Convert light frequency to RGB?

Question

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

Very technical questions in terms of physics and programming +1. — whatnick, Commented Sep 24, 2009 at 15:49

squ1dd13 · Accepted Answer · 2020-07-01 11:00:48Z

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 final double Gamma = 0.80;
static private final 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;
}

There seems to be a bug in your code. If the wavelength is for example 439.5, your function returns black. The original code on the site was working with integers, I believe (I don't know pascal at all). I suggest to change Wavelength<=439 to Wavelength<440. — Hassedev, Commented Feb 25, 2013 at 15:44
You're right! Thank you for pointing this out to me :) Already corrected. — Tarc, Commented Mar 2, 2013 at 20:30
Is it expected to have repeated RFB to some frequencies? (RED): 652 - rgb(255, 0, 0) | 660 - rgb(255, 0, 0) | 692 - rgb(255, 0, 0) | 700 - rgb(255, 0, 0) | ... — Rodrigo Borba, Commented Mar 4, 2020 at 17:07

amartynov · Accepted Answer · 2016-09-12 19:47:08Z

General idea:

Use CEI color matching functions to convert wavelength to XYZ color.
Convert XYZ to RGB
Clip components to [0..1] and multiply by 255 to fit in the unsigned byte range.

Steps 1 and 2 may vary.

There are several color matching functions, available as tables or as analytic approximations (suggested by @Tarc and @Haochen Xie). Tables are best if you need a smooth preсise result.

There is no single RGB color space. Multiple transformation matrices and different kinds of gamma correction may be used.

Below is the C# code I came up with recently. It uses linear interpolation over the "CIE 1964 standard observer" table and sRGB matrix + gamma correction.

static class RgbCalculator {

    const int
         LEN_MIN = 380,
         LEN_MAX = 780,
         LEN_STEP = 5;

    static readonly double[]
        X = {
                0.000160, 0.000662, 0.002362, 0.007242, 0.019110, 0.043400, 0.084736, 0.140638, 0.204492, 0.264737,
                0.314679, 0.357719, 0.383734, 0.386726, 0.370702, 0.342957, 0.302273, 0.254085, 0.195618, 0.132349,
                0.080507, 0.041072, 0.016172, 0.005132, 0.003816, 0.015444, 0.037465, 0.071358, 0.117749, 0.172953,
                0.236491, 0.304213, 0.376772, 0.451584, 0.529826, 0.616053, 0.705224, 0.793832, 0.878655, 0.951162,
                1.014160, 1.074300, 1.118520, 1.134300, 1.123990, 1.089100, 1.030480, 0.950740, 0.856297, 0.754930,
                0.647467, 0.535110, 0.431567, 0.343690, 0.268329, 0.204300, 0.152568, 0.112210, 0.081261, 0.057930,
                0.040851, 0.028623, 0.019941, 0.013842, 0.009577, 0.006605, 0.004553, 0.003145, 0.002175, 0.001506,
                0.001045, 0.000727, 0.000508, 0.000356, 0.000251, 0.000178, 0.000126, 0.000090, 0.000065, 0.000046,
                0.000033
            },

        Y = {
                0.000017, 0.000072, 0.000253, 0.000769, 0.002004, 0.004509, 0.008756, 0.014456, 0.021391, 0.029497,
                0.038676, 0.049602, 0.062077, 0.074704, 0.089456, 0.106256, 0.128201, 0.152761, 0.185190, 0.219940,
                0.253589, 0.297665, 0.339133, 0.395379, 0.460777, 0.531360, 0.606741, 0.685660, 0.761757, 0.823330,
                0.875211, 0.923810, 0.961988, 0.982200, 0.991761, 0.999110, 0.997340, 0.982380, 0.955552, 0.915175,
                0.868934, 0.825623, 0.777405, 0.720353, 0.658341, 0.593878, 0.527963, 0.461834, 0.398057, 0.339554,
                0.283493, 0.228254, 0.179828, 0.140211, 0.107633, 0.081187, 0.060281, 0.044096, 0.031800, 0.022602,
                0.015905, 0.011130, 0.007749, 0.005375, 0.003718, 0.002565, 0.001768, 0.001222, 0.000846, 0.000586,
                0.000407, 0.000284, 0.000199, 0.000140, 0.000098, 0.000070, 0.000050, 0.000036, 0.000025, 0.000018,
                0.000013
            },

