Hi Afif Fouzri,

I am assuming from your question that you actually have obtained the PL spectra of the rare earth doped ZnO in the relevant wavelength region to calculate the CIE coordinates (that is from 380 to 780 nm)?

If that is the case, then the calculation of the CIE coordinates is not that difficult. Here is a step by step guide:

1. You need to calculate the CIE tristimulus values X, Y, and Z. Basically, what you need to do is to multiply your PL spectrum L(lambda) with the respective color matching functions xbar(lambda), ybar(lambda), and zbar(lambda). The color matching functions can be found in the literature or via search engines.

Let's for example calculate X.

The product of your PL spectrum and the color matching function would then have to be integrated over the relevant spectral range. This yields:

X = integral L(lambda)*xbar(lambda) d lambda,

where the lower and upper bound of the integral are 380 nm and 780 nm, respectively. Accordingly, the other values can be obtained by:

Y = integral L(lambda)*ybar(lambda) d lambda,

Z = integral L(lambda)*zbar(lambda) d lambda.

2. Once you have X, Y, and Z, it is necessary to convert these CIE tristimulus values to the CIE xyY colorspace, which is commonly used. This is a simple calculation:

x = X / (X+Y+Z)

and

y = Y / (X+Y+Z).

With x and y, you can now pinpoint the position of your PL spectrum on the commonly used CIE chromaticity diagram.

A good write-up of this procedure can actually be found on wikipedia (https://en.wikipedia.org/wiki/CIE_1931_color_space#Meaning_of_X,_Y_and_Z).

Hope this helps.

Hello Afif Fouzri

You can try using this method http://www.ppsloan.org/publications/XYZJCGT.pdf after you obtained your PL-Spectrum by measurement.

Some matlab script implementing the calculation also available in matlab file exchange forum:

https://www.mathworks.com/matlabcentral/fileexchange/29620-cie-coordinate-calculator.

Thanks for your kind response Dear colleages.