I need an algorithm or function to map each wavelength of visible range of spectrum to its equivalent RGB values.
Is there any structural relation between the RGB System and wavelength of a light?
like this image:
(source: kms at www1.appstate.edu)
sorry if this was irrelevant :-]
First you consult a CIE 1964 Supplementary Standard Colorimetric Observer chart (archive)
and look up the CIE color matching function values for the wavelength you want.
For example, i want to get the color of 455 nm light:
For our desired wavelength:
| nm | CIE color matching functions | Chromacity coordinates |
| nm | X | Y | Z | x | y | z |
|-----|----------|----------|---------|---------|---------|---------|
| 455 | 0.342957 | 0.106256 | 1.90070 | 0.14594 | 0.04522 | 0.80884 |
Note: The chromacity coordinates are simply calculated from the CIE color matching functions:
x = X / (X+Y+Z)
y = Y / (X+Y+Z)
z = Z / (Z+Y+Z)
Given that:
X+Y+Z = 0.342257+0.106256+1.90070 = 2.349913
we calculate:
x = 0.342257 / 2.349913 = 0.145945
y = 0.106256 / 2.349913 = 0.045217
z = 1.900700 / 2.349913 = 0.808838
You have your 455 nm light specified using two different color spaces:
We can also add a third color space: xyY
x = x = 0.145945
y = y = 0.045217
Y = y = 0.045217
We now have the 455 nm light specified in 3 different color spaces:
So we've converted a wavelength of pure monochromatic emitted light into a XYZ color. Now we want to convert that to RGB.
XYZ, xyz, and xyY are absolute color spaces that describe colors using absolute physics.
Meanwhile, every practical color spaces that people use:
depends some whitepoint. The colors are then described as being relative to that whitepoint.
For example,
But there is no such color as white. How do you define white? The color of sunlight?
Some people use the white of their (horribly orange) incandescent bulbs to mean white. Some people use the color of their florescent lights. There is no absolute physical definition of white - white is in our brains.
We have to pick a white. (Really you have to pick a white.) And there are plenty of whites to choose from:
(FL8)I will pick a white for you. The same white that sRGB uses:
D65 (which has a color close to 6504K, but not quite because of the Earth's atmosphere), has a color of:
With that, you can convert your XYZ into Lab (or Luv) - a color-space equally capable of expressing all theoretical colors. And now we have a 4th color space representation of our 445 nm monochromatic emission of light:
Lab (and Luv) are color spaces that are relative to some white-point. Even though you were forced to pick an arbitrary white-point, you can still represent every possible color.
RGB is not like that. With RGB:
If you specify an RGB color of (255, 0, 0), you are saying you want "just red". But there is no definition of red. There is no such thing as "red", "green", or "blue". The rainbow is continuous, and doesn't come with an arrow saying:
This is red
And again this means we have to pick three pick three primary colors. You have to pick your three primary colors to say what "red", "green", and "blue" are. And again you have many different defintions of Red,Green,Blue to choose from:
I'll pick for you. I'll pick these three colors:
Those were also the primaries chosen for by an international committee in 1996.
They created a standard that said everyone should use:
And they called that standard sRGB.
Now that we have chosen our
we can now convert you XYZ color into RGB:
Unfortunately there are some problems with that RGB value:
So we have to round:
And now we have the closest approximation sRGB of wavelength 455 nm of light:
I'm not a programmer. I'm not a physician. I'm just a musician who has two eyes (as any human being has).
So... I know the electromagnetic waves have a logarythm scale pattern into the Radio and TV range. Why it should be differente in the visible light range?
Inside the Radio and TV world we use a simple equation: We divide a given range between two frecuencies into a given number of parts according to the ratio between the extreme frecuencies.
Let's say: If our range starts in 100 MHZ and ends in 200 MHZ, we have a ratio of 2 (200 is equal to 100 multiplied by 2).
So, if we have to divide that range in 10 equal parts, we have to use this equation:
The first frecuency (100 MHZ) multiplied by the 10th root of 2.
That new value multiplied by the 10th root of 2.
And so and on.
Why we use the 10th root of 2? Simple: Remember it is not a linear scale, it is a logarythm scale (exactly the same of musical notes).
So, based in that equation, as we know the visible light spectrum is between 780 and 380 nanometers (aproximately 384.02 THZ and 789.26 THZ; both values very aproximately, because it is a variable value according to the individual optical capability), we just to know the ratio between those frecuencies:
789.26/384.02=2,055
Also, we know that the RGB aproximately equivalent to that extreme frecuencies are:
384.02 THZ = 95,0,0 (hx=5F0000)
788.92 THZ = 97,0,97 (hx=610061)
Also, we know all the possible RGB combinations between that points are = 1595
So, with all those values we have a simple equation:
RGB = 95, 0, 0 = 384.02 THZ
RGB = 96, 0, 0 = 384.02 THZ multiplied by (1595th root of 2,055) = 384,19 THZ
RGB = 97, 0, 0 = 384,19 THZ multiplied by (1595th root of 2,055) = 384.37 THZ
And so and on
Simple scale.
