Spectral measurements and quantities

LED Flashlights – General Info
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I am looking into LED spectra and it has become very confusing. It is never good practice to have a graph with the y-axis unlabelled. However, this is the case with most spectral measurements of LEDs. So what exactly are we measuring?

Usually, radiation spectra are presented with spectral irradiance as the quantity on the y-axis, with units W/m^2/nm. When this is not followed nor specified, we run into some seemingly conflicting data.

Let us start with a question, is the red or blue peak higher in 4000K R9080 LEDs? I found the following measurements:

  1. Nichia 519A 4000K measured with HOPOOCOLOR HPCS-320 by huwenyupeter, blue peak higher
  2. Nichia 519A 4000K measured with X-Rite ColorMunki by zeroair, red peak higher
  3. Nichia E21A 4000K measured with unknown by maukka, red peak higher

I suspect the quantities being measured are different, leading to different answers. Specifically, zeroair’s graph says “Radiant Power (Equal Luminous Flux)” on the y-axis, which is ambiguous. It is a spectral measurement, so there is no way it is actually luminous flux. Could it be spectral luminous flux with units lm/nm? However, it also says says radiant power, which is measured in watts instead of lm. Radiant power is also not a spectral quantity, it should at least be spectral power/flux with units watts/nm. Which is it?

If it is spectral luminous flux, that would explain the red peak being higher, because the photopic efficiency function at the red peak is higher than at the blue peak, thereby inversing the height of the peaks than if one were to measure spectral irradiance.

However, this raises more questions than it answers. The photopic efficiency function at the red peak (~630 nm) is 0.265, and at the blue peak (~450 nm) is 0.038. With this huge difference, we should see the peak heights being drastically different between the measurements of different quantities, but we don’t. What is going on here?

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This is a very good thread full of important unanswered questions. I don’t have any definitive answers either but have some thoughts.

(1) The fact that the y axis is not just unlabeled but also unnumbered suggests that the plots involve some sort of automatic normalization, such as one that puts the peak of the plot at the upper boundary of the display, as seen in third plot. Thus there is no consistency in units between measurements by the same device of difference sources (or the same source just twice as bright). Thus the best unit one can assign to the y axis is “[some SI-derived unit], up to a normalization factor that depends on both the spectrum and power of the source”.

(2) It seems probable that these plots from different devices use the same unit from (1), since they produce almost-identical plots of the same emitter. Furthermore, it is likely that the implicit unit does not rely on lumens: a plot of a 6500K Optisolis features a tallest peak at 420nm violet, which is barely visible to the human eye compared to the other emission present.

(3) It is possible that the implicit unit is “some sort of relative watts-per-nm”, in the following sense: up to some normalization constant (hence “relative”), the power emitted between x nm and y nm is the integral of the plot over [x,y]. Why “some sort of”? Because it is difficult to directly interpret a probability density function.

Assuming the integrated plot has unit W: since integrating the plot over nm results in a unit of W, it seems reasonable for the plot to have the unit W/nm. But this leads to the issue of interpreting, say, what it means for the plot to say w W/nm at x nm. What it actually means is that “for a very small interval around x, the ratio of power emitted in this interval to the length of the interval is close to w”, which is not easy to conceptualize as anything other than the derivative of the cumulative power-over-nm function (cumulative distribution function).

(4) The plots you linked were very interesting. I worry, however, that the variance in emitter and device characteristics makes comparing the heights of blue/red peaks difficult. In the first image, the blue peak is unusually sharp and has an inflection point halfway to the cyan dip; this inflection point is not seen in the other plots. The second plot looks typical. The third plot reads an actual CCT of 3756K, noticeably lower than 4000K, which explains the higher red peak. It is possible that slight differences in the resolution of the device, and choice of smoothing/interpolation used to produce the final plot, may noticeably affect the height of the blue peak.

Curiously, I do observe the inflection point (as almost a secondary peak) looking at 519A through a homemade spectroscope. So it is possible that the other devices don’t have enough resolution to bring out this feature.

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Plots from this post hints at what the unit might be: 【图片】1688上定制的5050高显色【手电吧】_百度贴吧

The y-axis is labeled W/m^2/nm, which is technically incorrect, since summing over all wavelengths gives [infinity] W/m^2 (recall the difficulty of directly interpreting a probability density function). But the label does hint that integrating the plot over nm should yield a unit of W/m^2 (radiometric intensity), which seems sensible. This is equivalent to W up to a constant (being the intensity of the light source).