On Mixing Colors of Light

[DaveC426913]

I'm actually looking for somewhat high precision here, since it seems to be available. It does appear from the CIE chart, and its nearly straight line border that we should be able to generate what appears as an almost very precise yellow at 580-590 nm to the eye from wavelengths of green at 550 nm and red at 650 nm in the right combination. I would agree that everyone won't see precisely the same thing, but in this case it should be pretty close.

Pretty close to what?
There is no such thing as "The One True Yellow".

Heck, there's no such thing as "One True Red" or "One True Green"; how could there be a mixture that's true?

The very nature of colour is that occurs only in the mind of the observer. Each observer.

 

[DaveC426913]

I'm actually looking for somewhat high precision here, since it seems to be available. It does appear from the CIE chart, and its nearly straight line border that we should be able to generate what appears as an almost very precise yellow at 580-590 nm to the eye from wavelengths of green at 550 nm and red at 650 nm in the right combination. I would agree that everyone won't see precisely the same thing, but in this case it should be pretty close.

Here's your 580 and 590:

Photoshop thinks 580 is 98% yellow and 29% magenta, while 590 is 60% magenta.

 

[Charles Link]

Pretty close to what?

From what I have in my OP=to actually make a live demo instead of just a Gedanken experiment. From what the CIE chart has with 580-590 nm being on the almost straight like connecting 550 nm and 650 nm. To follow what I am referring to here, you would need to understand the CIE chart in depth=perhaps you already do, but it is something I only figured out in the last day or two=(see also my posts 23 and 24). The primary colors (edit: actually the amount of stimulation of each of the 3 color cones=I think this is now a more accurate description) are made as vectors in an XYZ space with the length being proportional to the intensity. Meanwhile the entire visible spectrum lies on the outside border of the color coordinate curve, which is on the plane $x+y+z=1$ of this space. Any visible light source will have a vector that passes through the interior of the CIE color coordinate curve. Individual sources are all treated as vectors, and the laws of vector addition apply to determine the result. Meanwhile where the resultant vector passes through the plane $x+y+z=1$ determines its color coordinates. Using this, the pure yellow of 580-590 nm (on the border of the CIE curve) is the vector sum of the right combination of green at 550 nm and red at 650 nm, (both also on the border), since the 580-590 nm lies almost on the straight line connecting the 550 nm to the 650 nm.

 

[DaveC426913]

From what I have in my OP=to actually make a live demo instead of just a Gedanken experiment. From what the CIE chart has with 580-590 nm being on the almost straight like connecting 550 nm and 650 nm. To follow what I am referring to here, you would need to understand the CIE chart in depth=perhaps you already do, but it is something I only figured out in the last day or two=(see also my posts 23 and 24). The primary colors are made as vectors in an XYZ space with the length being proportional to the intensity. Meanwhile the entire visible spectrum lies on the outside border of the color coordinate curve, which is on the plane $x+y+z=1$ of this space. Any visible light source will have a vector that passes through the interior of the CIE color coordinate curve. Individual sources are all treated as vectors, and the laws of vector addition apply to determine the result. Meanwhile where the resultant vector passes through the plane $x+y+z=1$ determines its color coordinates. Using this, the pure yellow of 580-590 nm (on the border of the CIE curve) is the vector sum of the right combination of green at 550 nm and red at 650 nm, (both also on the border), since the 580-590 nm lies almost on the straight line connecting the 550 nm to the 650 nm.

You're confusing the map with the territory, and doing your math on the map instead.
The CIE chart is just a map; it does not define the territory; it can only attempt to mimic it.

Witness the fact that there are dozens of competing colour maps, all vying to achieve the ideal.

 

[Charles Link]

You're confusing the map with the territory, and doing your math on the map instead.
The CIE chart is just a map; it does not define the territory; it can only attempt to mimic it.

Witness the fact that there are dozens of competing colour maps, all vying to achieve the ideal.

