Help understanding $X(T) = \sum_{j=0}^{471} M( λ_j ,T)\bar{x}(λ_j)$ needed.

Question

I'm trying to convert mathematic syntax for color calculation in C++ algorithms.

$X(T) = k\sum_{j=0}^{471} M(λ_j,T)\bar{x}(λ_j)$

$M(λ_j,T)$ is a function but what means $\bar{x}(λ_j)$?

The equation (No. 11) is from Accurate method for computing correlated color temperature, Section 3.

Thanx for any hint! :-)

Answer 1

$\bar{x}(\lambda_j)$ is the color-matching function (for the $x$ coordinate of the CIE color system), evaluated at the wavelength $\lambda_j$.

The idea of these color-matching functions is that if you compute all three of them, at some wavelength $\lambda$, the results you get will be three coefficients $c_x, c_y, c_z$ with the property that the spectrum $$ c_x X + c_y Y + c_z Z $$ (where $X$, $Y$, and $Z$ are the spectra of the CIE primaries) will produce the same color sensation as a pure spectrum of wavelength $\lambda$.

This is slightly sloppy, in the sense that there's a scaling constant hidden in here, but that's the main idea.

These color-matching functions are tabulated (at about a 1nm sampling rate, I believe) by CIE, and if you're writing a computer program, you need to grab some files containing the data and read them in.