July 20, 2012

Light emitting diodes (LED) have output intensities that are specified in two types of units: radiant intensity (mW/sr = milliWatts per steradian) and luminous intensity (photometric units) (mcd = millicandelas = millilumens per steradian = mlm/sr) at a typical forward current (e.g. 20 mA) and at the peak of the forward emission radiation pattern. The

Usually LEDs emitting in the visible (e.g. red, green, white) use the luminous (photometric) units while infrared LEDs use radiant units. However, photodiode sensitivity is often specified in terms of radiant units (e.g. mA/mW) so it is convenient to understand how to convert LED intensity specifications between systems. Since photometric units are based on a standard of an ideal black-body radiator at a specific temperature weighted with the response of the human eye, conversion of an arbitrary optical source from luminous to radiant units requires a calculation involving weighing the human eye response with the actual spectral intensity output of the source. However for LEDs with a relatively narrow band of emission wavelength, the conversion from photometric units (millicandelas) to radiant units (mW/sr) is relatively easy as described below. The relevant conversion factor is called the

where the definition is the ratio of luminous (or visible) flux Φ

Therefore to convert from luminous intensity to radiant intensity, it is simply a matter of looking up the K(λ) value for the peak emission wavelength of the LED. The graph and calculator below facilitate determination of K(λ)

Using tables (e.g. RCA Electro-Optics Handbook), K(625nm) = 200 lm/W = 200 mlm/mW. Therefore the corresponding radiant intensity is:

I

(2) A Si photodiode has a

The geometry is shown below:

The half-angle θ subtended by the photodiode is about 0.6 degrees. This is much smaller than the LED emission field width (~ 15 degrees) so the peak radiant intensity value applies over the entire detector area. The peak radiant intensity as calculated above is 25mW/sr. To determine the optical power received by the photodiode, we calculate the solid-angle subtended by the photodiode active area. For small angles such as this, the solid-angle Ω is approximately the area of the photodiode A divided by the distance-squared from LED to photodiode D:

so Ω = π/4*(4)^2/*(7*25.4)^2 = 4e-4 sr.

Therefore the received optical power at the photodiode is 25mW/sr * 4e-4sr = 10 µW. With the responsivity of 0.4mA/mW, the photocurrent is 4 µA.

To convert total radiant flux (in Watts) to total luminous flux (in lumens) for ANY source with any spectral radiance distribution, it is simply a matter of integrating K(λ) over the spectral radiance distribution

K is the ratio of luminance

(Note that only the RELATIVE intensity distribution of the source is required to calculate

For sources with narrow wavelength spreads (<20nm) in the visible region (such as single-color LEDs), integration isn't usually necessary (as discussed in the article above). One needs only use the value of K(λ) at the center wavelength of interest which will usually provide sufficient accuracy. The narrow spectral distribution simply "picks out" the value of K(λ) in the integration. In this case

(data for the relative eye response in this calculator is taken from the RCA Electro-Optics Handbook EOH-11, 1974 p.54-55)

- RCA Electro-Optics Handbook , EOH-11, 1974 pp. 53-57.

- Luminous Efficacy (Wikipedia)