I find it a little disappointing that most others don't seem to be able to follow the mathematics behind the CIE chart that I just figured out in the last couple of days and/or they haven't read my posts very carefully, especially posts 23 and 24. I knew of the CIE chart as much as 40 years ago or more, but only in the last couple of days did I figure out enough of what are perhaps somewhat hidden mathematical details that you normally don't even find except in a very good write-up of the CIE chart, which so far I haven't seen. Some others who already know these details simply may not be giving much or any feedback. Cheers. :)

 

[DaveC426913]

I find it a little disappointing that most others don't seem to be able to follow the mathematics behind the CIE chart

This did not start off there. This started off as discussion about the nature of yellow, and wandered into the weeds of what it is to be true yellow. (Mia culpa.)

But that's a far cry from the quantitative mathematics of the CIE chart. Perhaps you could take some time to compose your thoughts, separating out what is subjective from what is objective, so as to help us follow your thesis, and to engage the members you want to engage?

 

[Charles Link]

Here's your 580 and 590:
View attachment 352561
Photoshop thinks 580 is 98% yellow and 29% magenta, while 590 is 60% magenta.

Please see my post 33 where I "linked" another color chart=I do think this "linked" color chart is more correct =see also post 16 where that chart may also have some rather incorrect color to it.

I don't think very many people have tried to follow along my posts through the complete thread. The discussion then got off on a tangent about cotton. I would have preferred if it stuck more to the topic which I think I have presented reasonably well.

The diagram you presented in post 13 is a very good one as I mentioned in post 15. :)

 

[DaveC426913]

The discussion then got off on a tangent about cotton. I would have preferred if it stuck more to the topic

You could report and ask to have that diversion removed. Not sure if they will, but it's not unreasonable to ask.

 

[Charles Link]

You could report and ask to have that diversion removed. Not sure if they will, but it's not unreasonable to ask.

It really didn't matter much to me one way or the other. What I would like to see though as that you and others, including @sophiecentaur who has had some very good inputs, read through and study my posts in complete detail throughout the whole thread. That may be asking a lot, but otherwise the feedback I get may be rather mediocre, because you/they will have missed perhaps a couple things or more that I presented throughout the thread. (Post 33 is also one that I could enjoy getting some feedback on).

I wasn't the one who introduced the CIE color map in the thread, (I think @sophiecentaur did), but in hindsight it seems to be very useful for discussing how the colors mix. If you follow my posts throughout the thread, you will see that at first I had a very limited understanding of what the CIE color map is all about. In fact, after figuring out some of its finer mathematical details, (see posts 23, 24, 32, and 38), it seems IMO to be a very good way to proceed when discussing the mixing of any combination of colors of light. :)

 

[sophiecentaur]

I wasn't the one who introduced the CIE color map in the thread, (I think @sophiecentaur did), but in hindsight it seems to be very useful for discussing how the colors mix.

IMO, the point of the CIE chart is as a common discussion point when design colour reproduction systems.

One thing we haven't yet mentioned is the specification of the illuminant of a scene that's being reproduced. The CIE system allows colour matching between different technologies and different illuminants. Every modern camera / colour chain has software that tries to match the original scene to what's displayed for 'all' combinations of camera analysis and display synthesis, and the eye. Our brains manage a good job of colour matching for outdoor conditions, in and out of shadow (direct sunlight and light from the sky and surrounding objects (i.e. for different 'white points') but it can be confused. Camera software finds this more different, despite being very clever. Things are even harder now that there is a whole range of colour phosphors.

Pretty close to what?
There is no such thing as "The One True Yellow".

Exactly. this thread has already exposed the nonsensical generalised equivalent that used to be drawn between spectral yellow and 'what you get' when you mix red and green. Nothing is certain about colour but without well specified primaries and white point, you can't say how a coloured patch on an item in a scene will be displayed on a TV screen.

