 # Calculating Photon per Second Output of LEDs

Hello,

I have some LEDs that I am trying to calculate the photon per second output of. The method I am using involves dividing the radiant power (in Watts) by the energy of a single photon (using E=hc/lambda) (I realize there’s a range of wavelengths to take into account, but I am just choosing the peak wavelength for an approximation). The problem is some LEDs do not give the radiant power in the spec sheets. Instead, they give a quantity called the luminous intensity (given in Candelas). What I am trying to do for this method then, is convert Candelas to Watts. I am approaching this from a unit analysis standpoint. A Candela is a Lumen per Steradian, so I first multiply by the solid angle in Steradians to obtian Lumens (the spec sheets do list the half intensity angle, which is required to calculate the solid angle).

The next step seems to be to divide by a quantity known as the efficacy, which is given in Lumens per Watt. The final result is Watts. However, the problem I am running into is that spec sheets do not list the efficacy anywhere, and LED efficacies in general seem to take on a wide range of values.

How can I find out what the efficacy of my LEDs are? Is there maybe another way to calculate the photon per second output of the LEDs that doesn’t require needing to know this information? Any help would be appreciated.

Greetings,

“Luminous” is something of a signal word to indicate that a quantity in question is a perceptual measure that takes the wavelength-dependent sensitivity of human vision into account, rather than a radiometric one that’s concerned with energy. You can use that to convert luminous intensity values to radiant intensity values, based on the spectral characteristics of the LED.

Having thereby converted the luminous intensity vs. angle chart into a radiant intensity vs. angle chart, you’d set up an integral to evaluate the product of intensity and solid angle. Or you could approximate things using a piecewise method, figuring out the solid angle subtended between, for example, 0 to 5° viewing angle, 5 to 10°, etc. and multiplying each by the radiant intensity in that direction. At the end of the day, you should arrive at a figure in watts.

Thank you for the insight. How would you go about converting luminous intensity values to radiant intensity values? I would imagine the efficacy is a spectral characteristic of the LED needed to do it, but I do not have it. Perhaps it is not necessary?

“Luminous efficacy” describes how effective an LED or other lighting agent is at turning electrical input power into human-weighted optical output power. Not really relevant for what you’re doing.

Put “photopic luminosity function” into your search engine of choice, and you should find a variety of sources offering curves that relate the radiant and luminous realms as a function of wavelength.

Alright, I’ll look into it. Thank you!