Just my humble opinion.
A runnable example based on a popular answer:
function spectrogram() {
var svgns = 'http://www.w3.org/2000/svg';
var svg = document.createElementNS(svgns, 'svg');
var defs = document.createElementNS(svgns, 'defs');
var gradient = document.createElementNS(svgns, 'linearGradient');
var rect = document.createElementNS(svgns, 'rect');
var stops = spectral_gradient( 400, 700, 3 );
for( var i = 0, length = stops.length; i < length; i++ ) {
var stop = document.createElementNS(svgns, 'stop');
stop.setAttribute('offset', stops[i].offset);
stop.setAttribute('stop-color', stops[i].color);
gradient.appendChild(stop);
}
// Apply the <lineargradient> to <defs>
gradient.id = 'Gradient';
gradient.setAttribute('x1', '0');
gradient.setAttribute('x2', '1');
gradient.setAttribute('y1', '0');
gradient.setAttribute('y2', '0');
defs.appendChild(gradient);
// Setup the <rect> element.
rect.setAttribute('fill', 'url(#Gradient)');
rect.setAttribute('width', '100%');
rect.setAttribute('height', '100%');
// Assign an id, classname, width and height
svg.setAttribute('width', '100%');
svg.setAttribute('height', '100%')
svg.setAttribute('version', '1.1');
svg.setAttribute('xmlns', svgns);
// Add the <defs> and <rect> elements to <svg>
svg.appendChild(defs);
svg.appendChild(rect);
// Add the <svg> element to <body>
document.body.appendChild(svg);
}
function spectral_gradient( wl1, wl2, steps ) {
var stops = [];
var delta = Math.abs( wl2 - wl1 );
for( var wl = wl1; wl <= wl2; wl += steps ) {
var offset = Math.round( (1 - Math.abs( wl2 - wl ) / delta) * 100 );
stops.push({
"color": wavelength2hex( wl ),
"offset": offset + "%"
});
}
return stops;
}
function wavelength2hex( l ) {
var wl = wavelength2rgb( l );
var rgb = {
"r": Math.round( wl.r * 255 ),
"g": Math.round( wl.g * 255 ),
"b": Math.round( wl.b * 255 )
};
return rgb2hex( rgb.r, rgb.g, rgb.b );
}
function wavelength2rgb( l ) {
var t;
var r = 0.0;
var g = 0.0;
var b = 0.0;
if ((l >= 400.0) && (l < 410.0)) {
t = (l - 400.0) / (410.0 - 400.0);
r = +(0.33 * t) - (0.20 * t * t);
} else if ((l >= 410.0) && (l < 475.0)) {
t = (l - 410.0) / (475.0 - 410.0);
r = 0.14 - (0.13 * t * t);
} else if ((l >= 545.0) && (l < 595.0)) {
t = (l - 545.0) / (595.0 - 545.0);
r = +(1.98 * t) - (t * t);
} else if ((l >= 595.0) && (l < 650.0)) {
t = (l - 595.0) / (650.0 - 595.0);
r = 0.98 + (0.06 * t) - (0.40 * t * t);
} else if ((l >= 650.0) && (l < 700.0)) {
t = (l - 650.0) / (700.0 - 650.0);
r = 0.65 - (0.84 * t) + (0.20 * t * t);
}
if ((l >= 415.0) && (l < 475.0)) {
t = (l - 415.0) / (475.0 - 415.0);
g = +(0.80 * t * t);
} else if ((l >= 475.0) && (l < 590.0)) {
t = (l - 475.0) / (590.0 - 475.0);
g = 0.8 + (0.76 * t) - (0.80 * t * t);
} else if ((l >= 585.0) && (l < 639.0)) {
t = (l - 585.0) / (639.0 - 585.0);
g = 0.84 - (0.84 * t);
}
if ((l >= 400.0) && (l < 475.0)) {
t = (l - 400.0) / (475.0 - 400.0);
b = +(2.20 * t) - (1.50 * t * t);
} else if ((l >= 475.0) && (l < 560.0)) {
t = (l - 475.0) / (560.0 - 475.0);
b = 0.7 - (t) + (0.30 * t * t);
}
return {"r": r, "g": g, "b": b};
}
function rgb2hex( r, g, b ) {
return "#" + hex( r ) + hex( g ) + hex( b );
}
function hex( v ) {
return v.toString( 16 ).padStart( 2, "0" );
}<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<script src="js/spectrum.js"></script>
</head>
<body onload="spectrogram();">
</body>
</html>