Mean colour of visible spectrum?

[sophiecentaur]

our eyes do not have a linear response to equal power of different wavelengths

The most important aspect of the eye's response is that it has virtually no wavelength resolving facility - never mind its amplitude response. It is not a spectrometer.

 

[fizixfan]

To my simplistic way of thinking, the "mean" value for visible light would be the statistical average between the two extreme wavelengths of visible light, i.e., 400 nm (violet) and 780 nm (red), which would be 590 nm (orange). However, there does not appear to be any standard definition of the shortest or longest visible wavelengths. I took a range of estimates from several different sources from a Google search of "Visible Spectrum" and got an average value of about 560 nm (green-yellow).

 

[Shane Kennedy]

It also depends on how you measure it. Can we actually measure the amplitude of the wave, or do we measure by it's power ? Is there a device that can measure light without any colour bias ? I am sure that human eyes vary slightly in their sensitivity too.

 

[Drakkith]

It also depends on how you measure it. Can we actually measure the amplitude of the wave, or do we measure by it's power ?

Not of visible light. The wave alternates too fast for electronics to respond so we can't directly measure the amplitude of each alternation. Instead we measure the power over some amount of time.

Is there a device that can measure light without any colour bias ?

Of course. A properly calibrated spectrometer is one such device.

 

[sophiecentaur]

I wonder what would be the arithmetic mean of Tom, Dick and Harry?

 

[Shane Kennedy]

Not of visible light. The wave alternates too fast for electronics to respond so we can't directly measure the amplitude of each alternation. Instead we measure the power over some amount of time.
Of course. A properly calibrated spectrometer is one such device.

In order to calibrate anything, you need a reference. I was involved in setting up a production test for IR LEDs and sensors. We knew that a block of plastic would attenuate at a certain rate/mm, but where do you get a reference source, or a reference detector ? With light, it seems to be a chicken and egg situation. You need one to get the other ... in both directions.

 

[Shane Kennedy]

I wonder what would be the arithmetic mean of Tom, Dick and Harry?

When at college, learning about matrices, and since, I often wondered how you can get the value of a matrix. What defines what cell does what, and where does the information come from. A practical example would be good.

 

[sophiecentaur]

Not of visible light. The wave alternates too fast for electronics to respond so we can't directly measure the amplitude of each alternation. Instead we measure the power over some amount of time.
Of course. A properly calibrated spectrometer is one such device.

It is quite possible to use 'superheterodyne' (now there's a lovely old word) methods to beat down a CW signal from a laser to a manageable RF frequency and to 'look at' the variations of the fields in the light wave. You may say it's a bit of a cheat but no one (?) uses TRF (tuned radio frequency) receivers these days, so we do the same trick for RF measurement, in any case.
It is true, however, that the THz variations of fields in light waves can neither be detected by thermal sensors nor the output of photochemical or photoelectric devices - which are only aware of numbers of Photons.

Is there a device that can measure light without any colour bias ? I am sure that human eyes vary slightly in their sensitivity too.

All human senses are like this. With the exception of highly trained craftsmen and people with perfect pitch, all quantities have to be measured with instruments, if high accuracy is needed. I think you may still be missing the point that the eye is not a spectrometer. It can make a stab at estimating the wavelength of a single spectral line but it is completely unable to resolve the spectral components of any other light source. All it can do is to 'name the colour' of an object or light source - which is nothing like the spectral content. It is because of this that Colour TV works.

 

[fizixfan]

I am sure that human eyes vary slightly in their sensitivity too.

Good point Shane. I'm what you call "color blind," although "red-green deficient" or better yet "deuteranopia" are more accurate terms.

We have red, green and blue color receptors (cones) in our retinas. I probably have fewer red and green receptors than people with normal vision do.

But - and this is just a theory - color blind and color deficient people may have more rods (for light sensitivity, not color) than non-color blind people, and so may have better night vision. My night vision is pretty good.

I also wonder if the RGB cones distinguish colors and hues via a RGB (additive) or CMYK (subtractive) process. Probably additive, since computer screens use this method, whereas the color printing (pigmenting) process uses the subtractive colors.

 

[blue_leaf77]

Given a spectrum shape $A(\omega)$, the mean frequency is
$$ \omega_{av} = \frac{\int \omega |A(\omega)|^2 d\omega}{\int |A(\omega)|^2 d\omega} $$.
I don't see there is a way to calculate the spectrum if one has not been given a particular spectrum.

