I have a setup where I can measure the optical power, in watts, the current, the voltage and the spectrum of an LED. Is it possible from this to calculate the external quantum efficiency? I realise I can calculate the ratio between the optical and the electrical power from this but I think this is a different type of efficiency.
External quantum efficiency is the ratio of photons produced by the LED to electrons injected in. By measuring the optical power and dividing by the photon energy, you can get the total number of photons. Then divide by the current to get the ext QE.
More information can be found at this source from MIT OpenCourseWare. Page 4 seems to be what you're looking for.