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If I understand correctly, the cones in the human eye work as follows: the three types have a degree of sensitivity for each wavelength. A cone is activated in a one-dimensional "degree of activation", but by itself cannot detect the wavelength of light that activates it.

If we know that only one light frequency enters the eye, then we can easily deduce what this frequency is based on the degree of activation of the three cones.

But suppose we sample a spectrum of emission from all possible spectra. What can the eye infer from the three degrees of activation? It seems like it would not be able to distinguish between many different spectra. In particular, for any given wavelength, we can create many different "scrambled" spectra that result in the same activations.

This would mean the eye has only a quite limited capacity to distinguish between spectra of emission.

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  • $\begingroup$ @user56834, In the color printing business, they have a name for the inability of human eyes to "distinguish between many different spectra." They call it metamerism. That leads to another phenomenon, metameric failure in which, for example, two different inks or dyes that are indistinguishable from each other when illuminated by one light source (e.g., sunlight) can look dramatically different under some other light source (e.g., typical office lighting) $\endgroup$
    – Solomon Slow
    Commented Oct 21, 2019 at 16:45
  • $\begingroup$ @SolomonSlow You're right -- that was a silly mistake on my part! (I shouldn't write quickly; I've deleted that comment.) Thanks for catching this quickly. A better comment: "This would mean the eye has only a quite limited capacity to distinguish between spectra of emission." Yes. As an example, pure red light and pure green light are perceived in the same way as pure yellow light. $\endgroup$
    – Raghu Parthasarathy
    Commented Oct 21, 2019 at 16:57

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But suppose we sample a spectrum of emission from all possible spectra. What can the eye infer from the three degrees of activation?

The eye is limited to a three-way signal, where each type of receptor outputs the integral of the spectral power distribution of the stimulus $P(\lambda)$ weighted by the spectral sensitivity of the receptor, i.e. a signal of the form $$ A = \int_0^\infty P(\lambda) a(\lambda)\,\mathrm d\lambda $$ for $a\in\{r,g,b\}$, $A\in \{R,G,B\}$.

It seems like it would not be able to distinguish between many different spectra. In particular, for any given wavelength, we can create many different "scrambled" spectra that result in the same activations.

Yes.

This would mean the eye has only a quite limited capacity to distinguish between spectra of emission.

Yes. I don't know what else there is to say about that.

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