        Z = {
                0.000705, 0.002928, 0.010482, 0.032344, 0.086011, 0.197120, 0.389366, 0.656760, 0.972542, 1.282500,
                1.553480, 1.798500, 1.967280, 2.027300, 1.994800, 1.900700, 1.745370, 1.554900, 1.317560, 1.030200,
                0.772125, 0.570060, 0.415254, 0.302356, 0.218502, 0.159249, 0.112044, 0.082248, 0.060709, 0.043050,
                0.030451, 0.020584, 0.013676, 0.007918, 0.003988, 0.001091, 0.000000, 0.000000, 0.000000, 0.000000,
                0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
                0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
                0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
                0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000,
                0.000000
            };

    static readonly double[]
        MATRIX_SRGB_D65 = {
             3.2404542, -1.5371385, -0.4985314,
            -0.9692660,  1.8760108,  0.0415560,
             0.0556434, -0.2040259,  1.0572252
        };

    public static byte[] Calc(double len) {
        if(len < LEN_MIN || len > LEN_MAX)
            return new byte[3];

        len -= LEN_MIN;
        var index = (int)Math.Floor(len / LEN_STEP);
        var offset = len - LEN_STEP * index;

        var x = Interpolate(X, index, offset);
        var y = Interpolate(Y, index, offset);
        var z = Interpolate(Z, index, offset);

        var m = MATRIX_SRGB_D65;

        var r = m[0] * x + m[1] * y + m[2] * z;
        var g = m[3] * x + m[4] * y + m[5] * z;
        var b = m[6] * x + m[7] * y + m[8] * z;

        r = Clip(GammaCorrect_sRGB(r));
        g = Clip(GammaCorrect_sRGB(g));
        b = Clip(GammaCorrect_sRGB(b));

        return new[] { 
            (byte)(255 * r),
            (byte)(255 * g),
            (byte)(255 * b)
        };
    }

    static double Interpolate(double[] values, int index, double offset) {
        if(offset == 0)
            return values[index];

        var x0 = index * LEN_STEP;
        var x1 = x0 + LEN_STEP;
        var y0 = values[index];
        var y1 = values[1 + index];

        return y0 + offset * (y1 - y0) / (x1 - x0);
    }

    static double GammaCorrect_sRGB(double c) {
        if(c <= 0.0031308)
            return 12.92 * c;

        var a = 0.055;
        return (1 + a) * Math.Pow(c, 1 / 2.4) - a;
    }

    static double Clip(double c) {
        if(c < 0)
            return 0;
        if(c > 1)
            return 1;
        return c;
    }
}

Result for the 400-700 nm range:

This is really interesting to me. I have an idea to use something like this to give a normal response, but use a WXYZ response to mimic the response of tetrachromats who have a fourth cone which responds to a frequency far enough from any of the other normal three types of cones. That might let me take source images and infer the differences they see. N.B. they don't see new colors, it's that lights that blend, (sum), for example, to a particular yellow seems identical to a yellow of a particular frequency for most of us, but for them, the light wouldn't blend to that yellow at all. — phorgan1, Commented Nov 18, 2016 at 4:34
Of course, for a particular RGB color, it could have been arrived at in a lot of ways. The green of a leaf could come from the filtering out of everything but green, or the green could have been filtered out, but nano characteristics could cause blue and yellow to reflect and look identical to the green. Given an image rather than the light, is there any way that I can differentiate? — phorgan1, Commented Nov 18, 2016 at 4:36

Haochen Xie · Accepted Answer · 2016-06-25 15:05:13Z

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.