And by the way there have been a couple of measurement methods able to resolve electric field oscillation such as FROG, SPIDER, etc.

 

[sophiecentaur]

Good point Shane. I'm what you call "color blind," although "red-green deficient" or better yet "deuteranopia" are more accurate terms.

We have red, green and blue color receptors (cones) in our retinas. I probably have fewer red and green receptors than people with normal vision do.

But - and this is just a theory - color blind and color deficient people may have more rods (for light sensitivity, not color) than non-color blind people, and so may have better night vision. My night vision is pretty good.

I also wonder if the RGB cones distinguish colors and hues via a RGB (additive) or CMYK (subtractive) process. Probably additive, since computer screens use this method, whereas the color printing (pigmenting) process uses the subtractive colors.

You are using terms in colour synthesis here but colour analysis is not suited to those descriptions. It s a bit simplistic to describe the receptors as 'red', 'green' and 'blue' receptors because they are all sensitive to more or less the whole visual spectrum. This is essential for the way they work.
This link (and dozens others from Google) tells you the main points about the tristimulus colour vision theory. That theory works well enough for Colour TV and other displays to work very well. Those displays work on additive mixing and give pretty good colour fidelity. within their gamut. Subtractive mixing (colour film and colour printing) is not so good if you can only use three primaries on their own. Spot colours can be used in printing to improve reproducibility (e.g. the Red in the CocaCola adverts would never be done 'right' with a dot matrix printer)

 

[klimatos]

The wavelength of maximum intensity for insolation (incoming solar radiation) is generally given as 475 nanometers in most solar radiation studies. This wavelength is toward the green end of the visible spectrum. However, the scattering of a portion of the blue component of that greenish radiation by the intervening atmosphere (Rayleigh scattering) allows us to perceive sunlight as somewhat yellow. This was my standard explanation in my atmospheric science classes.

 

[mp3car]

The most important aspect of the eye's response is that it has virtually no wavelength resolving facility - never mind its amplitude response. It is not a spectrometer.

No wavelength resolving facility? No, it's not a spectrometer, but the various cone cells respond differently when we view one wavelength compared to another. No, we can't tell a difference between 532nm and 533nm, nor a difference between a surface illuminated with 70W/m^2 vs. 71W/m^2...

However, if a surface is emitting monochromatic 400nm, I am going to have a different cone response than I would it were 600nm. And as has been said, the perceived brightness depends not only on power, but also the wavelength. I am not sure what you mean by "no wavelength resolving facility" considering we can easily resolve a difference between the two different wavelengths in this example. As I said, of course we can't tell 532nm vs. 533 and maybe even 532 and 540nm. But in the big picture, taking the entire system into account of the eye and brain, 500nm and 600nm are "resolved" very differently (I am using the term "resolve" to mean separate, distinguish, discern).

 

[sophiecentaur]

No wavelength resolving facility? No, it's not a spectrometer, but the various cone cells respond differently when we view one wavelength compared to another. No, we can't tell a difference between 532nm and 533nm, nor a difference between a surface illuminated with 70W/m^2 vs. 71W/m^2...

However, if a surface is emitting monochromatic 400nm, I am going to have a different cone response than I would it were 600nm. And as has been said, the perceived brightness depends not only on power, but also the wavelength. I am not sure what you mean by "no wavelength resolving facility" considering we can easily resolve a difference between the two different wavelengths in this example. As I said, of course we can't tell 532nm vs. 533 and maybe even 532 and 540nm. But in the big picture, taking the entire system into account of the eye and brain, 500nm and 600nm are "resolved" very differently (I am using the term "resolve" to mean separate, distinguish, discern).

There is no way that the eye can distinguish between a Yellow Sodium line and an appropriate mix of Green and Red monochromatic light. I thing that demonstrates pretty well that the eye cannot resolve different wavelengths. I can't think why people feel it necessary to defend the abilities of the eye by suggesting it can do things that it can't Why should it matter?

 

[blue_leaf77]

All materials must exhibit dispersion (different response to frequency), this is guaranteed by Kramers-Kronig relation. The only way a "medium" behavior can be independent of frequency is that to have unit refractive index (again proved by Kramers-Kronig relation) which means vacuum, so the eye being sensitive to different wavelength is a must. Probably the more appropriate way to get around this discrepancy is to introduce resolution for the eye. Anyway what we call colors is actually how our brain gives its response to incoming stimulus, it doesn't output numbers like spectrometers. On the other hand spectrometers see numbers, not colors. Therefore we don't have to associate eye to spectrometers in all ways, only in some ways that it's sensitive to different wavelength.

