if possible, so candela would have the most parameters to take into account.

Were my two lux definitions correct? I'll requote, but use Wikipedia's definitions one on or two of them to reduce ambiguity:
Lux definition 1 (Illuminance): Depends on Light source size, Luminous emittance, distance from object (or observer).
Lux defintion 2 (Luminous emittance): Depends on Light source size, and Luminous emittance.

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Claude Bile
I respect the idea of the kind of simplification you're making. And thanks again for the insightful post - this thread is finally beginning to clear things for me.
No problem, it's refreshing this stuff in my mind as well.
I suppose one thing I might say though is that I find it easier to envisage "size and distance of object" rather than the exact equivalent "solid angle it radiates into". This is why I brought the observer/object into the picture to help clarify things.
You need to take into account that there might be power radiated that doesn't fall onto the observer. For example if the sun were to suddenly radiate all its power into a hemisphere (which would halve the solid angle it radiates into from 4*pi to 2*pi) we would get twice as much power falling on the Earth, even though the distance from the source and the size of the Earth has not changed.
By the way, are you using "luminosity" for what Wikipedia refers to as "Luminous emittance" (or "watt per square metre"), and for what I referred to in my earlier posts as "light-source-intensity" ?
I'm using luminosity as the photometric version of Power.
I would rather each type be split into its component units if possible, so candela would have the most parameters to take into account.
This is fine, but I think it is far easier to leave the observer out of the picture.
Were my two lux definitions correct? I'll requote, but use Wikipedia's definitions one on or two of them to reduce ambiguity:
Lux definition 1 (Illuminance): Depends on Light source size, Luminous emittance, distance from object (or observer).
Lux defintion 2 (Luminous emittance): Depends on Light source size, and Luminous emittance.
The definition for Luminous Emittance is a little odd since you say it depends on Luminous emittance! You should say it depends on Luminosity (in lm) and source size (in m^2), which makes a great deal of sense since lux = lm/m^2.

The definition of Illuminance (since it involves an observer) is far more complicated. Let's look at the potential variables.

Source Luminosity? - If the source doubles in power we would expect double the power to be incident on the observer.
Source Size? - I don't think it does - increasing the size of the source, provided the power incident on the observer stays constant, will not change the Illuminance.
Solid Angle source radiates into? - Most definitely - see my sun example above.
Observer Size? - No, increasing observer size will increase total power incident on the observer, but not the illuminance.
Observer distance from source? - Yes, a closer observer will capture more power over the same surface area.

So I would say Illuminance depends on Source Luminosity, the solid angle the source radiates into and the distance from the observer to the source.

What do you think?

Claude.

You need to take into account that there might be power radiated that doesn't fall onto the observer. For example if the sun were to suddenly radiate all its power into a hemisphere (which would halve the solid angle it radiates into from 4*pi to 2*pi) we would get twice as much power falling on the Earth, even though the distance from the source and the size of the Earth has not changed.
But surely if you're measuring the solid angle, that's still equivalent to "observer size and distance" in the context of candela? As an example, if we're measuring candela, we could replace:

Light source size, Luminous emittance (W/M^2), Solid angle
....with...
Light source size, Luminous emittance (W/M^2), observer surface size (facing the source), and observer distance from source

Okay quick question, given a constant solid angle size (but with variable direction), and the same light source, can the candelas vary according to the direction of the solid angle? (this light source would obviously have varying intensity according to the direction). If this is true, then the definition of candela is slightly more involved than I initially thought. Also, if it were true, it would not be enough to give the size of the solid angle, but also its direction/angle would be needed.

The definition for Luminous Emittance is a little odd since you say it depends on Luminous emittance! You should say it depends on Luminosity (in lm) and source size (in m^2), which makes a great deal of sense since lux = lm/m^2.
Sorry, my bad. Yes you're right, or I could have just said:
"Lux definition 2: Depends on Luminous emittance (i.e. lm/m^2 or radiometrically W/m^2)."

The definition of Illuminance (since it involves an observer) is far more complicated. Let's look at the potential variables.

Source Luminosity? - If the source doubles in power we would expect double the power to be incident on the observer.
Source Size? - I don't think it does - increasing the size of the source, provided the power incident on the observer stays constant, will not change the Illuminance.
Solid Angle source radiates into? - Most definitely - see my sun example above.
Observer Size? - No, increasing observer size will increase total power incident on the observer, but not the illuminance.
Observer distance from source? - Yes, a closer observer will capture more power over the same surface area.
Out of all of these, the only one I would question is the "Source Size?" one, since the power would actually increase, even that seen by the observer.

So I would say Illuminance depends on Source Luminosity, the solid angle the source radiates into and the distance from the observer to the source.
I think so, and I suppose that the "solid angle" variable can be replaced by: the light source size and luminous emittance. In other words, if the solid angle gets smaller, that's the same thing as saying: the light source size gets smaller + the luminous emittance gets greater (though I don't know about this second one to be honest).