@Baddack, you're right: it's just a fancy way to make some further transformation on the calculated values. I cannot remember exactly, but I think it first applies a gamma correction, then cuts off out of range values. Maybe I should have it done in a separate method, but I wasn't actually thinking about sharing the code while writing it, and it was a toy project in which I needed this conversion. — Haochen Xie, Commented Jun 24, 2016 at 18:39
@Baddack I've dug out the project that I needed this conversion, and rewrote this part without using java 8 lambda so the code is more clear. I actually remembered incorrectly about what the transfer DoubleUnaryOperator was doing (thus the explanation in my previous comment are not correct), so please check the new code. — Haochen Xie, Commented Jun 25, 2016 at 15:09
@Baddack i'm glad that the code helps you. and if you don't mind, could you please upvote it so it may potentially help more people? — Haochen Xie, Commented Jun 27, 2016 at 2:30
@Baddack Math.pow(c, 1. / 2.4) = c^(1/2.4), i.e. raise c to the power of 1/2.4; 1. is just 1 but the type will be double instead of int — Haochen Xie, Commented Jun 29, 2016 at 21:36
@Ruslan since this algorithm is a analytical fit of the CIE standard observer (which could be considered to be the "precise" model), there are errors. But from the paper, if you look at the Figure 1 on page 7 (compare (d) with (f)), this method provides quite a close approximation. Especially if you look at (f), you could see that there is also a bluish line even in the standard model. Also, color perception of pure light source varies personally, so this level of error is probably negligible. — Haochen Xie, Commented Sep 8, 2016 at 12:56

user151323user151323 · Accepted Answer · 2009-09-24 15:45:03Z

7

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

answered Sep 24, 2009 at 15:45

user151323

1

Just reading the same page "There is no unique one-to-one mapping between wavelength and RGB values" - so well you are stuck with a lookup table and heuristics. As a first cut I would look at HSV to RGB conversions since the "Hue" ranges from blue to red. With possibly a slight shift since in RGB domain red+blue = violet and violet has the shortest visible wavelength.
– whatnick
Commented Sep 24, 2009 at 15:49
3

isn't it practically the same? freq = c / wavelength
– Mauricio Scheffer
Commented Sep 24, 2009 at 15:56
1

@Mauricio Scheffer Yes it is EXACTLY the same.
– Joseph Gordon
Commented Jul 1, 2010 at 19:55
this Bruton's algorithm is rather aesthetic than realistic
– mykhal
Commented Sep 15, 2010 at 19:01
10

@ Joseph Gordon - Strongly disagree. Consider a greenish ray 400nm emitted in air hit the water surface and then propagates in water. Refraction coefficient of water is, say, 1.33, so a ray wavelength in water is now 300nm, which obviously doesn't change it's color. The matter that "colorizes" the rays is frequency, not wavelength. In the same substance (vacuum, air, water) frequencies (colors) map to same wavelengths. In different media - not.
– mbaitoff
Commented Jan 16, 2011 at 7:44

| Show 1 more comment

whatnick · Accepted Answer · 2009-09-24 15:53:10Z

3

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.

answered Sep 24, 2009 at 15:53

whatnick

5,4603 gold badges20 silver badges35 bronze badges

1

Your link is dead.
– Ruslan
Commented Sep 8, 2016 at 7:08

Add a comment |

Siddharth Rout · Accepted Answer · 2012-06-03 23:32:43Z

3

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.

edited Jun 3, 2012 at 23:32

Siddharth Rout

148k18 gold badges208 silver badges252 bronze badges

answered May 13, 2010 at 23:58

David Elm

311 bronze badge

Add a comment |

Shital Shah · Accepted Answer · 2018-08-23 09:49:01Z

Method 1

This is bit cleaned up and tested C++11 version of @haochen-xie. I also added a function that converts value 0 to 1 to a wavelength in visible spectrum that is usable with this method. You can just put below in one header file and use it without any dependencies. This version will be maintained here.

