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How do I calculate the Luminous Intensity (cd) of multiple LEDs spread across a 1.5m2 internally illuminated sign element?

I have done this by treating it as a point source and adding each led module, but from what I have read it doesn't work that way. such as mentioned in How to add lumens

ShawnH
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Lumens DO add directly.

If the illuminated area is common to two sources then
Lux (luminous intensity) = lumen per square metre also adds linearly.

If you has say 3 LEDs (each of say 1200 lumen output), each exactly and uniformly illuminating a 1m x 0.5 m area and you placed the areas side by side to make a single 1m x 1.5m area, then

  • Each area would have 1200 lumen of light shining on it
  • The total light would be 3600 lumen
  • Each sub area would have a luminous intensity of 1200/0.5 = 2400 lux
  • The 1.5 m^2 area would also be illuminated at 2400 lux ( (3 x 1200) / (3 x 0.5) )

In practice LEDs do not illuminate an area evenly so the lux level will vary across the 0.5 m^2 areas and across the overall 1.5 m^2 area. If light from a given LED falls outside it's 0.5 m^2 area (as it probably would) then at the boundaries with the other areas it would add to the light from the adjacent LED so the boundary areas would be brighter when the 3 areas were merged.

In practical situations where you have more or far more than one LED per 0.5 m^2 the level of illumination would be more even than with only 3 LEDs.

Russell McMahon
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  • Thank you for your response, I need to calculate the luminous intensity or luminance (cd or cd/m^2), not the illuminance (lux). Essentially I need to know how bright the sign appears when looking at it, not the amount of light it puts out onto other surfaces. – ShawnH Sep 29 '19 at 11:13
  • @ShawnH How bright it looks IS the amount of light that it puts out onto another surface (your eye). BUT knowing what light falls on it and summing sources will do what you want. You can complicate matters by dealing with reflectivity, incident angles, eye spectral response, eye logarithmic intensity response and quite a lot more. BUT what I said above does essentially what you want. If you have the distribution patterns of the LEDS you can work out the cd/m^2 across its area of illumination. For starters assume a barn door cut off even illumination per led. ... If – Russell McMahon Sep 29 '19 at 11:25
  • ... I am familiar with the relevant terminology but would have to go and check the correct terms. Advanced common sense really does work. || Total lumens = sum of individual lumens. Illuminate the same area with two sources and the lux add. || You start to get into complex issues which almost certainly don't matter here when you look at eg lumen definition - which is an eye-response tailored curve. Or at perceived brightness - which is logarithmic. || None of the terms you have mentioned so far deal with either the lumen eye response curve or the eye's amplitude response. See next comment: – Russell McMahon Sep 29 '19 at 11:29
  • @ShawnH I **STRONGLY** recommend that you describe in painstaking pedantic detail what you wish to achieve. No need to use technical terms - just common sense ones. I say this because the subject has many subtle aspects which largely do not matter in many cases and if you start on the terms for what you think you do or do not want "there will probably be trouble". I have been involved with producing 100's of thousands of solar lights for develping country applications. I have spent zillions of hours with lux meters, perception tests, 1 & N LED comparisons, various distribution patterns, ... – Russell McMahon Sep 29 '19 at 11:33
  • @ShawnH ... colour temperatures, CRIs ... et al. || So, really, describe your desires in simple words in such a manner that there is no chance of there being a misunderstanding. | Be aware that if you get into "increasing brightness such that the eye will see it s twice as bright" that the answer is even more complex than you'd imagine. Two lights viewed one at a time may be typically up to 2:1 in 'brightness before most people can be sure they are different. View both at once a few metres apart and it's maybe 1.5:1. Wall wash two adjacently and its maybe 1.1 - 1.2. Agh. – Russell McMahon Sep 29 '19 at 11:37