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Thought experiment: The 'perfect eye' (and a finite set of colours)

  1. Oct 22, 2008 #1
    Thought experiment: The 'perfect eye' (and a finite set of colours)


    Introduction:

    Human beings have trichromatic colour vision, our ability to distinguish different colours at different spectral frequencies, and wavelengths, of electromagnetic radiation, or combinations thereof, is enabled and limited by having three different colour receptors in our eyes. Red, green and blue receptors perceive light and allow us to distinguish colours through additive processes in an RGB colourspace.

    Most mammals and people with colour blindness have dichromatic colour vision, limiting their ability to distinguish different colours at different spectral frequencies, and wavelengths, or combinations thereof, perceiving what trichomats see as different colours (i.e. red and green in protanopia) as one colour.

    Birds have tetrachromatic colour vision, they have four different colour receptors, and are able to distinguish additional colours within the colours trichomats perceive, and to also see electromagnetic radiation from outside the range of what we consider the visual spectrum into the ultraviolet. There is new research suggesting that some woman may be tetrachromats.

    With each additional colour receptor an eye has, the more colours it is able to distinguish from different frequencies/wavelengths of the electromagnetic spectrum, or combinations thereof, and additional receptors may also expand the range of the electromagnetic spectrum that is visually perceivable.


    The thought experiment:

    Is it possible to build a 'perfect eye' that is able to perceive not only the entirety of the electromagnetic spectrum, but is able to distinguish between every colour that exists, that is, it has a colour receptor for every spectral colour (or hue) that exists so that the addition of another colour receptor would not enable the eye to distinguish additional colours (or hues)? Could we create totalchromats?


    I can envisage three approaches:

    First Approach:

    The first of which asks another interesting question:

    Are there a finite or infinite set of possible colours?

    For there to be a finite set of spectral colours (or hues) the electromagnetic spectrum would have to be discrete rather than continuous. That is, the difference between the frequency, or wavelength, of two different electromagnetic waves could not be infinitely small, otherwise additional colours could be created by simply adding a very small amount to the frequency, or length to the wavelength, necessitating an additional receptor for that frequency/wavelength to perceive an additional colour etc, ad infinitum. There would be an infinite set of colours needing an infinite number of receptors to build a 'perfect eye'.

    Secondly there would have to be upper and lower limits on the electromagnetic spectrum. Even if the spectrum is discrete, a spectrum with infinitely large or small frequencies, or infinitely short or long wavelengths, would have an infinite set of colours and need an infinite number of receptors to build a 'perfect eye'.

    Second Approach:

    Regardless of whether the electromagnetic spectrum is discreet or continuous, and whether there is a finite set of theoretical colours, a second approach to the experiment is:

    Are there inherent limits on the ability of a colour receptor to distinguish between different wavelengths and hence different colours (or hues)? If the spectral sensitivity of a colour receptor is unable to distinguish between different frequencies with infinite precision, then this uncertainty of the colour receptor has the practical effect of making the electromagnetic spectrum (as it is perceived) discreet, creating a finite set of perceivable colours (if there are upper and lower limits on the EM spectrum), and allowing us build a 'perfect eye' with a finite set of colour receptors.

    Third Approach:


    A third approach is the practical one, how could a 'perfect or almost perfect eye' be built? What real world limits to a 'perfect or almost perfect eye' are there? How many colours could be practically distingushed? How much of the electromagnetic spectrum could be seen? What would be needed to process the image? How would the image be processed? What would the colourspace look like? Would the phenomenon of dominant wavelength limit the practical number of colours seen?


    A 'more perfect eye'

    The concept of a 'perfect eye' also goes beyond colour recognition and into other ideas like:

    How else could an eye be perfect beyond distinguishing colours? What about perception of forces other than electromagnetic radiation? Could other forces have colours that a 'more perfect eye' could see and distinguish? Could it combine them with EMR or other 'force colours' to make a 'more perfect image'?


    Last thoughts:

    One additional question needs to be asked of the experiment no matter the approach. Even if there were a finite set of spectral colours (or hues) or colours (or hues) perceivable by colour receptors, would there be a finite or infinite set of additive colours in a 'perfect colour space'? Would there be a limit on the amount of colours that are able to be distinguished in the 'perfect brain' that processes the 'perfect eyes' image?


    Your thoughts please!...
     
  2. jcsd
  3. Oct 22, 2008 #2

    mgb_phys

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    Having three (or more) colour receptors with fixed bandpasses - as in a human eye or a colour CCD camera, isn't the only way to do it - or even the best.
    The visible spectrum is a continous range from UV to IR, you could just have a pair of receptors with a linear response, one measuring how much blue and the other how much red you get from a single source. You could also have detectors which measure the wavelength of each photon directly.