#ifndef common_utils_OnlineStats_hpp
#define common_utils_OnlineStats_hpp

namespace common_utils {

class ColorUtils {
public:

    static void valToRGB(double val0To1, unsigned char& r, unsigned char& g, unsigned char& b)
    {
        //actual visible spectrum is 375 to 725 but outside of 400-700 things become too dark
        wavelengthToRGB(val0To1 * (700 - 400) + 400, r, g, b);
    }

    /**
    * 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
    */
    static void wavelengthToRGB(double wavelength, unsigned char& r, unsigned char& g, unsigned char& b) {
        double x, y, z;
        cie1931WavelengthToXYZFit(wavelength, x, y, z);
        double dr, dg, db;
        srgbXYZ2RGB(x, y, z, dr, dg, db);

        r = static_cast<unsigned char>(static_cast<int>(dr * 0xFF) & 0xFF);
        g = static_cast<unsigned char>(static_cast<int>(dg * 0xFF) & 0xFF);
        b = static_cast<unsigned char>(static_cast<int>(db * 0xFF) & 0xFF);
    }

    /**
    * 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]
    */
    static void srgbXYZ2RGB(double x, double y, double z, double& r, double& g, double& b) {
        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;

        r = srgbXYZ2RGBPostprocess(rl);
        g = srgbXYZ2RGBPostprocess(gl);
        b = srgbXYZ2RGBPostprocess(bl);
    }

    /**
    * helper function for {@link #srgbXYZ2RGB(double[])}
    */
    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 * std::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]
    */
    static void cie1931WavelengthToXYZFit(double wavelength, double& x, double& y, double& z) {
        double wave = wavelength;

        {
            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 * std::exp(-0.5 * t1 * t1)
                + 1.056 * std::exp(-0.5 * t2 * t2)
                - 0.065 * std::exp(-0.5 * t3 * t3);
        }

        {
            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 * std::exp(-0.5 * t1 * t1)
                + 0.286 * std::exp(-0.5 * t2 * t2);
        }

        {
            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 * std::exp(-0.5 * t1 * t1)
                + 0.681 * std::exp(-0.5 * t2 * t2);
        }
    }

};

} //namespace

#endif

The plot of colors from 375nm to 725nm looks like below:

One issue with this method is the fact that it works only between 400-700nm and outside of that it sharply falls down to black. Another issue is narrower blue.

For comparison, below is the colors from Vision FAQ at maxmax.com:

I used this to visualize depth map where each pixel represents depth value in meters and this looks like below:

Method 2

This is implemented as part of bitmap_image single file header-only library by Aeash Partow:

inline rgb_t convert_wave_length_nm_to_rgb(const double wave_length_nm)
{
   // Credits: Dan Bruton http://www.physics.sfasu.edu/astro/color.html
   double red   = 0.0;
   double green = 0.0;
   double blue  = 0.0;

   if ((380.0 <= wave_length_nm) && (wave_length_nm <= 439.0))
   {
      red   = -(wave_length_nm - 440.0) / (440.0 - 380.0);
      green = 0.0;
      blue  = 1.0;
   }
   else if ((440.0 <= wave_length_nm) && (wave_length_nm <= 489.0))
   {
      red   = 0.0;
      green = (wave_length_nm - 440.0) / (490.0 - 440.0);
      blue  = 1.0;
   }
   else if ((490.0 <= wave_length_nm) && (wave_length_nm <= 509.0))
   {
      red   = 0.0;
      green = 1.0;
      blue  = -(wave_length_nm - 510.0) / (510.0 - 490.0);
   }
   else if ((510.0 <= wave_length_nm) && (wave_length_nm <= 579.0))
   {
      red   = (wave_length_nm - 510.0) / (580.0 - 510.0);
      green = 1.0;
      blue  = 0.0;
   }
   else if ((580.0 <= wave_length_nm) && (wave_length_nm <= 644.0))
   {
      red   = 1.0;
      green = -(wave_length_nm - 645.0) / (645.0 - 580.0);
      blue  = 0.0;
   }
   else if ((645.0 <= wave_length_nm) && (wave_length_nm <= 780.0))
   {
      red   = 1.0;
      green = 0.0;
      blue  = 0.0;
   }

   double factor = 0.0;

