How to calculate the daylight spectrum (D illuminant)

Measuring and characterizing the daylight spectrum can be challenging due to the fact that many factors affect it, including time of day, season and weather. That being said, it is oftentimes necessary to standardize the daylight spectrum and this is what the D illuminant attempts to do.

The D illuminant can be used to approximate the daylight spectrum between 4000K and 25,000K. The inputs needed are the xy coordinates from the 1931 CIE coordinate system, along with the three functions named S0 (blue), S1 (green) and S2 (red). You will likely need to convert CCT to CIE 1931 xy first.

The S0, S1 and S2 functions are available as a text file for download.

Alternatively, you can find our online calculator here.

To calculate the irradiance of daylight at a particular xy coordinate, use the following formulas for M1 and M2:

M1 = (-1.3515-1.7703*x+5.9114*y)/(0.0241+0.2562*x-0.7341*y)
M2 =(0.03-31.4424*x+30.0717*y)/(0.0241+0.2562*x-0.7341*y)

Then, for each wavelength, use the following formula to get the irradiance value:

S = S0 + S1*M1 + S2*M2

That's it!