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Paraphrasing from here:

A purely monochromatic 575nm wavelength light would be "perceived" as yellow, as would a light that has equal components in red and green (but no yellow). However, the actual waveform for the latter would be different than a pure yellow waveform.

However, we could, theoretically, use a Fourier Analysis to determine the frequencies at which the second light (red/green) has peaks in intensity. I am wondering if there would be any such case where an FFT would mislead us in how that light is perceived by most humans. For example, maybe you input some waveform to an FFT and the results show peak intensities in the red and green wavelengths, but for some reason that light is actually perceived as blue or something... discounting variances in the perception of color between humans (talking general case here).

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    $\begingroup$ physics.stackexchange.com/q/673991/123208 has a graph of human cone response spectra, but note that the curves are normalised so that they all peak at 1.0, which is a bit misleading, IMHO. $\endgroup$
    – PM 2Ring
    Commented Nov 19, 2023 at 2:34
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    $\begingroup$ FYI: The input to the FFT is supposed to be a sequence of samples of some continuous waveform. Light can be understood as an electromagnetic wave, but how are you going to sample the value of that wave at sufficiently high rate to recover frequency information? $\endgroup$
    – Solomon Slow
    Commented Nov 19, 2023 at 15:15
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    $\begingroup$ Following up on the comment below an answer, we typically use a spectrometer or spectrograph to disperse light and get spectra, i.e., intensities as a function of wavelength or wavenumber. I did this for dispersing the “purple” light emitted by a long-obsolete GE AR-1 glow lamp: physics.stackexchange.com/a/754027/313612. The two dimensional spectra, called echellograms, clearly show that the light is mostly violet and red, with less green. Our brains, mine anyway, perceives this very rich spectrum as plain old purple. The lamp’s fill gas is 90% argon and 10% nitrogen. $\endgroup$
    – Ed V
    Commented Nov 19, 2023 at 15:19
  • $\begingroup$ Related: There is a device called a Fourier transform spectrometer (en.wikipedia.org/wiki/Fourier-transform_spectroscopy) which uses a pair of glass plates with a small controllable gap between them (etalon). The light transmitted through the etalon is the sum of the light that is reflected no times, the light reflected twice, four times, etc. At some distances, the reflections destructively interfere with the transmission and less light gets through. It turns out that the plot of transmission vs distance is the Fourier transform of the spectrum. $\endgroup$
    – kwan3217
    Commented Nov 19, 2023 at 18:02

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The Fourier transform does tell you the mix of frequencies in the light. From that, you can calculate the relative stimulations of the three types of cones in your eye. That mix tells you the amount of red, green, and blue you perceive, and hence the color. See Conversion formula from spectrophotometer readings to any standard color space profile?

But color happens in the mind. Gotchas are always possible:

  • Some people are colorblind. They only have two types of color receptors—or, rarely, just one.
  • You can saturate the receptors and see after-image colors.
  • Colors in the surrounding area affect perception. See What is Gray, from a physics POV? for an example.
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  • $\begingroup$ That helped, thank you. Theoretically, could you derive the - emprically obtained - spectral power distribution of the light entering the retina, by doing a FFT of the signal from some light-sensor, or would this be a completely different "mathematical" breakdown of the component waveforms vs. the true wavelengths present in the physical light. $\endgroup$
    – codecitrus
    Commented Nov 19, 2023 at 3:46
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    $\begingroup$ Typically you don't know the waveform of visible light. You might for the radio spectrum. For visible, you would likely measure the intensity of each wavelength directly with a spectrograph. $\endgroup$
    – mmesser314
    Commented Nov 19, 2023 at 4:27
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Spectral analysis of light is the basis of precision colour matching - although the problem in reality is made very much worse by the diffuse reflection component of real surface textures and fluorescence of some dyes. Spectral analysis is equivalent to taking the FT of the incoming waveform just implemented differently. Giving measured intensity as a function of wavelength.

Colorimetry has a long history - more than you probably ever want to know available here Basic Principles of Colour Measurement and Colour Matching of Textiles and Apparels

The best examples of objects that exhibit brain confusing colour behaviour are the natural gemstone Alexandrite (chrysoberyl) and the neodymium doped glass used by glass blowers to block the sodium D lines (effectively a narrow band stop filter against yellow light). The latter also found use in early colour TVs to improve the blue phosphor. In both cases the perceived colour of the material depends strongly on the colour temperature of the "white" light used to illuminate it. Such objects are rare but do occur both in nature and manufactured filters.

Looking through Nd doped glasses in particular can produce out of gamut colours in the brains perception of colour which although normally thought of as RGB is actually YGB raw sensor data with the red channel computed by the brain as Y-G for spotting ripe fruit. The effect is exaggerated red/green colour saturation. It even works on photography and such filters are sold to enhance fall colours.

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  • $\begingroup$ "Spectral analysis is equivalent to taking the FT of the incoming waveform just implemented differently." - This helped. Thank you. $\endgroup$
    – codecitrus
    Commented Nov 19, 2023 at 17:51

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