By the way, I had another good think about all this again a couple of days ago, and to really simplify things, I thought one may be able to scrap candela and nits completely (apart from for mathematical purposes), and just go with lux (luminous emittence type) and lumens. Basically, we would speak about the lux and lumens received and emitted by a "light source" (where "light source" could be a real light, or actually an object which merely emits reflected light; in other words, everything becomes a light source).

Think about it, every possible practical situation could be described using lumens and lux alone:
Want to measure the lumens of the moon? Fine, it would be quite a lot, compared to even the brightest bulb on Earth.
Want to measure the lux of the moon? It would be very dim, probably 1 watt bulb standard as a guess.
Want to measure the lumens on Earth given off as a direct result of the moon. That would a fraction of the moon's lumens, but still quite a bit.
Want to measure the lux of the Earth given moonlight. This would be tiny. ). As a wild guess, maybe the same as a 0.01 watt bulb :)

And all of those four again, but measuring the light received instead of emitted. These would usually be the same were it not for light absorption into the material etc.

That's all eight possible measurments you could possibly wish to make about the moon, earth, and the light coming to/from each one. I suppose candela and nits might have some use, but television/light bulb/laser/flashlight etc. manufacturers, along with say, light fitters for buildings, should stick to lumens and lux when giving stats about their products. Would you agree?

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Claude Bile
But surely if you're measuring the solid angle, that's still equivalent to "observer size and distance" in the context of candela? As an example, if we're measuring candela, we could replace:

Light source size, Luminous emittance (W/M^2), Solid angle
....with...
Light source size, Luminous emittance (W/M^2), observer surface size (facing the source), and observer distance from source
If I have a source and halve the solid angle it radiates into, then I have doubled its intensity (or cd in photometric), irrespective of the observer characteristics.
Okay quick question, given a constant solid angle size (but with variable direction), and the same light source, can the candelas vary according to the direction of the solid angle? (this light source would obviously have varying intensity according to the direction). If this is true, then the definition of candela is slightly more involved than I initially thought. Also, if it were true, it would not be enough to give the size of the solid angle, but also its direction/angle would be needed.
Absolutely! To get the amount of power incident on an observer from such a source, yes we do need to know specifics about what bearing the observer is relative to the source. I have neglected these types of possibilities up until now for simplicity.
Out of all of these, the only one I would question is the "Source Size?" one, since the power would actually increase, even that seen by the observer.
I was comparing a (say) 2W source with another 2W source that is double the size. Essentially, I was looking at each variable on its own, not in conjunction with other variables.
I think so, and I suppose that the "solid angle" variable can be replaced by: the light source size and luminous emittance. In other words, if the solid angle gets smaller, that's the same thing as saying: the light source size gets smaller + the luminous emittance gets greater (though I don't know about this second one to be honest).
Solid Angle is not determined by source size or anything like that, it depends on the physical radiation mechanism and whatever optics may be in place. I can change the solid angle of a source without changing its size and I can change the size of a source without changing its solid angle.
By the way, I had another good think about all this again a couple of days ago, and to really simplify things, I thought one may be able to scrap candela and nits completely (apart from for mathematical purposes), and just go with lux (luminous emittence type) and lumens. Basically, we would speak about the lux and lumens received and emitted by a "light source" (where "light source" could be a real light, or actually an object which merely emits reflected light; in other words, everything becomes a light source).

Think about it, every possible practical situation could be described using lumens and lux alone:
Want to measure the lumens of the moon? Fine, it would be quite a lot, compared to even the brightest bulb on Earth.
Want to measure the lux of the moon? It would be very dim, probably 1 watt bulb standard as a guess.
Want to measure the lumens on Earth given off as a direct result of the moon. That would a fraction of the moon's lumens, but still quite a bit.
Want to measure the lux of the Earth given moonlight. This would be tiny. ). As a wild guess, maybe the same as a 0.01 watt bulb :)

And all of those four again, but measuring the light received instead of emitted. These would usually be the same were it not for light absorption into the material etc.

That's all eight possible measurments you could possibly wish to make about the moon, earth, and the light coming to/from each one. I suppose candela and nits might have some use, but television/light bulb/laser/flashlight etc. manufacturers, along with say, light fitters for buildings, should stick to lumens and lux when giving stats about their products. Would you agree?
For light source manufacturers, the nit is actually the most widely used in terms of standards, because it is synonymous with how bright we perceive something to be. This is because we, unlike ordinary objects can tell, via our lens and retina which direction light comes from in addition to how much (within the visible spectrum at least) light there is. Now, if we were to constrain ourselves to omni-directional sources, I agree, candela and nit would not be much use since the only difference between these units and lm and lux would be a factor of 4*pi. But light sources are not omnidirectional, even light bulbs - which is why we need to use candela and nits when it comes to making specifications and the properties of a source.

