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Member Since: August 29, 2015

Country: United States

  • Hey Pete!

    So as another EE who fell down the rabbit hole that is color science a few months back, I think I can help you out here.

    To understand candelas and lumens, you can think of candelas as like a pressure and lumens as like the force behind it. You're only applying this pressure in a set area (well, solid angle) so you only need to apply the force to that area, not everywhere! This means the same amount of lumens over a smaller solid angle results in a higher intensity (candelas), like how the same force over a smaller area results in higher pressure.

    Another way to look at it is candelas are analogous to Watts per steradian in the equations, so they are an intensity. Lumens are then analogous to Watts in the equations and represent total light output, like how Watts represent total power output. They aren't exactly the same or fully proportional due to the luminosity function, but they are similar enough.

    So back to that equation, you start with your magic number of 683.002(lm/W), which knowing that lumens and Watts are similar, you can see it now as a sort of unit converter. Then have your luminosity function which weights the light based on how well people perceive it's frequency (the peak at 555nm means that eyes have the strongest response to green light). Then you've got this radiant intensity function, which is about how much actual light energy the source is putting out, per steradian.

    Now for a single wavelength LED, just find the value of the luminosity function at the wavelength, assume all power is at that exact wavelength, multiply by our magic number, and you've got your candelas. However, to use this equation on any sort of broader spectrum or white LED, you'll need some calculus and the spectral power density (which you can find among the pretty pictures on the datasheet).

    If you want to go further, take a look at the "radiation pattern characteristics" (angular distribution) of a wide angle LED to see why they tend to only have luminous flux data (lumens) rather than luminous intensity data (candelas). You can also find certain deep red LEDs give out a radiant flux/intensity (Watts) instead of a luminous one, because they fall off the high end of the luminosity function.

    Let me know if this helps any, or if you have further questions on this and/or anything else you couldn't quite wrap your head around!

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