When first approaching photographic science a photographer is often confused by the unfamiliar units used.  In high school we were taught energy and power in radiometric units like watts () – while in photography the same concepts are dealt with in photometric units like lumens ().

Once one realizes that both sets of units refer to the exact same physical process – energy transfer – but they are fine tuned for two slightly different purposes it becomes a lot easier to interpret the science behind photography through the theory one already knows.

It all boils down to one simple notion: lumens are watts as perceived by the Human Visual System.

They both indicate a certain amount of energy transferred per second, except that the lumen counts only the portion of energy as perceived by humans.  Once this concept is absorbed the rest is easy because every single photometric SI unit is just a lumen over a period of time or space – therefore if one knows how to convert watts to lumens one can convert virtually all radiometric units relevant to photography to photometric units in exactly the same way (space and time are assumed to stay the same:-)

For instance a certain Radiance in units of watts per steradian per meter squared () becomes Luminance in units of .  But are defined as candela , so Luminance is normally expressed in , the units that photographers are usually familiar with.  And so on.

Converting  a radiometric function in watts (per whatever) to a photometric function in  lumens (per whatever) is simple: it is the energy flux in watts (per whatever) weighted by the eye response to light intensity function .  In mathematical terms:

(1)  

where in lumens (per whatever) is the photometric version of in watts (per whatever), a conversion constant equal to 683.002 and represents element-wise multiplication.

The key to conversion is the adapted eye response function which looks as follows for daylight as determined by Sharpe et al. (2005)*

That’s the CIE ‘physiologically relevant’ daylight-adapted photopic version , there is also a dark-adapted scotopic one that is less relevant to photographers. Because it is multiplied together with the radiometric  function that we are trying to convert, when is zero the output in lumens is also zero no matter what the input in watts.  Its value at 395nm and 718nm is 10 stops below the peak at 556nm, and it gets only smaller from there, so the integration in Color Science is typically limited to the 380-780nm ‘visible’ range.

For instance a 1mW laser that emits all its power at 556 nm produces 0.683 lumens, while an infrared 1mW laser that emits all its power at 750nm produces virtually none.  You get the idea: same power, different lumens based on eye response.

That’s for lasers which are not often found in nature by a photographer.  In the typical case of broad spectrum sources one needs to know their Spectral Power Distribution in watts per whatever as a function of wavelength and plug it into formula (1) as  to convert it to photometric units.  Next a practical example.

 

* Interestingly, photopic is usually considered to be the same as the CIE Color Matching Function for the color space, you can see the correspondence in Figure 1 here.