# Is there a relationship between the driving current and the optical power emitted by a light source?

If we have an LED light source which is driven by 0.5 Ampere can we infer what is the optical power (aka radiant flux, radiant power) emitted by that light source?

Furthermore is there a way to convert Illuminance (measured in lux) to optical power (measured in Watt)?

## 2 Answers

Short answer - no, the current is not sufficient.

At the very least, you need both the driving current and the voltage (which depends on the band gap, and thus the wavelength) to know the input power. But the actual efficiency of a light source (LED, or any other light) is a function of many factors. The output of most LEDs is a function of temperature, and is not even linear with current (because of certain saturating self-absorption phenomena).

Conversion of illuminance (lux) to power requires you to know the "luminous efficacy per Watt" (which is a function of the wavelength distribution). It's complicated. This is coverend in this answer

You want to convert from photometric luminous power to radiometric power.

Radiometric power, measured in Watts, emitting from an LED is a measurement total amount of photons emitted.

lm is the photometric equivalent of the radiant power which is the luminous flux or luminous power measured in lumens.

Photometrics is how the human eye perceives the photons emitted from a light source.

In addition to power there is the intensity which is the measure of photon at a single point at a particular angle.

There is also the concentration of photons within a given area within a cone where the cone has a given angle.

Radiometric units                              Photometric units
Radiant power Watts                            Luminous flux Lumens (lm)
Radiant intensity Watts per steradian (W/ster) Luminous intensity Candelas (cd)
Irradiance Watts per square meter (W/m2)       Illuminance Lux (lx)


The conversion is easier for a narrow band LED (e.g. red green blue) within the visible bandwidth. It is not possible for a narrow band LED outside the visible spectrum (e.g deep & far red, royal blue, UV, or ultraviolet).

It is very difficult to convert a wide band LED like white. The radiometric power of a white LED varies for each wavelength in the visible spectrum for the measured photometric lumens.

You can approximate the radiant power if the LED's datasheet publishes the efficacy in lm/Watt. The conversion is still bandwidth dependent where you have to account for how the human eye perceives each wavelength emitted.

That is just the beginning. The characteristics of an LED as indicated in the LED's datasheet are min, max and typical. No LED is typical. The amount of current, the forward voltage, the junction temperature, and the view angle all come into play. All of these characteristics vary widely even if the LED's dies (chips) were produced on the same wafer.