Source: http://gizmodo.com/5649389/giz-explains-brightness
The first thing to know about brightness is that, most of the time, it's not brightness. This is a semantic point, but also an important one. We (meaning basically everybody) use "brightness" to describe two distinct concepts: Brightness and luminance. One is subjective, and the other is objective. One is measured by our brains, and the other by instruments. One is the term we use, and the other is the term we mean.
Brightness vs. Luminance
Nearly everything we refer to as brightness is in fact luminance. The measurements companies use to sell the brightness of a screen, the power of a projector or the strength of a flashlight—those numbers above, the nits and the lumens—refer to objective measurements of light from a screen or a bulb, as taken by specific instruments.
So what is brightness? Let's crack a dictionary:
The effect or sensation by means of which an observer is able to distinguish differences in luminance.
In other words, brightness describes the experience of a phenomenon (luminance), not the phenomenon itself. A slightly more helpful crack at a definition, by Charles P. Halsted, engineer and fellow at the Society for Information Display:
Brightness is a subjective attribute of light to which humans assign a label between very dim and very bright (brilliant). Brightness is perceived, not measured.
The term is entirely subjective. You are never incorrect to refer to an item as bright or not bright, in the same way that you can't be wrong about the deliciousness of a piece of cake—at its most scientific, it's a measurement of a personal experience, made by the person having it. Even more jarring is that without humans, eyes, optical nerves, brains and judgment, brightness ceases to exist. If an HDTV flips on in the forest...
Measuring Light
Thankfully, there is a coherent way to talk about the amount of light that comes out of our gadgets. We talk about nits in our gadgets' screens, and lumens in our projectors, both of which refer to luminance, albeit indirectly. And they're intuitive! Higher is brighter; more is better. This is why manufacturers even bother to talk about them.
You've probably heard the term "candlepower" before, and you may hear it again. Like the candela, it's a measure of light intensity. Its definition is exactly what it sounds like: The measure of the "power" of a candle. In particular, according to the British Government circa 1860, one candlepower is the intensity of light produced by a spermaceti (whale oil) candle burning at a specific rate. Other countries defined it slightly differently.
The units has since fallen out of use. Well, sort of. The candela, which replaced the various different candlepowers as the standard unit for luminous intensity, is deliberately close to the British Candlepower. The way the sperm whale's brain-juice burns has in no small way determined how we talk about light to this day.
If you see someone advertising candlepower today, they're actually just talking about the candela, the accepted standard unit for luminous intensity. In common usage, the two have become one and the same.
Talking about luminance isn't exactly straightforward. Watts, a measure of power, are often used as shorthand for a light's brightness. A 40 watt bulb uses twice as much power as a 20 watt. It's simple! But it also isn't very helpful. Chuck Halsted again:
The response [of human eyes to light] is non-linear and complex. The sensitivity of the eye decreases as the magnitude of the light increases.
So even though 40 watts is about twice as radiant as 20 watts, it won't seem that way to you and me.
This is where candelas come in. A two-candela light will seem half as bright as a four-candela light, and twice as bright as a one-candela bulb. That's because the candela doesn't strictly measure intensity—it's a combined measure of light emitted, and its (approximated) significance to us, the humans, according to average sensitivity of our eyeballs to specific wavelengths of light.
This sounds sort of like what most people mean by "brightness!" Actually, it sounds a lot like that. The candela gives us a way to say, in broad terms, how bright, how glow-y, or how intense a single light is. What it doesn't do is speak to the size of our screens, or the way our projectors spray light. For this, we need nits and lumens.
Everything Is Il-lumen-ated
To use the candela to talk about gadgets and screens and bulbs, it's got to be wrapped up inside new terms. These terms take into account where the light is coming from, and where it's going.
The term nit is actually slang for the standard measurement for luminance, the candela per square meter. Put simply, a nit, is a measurement of light emissions and surface area. Think of it this way: The candela basically tells us how much light energy is coming from a source. (Or more specifically, how this light energy is likely to be perceived by people.) Nits tell us how this energy is distributed over an area, or to put it (too) crudely, how dense the light of a certain screen is. That's why 400 nit smarpthone screen will seem as bright as a 400 nit laptop screen, even though the laptop screen is emitting more light in total.
Lumens measure something similar, but they do it differently. A lumen is essentially a measure of light intensity that includes a consideration of the area the light is hitting—the cone of the projection, basically. Imagine a light source emitting light in all directions. Now imagine surrounding that light source with a sphere that absorbs all light. Cut a little circle out, and you'll get a beam of light. A smaller opening will mean fewer lumens, assuming the light doesn't change intensity. A larger opening, more lumens. See how this works?
The lumen is helpful in describing projectors, because it measures both light intensity in a way that has practical advantages: Knowing how many lumens a projector emits, and how far away from a projection surface you are, you can figure out how bright a projection will be, more or less. It's... nit-like.
All this said, simply knowing what nits and lumens are won't give you an intuitive sense of how many of either your display or projector needs. The fellas over at ProjectorPeople have put together a chart to determine how many lumens you should aim for in a new projector, depending on setting and display size:
In most conditions, a 250 nit screen will appear plenty bright. Many cheaper or older display will dip below that, and a some new ones—particularly LED-backlit screens—measure in at over 400 nits. That said, choosing a monitor or smartphone shouldn't necessarily be a calculation. Sometimes, you're best off just trusting your eyes.
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Bulb/exit image by Flickr user hryckowian