Meanwhile, after looking at dozens of LED data sheets online I was a bit disconcerted that the LEDs that claim to be 3200k (tungsten) and 5600k (daylight) weren't quite perfect - in theory. Thus is was off to Excel that I went; and down the Internet rabbit hole.
My first stop was the plateau of "black-body radiation". Color temperature is really described as the color spectrum a black body would emit if it was heated to a defined temperature, say 3200 Kelvin. Obviously our household tungsten bulbs aren't anywhere near 3200 Kelvin, otherwise every house in America would have caught on fire by now. However, the spectrum that the tungsten bulb emits is commonly thought of as close to 3200K or sometimes 2700K. I used Excel to calculate the spectrum of a "ideal" black body radiator using Planck's equation.
After some research I made the graph calculate from 390nm (violet) to 700nm(deep red). As you would suspect from a tungsten bulb, blue is quite a bit lower on the graph than red. After doing a quick Google search I found someone who has actually measured a tungsten light bulb's spectrum and in the name of science I ripped off their picture. However, as a courtesy, you can read the original article at this link. The two graphs seem to agree within reason. I guess that's one of the reasons why tungsten lights remain the industry standard to this day - very predictable color representation.
However, when we look at LEDs that claim to be around 3200K-ish then things get a bit interesting. What I found is that LEDs tend to come in 3000K and 3500K more commonly, but the example below is still effective at showing my point. The graph is from a data sheet for a Cree CXA3050 LED, as you might find in a hardware store "warm white" LED bulb that is meant to replace a tungsten bulb. With a color rendering index of 93 you would expect this to match a black body radiator pretty well, but it's no where near the same spectrum. Please note that the Cree LED graph extends beyond 700nm, so this isn't a 1-to-1 graphical representation. The LED is all lumpy with a large spike in blue, a dip in green, and precipitously falling deep red response. Somehow that spectrum comes out sort of looking like 3000K.. The second picture is the spectrum of an ideal 3000K light bulb.
So how can this be? Well...let's start with a simple concept - the spectral response of the human eye. Again, I stole some graphs from Wikipedia at this link. The human eye is most sensitive to light at 555nm (green). Interestingly enough, our peak sensitivity drops to about 507nm at night. A blue shift...hmmm, wonder why we would do that at night? Notice how the graph barely leaves zero around 420nm? In fact, it barely leaves 1% around 430nm. The same goes for the other end of the spectrum. We barely see anything above 690nm and it drops to zero around 700nm.
So just because the LED doesn't produce much light below 420nm doesn't mean that much to human perception of the light source. Relatively speaking, it's difficult to see! What is of greater concern is the area up around 650-690nm. Notice how the "ideal" 3000K bulb is still rising around that area of the spectrum, yet the LED is falling away?
For an explanation of why this bulb appears like a 3000K light bulb we have to dig much deeper into how we, as humans, perceive the different spectrums of light. There are three types of cones in our eyes: short, medium, and long - identified by the wavelengths they are sensitive to. So when we see violet or blue it's mostly the short cones that are being stimulated. As you can see in the picture below (also stolen from the Wikipedia "color vision" article), each cone type has its own spectral sensitivity. The cone integrates light over the range of wavelengths its sensitive to.
So when you provide a spectrum like the 3000K LED shown previously, it is stimulating each cone and the cone in turn integrates the light over that spectrum. For instance, the long (L) cone can't tell the difference between 500nm and 600nm - both frequencies and everything in between stimulate that cone. The long cone throws both of those frequencies into its stimulus "bucket", but with different weighting. You could have a light like the "ideal" 3000K black body radiator as shown in my spreadsheet graph, or you could provide an equivalent weighted spectrum like the LED has, that throws enough light into each cone "bucket" to make the two lights perceptually equivalent.
Oh...so that's not so bad, you're probably thinking. Well...sort of. It depends on if it's you or a CMOS/CCD sensor looking at the light. Image sensors do not necessarily mimic the human sensitivity to wavelength. Also, the dye based filters that are used in Bayer patterns on all our favorite cameras do not necessarily match the cone sensitivity of our eyes. Your camera may disagree with your estimation/perception of a color temperature based on how it sees color!
The only clear way I see to work around this with the state of the art LED technology is to mix different LEDs to match color temperature spectrum, however that's fraught with inefficiency in light integration and color mixing light guides. LEDs are just barely getting to be powerful enough for video lighting, so most vendors would probably argue that it's better to have enough light than perfect light.
Hopefully I haven't gone off the deep end. I DO have a video project this weekend, so I can put my nerd hat back on the rack and my geek member club ID back in my wallet for a while. Now you know what sort of weird stuff keeps me up at night.