   if ((380.0 <= wave_length_nm) && (wave_length_nm <= 419.0))
      factor = 0.3 + 0.7 * (wave_length_nm - 380.0) / (420.0 - 380.0);
   else if ((420.0 <= wave_length_nm) && (wave_length_nm <= 700.0))
      factor = 1.0;
   else if ((701.0 <= wave_length_nm) && (wave_length_nm <= 780.0))
      factor = 0.3 + 0.7 * (780.0 - wave_length_nm) / (780.0 - 700.0);
   else
      factor = 0.0;

   rgb_t result;

   const double gamma         =   0.8;
   const double intensity_max = 255.0;

   #define round(d) std::floor(d + 0.5)

   result.red   = static_cast<unsigned char>((red   == 0.0) ? red   : round(intensity_max * std::pow(red   * factor, gamma)));
   result.green = static_cast<unsigned char>((green == 0.0) ? green : round(intensity_max * std::pow(green * factor, gamma)));
   result.blue  = static_cast<unsigned char>((blue  == 0.0) ? blue  : round(intensity_max * std::pow(blue  * factor, gamma)));

   #undef round

   return result;
}

Plot of wavelength from 375-725nm looks like below:

So this is more usable in 400-725nm. When I visualize same depth map as in method 1, I get below. There is an obvious issue of those black lines which I think indicates minor bug in this code which I haven't looked more deeply. Also violets are bit narrower in this method which causes less contrast for far away objects.

Community · Accepted Answer · 2020-06-20 09:12:55Z

Project the wavelength's CIExy towards the D65 white onto the sRGB gamut

#!/usr/bin/ghci
ångstrømsfromTHz terahertz = 2997924.58 / terahertz
tristimulusXYZfromÅngstrøms å=map(sum.map(stimulus))[
 [[1056,5998,379,310],[362,4420,160,267],[-65,5011,204,262]],
 [[821,5688,469,405],[286,5309,163,311]],
 [[1217,4370,118,360],[681,4590,260,138]]]
 where stimulus[ω,μ,ς,σ]=ω/1000*exp(-((å-μ)/if å<μ then ς else σ)^2/2)

standardRGBfromTristimulusXYZ xyz=
 map(gamma.sum.zipWith(*)(gamutConfine xyz))[
 [3.2406,-1.5372,-0.4986],[-0.9689,1.8758,0.0415],[0.0557,-0.2040,1.057]]
gamma u=if u<=0.0031308 then 12.92*u else (u**(5/12)*211-11)/200
[red,green,blue,black]=
 [[0.64,0.33],[0.3,0.6],[0.15,0.06],[0.3127,0.3290,0]]
ciexyYfromXYZ xyz=if xyz!!1==0 then black else map(/sum xyz)xyz
cieXYZfromxyY[x,y,l]=if y==0 then black else[x*l/y,l,(1-x-y)*l/y]
gamutConfine xyz=last$xyz:[cieXYZfromxyY[x0+t*(x1-x0),y0+t*(y1-y0),xyz!!1]|
 x0:y0:_<-[black],x1:y1:_<-[ciexyYfromXYZ xyz],i<-[0..2],
 [x2,y2]:[x3,y3]:_<-[drop i[red,green,blue,red]],
 det<-[(x0-x1)*(y2-y3)-(y0-y1)*(x2-x3)],
 t <-[((x0-x2)*(y2-y3)-(y0-y2)*(x2-x3))/det|det/=0],0<=t,t<=1]

sRGBfromÅ=standardRGBfromTristimulusXYZ.tristimulusXYZfromÅngstrøms
x s rgb=concat["\ESC[48;2;",
               intercalate";"$map(show.(17*).round.(15*).max 0.min 1)rgb,
               "m",s,"\ESC[49m"]
spectrum=concatMap(x" ".sRGBfromÅ)$takeWhile(<7000)$iterate(+60)4000
main=putStrLn spectrum

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Project the wavelength's CIExy towards the D65 white onto the sRGB gamut

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Project the wavelength's CIExy towards the D65 white onto the sRGB gamut

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