After having learned the theoretical definition of light intensity, let's see how to apply it to LEDs.
1 - intensity profile
It's simply the graph showing the light intensity vs. the angle. It can be displayed either in Cartesian or in polar coordinates. This graph usually appears in all reliable LED's specifications.
2 - intensity profile of LEDs dice
The emitted light fr om the die itself (without any optics) is usually very close to a Lambertian emission. Nice word, but what does it mean?
A Lambertian emission (http://en.wikipedia.org/wiki/Lambert%27s_cosine_law) refers to a source emitting the same quantity of light in all directions. When you look at this source, the quantity of light (intensity) you will see is proportional to the seen surface. And this seen surface is equal to S.cos(teta) where S is the total surface of the source, and teta the viewing angle.
Now we know why the intensity profile of a die without optics is a cosine curve, as simple as that!
Another interesting equation to know is the power emitted by a Lambertian source within a given cone:
Where P0 is the total power emitted by the LED and phi the half-angle of the cone.
Finally, let’s calculate the intensity of a die for small angle cones, normal to the surface:
3 – adding optics to the die…
The optics integrated in the encapsulated LEDs is usually intended to collimate the light (send all the rays towards a parallel direction). Light that should have gone to the sides is now redirected to the center. The intensity graph is therefore changed so that the intensity is stronger at the center (teta=0), but at the price of a reduced intensity on the sides (the integrals of both curves, before and after the lens, are of course equal).
Let’s calculate now the intensity of the system LED + optics, wh ere the optics collimates 50% of the energy within a +/-3deg cone:
And for a system collimating 30% of the light within +/-1deg cone:
which is 1000 times (!) stronger than the original intensity without lens!
Thus, a significantly weak LED can exhibit a much higher intensity value than real power LEDs, only with the use of a simple lens. It sometimes seems to be a method to artificially enhance the power (and the sales to those who are not “skilled in the art”) of old and low-power LEDs.
Conclusion: NEVER USE THE INTENSITY VALUE (CANDELA) TO COMPARE THE TOTAL POWER EMITTED BY LEDS.