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post #1 of 24 Old 10-02-2013, 07:07 PM - Thread Starter
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I've just started reading János Schanda's text, and noticed something strange, and I think this reflects a misunderstanding on my part.

In the early experiments, the "red" primary was 700 nm. It's not fully clear how narrow the spectral bandwidth of these primaries were, but the text does say that "single wavelengths were used..." (p 29). I also gather that the test stimuli comprised single wavelengths.

Now, take a look at the CMF that was derived from these primaries.



Look at what happens when the test stimulus was 700 nm. Hardly any response at all. I interpret this to mean that the red primary itself (which was also 700 nm) is barely visible to the human visual system (which is the first thing I find strange).

Now look a little bit to the left of that point - say around 670 nm. This particular spectral color is matched by increasing the intensity of the 700 nm primary. But this makes no sense to me! How can increasing a single primary's intensity (while leaving the other primaries at zero), change the perceived chromaticity of the stimulus?
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post #2 of 24 Old 10-02-2013, 07:19 PM
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Quote:
Originally Posted by spacediver View Post

How can increasing a single primary's intensity (while leaving the other primaries at zero), change the perceived chromaticity of the stimulus?

First off that graph is of cone fundamentals, not a color matching function.

670-700nm would subtly shift, they wouldn't match perfectly. There in the XYZ where red is loosely the X curve and Y is loosely the green curve. But Y is more closely associated with luminance and there is some Y value for every perceivable color. So since there is some amount of Y that is always slightly different for any point on the visible spectrum, every single wavelength of light produces a different ratio of XYZ. Some do have a zero value for Z, but every combination has different amounts of Y and X.

So shifting from 670 to 700 and changing the intensity you might be able to keep the X constant, but the ratio between X and Y would change and so would your perception chromaticity.
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post #3 of 24 Old 10-02-2013, 07:20 PM - Thread Starter
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It looks as if you can change the perceived chromaticity by increasing the intensity of the red primary while the other primaries are at zero. In other words, the spectral signature has only changed in amplitude.
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post #4 of 24 Old 10-02-2013, 07:26 PM - Thread Starter
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ah, I just looked at the original tables (rather than the graph), and it appears that the other primaries were NOT at zero.

Here is the data:

for test wavelength of 700 nm:

R = 1.0000
G = 0.0000
B = 0.0000

for 695:

R = 0.9999
G = 0.0001
B = 0.0000

for 690:

R = 0.9996
G = 0.0004
B = 0.0000

Goes to show how graphs can sometimes be misleading. Also goes to demonstrate how sensitive we are to the green primary.
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post #5 of 24 Old 10-02-2013, 07:32 PM
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Quote:
Originally Posted by spacediver View Post

ah, I just looked at the original tables (rather than the graph), and it appears that the other primaries were NOT at zero.

Here is the data:

for test wavelength of 700 nm:

R = 1.0000
G = 0.0000
B = 0.0000

for 695:

R = 0.9999
G = 0.0001
B = 0.0000

for 690:

R = 0.9996
G = 0.0004
B = 0.0000

Goes to show how graphs can sometimes be misleading. Also goes to demonstrate how sensitive we are to the green primary.

It's really a misnomer to consider them red, green and blue primaries.

They are long, medium and short wave cones. With the medium cones being broad enough that if they aren't being stimulated we don't perceive illumination.

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post #6 of 24 Old 10-02-2013, 07:42 PM - Thread Starter
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Quote:
Originally Posted by sotti View Post

It's really a misnomer to consider them red, green and blue primaries.

They are long, medium and short wave cones. With the medium cones being broad enough that if they aren't being stimulated we don't perceive illumination.

I'm referring to the actual primaries that they used, though. Why would you want to call them cones? I get that the S M L cone responses in the human visual system will say something about how the chosen primaries and the derived CMF interact, but primaries in the context I've been using them doesn't seem to be a misnomer.
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post #7 of 24 Old 10-02-2013, 08:05 PM
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Quote:
Originally Posted by spacediver View Post

I'm referring to the actual primaries that they used, though. Why would you want to call them cones? I get that the S M L cone responses in the human visual system will say something about how the chosen primaries and the derived CMF interact, but primaries in the context I've been using them doesn't seem to be a misnomer.

