Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2022 / Paper 1 / 4 / b

A band ratio image emphasizes differences in spectral reflectance rather than overall brightness. If two corrected band signals are $L_1=k{\rho }_1$ and $L_2=k{\rho }_2$, with the same multiplicative illumination factor $k$, their ratio is ${\rho }_1/{\rho }_2$: common shading or exposure factors cancel. Materials with different spectral slopes or absorption features can therefore separate more clearly than in either band alone.

The cancellation is approximate. Additive atmospheric path radiance, different angular reflectance responses and different band noise do not cancel, and division by a small denominator amplifies errors. Use calibrated, co-registered bands and mask cloud, deep shadow and invalid pixels before interpreting a ratio as a material or vegetation contrast.