    Expanding vision into the UV and IR doesn't require more colour recpetors it just means extending the response range of the current ones, making the blue one sensitive to shorter blue and the red one sensitve to longer red. There are obviously limits, as you go further into the infrared red the photon energies become lower and so unless you want a cryogenically cooled eye the light will be swamped by thermal noise - similairly as you go into shorter wavelengths you have to find materials that will transmit the light.

    Other animals have usefull visual features outside colour - some insects and crustaceans can see polarisation which helps distinguish different surfaces that look the same to us.
     
  4. Oct 22, 2008 #3
    A Forth approach:

    Another approach to the 'perfect eye' is; rather than attempt to have a colour receptor for every colour, instead have simulated colour channels from a limited number of receptors that when processed as an image in a 'perfect brain' are able distinguish between all possible colours.

    A receptor than is sensitive to all electromagnetic radiation, or a number of sensors than together have a range across the entire electromagnetic spectrum, could be processed in such a way as to create additional simulated colour channels across different sections of wavelengths. If that 'section of wavelengths', from which a simulated colour channel were created, was reduced to the minimum resolving ability of the receptors, then a maximum amount of 'spectral' colours that could be possibly distingushed would be created, simulating the image of a 'perfect eye' within the 'perfect brain'.

    If we set arbitrarily limits on wavelengths in the EM spectrum at 1 Pictometre and 100 Megametres, and say that our receptors are able to resolve the size of the wavelengths it receives to within 1 Pictometre difference, then we would arrive at a spectral, simulated colour set of 10 to the power of 23 different spectral colours (10^23) and then we have the additive colours...

    Spectral sensitivity may not be fundamentally consistent across the spectrum, and neither may more 'real world' arrangements of receptors, placing fundamental limits on distinguishable colour channels, and/or additional demands on image processing.

    A relevant question is; what scale of processing power would be needed for a perfect eye to be processed? Just enough to fit in my robots/transhumans head? Enough to fill a Jupiter brain? Or beyond the resources of the entire universe?
     
  5. Oct 22, 2008 #4
    The idea behind this is not mainly concerned with extending the range of what is 'visible' within the EM spectrum, though it is an important part, but how many more 'colours' could be perceived and distinguished within what is visible. The larger question being posed is, could we reach a point were we could 'see' all the colours that are there to be seen?

    Would having a detector that is able to measure the wavelengths individual photons directly be similar to the points outlined in the second approach; that because a detector, even an ideal one(?), is unable to determine the size of an incoming photons wavelength with infinite precision, it has the practical effect of making the EM spectrum, as is perceived, discreet, thus limiting the set of possible colours (if there are upper and lower constraints on the spectrum).

    So thermal noise to longer wavelengths, and opacity to shorter ones, are big challenges to a 'perfect eye'... Maybe a composite eye, with different and separate parts being sensitive to different sections of the spectrum and tailored to their particular characteristics, with the total image being formed in processing, could get around those problems?

    I'll have a look into polarisation, a 'perfect eye' has got a big expectations to live up to!
     
  6. Oct 22, 2008 #5

    Claude Bile

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    This is a good thought experiment, mainly due to the number of theoretical constraints you run into when you start to think about it.

    Essentially, what you are trying to implement with the perfect eye is complete characterisation of an electromagnetic wave. In order to do this (classically at least) we need to know;
    - The spectrum of the wave, including relative phases. The Fourier transform yields the temporal evolution of the wave.
    - The spatial distribution of the wave. The Fourier transform yields the momentum distribution (k-spectrum) of the wave, i.e. the direction(s) the wave is propagating.
    - Polarisation, linear and elliptical.

    The spectrum of the wave is gathered by obtaining a power measurement for each frequency - the most practical way this is achieved is by using a diffraction grating, however to cover the entire spectrum, the grating would have to be infinitely long (and thus have an infinite free spectral range). Unfortunately, the bigger the free-spectral range, the lower the resolution, so our infinitely long grating might not be so useful after all. Bummer.

    Resolving the spatial distribution requires a lens, which, practical issues aside (such as being transparent over the entire spectrum) still has some fundamental problems, the most pressing problem being that the resolution we can obtain using a lens is dependent on the size of the actual lens with respect to wavelength. In other words, for very long wavelengths, we need a massive lens (that's why we need giant antenna arrays for radio astronomy). Since we are attempting to resolve the entire spectrum, the lens will need to be as big as the known universe in order to resolve any spatial detail of the longest EM wavelengths.