I also have to mention the importance of subtractive mixing of colours in dyes and pigments and also in some CMY displays like colour film. The advertising industry is obsessed with that.

Then there's the fact that the everyone's eyes are totally individual and that there is a huge spread in colour perception. This has allowed the high levels (as with HiFi) of BS that has gone into comparisons of cameras and displays. I recently bought a new telly with an OLED screen and its pictures can be really stunning (source dependent, of course) but I'd hesitate to make an objective comparison between the best displayed pictures and the original scenes. I remember being told (65 years ago , at least) that colour film colourimetry is simply awful but cinema audiences accept it because they are in an isolated darkened room with no comparison with real life.

 

[Charles Link]

Very good inputs @sophiecentaur Thank you. :)

I'm still looking for some feedback on the mathematics though=to me it isn't readily apparent the things that I mentioned in post 32. Perhaps you have already known this concept (that $x+y+z= 1$ as being the plane on which the CIE map is located) and the vector addition for two or more sources of the $X$ , $Y$, and $Z$, etc. for the 3 color cones of the eye, but for me this is something I finally figured out just this past week, and I wouldn't be surprised if it is a new concept for many others. Hope you find this part of interest. :) See also post 38.

[Edit: Note also that the color coordinates $(x,y,z)$ for any source is the location where the vector formed by the intensities $X, Y$ and $Z$ seen by the 3 color cones crosses the plane $x+y+z=1$. Thereby the CIE chart maps out each and every possible color, (each with its color coordinates $(x,y, z)$), right in this plane.]

Note that they could have normalized the $X,Y,Z$ vector and let its direction cosines determine the $(x,y,z )$ color coordinates of the color, but instead they used the location where the vector crosses the plane $x+y+z=1$, (instead of where the vector crosses the unit sphere $x^2+y^2+z^2=1$). It really makes for easier arithmetic=given the $x$ and $y$ on the color map (=red and green cones contributions/coordinates to the color ), we can very easily compute the blue cone contribution/coordinate as being $z=1-x-y$.

 

[Charles Link]

I'm still looking for some feedback on the mathematics of the CIE color chart as I presented in post 46 above, and in other posts in this thread. I think I came up with a good way of explaining it.

I find it somewhat disappointing these days that so few seem to take much interest in any mathematics. When I meet others in my neighborhood Starbucks, it is difficult to find anyone who can even work something simple like finding the hypotenuse of a right triangle whose sides are 35 and 12. I'm hoping at least a couple people are able to follow the explanation in post 46, but I guess if I don't get a whole lot of feedback, that is ok too. Cheers. :)

 

[DaveC426913]

When I meet others in my neighborhood Starbucks, it is difficult to find anyone who can even work something simple like finding the hypotenuse of a right triangle

What? Like strangers?

 

[DaveC426913]

That was a serious question.

 

[Charles Link]

That was a serious question.

Yes, and thank you for asking. Yes, I have a Starbucks about one block away from my house and I get coffee there almost every day. I meet a fair number of people there=not a huge number because many keep to themselves, but in any case I look for people who might understand some mathematics beyond high school algebra, and most of them that I meet have almost zero math skills. If I can get them to even work a right triangle with the Pythagorean theorem, I consider it a victory. Trying to get them to do something more difficult like the law of cosines is like asking for a miracle.

 

[DaveC426913]

I'm dying to ask about your pickup line intro.

 

[Charles Link]

I'm dying to ask about your pickup line intro.

I'm really too old to have much success with the younger generation, but if I have someone who I like, I might try a riddle on them that I got from the wife of one of my Saturday morning baseball players: "What type of fish does a bird like to sit on?" (You should be able to come up with the answer.) LOL

We got off topic here. Back to the physics=I'd still enjoy some feedback on the mathematics of the CIE map that I came up with=maybe people already have it figured out, but it took a google on my part, and one of the key things that I found in the google and applied it is that for any and all of the $(x,y,z)$ color coordinates $x+y+z=1$.

