Let two sensors of interest be sensor-1 and sensor-2. The TOA reflectance of sensor-1 at the wavelength $\lambda 1$ [Eqs. (2) and (3) for $\lambda 1$] and that of sensor-2 at the wavelength $\lambda 2$ [Eqs. (2) and (3) for $\lambda 2$] can be related using the relationship for the soil layer, known as the soil line.^{46} The linear relationship between any two bands for soil reflectances were assumed as Display Formula
$Rs(\lambda 2)=a(\lambda 1,\lambda 2)Rs(\lambda 1)+b(\lambda 1,\lambda 2),$(4)
where the two parameters $a(\lambda 1,\lambda 2)$ and $b(\lambda 1,\lambda 2)$ are the slope and offset of the soil line, respectively. After truncating the higher-order interaction terms between the atmosphere and vegetation layers [Eq. (2)] and between the vegetation and soil background layers [Eq. (3)] for $\lambda 1$ and $\lambda 2$, $Rs(\lambda 1)$ and $Rs(\lambda 2)$ are eliminated using Eq. (4), which derives the vegetation isoline equations.^{40}Display Formula$\rho (\lambda 2)=A(\lambda 1,\lambda 2)\rho (\lambda 1)+D(\lambda 1,\lambda 2),$(5)
where Display Formula$A(\lambda 1,\lambda 2)=a(\lambda 1,\lambda 2)\alpha (\lambda 1,\lambda 2)\gamma (\lambda 1,\lambda 2),$(6)
Display Formula$\alpha (\lambda 1,\lambda 2)=Ta2(\lambda 2)Ta2(\lambda 1),$(7)
Display Formula$\gamma (\lambda 1,\lambda 2)=\omega Tv2(\lambda 2)+1\u2212\omega \omega Tv2(\lambda 1)+1\u2212\omega ,$(8)
Display Formula$D(\lambda 1,\lambda 2)=D2(\lambda 2)\u2212A(\lambda 1,\lambda 2)D1(\lambda 1),$(9)
Display Formula$D1(\lambda )=\rho a(\lambda )+Ta2(\lambda )\omega \rho v(\lambda ),$(10)
Display Formula$D2(\lambda )=\rho a(\lambda )+Ta2(\lambda )\omega \rho v(\lambda )+Ta2(\lambda )b(\lambda 1,\lambda 2)(\omega Ta2(\lambda )+1\u2212\omega ).$(11)