Convert light frequency to RGB?

Question

Does anyone know of any formula for converting a light frequency to an RGB value?

Answer 1

I guess I might as well follow up my comment with a formal answer. The best option is to use the HSV colour space - though the hue represents the wavelength it is not a one-to-one comparison.

Answer 2

Here's a detailed explanation of the entire conversion process: http://www.fourmilab.ch/documents/specrend/. Source code included!

Answer 3

For lazy guys (like me), here is an implementation in java of the code found in @user151323 's answer (that is, just a simple translation from pascal code found in Spectra Lab Report):

static private double Gamma = 0.80;
static private double IntensityMax = 255;

/** Taken from Earl F. Glynn's web page:
* <a href="http://www.efg2.com/Lab/ScienceAndEngineering/Spectra.htm">Spectra Lab Report</a>
* */
public static int[] waveLengthToRGB(double Wavelength){
    double factor;
    double Red,Green,Blue;

    if((Wavelength >= 380) && (Wavelength<440)){
        Red = -(Wavelength - 440) / (440 - 380);
        Green = 0.0;
        Blue = 1.0;
    }else if((Wavelength >= 440) && (Wavelength<490)){
        Red = 0.0;
        Green = (Wavelength - 440) / (490 - 440);
        Blue = 1.0;
    }else if((Wavelength >= 490) && (Wavelength<510)){
        Red = 0.0;
        Green = 1.0;
        Blue = -(Wavelength - 510) / (510 - 490);
    }else if((Wavelength >= 510) && (Wavelength<580)){
        Red = (Wavelength - 510) / (580 - 510);
        Green = 1.0;
        Blue = 0.0;
    }else if((Wavelength >= 580) && (Wavelength<645)){
        Red = 1.0;
        Green = -(Wavelength - 645) / (645 - 580);
        Blue = 0.0;
    }else if((Wavelength >= 645) && (Wavelength<781)){
        Red = 1.0;
        Green = 0.0;
        Blue = 0.0;
    }else{
        Red = 0.0;
        Green = 0.0;
        Blue = 0.0;
    };

    // Let the intensity fall off near the vision limits

    if((Wavelength >= 380) && (Wavelength<420)){
        factor = 0.3 + 0.7*(Wavelength - 380) / (420 - 380);
    }else if((Wavelength >= 420) && (Wavelength<701)){
        factor = 1.0;
    }else if((Wavelength >= 701) && (Wavelength<781)){
        factor = 0.3 + 0.7*(780 - Wavelength) / (780 - 700);
    }else{
        factor = 0.0;
    };


    int[] rgb = new int[3];

    // Don't want 0^x = 1 for x <> 0
    rgb[0] = Red==0.0 ? 0 : (int) Math.round(IntensityMax * Math.pow(Red * factor, Gamma));
    rgb[1] = Green==0.0 ? 0 : (int) Math.round(IntensityMax * Math.pow(Green * factor, Gamma));
    rgb[2] = Blue==0.0 ? 0 : (int) Math.round(IntensityMax * Math.pow(Blue * factor, Gamma));

    return rgb;
}

By the way, this works fine for me.

Answer 4

I did a linear fit of known hue values and frequencies (dropping out red and violet because they extend so far in frequency values that they skew things a bit) and I got a rough conversion equation.

It goes like
frequency (in THz)=474+(3/4)(Hue Angle (in degrees))

I've tried to look around and see if anyone has come up with this equation, but I haven't found anything as of May 2010.

Answer 5

You're talking about converting from wave length to an RGB value.

Look here, will probably answer your question. Thy have an utility for doing this with the source code as well as some explanation.

WaveLengthToRGB

Answer 6

Although this is an old question and already gets a handful good answers, when I tried to implement such conversion functionality in my application I was not satisfied with the algorithms already listed here and did my own research, which gave me some good result. So I'm going to post a new answer.