 

[Charles Link]

Just a brief comment or two about the CIE color chart: I had seen this chart 40+ years ago, but it isn't at all obvious=I found this by googling it last week, that there is a 3rd variable z that is part of the color coordinate description, and I figured out that the chart is a cross section in the plane $x+y+z=1$ of an $X,Y,Z$ vector space , where the $X$ is the red cone response or intensity of a light source, the $Y$ is the green cone intensity, and the $Z$ is the blue cone intensity. Any visible light source is characterized by these 3 terms, and the color is characterized by where the $X,Y,Z$ vector crosses the plane $x+y+z=1$. For a given $x$ and $y$, the $z$ is found by $z=1-x-y$.

They would really do well to mention/footnote about the 3rd variable when displaying a CIE chart. One other item is that ordinarily the direction of a vector is characterized by the direction cosines of its normalized unit vector. Instead, with the CIE system they characterize the direction of the vector by giving the coordinates $(x,y,z)$ where the vector (with its tail at the origin), crosses the plane $x+y+z=1$, (instead of where it crosses the unit sphere $x^2+y^2+z^2=1$).

I'm mostly repeating/ summarizing what I have previously posted in the above thread. I think there may be others who have also seen a CIE color chart, who also didn't have a clue that it represents 3 variables=many might think that it is just an x-y graph. It is actually a view from above of the cross section of a 3-D space that lies in the plane $x+y+z=1$.

See post 16 above for the CIE color chart with its x-y axes.

I am hoping that there are at least a couple of people that find this of interest. I welcome your feedback. :)

Edit: Just an additional comment=to see what this whole thread is about, you really only need to read the OP and this last post 53, where I summarized how to read the CIE color chart. (The chart can be found in post 16). One minor correction is that it seems that yellow light occurs in the narrow band from 580-590 nm, rather than at 600 nm, but in any case, as is seen by reading the CIE chart, light that appears yellow can indeed be made in a composite manner by the right combination of green at 550 nm and red at 650 nm, even though a prism spectrometer will be able to tell the difference with complete certainty where our eye cannot.

Edit 2: One detail that might be worth mentioning in reading the OP , especially for those not very familiar with optics, is how you can sample the output of a prism at a given angle. To do this, right after the prism you place a converging lens, and parallel rays will come to a focus in the focal plane of the lens. Parallel rays at a different angle will focus at a different location in the focal plane. In this way the rainbow of colors is generated in the focal plane of the lens.

 

[sophiecentaur]

It is actually a view from above of the cross section of a 3-D space that lies in the plane x+y+z=1.

The CIE chart only shows chrominance, which can actually produce very different perceived 'colours' when Luminance changes. Two areas with the same XY co ordinates can often look very different with different Z. For, high and low luminanceareas can look yellow and brown. Pale 'European' skins tend to have very similar chrominance values to darker skins because the dark pigment is a pretty good neutral grey. Hardly surprising really because the tissues , fat, blood etc. are much the same for all skins.

When the eye sees coloured light it also takes into account the other light sources around and 'integrates to grey' , which is the best it can do so the actual chrominances in a scene can look almost the same in bright light or dim light There are hundreds of made-up images (illusions) that totally confuse the eye because surrounding areas affect what you 'see'.

 

[Charles Link]

The CIE chart only shows chrominance, which can actually produce very different perceived 'colours' when Luminance changes. Two areas with the same XY co ordinates can often look very different with different Z. For, high and low luminanceareas can look yellow and brown. Pale 'European' skins tend to have very similar chrominance values to darker skins because the dark pigment is a pretty good neutral grey. Hardly surprising really because the tissues , fat, blood etc. are much the same for all skins.

When the eye sees coloured light it also takes into account the other light sources around and 'integrates to grey' , which is the best it can do so the actual chrominances in a scene can look almost the same in bright light or dim light There are hundreds of made-up images (illusions) that totally confuse the eye because surrounding areas affect what you 'see'.

