Comment by thaumasiotes
1 year ago
> Irradiance is a density function - it's telling you how much energy or how many photons are hitting a given area per unit of the [in]dependent/spectral variable (you can see this by inspecting the units in the plots, for instance).
Well, I can see that in the labels on the y-axis, but I assumed it was a mistake.
So you have a graph that tells you that, for light of wavelength 1000 nm, measured irradiance is 3.5e+18 photons per square meter per second per nanometer.
And since there "are" 1000 nanometers (?!?), this means that the actual irradiance is 3.5e+21 photons per square meter per second.
Or does the "per nanometer" really mean something less stupid than that? What's being measured? What kind of nanometers are those on the y-axis?
Not quite - the nanometres on the y-axis are "deltas" of your spectral variable. The density allows you to answer questions like "how much power am I getting per square metre in a range [A, B] of wavelengths". You would integrate your density between A and B to obtain the value.
For example, pick some small value "k" close to 0 in units of nm. Then in your example, the amount of irradiation contributed by the small window [1000-k, 1000+k] nm of wavelengths is roughly equal to k*3.5e18 photons per square metre per second (you can check that the units work out). The smaller k is, the more accurate the approximation. If you want to get an answer for a larger interval you can break it up into lots of k-sized pieces and sum the results up. Recall from calculus that this is exactly what integration is (yes, I know the truth is a little more complicated in general measure theory).
Does that help? It's a bit like a continuous probability distribution, in the sense that to get an actual probability out of it you have to integrate. Formally a mathematician would say that a density corresponds to a "measure" over the space of all possible values of your spectral values.