    Finally, polarisation. This is probably the most practical to measure of the lot, since we don't have infinite domains here! We can characterise any polarisation state using only a handful of parameters. The tricky part here will be resolving left-handed and right-handed polarisation states, to do this we need a chiral medium, which do exist! Thus there are no real classical constraints when it comes to measuring polarisation.

    The other fundamental constraints we must be mindful of are those of a quantum nature, I am not qualified to really comment on those in detail.

    If you remove the constraint that we need to do the entire EM spectrum, many fundamental constraints are relaxed substantially. For a finite spectrum, we can partition our perfect eye into a number of eyes that each look at one portion of the spectrum - i.e. one for the visible, one for the UV, one for infrared etc. Because the practical challenges very substantially from one part of the spectrum to another, this would be the best way to implement it (indeed, this is what we do in the real world!).
     
  7. Oct 23, 2008 #6

    Andy Resnick

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    It's not clear what the biological advantage is to have a much more complex eye. In fact, extremely good color discrimination can be easily acheived by having a small number of broad-band detectors with considerable spectral overlap: by taking ratios of detectors, extremely fine spectral discrimination is achieved.
     
  8. Oct 23, 2008 #7

    HallsofIvy

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    What do you mean by "every color"? The color of light is determined by its frequency and that is "continuous".
     
  9. Oct 23, 2008 #8
    Use optical nanoantennas:

    http://repository.upenn.edu/dissertations/AAI3292048/

    In the eye you have a phased array consisting of billions of such nanoantenas. The signal from each antenna is detected as a function of time. By combining the signals from the antennas you can have a good angular resolution and sensitivity.
     
  10. Oct 23, 2008 #9
    I think that's the best way to put what a 'perfect eye' should be able to do; a complete characterisation of an electromagnetic wave.

    Would it be correct to say that an upper limit spectrum that would be visible to a perfect eye would be the size of the eye itself? It's a fair assumption that a perfect eye, outside of a pure thought experiment, is not going to be the size of the universe. Maybe the best way is to add an additional qualifier when we talk about a 'perfect eye', that is, a perfect eye at a certain (lens) size, because that upper constraint would appear to more fundamental than any other practical difficulties in trying to measure the entire EM spectrum.

    Now we have a practical upper wavelength limit on the EM spectrum, is there a lower one? Is it a case of classically no, and quantum maybe? With a probable practical limit much like the upper one we have just made?

    The Chiral medium looks very interesting as a way to measure polarisation, are there any limits on the polarisation states it could measure?

    What about the practical difficulties of measuring the different sections of the EM spectrum? Are there any sections have have proven exceptionally difficult or impossible to measure? Does the precision of measurement change at different wavelengths with current or envisioned technologies at different parts of the EM spectrum? (even with devices designed for that particular section?)
     
  11. Oct 23, 2008 #10
    That's true, there may or may not be a much of a biological advantage to a more complex eye, and the additional computation needs in image processing may be staggering and debilitating, biologically and/or economically. On the practical side it places limits on how complex an 'almost perfect eye' could be. Once there's a rough consensus on how much information a 'perfect eye' could or should collect, it would be very interesting to see how many binary bits would be needed to carry the information of a single pixel, and larger images and video. Compression would help, but it might defeat the purpose.

    Detectors with spectral overlap seems to be the most practical solution, and would much more efficiency achieve wide coverage with good spectral discrimination. The idea in the forth approach I wrote was to use that spectral discrimination in image processing to create additional simulated colour channels. At a particular wavelength, instead of that colour, as perceived, being an additive result of other primary colours (red, green and blue in normal colour vision), it becomes a primary colour in its own right, as would all single wavelength spectral colours, with the only additive colours being combinations of primary, spectral colours (like purple).

    The point being that if you can achieve good spectral discrimination with a limited, even small, number of detectors, there is no need for the inevitable task of having a detector for each and every wavelength, which would probably need infinite detectors, to see 'all or almost all the possible colours'.

    What's the forums thoughts on creating additional simulated primary colour channels in image processing, out of the spectral overlap out of a limited number of EMR detectors, utilising the fine spectral discrimination they could achieve?
     
  12. Oct 23, 2008 #11
    That's one of the big questions posed by the thought experiment, is there a finite or infinite set of colours?

    I thought of a few different approaches, the first asking is the EM spectrum continuous or discreet? Classically it is, do any Quantum theories suggest it is discrete?

    The second approach asking; does the imprecision with which we (or a detector, or an ideal detector) perceive or measure a continuous EM spectrum, have the practical effect of chopping it up into discrete packets, and thus making a finite colour set (with upper and lower constraints)? Say we could only measure the frequency of a wavelength to a precision of 1ym (10-24m), then two different waves whose frequencies differ by less that 1ym(?) will be spectrally indistinguishable, and will be perceived as the same colour.