 

[sophiecentaur]

All materials must exhibit dispersion (different response to frequency), this is guaranteed by Kramers-Kronig relation. The only way a "medium" behavior can be independent of frequency is that to have unit refractive index (again proved by Kramers-Kronig relation) which means vacuum, so the eye being sensitive to different wavelength is a must. Probably the more appropriate way to get around this discrepancy is to introduce resolution for the eye. Anyway what we call colors is actually how our brain gives its response to incoming stimulus, it doesn't output numbers like spectrometers. Therefore we don't have to associate eye to spectrometers in all ways, only in some ways that it's sensitive to different wavelength.

I'm not sure what you are implying about the way the sensors work but the accepted theory is that each of the three sensors have a very wide band sensitivity. Taken on its own, a sensor will not 'know' whether it is receiving low level light of wavelength near its peak of sensitivity or high level light way off its peak. It is only when the brain has information about all three sensors that a sense of 'Colour' (not necessarily wavelength) can be deduced by comparing the relative output levels of the sensors. Dispersion doesn't come into it. Indeed, how can it with non spectral incident light?
Have you read about the tristimulus theory of colour vision (links given earlier in this thread or Google it). Look at the graphs of the three responses and then read how the three signals are processed together. Colour TV mimics the process very well and can synthesise a display colour with a combination of Three Primary Phosphors, producing an entirely different spectrum from the original object that will give a near-perfect match to the eye. You may need to suspend your disbelief until the end of what you read as it seems to fly in the face of what you are saying.
Not only is the eye not a spectrometer, it is not an uncalibrated spectroscope either. The ear, on the other hand - but one thing at a time.

 

[mp3car]

No disagreement that we can't isolate specific lines in a multi-frequency composition. My example I gave most recently specifically said monochromatic, because I thought you were even saying we don't differentiate wavelengths, which obviously isn't what you were saying! I think I'm on the same page with you now... And I think I know what you're alluding to with sound... Two or more audio frequencies together is, as far as I know, impossible to recreate with a single frequency, but with light, your eye can be "tricked" into thinking two or more are a single wavelength...

 

[fizixfan]

You are using terms in colour synthesis here but colour analysis is not suited to those descriptions. It s a bit simplistic to describe the receptors as 'red', 'green' and 'blue' receptors because they are all sensitive to more or less the whole visual spectrum. This is essential for the way they work.
This link (and dozens others from Google) tells you the main points about the tristimulus colour vision theory. That theory works well enough for Colour TV and other displays to work very well. Those displays work on additive mixing and give pretty good colour fidelity. within their gamut. Subtractive mixing (colour film and colour printing) is not so good if you can only use three primaries on their own. Spot colours can be used in printing to improve reproducibility (e.g. the Red in the CocaCola adverts would never be done 'right' with a dot matrix printer)

Thanks for this link. It helped me to understand that the three different types of cone cells in our retina respond to a range of wavelengths, and actually overlap, but have fairly discrete peaks. This has broadened my understanding of the subject.

It's interesting to note that some women (and possibly even some men) may actually have tetrachromatic vision. http://en.wikipedia.org/wiki/Tetrachromacy

 

[sophiecentaur]

The peaked shape of the responses makes it possible to position the UV co ordinates of a colour on the CIE chart (which is a simplified description of what the brain does). If the responses were flat topped, it would not be possible to solve the equation with the given output signal levels. The peak is a necessary feature and is not there so that we have special sensitivity at three particular wavelengths.
On the subject of variations on the basic tristumulus system, it would be interesting to know whether it is racially differentiated, too.

 

[fizixfan]

On the subject of variations on the basic tristumulus system, it would be interesting to know whether it is racially differentiated, too.

