I just bought a projector fog light. The thing is amazingly bright, but what’s really incredible is: all that brightness is generated by a tiny SMT LED, maybe 4mm x 2mm. The LED is way too bright to look at (even without the lens), I was wondering how it’s brightness / surface area compared with other light sources, like a Tungsten-Halogen filament, or the Sun. Poking around the Internet wasn’t very helpful.
Various sites claim the sun produces 3.573e28 lumens. It also has a surface area of 6.07e18 m^2, for a luminous intensity of 5.9e9 lum/m^2.
Since the provenance of the lumen estimate is uncertain, let’s try this another way. The Stefan–Boltzmann law says the luminous intensity of a blackbody is σT^4, where T is the temperature and σ is the Stefan–Boltzmann constant. T is about 5778 K and σ is 5.57e-8 W/m^2-K^4, for 6.2e7 W/m^2. Converting watts to lumens depends on the frequency distribution (how much goes into visible light vs UV, etc.), but 100 lumens/W is in the ballpark, giving 6.2e9 lumen/m^2. Close enough to the 5.9e9 lum/m^2 from before; that seems legit.
As for the LED, here’s one of the brighter models I found:
From the datasheet, that’s a peak of 585 lumens from a chip that’s 1.15 mm on a side. That gives a surface brightness of 4.4e8 lumen/m^2, or a bit under a tenth that of the sun.
As for the filament: that runs at about 2800 K for a standard bulb. By the Stefan–Boltzmann law again, that means a ratio of (2800/5778)^4=1/18. So the LED has a somewhat higher surface brightness than the filament. Halogen bulbs run a little hotter at 3000 K for a ratio of 1/14 vs the sun.
It depends on how you’re defining the surface brightness, but surface brightness of the filament wire itself isn’t really very useable for most applications. The wire occupies some of the area of the region we can stop down to on a lamp. I mean, if for example you’re precisely refocusing it on a fiber optic, the wire will be some zigzag or coil shape surrounded by darkness. Well, what people do instead is refocus or reimage the filament softly, to get a uniformly bright spot, but that spot is averaging together wire and empty space.
The LED, on the other hand, is a full rectangle, and every point inside it has the full intensity. Its surface brightness happens on a more available surface, you might say.
Agreed that a compact rectangle of emission has more practical uses than a zig-zag filament. Still, surface brightness has a clear definition that we can compute explicitly from the temperature (for blackbodies). beowulff seemed interested in how bright the emitting elements looks visually, and for that, shape isn’t much of a consideration.
Not exactly–it’s just that the surface is more conveniently shaped. Even with the LED, you probably want to defocus slightly, as otherwise you might image some of the patterns on the LED itself. I had a projector flashlight that could do this, where you could see bondwires and the surface pattern of the conductors if you focused it just right. Kinda cool but not really what you want. But it requires less defocusing to make the LED look smooth and symmetrical than it does a filament.
I can remember some old flashlights where the filament orientation was just right (or wrong) so that the shape of the filament was projected. Made for a lousy light at certain distances.
As for brightness, is this the same as color temperature? When I built my auxiliary garage I used LED ceiling lights at 4000K and really liked them. I then replaced all the lamps in the old garage fluorescent fixtures. with LED replacements. The ones I bought have adjustable color temperatures in 3 stages. I ended up with them all the way up to 6500K and they are fantastic.
For incandescent emitters–whether an incandescent bulb, the sun, lava, etc.–brightness goes up with temperature (and here, color temperature is the same as actual temperature). The power output actually goes with the fourth power of temperature, but the perceived color goes up to higher frequencies as well (from red to blue). The visual brightness still goes up, even as the peak energy goes into the ultraviolet and beyond (make sure to wear your goggles). I’m not quite sure about that relationship but I’d spitball it’s more like the second or third power.
With LEDs, CFLs, and other non-incandescent emitters, there’s no direct relationship. You can have any brightness at any color temperature. And color temperature no longer is the same as actual temperature, but just means that visually, it looks similar to how an incandescent emitter would look. So 2700 K LED bulbs look pretty close to a normal incandescent bulb, since those run at 2700 K, and “cool white” bulbs tend to be at around 3000 K, which is what halogens run at. Above that , you get “daylight” bulbs which might be 4000 K or more. Again, there’s nothing actually operating at that temperature, but it looks like something that was. 6500 K would be the actual daylight temperature, and is a bit bluish for most people, but everyone has different tastes.
More emphatically, the idea of color temperature can be thought of in two steps:
If you are using incandescent lamps, and if they act as graybodies (meaning their emissivity is the same at all wavelengths), you can completely describe the spectrum of light they emit and their apparent color by stating the temperature of the filament. This is helpful, for example, for photographers who can accurately imitate what a photographed subject would look like in daylight if they use incandescent lamps operating at a known temperature.
If you are using a lamp that isn’t incandescent, then you can’t completely describe the spectrum and color this way, and some lamps are extreme misfits for this way of approximating spectrum and color. Fluorescent tubes that have a very strong green emission, and sodium street lighting, are examples.
The underlying issue is whether the blackbody or graybody model is accurate, close, or way way wrong, for a lamp. It’s a model comprising a family of curves with only one degree of freedom. Since we have two degrees of freedom in our color vision, something’s gotta give somewhere.