After some researchs I came across this paper, Simple Analytic Approximations to the CIE XYZ Color Matching Functions, and tried to adopt the introduced multi-lobe piecewise Gaussian fit algorithm in my application. The paper only described the functions to convert a wavelength to the corresponding XYZ values, so I implemented a function to convert XYZ to RGB in the sRGB color space and combined them. The result is fantastic and worth sharing:

/**
 * Convert a wavelength in the visible light spectrum to a RGB color value that is suitable to be displayed on a
 * monitor
 *
 * @param wavelength wavelength in nm
 * @return RGB color encoded in int. each color is represented with 8 bits and has a layout of
 * 00000000RRRRRRRRGGGGGGGGBBBBBBBB where MSB is at the leftmost
 */
public static int wavelengthToRGB(double wavelength){
    double[] xyz = cie1931WavelengthToXYZFit(wavelength);
    double[] rgb = srgbXYZ2RGB(xyz);

    int c = 0;
    c |= (((int) (rgb[0] * 0xFF)) & 0xFF) << 16;
    c |= (((int) (rgb[1] * 0xFF)) & 0xFF) << 8;
    c |= (((int) (rgb[2] * 0xFF)) & 0xFF) << 0;

    return c;
}

/**
 * Convert XYZ to RGB in the sRGB color space
 * <p>
 * The conversion matrix and color component transfer function is taken from http://www.color.org/srgb.pdf, which
 * follows the International Electrotechnical Commission standard IEC 61966-2-1 "Multimedia systems and equipment -
 * Colour measurement and management - Part 2-1: Colour management - Default RGB colour space - sRGB"
 *
 * @param xyz XYZ values in a double array in the order of X, Y, Z. each value in the range of [0.0, 1.0]
 * @return RGB values in a double array, in the order of R, G, B. each value in the range of [0.0, 1.0]
 */
public static double[] srgbXYZ2RGB(double[] xyz) {
    double x = xyz[0];
    double y = xyz[1];
    double z = xyz[2];

    double rl =  3.2406255 * x + -1.537208  * y + -0.4986286 * z;
    double gl = -0.9689307 * x +  1.8757561 * y +  0.0415175 * z;
    double bl =  0.0557101 * x + -0.2040211 * y +  1.0569959 * z;

    return new double[] {
            srgbXYZ2RGBPostprocess(rl),
            srgbXYZ2RGBPostprocess(gl),
            srgbXYZ2RGBPostprocess(bl)
    };
}

/**
 * helper function for {@link #srgbXYZ2RGB(double[])}
 */
private static double srgbXYZ2RGBPostprocess(double c) {
    // clip if c is out of range
    c = c > 1 ? 1 : (c < 0 ? 0 : c);

    // apply the color component transfer function
    c = c <= 0.0031308 ? c * 12.92 : 1.055 * Math.pow(c, 1. / 2.4) - 0.055;

    return c;
}

/**
 * A multi-lobe, piecewise Gaussian fit of CIE 1931 XYZ Color Matching Functions by Wyman el al. from Nvidia. The
 * code here is adopted from the Listing 1 of the paper authored by Wyman et al.
 * <p>
 * Reference: Chris Wyman, Peter-Pike Sloan, and Peter Shirley, Simple Analytic Approximations to the CIE XYZ Color
 * Matching Functions, Journal of Computer Graphics Techniques (JCGT), vol. 2, no. 2, 1-11, 2013.
 *
 * @param wavelength wavelength in nm
 * @return XYZ in a double array in the order of X, Y, Z. each value in the range of [0.0, 1.0]
 */
public static double[] cie1931WavelengthToXYZFit(double wavelength) {
    double wave = wavelength;

    double x;
    {
        double t1 = (wave - 442.0) * ((wave < 442.0) ? 0.0624 : 0.0374);
        double t2 = (wave - 599.8) * ((wave < 599.8) ? 0.0264 : 0.0323);
        double t3 = (wave - 501.1) * ((wave < 501.1) ? 0.0490 : 0.0382);

        x =   0.362 * Math.exp(-0.5 * t1 * t1)
            + 1.056 * Math.exp(-0.5 * t2 * t2)
            - 0.065 * Math.exp(-0.5 * t3 * t3);
    }

    double y;
    {
        double t1 = (wave - 568.8) * ((wave < 568.8) ? 0.0213 : 0.0247);
        double t2 = (wave - 530.9) * ((wave < 530.9) ? 0.0613 : 0.0322);

        y =   0.821 * Math.exp(-0.5 * t1 * t1)
            + 0.286 * Math.exp(-0.5 * t2 * t2);
    }

    double z;
    {
        double t1 = (wave - 437.0) * ((wave < 437.0) ? 0.0845 : 0.0278);
        double t2 = (wave - 459.0) * ((wave < 459.0) ? 0.0385 : 0.0725);

        z =   1.217 * Math.exp(-0.5 * t1 * t1)
            + 0.681 * Math.exp(-0.5 * t2 * t2);
    }

    return new double[] { x, y, z };
}

my code is written in Java 8, but it shouldn't be hard to port it to lower versions of Java and other languages.