It’s hard to explain what exactly I need. Look at this picture. It looks at a color and gives the intensity of each wavelength. I need the opposite where I give the intensity of the wavelength (can be either by providing a function or entering discrete data) and it will give me the color that is produced.
Barring that, is there a way mathematically that if I know the equation for intensity I for each wavelength w that I can calculate how it would appear i.e. monocromatic light w[sub]m[/sub] at intensity I[sub]m[/sub]. And if so, is there an app that if I give w[sub]m[/sub] it will show me what color it is?
The visual display is important because an important part of what I’m looking for is not only the color as a theoretical function of wavelength but also how that color is perceived through our eyes RGB (or for some women RGBUV) receptors. IIRC those are not exactly the same if intensity of the wavelengths is variable.
If you want something that can take an arbitrary ‘graph’ of intensity v wavelength and show you what it looks like, that would be somewhat complicated by the fact that the display device probably isn’t capable of emitting light at every arbitrary wavelength.
Most computer color monitors, as you probably know, simulate many different colors by emitting at three different wavelengths that more-or-less match the capacities of the three cones in the human eye. You can in theory use this to approximate how people would perceive more complex colors, but I think that there are differences in individual color perception which would throw that off.
Thinking about it, probably the best way to approximate would be to get an RGB triplet by taking the sum of the intensities under the range that the red cones can perceive, multiplied by how strongly they perceive that wavelength, and then show that RGB triplet. I don’t know offhand of any tool that does this though.
The mere mixture of wavelengths of various intensities is not enough to specify colors. The actual appearance of a color can vary a great deal depending on what other colors are close to it in the overall field of view. For instance, no mixture of wavelengths will give yo a brown. There is no such thing as beam of brown light, and you can’t experience brown filling your visual field. The nearest you can get is a dull orange or yellow. Nevertheless, brown is one of the commonest colors in ordinary visual experience, and is produced by the contrast between differently colored areas in the visual field, and an area of color that, if it completely filled the field, would appear orange or yellow. See this image for an illustration. Tiles A, B, and C are all, in fact causing your screen to emit the same mixture of wavelengths, at the same intensity, but A and C clearly look brown, whereas C is clearly yellow. This page (from which that image is taken) gives several more color illusions of similar type.
In real life, of course, as opposed to circumstances contrived in the laboratory, we never experience one color entirely filling the visual field, and this sort of contrast effect does not only apply to brown. That is just a particularly striking case of a common color that does not exist at all absent the contrast with other colors. In practice, however, the appearance of all colors is strongly affected by the other colors near them within the visual field, and patches of surfaces emitting or reflecting exactly the same mixture of wavelengths can look to be quite different colors depending on what other colors are close to it.
yes but when we have cameras and displays, we have a more objective definition of colours.
The analog of that in biological terms is the retina response… like this
Two spectrum are the the colour if the spectrums produce the same values of S,M and L response. You might consider blue as a more simple case to look at first.
Then consider how the M and L overlap complicates ? or makes more simple ? the situation.
I think that might be what I am questioning. When we look at light from a star, it has a color. That color can be defined 2 ways. One way is by the wavelength of the peak using Wien’s Displacement so the Sun at 5800K has a peak at 550 nm making it a yellow star. The other end is the 3 (or 4 in tetrachromats) sets of cones that combine the individual responses and is interpreted by the brain as a color which in the the case of sunlight is white and not yellow.
What I’m interested in is the middle ground meaning can “color” (whatever that means) of a spectrum where the various wavelengths have different intensities be an average if the wavelengths/intensities. I know that this “color” may not be the same “color” we perceive because of the way the cones process but that’s not what I’m worried about (yet).
Let’s go back to the Planck’s Law curve of the Sun through the visible spectrum. Suppose the “average” of the wavelengths weighted by the intensities is 580 nm. Does saying the “color” of the Sun is 580 nm (yellowish-orange) have any theoretical meaning?
Equations here (click math). You’ll want to do Spectrum to XYZ, then XYZ to RGB if you want to display it on a monitor, or one of the other color spaces. As stated/alluded above, RGB has a restricted range compared to what we can see (the triangle is the range for one implementation of RGB).
The functions they mention can be found here. You might have to scale the range of your sample with the range and step sizes they give.
ETA: I’m pretty sure the 4th cone in tetrachromacy is a skewed copy of a L or M cone. An the S cone isn’t X linked anyway so it would effect males and females equally. And calling it UV would only be a shorthand as we cannot see far into UV because our lens absorbs that light before it even reaches our retina.
This bit has you screwed. The equations linked to above are based upon a normalised human perception. Roughly our eyes can perceive differences to a limit of about 3nm difference in wavlength, and if you create a histogram from the spectrum binned at 3nm, and then multiply each bin by a given magic constant for each bin, then integrate across the bins you get the three values that describe the human colour perception. But those magic constants are exactly what you are worrying about being different between different subjects.
You could create a device to create a light mix, but you would need to create a continuous spectrum, modulate the light in those 3nm intervals, and remix the light. Doable, and such devices probably exist (but are probably bespoke, and not off the shelf items.)
There is a lot more to color science than either wavelengths or cone responses. Most of what determines the colors we experience is in the brain and is very far from fully understood. Some colors we can see do not correspond to any mixture of wavelengths. Sometimes the same mixture of wavelengths will look like very different colors in different circumstances. I am not exactly sure what you are trying to achieve, however. Maybe a machine to do whatever it is you actually want is possible. In principle, at least, it should be possible to build a machine capable of outputting a light beam of any desired mixture of wavelengths. (Maybe it is whatever thelurkinghorror is referring to.)
I am not quite sure why you are so concerned with tetrachromats. It is far from certain that functional human tetrachromats exist at all. If they do, all the indications are that their discriminatory ability is not all that much superior to normals (the response curve of the fourth cone type is not going to peak very far away from the normal peak), and, anyway, they are going to be pretty rare individuals. For most practical and theoretical purposes, the possibility that they exist can be ignored. You seem to be obsessing about a triviality without having any serious grasp of the much more serious issues (neurological, psychological, and even philosophical) that make the relationship between wavelength mixtures and actual experienced colors so very complex.
No, you are mistaken. There is no objective definition of colors, not one that does not badly distort the actual empirical reality of the situation (or, at any rate, if such a definition exists in principle, we are nowhere near knowing what it might be).