I don't know that you have completely followed my explanation of the chart. There is the capital $(X,Y,Z)$, and the small $(x,y,z)$. The chart itself is small $(x,y,z)$, and for a given $(x,y)$, there is only one $z$ which is computed to be $z=1-x-y$.

From what I can tell, I think the chart has been somewhat misunderstood or not fully understood by many. If we go to a different brightness level, we do scale up the $(X,Y,Z)$, but the $(x,y,z)$ stays the same. (The $(x,y,z)$ is found by where the vector $(X,Y,Z )$ crosses the plane $x+y+z=1$.) That of course is then what you are saying, that the $(x,y,z)$ for the scaled up case should really take on a different position on the chart=the chart assumes linearity of the system at all light levels, and that is only good to a very rough approximation at best. In any case, I find the chart to be based on some very good mathematics.

Edit: Computing where the $(X,Y,Z)$ crosses the plane $x+y+z=1$, it is given by $x=X/(X+Y+Z)$, $y=Y/(X+Y+Z)$, and $z=Z/(X+Y+Z)$. The $(x,y,z)$ are the color coordinates, where the $(x,y)$ is found on the chart, and it is simple arithmetic to compute the $z$ which is $z=1-x-y$. The chart is a map on the plane $x+y+z=1$ of the color that is found for each vector $(X,Y,Z)$ where each vector's color/direction is determined by where it crosses the plane $x+y+z=1$.

(They really IMO would do well to footnote that $z =1-x-y$ when showing the chart. The chart is actually a view from above of the plane $x+y+z=1$ that is colored in showing the colors of each $(x,y,z)$). .



Scaling up the $(X,Y,Z)$ gives the same $(x,y,z)$ on the color chart, which is really the best we can do with a linear model. It is not expected to be perfect, but it is reasonably accurate for many cases.

 

[sophiecentaur]

From what I can tell, I think the chart has been somewhat misunderstood or not fully understood by many.

Very true. The CIE chromaticity chart seems to be the result of several steps to produce a practical way into colourimetry without going into the details that you find in the Wiki Article, in which I (today) re-visited what I learned in the late 60s. (Not explicitly used since I moved departments soon afterwards.) Wiki can't always be relied upon but that article seems ok. The misunderstanding that you refer to is probably because it's not something you can reverse engineer - and it's much better than near enough for Jazz.
The experiments to determine the sensitivity curves are a great example of pulling yourself up by your own bootstraps but the end product (CIE chart) has proved itself to be useful. No lasers in those days.
The negative sensitivity values in the normalised sensitivity curves need thinking about!
The "similar threads" below are worth while looking through.

 

[pinball1970]

Good answer, but you reversed rods and cones.

Cones colour??

Operate in bright light and rods in dim, peripheral but 'grey' vision in the dark/low light.

 

[pinball1970]

Let's not forget that "yellow" is highly subjective. It's different for everyone, and even different depending on context.
View attachment 352556View attachment 352555

Anyone encountered this little test?
https://ismy.blue/
My score (today) is 172.

Pantone split them out and assign a hue, "lightness" and "C"
TPX is printed usually for textiles.
"C" is coated for paper.
The number make sense but the names as you can see are design centric madness.

 

[Charles Link]

The experiments to determine the sensitivity curves are a great example of pulling yourself up by your own bootstraps but the end product (CIE chart) has proved itself to be useful. No lasers in those days.
The negative sensitivity values in the normalised sensitivity curves need thinking about!

Yes, very good. I also thought the sensitivity curves that had some negative numbers were something that looked to be in error. That could be one of the reasons why, from what I could tell through the Wiki article, that they redid the original R,G,B response with X,Y,Z responses. I also "linked" the Wiki article in post 32 above.

and thank you very much for your interest in the topic. :)