From: boxman@voyager.net   
      
   On 7/14/2013 8:08 PM, Skywise wrote:   
   > I'm trying to compare brightnesses of LED's based on specs   
   > given in mcd (milli-candela). I have some samples of known   
   > mcd and viewing angle and want to use them as a reference   
   > to spec sheets I'm reading.   
   >   
   > I understand that luminous intensity is in part a function   
   > of the viewing angle.   
   >   
   > Am I right in understanding that, assuming all else being   
   > equal, if I cut the viewing angle in half the luminous   
   > intensity goes up by 4? That is, a given LED at 1000mcd and   
   > 60° viewing angle will be 4000mcd at 30° viewing angle?   
   >   
   > My reasoning is that since the area of a circle goes as the   
   > square of the radius, so if the radius of a circle doubles   
   > it's area increases by 4 times, and since the viewing angle   
   > is a light cone which projects a circle...   
   >   
   > Or, am I still a noob? :)   
   >   
   > The goal is to be able to read the specs and say to myself,   
   > "WOW!! This LED will appear about X times brighter than the   
   > one I have in my hand."   
   >   
   > Brian   
   >   
      
   It's not exactly as you describe, here are a few things that might help   
   you to make better comparisons.   
      
   1.  The viewing angle isn't necessarily standard from manufacturer to   
   manufacturer.  It is common to use the full width half maximum (FWHM)   
   which means that the viewing angle is the angle at which the intensity   
   drops to 50% of the maximum intensity on axis.  However some   
   manufacturers will use the 10% level to define their viewing angles in   
   which case the same LED would have larger quoted viewing angles if using   
   the 10% criteria.  It is often not stated on the data sheet as to which   
   one was used, so if there is an intensity vs. angle curve you can verify   
   it by looking at that or assume that the more common FWHM metric was   
   used.   
      
   2.  It is nearly universal that the intensity quoted on spec sheets by   
   manufacturers is the intensity measured along the LED optical axis and   
   is the maximum intensity (unless you have LEDs with specialized   
   radiation patterns such as a batwing or side emitter).   
      
   3.  Intensity as you are referring to it is a photometric quantity   
   defined by the differential flux contained within a differential solid   
   angle.  If you can treat your source as lambertian, you can approximate   
   the maximum intensity along the axis by using the formula for the solid   
   angle of a centered cone which is pi*sin^2(theta) where theta is your   
   FWHM value divided by 2.  To get intensity divide the flux (power in   
   lumens of the LED) by the calculated solid angle.   
      
   This will only be approximate because most LEDs are not true lambertian   
   sources, especially if they have lenses over them used to narrow the   
   beam.   
      
   4.  If you are really looking to compare brightnesses, you have to   
   consider one other factor which is the physical area of the emitter.   
   Intensity is not the quantity that identifies brightness, rather   
   luminance is the photometric quantity related to brightness. So for   
   example if you have a 3mm and a 5mm led with the same itensity in mcd,   
   the 3 mm LED will appear brighter.  The luminance is inversely   
   proportional to the square of the area of the emitter.   
      
   To be totally nitpicky, brightness is a sensation that depends on   
   several factors (background luminance, adaptation levels etc) and   
   doesn't necessarily behave linearly, so luminance on it's own doesn't   
   specify brightness. If however you are observing the different LEDs in   
   the same conditions over a small range of luminances, then luminance can   
   be a reasonable surrogate to approximate the X times brightness   
   increase.   
      
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