Back to Basics with LEDs

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Intensity profile, Lambertian emission and... Candela artifacts

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 ( 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.


the candela: the weapon of the poors

Now that we all know the difference between Watt and Lumen, it’s time to learn about another unit you can sometime find in LEDs’ specifications: the candela.

We have first to remember an old story from school: the solid angle. Roughly, it can be compared to “3D angle”; Wikipedia ( describes it as a “measure of how large an object appears to an observer”. And in the same way that “2D angles” do not have physical units but are still measured in degrees or radians, the solid angle has no physical unit and is measured in steradian (abbreviation: sr). The most useful equation to remember is, by far, the solid angle of a cone:

And the 2 values to remember are:
- the solid angle of an entire sphere:

- the solid angle of a half-sphere:

And now, back to our candela: the “light intensity” is the quantity of photons passing through a given solid angle. The units are W/sr in radiometric system, and lumen/sr in photometric system. The latter is also called candela.

In a LED’s specification, this value is intended to tell you how much light is directed in the LED-axis direction.

Seems easy, isn’t it? Next time, we will speak about optics and intensity diagram, and you will understand why this parameter is so much misleading if you don’t use it properly…

Watt, Lumen, Candelux and Steralux…

The most important item in a LED specification is also the most obscure one: this is the “Optical Power”. It seems that the LEDs’ manufacturers do it on purpose to confuse their customers! How can you compare the emitted energy when it’s called sometimes “Watt”, other times “Lumen” or “Candela”??? Isn’t it like searching the most beautiful woman with deforming glasses???

Let’s put all this in order, and let’s remember:

1 – there are 2 scales for optical power measurement:

a) radiometric scale (units: WATT): this is the absolute and objective scale (my preferred one!). It’s simply proportional to the number of photons and their energy!

b) photometric scale (units: LUMEN): this is the physiological and subjective scale, the sensitivity of your eyes. In other words, how strong YOU will see the light.

2 - The sensitivity of the eyes does not depend on their color, but on the wavelength of the light reaching them. As you may know, the eyes are the most sensitive to green, less sensitive to blue and red, and blind to UV and IR.
So, how can I compare radiometric and photometric scales? The following graph is the conversion from Lumen to Watt. Let’s take the red dot as an example: 350 lumen at 610 nm are equal to 1 watt. Easy, isn’t it?

3 – Quiz
question 1: how does it make sense that the UV that burns your skin and your eyes is as strong as 0.0 lumen?
question 2: Take a blue LED that emits 1 lumen. Cover it with phosphor. This LED emits now 10 lumen. Did we discover the optical perpetuum mobile (source of perpetual energy)???

What you don’t have the right to ignore about LEDs

My goal here is not to bombard you with frightening physics equations and terms, you can find them by yourself in many sites. You can also read the Wikipedia 10 pages article ( I only want to compile some essential concepts that will allow Newcomers to understand the “basics of basics”.
Here is a small list of what you don’t have the right to ignore. The real world is of course a little bit more complex than that, but this list is a good starting point:

L.E.D. is for Light Emitting Diode. It’s a small die that emits light when crossed by a current. This die needs to be electronically connected and mechanically protected, and that’s why it’s usually sold as an encapsulated device. By extension, this encapsulated device is called LED too.

about the die:
- usually square, between 250 and 1000 microns. The larger sizes are called High Brightness (HB)
- there are roughly 2 families of materials, one for the higher part of the spectrum (yellow to IR), the other one for the lower part (UV to green). Those 2 families differ in their electrical behavior.

electrical facts:
Like usual electronic diodes, the current can travel only in one direction inside the LED, and is blocked in the other direction. But, even in the right direction, there is a voltage threshold:
- below the voltage threshold, no light is emitted
- above the voltage threshold, the LED emits light, and the optical power goes with the current (and NOT with the voltage)

optical facts:
- the spectrum emitted by a die is close to a Gaussian curve, FWHM is between 25 and 40 nm
- you can find LEDs in numerous wavelengths and optical powers (but not all) from the UV to the near IR. There are even some LEDs in the 200+ nm region
- the die itself emits a Lambertian beam (half-sphere emission)
- the encapsulation can act as a lens, and the emitted beam is narrowed
- a “white LED” is either an encapsulated LED composed of 3 RGB (Red Green Blue) dice, or a blue / UV LED covered with phosphor.

What did I forget in this list?

my first blog

I am completely new in this world of “blog”, I never read them, I of course never wrote any, and in fact I even don’t know what it really is… And that’s exactly the reason why I decided to accept this challenge (Yaroslav, thank you for this opportunity!).

My name is Elie Meimoun, I am a physicist (does “electro-optical architect” sound better?), and my hobbies are 3D CAD optical design (in other words everything except standard lens design), plastic optics, illumination technologies, and …… LEDs.

I grew up in France and have a diploma of “Physics Engineer” from “Ecole Centrale de Marseille”. After my military service near Verdun (a really depressing place), I decided to emigrate to Jerusalem.
With such background, you will probably forgive me for my low-level English. You will not be able to correct my heavy accent, but you are invited to correct the grammar.

I asked Yaroslav to let me write an “educational blog”. This is a kind of “back to basics” about LEDs and their interfaces with the surrounding (optics, thermal, driving….). I am open to any comment and question.