Claude.

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Hi Claude,

Sorry for the delay, I get distracted by other things as usual.

In light of the fact that the direction is a factor on top of the size of the solid angle, then, like you suggested, it seems perhaps more sensible to disregard the object/observer. I suppose otherwise one would have to speak about the exact XYZ position and size of the observer, which becomes a bit of a headache.

I was comparing a (say) 2W source with another 2W source that is double the size. Essentially, I was looking at each variable on its own, not in conjunction with other variables.
I see. Yeah that makes sense.

Solid Angle is not determined by source size or anything like that, it depends on the physical radiation mechanism and whatever optics may be in place. I can change the solid angle of a source without changing its size and I can change the size of a source without changing its solid angle.
Yes, reading my old quote, I think I was referring to the actual power/total light output of the combined variables, rather than the mechanism being the same. But I was a bit unclear regardless.

Now, if we were to constrain ourselves to omni-directional sources, I agree, candela and nit would not be much use since the only difference between these units and lm and lux would be a factor of 4*pi. But light sources are not omnidirectional, even light bulbs
For exact, hard, measurements, that's true. But for most purposes, and for the average consumer of said light bulb, lumen would be all that's really needed, since most of the light will be seen as reflected light anyway (off walls etc.) which more or less evenly disperses the light omni-directionally.

Often, when definitions are given for nit and candela, they exclude any mention of the direction angle. Is this because they are stretching the chosen (possible cherry-picked) angle to a full 360 solid angle, or is it because they take the estimated average of all possible solid angles, and call that the number of nits (or candela)? The latter effectively becomes a measurement of lux or lumens again btw.

Anyway, using just the light source, I'll give the variables once more (I hope!), and it's just the last two that need double checking.

Lux (radiometrically; W/m^2) - Depends on Luminous emittance.
Lumen (radiometrically; Watt) - Depends on Luminous emittance and light source size.
Nit (radiometrically; W/sr/m^2) - Depends on Luminous emittance, and size of solid angle.
Candela (radiometrically; W/sr) - Depends on Luminous emittance, light source size, and size of solid angle.

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Claude Bile
Often, when definitions are given for nit and candela, they exclude any mention of the direction angle. Is this because they are stretching the chosen (possible cherry-picked) angle to a full 360 solid angle, or is it because they take the estimated average of all possible solid angles, and call that the number of nits (or candela)? The latter effectively becomes a measurement of lux or lumens again btw.
No, as you said, if they did this it just reverts back to lux and lumens again, so it wouldn't provide any information. Some "definitions" of nits and candela can be very obtuse (the wiki one you provided before is a good example). That is why it is best to stick with SI definitions!

When you say a light source is X nit, you are really saying one of two things, it is X nit average within the range of directions the source actually emits into, OR that X nit is the maximum brightness. This is because rarely is the "nittage" constant over a given range of angles. Sometimes it makes practical sense to quote an average, whereas on other occasions (particularly where safety is concerned) a maximum is more appropriate.

Claude.

P.S. I agree with your dependencies.

Okay, thanks for all your answers so far - you've been a great help! Just a few quick Q+A just to make sure I understand everything 100%:

1: Given a constant luminous emittance, and assuming an evenly spread light source, does the number of nits increase proportionally to the size of the solid angle?
2: Given a constant Luminous emittance and light source size, and assuming an evenly spread light source, does the number of candela increase proportionally to the size of the solid angle?
3: Is another name for Luminous emittance - "Irradiance"?
4: If a laptop manufacturer say their LCD screen is 300 nits, in general, does this mean the average of the 180 degree solid angle the laptop emits, or is it referring to the brightest angle?
5: If it's the latter, then shouldn't they state the size of the solid angle which would presumably change massively according to whether it's say... 1 degree or 2 degrees?

Claude Bile
1. The "nittage" would increase as you reduce the solid angle (because it is in sr^-1).
2. Ditto.
3. Irradiance is the radiometric equivalent of Illuminance - The radiometric equivalent of Luminous Emittance is Radiant Exitance or Radiant Emittance (There are 2 names for the same thing).
4. Laptop screens are designed to have a constant "nittage" over a wide solid angle (because it would be annoying if the screen brightness varied depending at what angle you viewed it from. The quoted value of 300 nits is probably a maximum, but since the brightness should be pretty constant over the range of viewing angles, it wouldn't be much different to an average measurement.
5. Typically LCD screens and the like specify a "maximum viewing angle" or something of that sort, this is the quantity that defines the solid angle the screen emits into. (Even if no angle is specified, a consumer can easily obtain a rough measure by simply viewing the screen from different angles).

Claude.