    The third approach asks how many colours could it be practical to see with an 'almost perfect eye', with practical being judged by different standards. It does not depend on whether there is a finite or infinite set of possible colours.

    In these approaches it may well be that there are infinite colours, and that therefore at some point in the perfect eyes design require an infinite answer to see "all the colours".


    I should clarify when I talk about "all the colours", the idea is that a perfect eye would turn each different wavelength into its own primary colour, so that when we see the spectral colours (or any wavelength of the EM spectrum), instead of seeing an additive colour (in RGB colourspace), we instead see a colour in its own right, independent and not the combination of any other. Combinations of spectral colours would then produce additive colours together with other colourspace concepts like saturation, lightness, luminance etc... and as we have added, polarisation.
     
  13. Oct 23, 2008 #12
  14. Oct 23, 2008 #13

    Vanadium 50

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    There is no dispute about this. Light has an infinite possible range of frequencies. Of course, to determine that you have a frequency of f and not f + epsilon takes increasingly longer as epsilon gets smaller, so if you require that two colors be distinguished within a fixed time window, that reduces the number of distinguishable colors to some number of trillions.
     
  15. Oct 23, 2008 #14
    If you had an infinite amount of time would you be able to determine, with an ideal detector, the frequency (or wavelength) of a photon with infinite precision?

    Aren't there uncertainty problems, even with unlimited time? Would you just be measuring a probability distribution?

    In any case, for a colour to be seen by an eye, it would need to be perceived within some sort of a time limit. And a time limit would break up a continuous EM spectrum into discrete parts of perceivable colours.

    How would you go about determining the mathematical relationship between a time limit and the resolving precision of a detector?

    Also, does a time limit, in and of itself, place any upper or lower constraints on how much of the EM spectrum would be perceivable? Even if it made the perceivable colours in the spectrum discrete, if the spectrum continues indefinitely in either direction, there would be an infinite number of discrete colours.
     
  16. Oct 23, 2008 #15

    Andy Resnick

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    Radiometry (the physical properties of light) is not the same thing as Photometrics (how light is perceived by the human (or animal) eye). Radiometrically, the 'color' of the light is simply the specified wavelength (or center wavelength for dispersed pulses). Photometrics deals with perceived color- the chrominance, luminance, etc. I don't think polarization plays a role in how color is perceived. Thus, we can speak of browns and pastel hues in photometrics whereas those colors do not exist radiometrically.

    The electromagnetic spectrum is both continuous and is a radiometric quantity. Certain objects only emit in a discrete (or very narrowly peaked) spectra, but the energy spectrum itself is continuous. Color space in photometrics is more complex, covering a 2- or 3- or even higher dimensional space, and there is no unambiguous 1-to-1 mapping between the two ways to define color.

    This is the key concept- chromaticity does not have a simple mapping to wavelength, and vice-versa.

    Does that help?
     
  17. Oct 23, 2008 #16

    Vanadium 50

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    I haven't been thinking about a single photon, but rather a continuous source. (Note that the eye is not sensitive to single photons).

    We always measure "just" probability distributions. There's always a chance that one will mismeasure a given quantity and assign it to the wrong bin. We can only talk about making this probability arbitrarily small.

    "Discrete parts of perceivable colours" sounds like there is an exact number. I don't believe that's true: it's more likely that with N colors, once can resolve 2 adjacent colors 90% of the time, but with 2N that drops to 50% and with 3N maybe 10%.
     
  18. Oct 23, 2008 #17
    Thanks, that definitely helps, especially the correct definitions and terms.

    Let me express the idea more clearly. When I speak of colours I'm referring to Photometric rather than Radiometric colours. What I'm suggesting in this thought experiment is that it may be possible to map the Radiometric colours, across the EM spectrum, more thoroughly to additional Photometric primary colours in an additive n-dimensional colour space, and that furthermore the Radiometric colours could in some way be mapped in their entirety to primary Photometric colours in an additive n-dimensional colour space, so that the subsequent addition of more Photometric primary colours into the proposed colour space (i.e. adding another dimension), would not result in any more colours being perceived.

    The 'perfect eye' is in all likelihood not for humans as they are now, and shouldn't be thought of as limited by our faculties, its probably a transhumanist idea, and a far out one at that.

    The idea of polarisation comes from a suggestion earlier in the thread that some animals can see polarisation, and that a perfect eye, whilst expanding the gamut of its Photometric colour space, may as well try to expand that colour space to other wave properties, such as polarisation.

    I'm not sure if I'm expressing the idea correctly in terms of the colour space envisioned or the the relationship envisioned between the Radiometric and Photometric colours, so I may rephrase it later. I'd also like to describe the colour space in terms other than additive.

    Does that make the idea clearer? What are your thoughts?
     
    Last edited: Oct 23, 2008
  19. Oct 23, 2008 #18
    Apparently the rods in our eyes are sensitive to single photons, whilst the cones are not, so a single photon in our imperfect eyes can let us see something. In any case, a perfect eye should not be thought of as limited by our human faculties, and unless there is a reason why its hypothetical detectors would not be sensitive to single photons, the question remains; would a detectors precision of radiometric colour recognition be different if the EM source was a single photon?

    How small is arbitrarily small? The idea behind the question is that the imprecision of a detector would mean that a certain range of radiometric colours would be perceived as a single photometric colour (or chroma) in the proposed colour space, equal to the imprecision of the measurement; thus creating a discrete photometric chroma spectrum out of a continuous radiometric colour spectrum; and that furthermore, could the imprecision in measurement be an inherent quantum effect rather than the result of a time limit or technological shortcoming?

    Could you explain the N colours and probabilities again, I didn't understand it.
     
  20. Oct 25, 2008 #19
    I like your idea of the perfect eye. An important distinction to make between all EM spectra vs. just the visible range, is that the visible range is perceived by humans to have hues. This cannot be said for the rest of the EM spectra. Sure you could build a perfect eye (well near perfect, but obviously we don't have the tech to attenuate the longest radio waves, or the shortest cosmic waves) but detecting EM radiation and actually perceiving it in colored hues as our human eye does, is quite unfathomable.

    The human eye detects incident photons in the retina, in which a slew of cells, most notably the cones and rods are used to detect the light. Cones and rods detect light in the exact same manner. Within each is a light sensitive protein called an opsin which in turn contains the molecule cis-11-retinal. When an incident photon strikes this molecule, the photon powers a conformational change of the molecules atomic bonds and its transformed into trans-retinal. This conformational change can be thought of not metaphorically, but literally, as the opening of a gate. Once the gate is open, a chemical cascade is set into motion, in which the end result is neurotransmitters like Ca2+, Na+, and CL- flow through ion channels and enter the next strata of the retina, the strata where horizontal cells are located. Then various other cells in the strata in turn receive the signal and do intensive signal processing on it, these cells include, in order, Bipolar cells, Amacrine cells and finally Ganglion cells. After the signal leaves the ganglion cells it enters the optic nerve and is en route to the brain's visual cortex where further less well understood processing occurs and the perception of color is formed. I am simplifying the process because its extremely complex, but suffice it to say cones and rods are just the inital phase of perceiving incident light, one must also consider the complex circuitry of the retinal strata cells and then the even more complex circuitry of the visual cortex.

    My point being, your perfect eye needs a perfect brain too.

    Plus as you pointed out, the EM spectra unless precisely defined to have limits, is infinite in expanse. Also, as another poster pointed out, a single rod can detect a single photon, this is true. But to perceive a single photon, you require two adjacent rods for contrast. In other words, for you to see a single photon you need Rod-OFF | Rod-ON | Rod-OFF. Essentially, a diffraction grating is needed. Try making a diffraction grating for gravity waves (if they exist) and you will require a network of 100s of satellites like LISA to achieve resolutions better than a blur. Consider the retina, which has 120,000,000 rods, and 6 million cones in an average adult male.

    That said, I really enjoyed your idea of the perfect eye and with unlimited funds and a discrete limit on the EM spectra, I see no barrier to achieving it some day.

    Cheers.
     
  21. Oct 25, 2008 #20
    Some good points. I see the perfect eye, at its grandest scales, as something for a type 3 civilisation to do when it gets bored!

    Have a read of my new post (after this one) in regards to hues, I go into more detail on the colour space model involved, see how that relates to the points you raised.

    I'm getting a little closer to working out just how much computational power would be needed.. LOTS. Even if you couldn't fit it all into your transhuman's or robot's head you could imagine a perfect eye observatory that has a perfect brain or very powerful computer that you 'plug into' so to speak, so that all the processing is done remotely with the being that perceives the colours being a 'thin client'.

    I'm not sure about single photons, it was more of a way of asking for a QM answer rather than classical one.

    I still have some QM related questions about a discrete EM spectrum and upper and lower limits of radiometric and spectrometric EM spectrums, but I'm doubtful there is any QM saviour for a truly perfect eye, and as you say, any practical perfect eye would have to have upper and lower limits on the EM spectrum it surveyed.
     
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