Metamerism (vector-matrix representation of color perception)

Click For Summary
The discussion revolves around explaining metamerism using vector-matrix representation of color perception under different illuminants. The user seeks confirmation on their understanding of how two objects can appear the same color under illuminant A but differ under illuminant B. Participants emphasize the importance of defining variables and functions to facilitate better assistance. Providing standard references or links related to the topic is suggested for clarity. Overall, the focus is on accurately representing color perception in varying lighting conditions.
nao113
Messages
68
Reaction score
13
Homework Statement
I want to explain metamerism by using vector-matrix representation of color perception. So, here, there are 2 conditions where the both objects produce the same color with illuminant spectrum A, and the both objects produce the different color with illuminant spectrum B
Relevant Equations
in the picture below
For the illuminant A

Screen Shot 2022-06-22 at 13.01.31.png

for the illuminant B
Screen Shot 2022-06-22 at 13.01.37.png

Did I got them correct? Thank you
 
Physics news on Phys.org
nao113 said:
Homework Statement:: I want to explain metamerism by using vector-matrix representation of color perception. So, here, there are 2 conditions where the both objects produce the same color with illuminant spectrum A, and the both objects produce the different color with illuminant spectrum B
Relevant Equations:: in the picture below

For the illuminant A

View attachment 303155
for the illuminant B
View attachment 303156
Did I got them correct? Thank you
You are much more likely to get help with this if you take the trouble to define the variables and functions. If they’re standard within the topic, perhaps you can provide a link.
 
At first, I derived that: $$\nabla \frac 1{\mu}=-\frac 1{{\mu}^3}\left((1-\beta^2)+\frac{\dot{\vec\beta}\cdot\vec R}c\right)\vec R$$ (dot means differentiation with respect to ##t'##). I assume this result is true because it gives valid result for magnetic field. To find electric field one should also derive partial derivative of ##\vec A## with respect to ##t##. I've used chain rule, substituted ##\vec A## and used derivative of product formula. $$\frac {\partial \vec A}{\partial t}=\frac...