Signal decomposition

The Rayleigh-corrected reflectance is obtained from the TOA reflectance as:

\[\rho_{\text{rc}} = \rho_{\text{TOA}} / t_g - \rho_r\]

Alternatively, it can also be divided by the Rayleigh diffuse transmittance:

\[\rho_{\text{rc}}^\prime = \frac{\rho_{\text{TOA}} / t_g - \rho_r}{t_r}\]

Symbol Description
\(\rho_{\text{TOA}}\) Top-of-atmosphere reflectance: \(\rho_{\text{TOA}} = \pi \, L_{\text{TOA}} / (F_0 \, \mu_0)\)
\(L_{\text{TOA}}\) TOA radiance
\(F_0\) Extraterrestrial solar irradiance
\(\mu_0\) Cosine of the solar zenith angle
\(\rho_r\) Rayleigh reflectance
\(t_g\) Gaseous absorption transmittance along the downward + upward (solar and sensor) path
\(t_r\) Rayleigh diffuse transmittance along the solar+sensor view path