A few years ago a colleague asked me how to calculate total luminous flux emitted from an LED, when the only information you have is maximum intensity. Often those cagey LED manufacturers omit this critical information which you may need in order to design for a certain target light output.
First we’ll review the short answer and later we will go into more detail.
The Short Answer:
It turns out that for a lambertian source the relationship between max intensity and total lumens is very simple.
- Φ is total luminous flux emitted from the lED in lumens (lm)
- Imax is the maximum intensity of the LED in candelas (cd), which is usually specified on the datasheet if intensity is specified at all.
- the units of the constant pi is steradians (sr)1
See below for a derivation of Equation 1.
The Detailed Answer:
let’s talk for a moment about δω.
from figure 2 we can see that
since the radius of the circle that δh lies on is equal to rsin(θ),
thus, combining equations 3, 4, and 5:
We integrate δγ from 0 to 2π because we are interested in the light emitted around the entire circumference of the source, and our integration results as follows:
now, if the source is lambertian, then we know from a previous discussion that
Next time, we will talk about what happens when you want to calculate flux for an intensity distribution other than lambertian. Questions? Contact me at Rachel@HowYouLightIt.com or comment below.
1. Murdoch, Joseph B. Illuminating Engineering: From Edison’s Lamp to the LED. 2nd ed. New York: Visions Communications, 2003.
2. Sahiner, A. V. Computer Graphics, Boğaziçi University, Spring 2010. Web. 15 January 2011. (Radiometric Terms and Radiance at: http://www.cmpe.boun.edu.tr/courses/cmpe535/spring2010/)