Here's an study which finds that "Caucasian Boys Show Highest Prevalence of Color Blindness Among Preschoolers" http://www.aao.org/newsroom/release/color-blindness-among-preschoolers-ophthalmology-journal-study.cfm

"Researchers from the Multi-Ethnic Pediatric Eye Disease Study Group tested 4,005 California preschool children age 3 to 6 in Los Angeles and Riverside counties for color blindness. They found the following prevalence by ethnicity for boys:

• 5.6 percent of Caucasian boys
• 3.1 percent of Asian boys
• 2.6 percent for Hispanic boys
• 1.4 percent of African-American boys"

 

[sophiecentaur]

Here's an study which finds that "Caucasian Boys Show Highest Prevalence of Color Blindness Among Preschoolers" http://www.aao.org/newsroom/release/color-blindness-among-preschoolers-ophthalmology-journal-study.cfm

"Researchers from the Multi-Ethnic Pediatric Eye Disease Study Group tested 4,005 California preschool children age 3 to 6 in Los Angeles and Riverside counties for color blindness. They found the following prevalence by ethnicity for boys:

• 5.6 percent of Caucasian boys
• 3.1 percent of Asian boys
• 2.6 percent for Hispanic boys
• 1.4 percent of African-American boys"

Interesting figures. From a very simplified viewpoint, it might imply that it relates to the amount of Sunlight experienced in the different regions.

 

[fizixfan]

Interesting figures. From a very simplified viewpoint, it might imply that it relates to the amount of Sunlight experienced in the different regions.

That makes a lot of sense. An exception is Eskimos (Inuit), who are only about 1% color blind, but "it is logical to assume that less of the ‘original Eskimos’ carried the defective gene, so the likelihood of it infecting the gene pool was quite a lot lower." http://www.colour-blindness.com/general/prevalence/

 

[sophiecentaur]

That makes a lot of sense. An exception is Eskimos (Inuit), who are only about 1% color blind, but "it is logical to assume that less of the ‘original Eskimos’ carried the defective gene, so the likelihood of it infecting the gene pool was quite a lot lower." http://www.colour-blindness.com/general/prevalence/

Of course, when you say "defective", it may be more to do with the actual need for that particular characteristic and a consequential (Lamarckian style of )adaptation. Lamarck is not as far out of favour these days as he was.

 

[fizixfan]

Of course, when you say "defective", it may be more to do with the actual need for that particular characteristic and a consequential (Lamarckian style of )adaptation. Lamarck is not as far out of favour these days as he was.

I agree absolutely. I was just quoting the source. "Abnormal" may be more to the point. Epigenetics seems to be lending more credibility to the inheritance of acquired traits. I've always thought that the Darwinian view of evolution as nothing more than random mutation and natural selection was incomplete. It completely ignores self-organization and emergent order.

 

[sophiecentaur]

Read Arrival of the Fittest by Andreas Wagner. It's a good read and shows, with computational evidence, that there are many pathways to the same end result so that the actual statistical probability of evolution in a particular direction can be much higher than intuition (on a simple Darwinian basis) would suggest. It 'explains' convergent and parallel evolution. Great stuff but not Physics.

 

[fizixfan]

Read Arrival of the Fittest by Andreas Wagner. It's a good read and shows, with computational evidence, that there are many pathways to the same end result so that the actual statistical probability of evolution in a particular direction can be much higher than intuition (on a simple Darwinian basis) would suggest. It 'explains' convergent and parallel evolution. Great stuff but not Physics.

Sounds interesting. I read the intro, and it's a tease. I probably will buy the book to see if he really does explain HOW nature innovates.

Stephen Jay Gould's "Punctuated Equilibrium" introduced the idea that genetic changes accumulate over time with no changes in phenotype, and will sometimes be expressed suddenly (relatively speaking) when the right amount of environmental pressure is brought to bear.

I would also recommend Stuart Kauffman's "At Home in the Universe," a groundbreaking book that looked into the roles that self-organization and emergent order play in evolution. Kauffman was a MacArthur Fellow, so he's no slouch. This book was quite revelatory to me.

 

[sophiecentaur]

if he really does explain HOW nature innovates

What he does do is to show the results of a vast amount of statistical work on computers which has revealed that there are many different pathways to achieve a seemingly 'singular' result. The numbers / probabilities leads to the conclusion that evolution does;t have to rely on such low probabilities which would be associated with single random events. I guess, when you get down to it, it's akin to comparing _nC_m and _nP_m (Combinations and Permutations). He writes numbers down with a lot of zeros in them, when he wants to make a point - to appeal to the non-mathematical amongst his readership- but it's quite a good read and I came away 'feeling' I had a better grasp of the situation. Kindle prices are always better than hardback, of course. Fine for a book with very few diagrams in it.