# Photoreceptors and light with mixed frequencies

I am interested in how the activation of a, say, blue cone depends on the incident light. Wikipedia tells me this: , which describes how strong the activation of the blue cone is for light with a single wavelength and a given intensity. But what happens if the incident light has several frequencies?

My question is: given the intensity i(f) of the incident light at frequency f, what is the activation of the blue cone?

(A natural guess would be that if b(f) is the activation curve in the figure, then the activation of the blue cone should be the integral of b(f)*i(f) over f. But I have not found any confirmation of this guess. For example, in the reference for the picture above, only pure light was used in the experiments.)

• I'm confused. Your question seems to ask for a simple reading of the graph at a particular frequency but your comment implies otherwise. Also, what do you mean by pure light? I gather the vertical axis is fraction of maximum possible? If so, would integrating under the curve make sense? – bpedit Oct 10 '16 at 16:31

## 1 Answer

Yes, current color models assume a linear response in the spectrum.

Given a light with mixed spectrum $\Phi(\lambda)$, the response of a cone with spectral sensitivity $\Psi_i(\lambda)$ is a (nonlinear) function of the L2 inner product: This is how CIE XYZ color space is defined.

Reference: