Comparison -- Necessary Condition for Color Vision

• Monochromatic System:

  If there is only one type of photoreceptors with sensitivity as a function of wavelength $S(\lambda)$, such as the rod cells in the retina, then only one value is produced as the response to a given color $L(\lambda)$ (see
  

  $$r=\int S(\lambda) L(\lambda) d\lambda$$
  
  
  and the visual system perceives an image of different gray levels. Moreover, it is possible that some two colors $L(\lambda)$ and $L'(\lambda)$ are responded to by the same value, so long as
  
  $$r=\int S(\lambda) L(\lambda) d\lambda= r'=\int S(\lambda) L'(\lambda) d\lambda$$
  
  
  

• Dichromatic System:

  The necessary condition for color perception is to have more than one type of photoreceptor with different sensitivity functions $S_i(\lambda)\;\;\; (i=1,2)$, so that each color is represented by two or more values and some comparison can be made between the two types of receptors.

  Almost all mammals except primates have only two types of photoreceptors (S type and LM type). It is again possible, although less likely than the monochromatic case, for two colors $L(\lambda)$ and $L'(\lambda)$ to be indistinguishable if the two types of receptors respond to the colors in the same way, i.e.,
  

  $$r_i=\int S_i(\lambda) L(\lambda) d\lambda =r'_i=\int S_i(\lambda) L'(\lambda) d\lambda\;\;\;\;(i=1,2)$$
  
  

  

• Trichromatic System:

  In the primates the LM type photoreceptor is separated into M and L types. These three different types of photoreceptors respond to a given color $L(\lambda)$ with different intensities:
  

  $$r_i=\int S_i(\lambda) L(\lambda) d\lambda\;\;\;\;(i=1,2,3)$$
  
  
  As the result, more comparisons can be made to distinguish more colors. But can three types of receptors resolve all possible colors? As before, if it so happens that all three types of receptors respond to some two colors $L(\lambda)$ and $L'(\lambda)$ with identical outputs:
  
  $$r_i=\int S_i(\lambda) L(\lambda) d\lambda =r'_i=\int S_i(\lambda) L'(\lambda) d\lambda\;\;\;\;(i=1,2,3)$$
  
  
  the colors are still indistinguishable, and they are called metamers.

  

• Tetrachromatic System:

  Some animals have four different types of photo receptors that are sensitive to red, green, blue and ultraviolet light. These animals have much richer color sensation than humans.