I don't think you are correctly understanding their experiments.

If you have a monochromator to generate individual wavelengths of light, you don't have primaries.

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post #8 of 24 Old 10-02-2013, 08:17 PM - Thread Starter
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my understanding of the experiment is that this was a psychophysical experiment, where various test wavelengths (the reference) were presented one at a time on one part of the visual field. On a neighbouring part of the visual field was the "matching" stimulus. This was formed by a combination of the three primaries, and the task was to adjust the relative levels of these primaries until the two samples matched. These red green and blue primaries had defined wavelengths of 700, 546.1, and 435.8 nm, respectively.

The X-axis on the CMF graph represents the various test wavelengths used, and the values of each of the three curves at a given test value represents the relative intensities of the three primaries that were required to form a perceptual match.

Are you saying that the term "primary" is being misused here? This is what Schanda is calling them, as far as I can understand.
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post #9 of 24 Old 10-02-2013, 08:22 PM
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So what is your question?

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post #10 of 24 Old 10-02-2013, 08:32 PM - Thread Starter
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I already answered it, when I figured out that, contrary to what the curves look like, if you look at the actual raw data, the curve for the green primary is actually not at zero at 690 nm.

Which means that at the test value of 690 nm, the spectral signature of the matching sample actually does change - there's a tiny amount of green being introduced.

I just noticed that you edited one of your posts:
Quote:
Originally Posted by sotti View Post

First off that graph is of cone fundamentals, not a color matching function.

No, that graph depicts the three color matching functions of the primaries used in those experiments. This is before they were transformed into XYZ.
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post #11 of 24 Old 10-02-2013, 11:14 PM - Thread Starter
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Here's another brain teaser:

from the text:
Quote:
"To be able to define a standard observer, the spectral compositions and the luminances of the primaries have to be specified. Single wavelengths were used: 700 nm for the red, 546.1 nm for the green, and 435.8 nm for the blue primary. The "unit intensity" of the primaries was defined by stating their luminances. The requirement was that for an equienergy spectrum [i.e. illuminant E] the addition of the unit amounts of the three primaries should give a color match. If 1 cd/m2 of red light was used, then 4.5907 cd/m2 of green and 0.0601 cd/m2 of blue light was needed to match the color of an equienergy spectrum"

Here, we see how the luminance units of the three primaries are scaled so that when equal amounts of the scaled units are added together, the color matches that of illuminant E (I take it that illuminant E is a purely theoretical entity, but they may have approximated it by adding a series of monochromatic wavelengths together).

The thing is, it requires almost two orders of magnitude less of the blue light than it did the green light. This, to me, makes it seem as if we are much more sensitive to blue light (since we need so little of it to have an effect). However, everything else I've read on the relative sensitivities of blue vs. green light indicates the exact opposite.

I'll try to find an answer to this, and report back (unless someone here can figure it out).
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post #12 of 24 Old 10-03-2013, 12:20 AM
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Quote:
Originally Posted by spacediver View Post

Here's another brain teaser:
The thing is, it requires almost two orders of magnitude less of the blue light than it did the green light. This, to me, makes it seem as if we are much more sensitive to blue light (since we need so little of it to have an effect).

That would be correct. This is why "blue-filter" techniques have been used for years. Also why TV manufacturers started cranking up the blues to win the "brightness" battles.

In contrast, trying to use a "green-filter" or green isolation for setting color/tint can be quite frustrating since we are not as sensitive to changes in intensity in the "green" spectrum. Red sensitivity falls somewhere between green and blue. ... At least in my case. YMMV.
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post #13 of 24 Old 10-03-2013, 12:31 AM - Thread Starter
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interesting!
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post #14 of 24 Old 10-03-2013, 07:27 AM
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To really answer your question you need to be looking at the spectral to XYZ color matching function. Here's the 1931 function.




Illuminant E is equal parts X, Y, and Z. If you were going to integrate 3, 1nm wavelength and balance them to produce equal parts X,Y,Z the wavelength that contributes Z needs to be precisely aligned with the Z curve, or ti's going to take a lot more energy to create the same stimulus. But if it was correctly centered, then it should take a little less energy.

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post #15 of 24 Old 10-03-2013, 09:36 AM - Thread Starter
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I'm trying to fully understand everything they did before the XYZ transformation part of the story.

One thing I'm having trouble with is the idea that if we are indeed more sensitive to blue light, then shouldn't an equal energy spectrum look very blue?

And if that is the case, then shouldn't they have required equal energy from each of the three R G B primaries to match an equal energy spectrum?


In other words, sure, I can see how a tiny bit of blue added to a lot of green and a moderate amount of red, can yield a perception of "white". But an equal energy spectrum does not have this relative scaling incorporated into it, so shouldn't it look very blue?
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post #16 of 24 Old 10-03-2013, 09:53 AM
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The XYZ tells you far more about how we actually perceive the color than the work getting to there.

What you see when you look at the color matching function is that for a very narrow band of blue our eyes are extremely sensitive, off that peak, not so much.

Also our visual system is weighted in a way where illuminant E isn't even all that neutral.



Assuming you've got an sRGB calibrated monitor that is the difference between illuminant E on the left and d65 on the right.


I would stop trying to think of RGB in terms of what your eye sees. It's stimulated by different wavelengths of light, red, green and blue are too abstract to be meaningful, with out very specific context.

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post #17 of 24 Old 10-03-2013, 09:57 AM - Thread Starter
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interesting, thanks that makes sense.
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post #18 of 24 Old 10-03-2013, 08:51 PM - Thread Starter
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Found this to be a useful visualization of the relationship between R G B, X Y Z, and the cie chart:

http://www.youtube.com/watch?v=x0-qoXOCOow

craig blackwell's youtube series is also very good
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post #19 of 24 Old 10-08-2013, 04:33 PM - Thread Starter
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just thought I'd share something.

I found some details of Schanda's chapter on CIE colorimetry to be unnecessarily obtuse. While it is fairly comprehensive in its detail, it could have explained a few things better.

I gained some very valuable insight by reading through the colorimetry chapter in Ross Mcluney's text on radiometry and photometry. It is not as detailed as Schanda's account, but it introduces the concepts much more clearly. The first two chapters of that book are also excellent, and I would recommend reading them before reading the colorimetry chapter (they deal with radiometry and photometry).

I know have a MUCH firmer grasp on what the x y and Y are!
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post #20 of 24 Old 10-18-2013, 02:53 PM
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Quote:
Originally Posted by spacediver View Post

Here's another brain teaser:

from the text:
Here, we see how the luminance units of the three primaries are scaled so that when equal amounts of the scaled units are added together, the color matches that of illuminant E (I take it that illuminant E is a purely theoretical entity, but they may have approximated it by adding a series of monochromatic wavelengths together).

The thing is, it requires almost two orders of magnitude less of the blue light than it did the green light. This, to me, makes it seem as if we are much more sensitive to blue light (since we need so little of it to have an effect). However, everything else I've read on the relative sensitivities of blue vs. green light indicates the exact opposite.

I'll try to find an answer to this, and report back (unless someone here can figure it out).

I think you are drawing the conclusion that 4.5907 cd/m2 of green has more energy than 0.0601 cd/m2 of blue by direct comparison of the numbers. This is not correct. Remember that cd/m2 is a measure of luminance, not radiant energy. In essence, that measurement already has the spectral sensitivity weighting built into it. You have to back out the luminous efficiency function, y(lambda), to find out how much energy is really in that particular blue. If you do that, you'll find that the blue light is not two orders of magnitude less energetic than the green.
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post #21 of 24 Old 10-18-2013, 09:52 PM - Thread Starter
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Quote:
Originally Posted by EvLee View Post

I think you are drawing the conclusion that 4.5907 cd/m2 of green has more energy than 0.0601 cd/m2 of blue by direct comparison of the numbers. This is not correct. Remember that cd/m2 is a measure of luminance, not radiant energy. In essence, that measurement already has the spectral sensitivity weighting built into it. You have to back out the luminous efficiency function, y(lambda), to find out how much energy is really in that particular blue. If you do that, you'll find that the blue light is not two orders of magnitude less energetic than the green.


yep, thanks for pointing this out. I ended up learning what the spectral luminous efficiency function - V(lambda) - actually was through the photometry chapter from McCluney. There was no hint of an explanation of it in Schanda's chapter, although it was referenced. Also pretty cool that Y(lambda) turns out to equal the same function.


