LED/LED Flashlight Beam and Field Angles?

[bristle]

I believe the beam angle for lights can be calculated by the following formula -

α = 2 arcCos ( 1 - Lm ÷ ( 2 π Cd ) )

where,
α = beam angle in degrees; and where beam intensity falls off to 50% of maximum (apparently)
Lm = luminous flux in lumens
Cd = luminous intensity in candelas

The difficulty I have is understanding where the "50%" comes in to it?

I thought the above formula calculates the TOTAL beam angle where the beam intensity falls off to 0 or near 0!?

First question :

Where does this 50% figure come from? Is it just some random figure? Or is it calculated from somewhere?

The "field angle" of light beams is apparently the light beam angle where the beam intensity falls off to 10% of maximum. This field angle is greater than the beam angle.

Second question :

What is the formula for calculating the field angle?

Thank you for any helpful replies!

 

[dave9]

I don't understand your question. A 50% figure comes from measuring MCD in the beam pattern relative to the hot spot center of the beam.

How are you going to calculate anything? The beam pattern is a spec based on the reflector or optics put in front of the LED or from the LED manufacturer itself, no calculation needed.

Yes, of course a 10% so-called "field angle" MCD value would be wider than a 50% MCD value, given any kind of reflector or optics that attempts to focus the beam, and most that don't.

Total beam angle falling off to zero, is a highly variable thing, with many lighting systems exhibiting varying degrees of light output, some useful and some not, between the 50% to 10% and between 10% to zero.

You seem to be trying to tackle this backwards, in lacking other variables you defer to the manufacturer who has already included the other variables for their specific product and since they typically don't disclose those, just provide the solution to the equation, it is usually not needed to know them for an implementation towards a lighting solution.

Perhaps there is a more application-targeted issue you are having where answers could be more tailored towards that?

 

[bristle]

Comments noted.

Actually I am aware how beam angle is measured to 50% of initial intensity.

My questions are more related to LED driven flashlights. And yes, I am aware that flashlight reflectors and lens will affect type of light (flood, narrow/spot).

Manufacturers do not usually provide beam angle data, this is where the formula I mentioned previously becomes useful in that beam angle (to 50%) can be calculated from lumen and candela or beam throw (until 0.25 lux). This latter data is usually provided by manufacturers. But the supplied data usually consists of total lumen output and maximum candela, and does not provide the 50% candela data.

This formula can then calculate "beam angle" based on total lumen and maximum candela. However, as mentioned previously, on first inspection of the formula, it suggests this formula calculates the total (maximum) "beam angle" down to where the candela intensity has dropped to zero or near to it. But in reality, this formula calculates only to 50% of maximum candela!?

So how is it that this formula only calculates beam angle down to 50% of maximum candela, when no 50% candela data is provided by manufacturers to begin with? As far as I can tell, even from the derivation of this formula, the calculated "beam angle" appears to be for the entire beam!?

The "beam angle" is important as it gives an indication of how much light is available for certain specific tasks. Some tasks require a spot type beam, where other tasks require a more flood type beam. Also important (to a slightly lesser extent) is the "field angle" where this data gives an indication of how much "spill" light is also available. So a formula that calculates this field angle when candela intensity drops to 10% is also very useful.

So my two initial questions still remain to be answered.