Equations for Color

  • The color is presented as a difference in the magnitude, $m$, in the red and blue filters: \[\text{color} = m_{\text{blue}} - m_{\text{red}} = -2.5 \cdot \log_{10} \Big(\frac{\text{brightness_blue} }{ \text{brightness_red}} \Big) \] Note that the modeling has been done for a white light of the source, i.e., the solar color is not included here; it should be subtracted from the observational data to fit the modeling results. As usual, positive color is called red, and negative color is called blue, neutral color is equal to zero.
  • For a mixture of two materials, the resulting color is calculated as: \[\text{color} = -2.5 \cdot \log_{10}\Big(\frac{\text{brightness_blue_1}\cdot r +\text{brightness_blue_2}\cdot (1-r)} {\text{brightness_red_1}\cdot r+\text{brightness_red_2}\cdot (1-r)} \Big) \] where 1 and 2 correspond to material 1 (e.g., water ice) and material 2 (e.g., olivine) and $r$ is the fraction of the particles of the material 1 in the mixture, e.g., 0.1 means that each 10 particles in the mixture contain 1 particle made of material 1 and 9 particles made of material 2; 0.9 means that among 10 particles 9 are made of material 1 and 1 is made of material 2.