It is interesting. Intuitively you might suppose that, with this efficiency function taken into account, you would need equal nits of red green and blue to produce a perceptual sensation of whiteness.

But perhaps it has more to do with the balance of actual photons. If you combine the luminance ratios they used to get white (1:4.5907:0.0601) with V(lambda), you can find out the radiance ratios they used to get white.

Original RGB primary wavelengths:

R: 700 nm
G: 546.1 nm
B: 435.8 nm

R: V(700) = 0.004102
G: V(546.1) = 0.978980
B: V(435.8) = 0.00334487 (this value and above through linear interpolation)


Luminance ratios to get white:

R: 1
G: 4.5907
B: 0.0601


To get the radiance ratios, we divide the luminance ratio (R) by V(R), and luminance ratio(G) by V(G), and so on for B. (we need not divide by the factor of 683 to get radiance, since we're not interested in watts/m^2 but rather relative radiance).

We get

R: 1/0.004102 = 243.78
G: 4.5907/.97898 = 4.689
B: 0.0601/0.00334487 = 17.968


Let's normalize them so that the radiance ratio has R = 1:


R: 1
G: 0.0192
B: 0.0737


So, when you ignore the fact that our eyes are more sensitive to green light, and are just interested in the relative amounts of raw power from each of the three wavelengths that are required to produce a sense of whiteness, you get 1:0.0192:0.0737 (R:G:B), or, very roughly, about 50:1:4

This means you need roughly 50 times as many photons of red light than you do green light to produce a sense of whiteness, and four times as much blue as you do green. So this resolves the apparent paradox I thought existed when I didn't take into account V(lambda) - thanks EvLee!

So what I think this tells us is that it's not about the balance of photons that produces white (the radiance ratio is not 1:1:1) , and it's not about the balance of stimulation that produces white (the luminance ratio is not 1:1:1). I think this suggests that whiteness, perceptually speaking, is not only about energy balance, whether that be radiant energy, or cortical stimulation "energy".
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post #22 of 24 Old 10-19-2013, 10:13 PM
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700nm is red, but 630nm would also appear red and change your math quite a bit. Red and Green and Blue are abstract, there is no universal definition for red. It is conceptually inaccurate to intermix specific wavelengths of light for individual colors. What you said is ONLY valid for those wavelengths, which basically means that what you are saying is nonsense in the real world.

To put it another way, if what you stated above was even remotely true, then E the equal energy point that has a flat spectral response would have an incredible cyan tint, since so much more red is required, yet in truth, E is quite a bit more red than D65.

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post #23 of 24 Old 10-19-2013, 10:37 PM - Thread Starter
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that's a great point - these were primaries that were chosen because they were physically realizable in a consistent manner in that period (I think using a mercury vapor lamp), and also because the green and blue (actually violet) were very prominent in the underlying spectrum. I was tacitly making the assumption that the conjunction of these primaries represented a "balanced" spectrum.

I see your point - it's better not to get hung up on primaries. Instead, illuminant E would be a better test of how our bodies combine energy.
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post #24 of 24 Old 10-23-2013, 06:01 PM
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Y doesn't really say anything about whiteness. In the HVS, the photoreceptors are followed by ganglion cells in the retina that perform color processing to turn the cone responses into color opponent signals. The color opponent signals are where an achromatic component (that eventually contributes to the perception of whiteness) is first introduced. This processing is also responsible for chromatic adaptation, which is similar to white balance in a camera except on a local scale, so whiteness is not a function of the light alone. It depends on the configuration of the scene. In reality, colorimetry is very limited in what it tells us and is a big step away from color appearance.
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