Calculate colour temperature in K

Question

I have written a lib for working with colours and stuck trying to calculate Tc(k). From what I have read working in the CIE 1931 XYZ colour space i

Answer 1

I done some digging in some open source apps and found something in UFRaw. I have not quite figured out what is going on exactly.

Also found a paper that seems to cover the topic quite well.

Converted to php and this is what I have so far:

$temp = array(9500, 7000, 5500, 3750, 3000, 2700, 2250, 1800, 1500);
$hex = array('9DBEFF', 'E4EEFF', 'FFE4BE', 'FFA04C', 'FF7A26', 'FF6A19', 'FF500B', 'FF3403', 'FF2300');

echo '
K -> RGB
';
foreach ($temp as $k) {
    $rgb = ColourConverter::temperature2rgb($k);
    echo sprintf('
%s
', implode(', ', $rgb), $k);
}

echo '
RGB -> K
';
foreach ($hex as $v) {
    $rgb = array_values(ColourConverter::hex2rgb($v));
    $k = round(ColourConverter::rgb2temperature($rgb[0], $rgb[1], $rgb[2]));
    echo sprintf('
%s
', implode(', ', $rgb), $k);
}

My output:

Pretty close but not 100% yet. (Found a bug in my code and it is now almost perfect)

• The colours are slightly off going from k -> rgb
• It does not work doing k -> rgb -> k. You don't get back to the same value.

Code

UFRaw line 246-294

void Temperature_to_RGB(double T, double RGB[3])
{
    int c;
    double xD, yD, X, Y, Z, max;
    // Fit for CIE Daylight illuminant
    if (T <= 4000) {
        xD = 0.27475e9 / (T * T * T) - 0.98598e6 / (T * T) + 1.17444e3 / T + 0.145986;
    } else if (T <= 7000) {
        xD = -4.6070e9 / (T * T * T) + 2.9678e6 / (T * T) + 0.09911e3 / T + 0.244063;
    } else {
        xD = -2.0064e9 / (T * T * T) + 1.9018e6 / (T * T) + 0.24748e3 / T + 0.237040;
    }
    yD = -3 * xD * xD + 2.87 * xD - 0.275;

    // Fit for Blackbody using CIE standard observer function at 2 degrees
    //xD = -1.8596e9/(T*T*T) + 1.37686e6/(T*T) + 0.360496e3/T + 0.232632;
    //yD = -2.6046*xD*xD + 2.6106*xD - 0.239156;

    // Fit for Blackbody using CIE standard observer function at 10 degrees
    //xD = -1.98883e9/(T*T*T) + 1.45155e6/(T*T) + 0.364774e3/T + 0.231136;
    //yD = -2.35563*xD*xD + 2.39688*xD - 0.196035;

    X = xD / yD;
    Y = 1;
    Z = (1 - xD - yD) / yD;
    max = 0;
    for (c = 0; c < 3; c++) {
        RGB[c] = X * XYZ_to_RGB[0][c] + Y * XYZ_to_RGB[1][c] + Z * XYZ_to_RGB[2][c];
        if (RGB[c] > max) max = RGB[c];
    }
    for (c = 0; c < 3; c++) RGB[c] = RGB[c] / max;
}

void RGB_to_Temperature(double RGB[3], double *T, double *Green)
{
    double Tmax, Tmin, testRGB[3];
    Tmin = 2000;
    Tmax = 23000;
    for (*T = (Tmax + Tmin) / 2; Tmax - Tmin > 0.1; *T = (Tmax + Tmin) / 2) {
        Temperature_to_RGB(*T, testRGB);
        if (testRGB[2] / testRGB[0] > RGB[2] / RGB[0])
            Tmax = *T;
        else
            Tmin = *T;
    }
    *Green = (testRGB[1] / testRGB[0]) / (RGB[1] / RGB[0]);
    if (*Green < 0.2) *Green = 0.2;
    if (*Green > 2.5) *Green = 2.5;
}