add_layers_basic

iadpython.combine.add_layers_basic(sample, R10, T01, R12, R21, T12, T21)

Add two layers together.

The basic equations for the adding-doubling sample (neglecting sources) are

\[T_{02} = T_{12} (E - R_{10} R_{12})^{-1} T_{01}\]

\[R_{20} = T_{12} (E - R_{10} R_{12})^{-1} R_{10} T_{21} +R_{21}\]

\[T_{20} = T_{10} (E - R_{12} R_{10})^{-1} T_{21}\]

\[R_{02} = T_{10} (E - R_{12} R_{10})^{-1} R_{12} T_{01} +R_{01}\]

Upon examination it is clear that the two sets of equations have the same form. These equations assume some of the multiplications are star multiplications. Explicitly,

\[T_{02} = T_{12} (E - R_{10} C R_{12} )^{-1} T_{01}\]

\[R_{20} = T_{12} (E - R_{10} C R_{12} )^{-1} R_{10} C T_{21} +R_{21}\]

where the diagonal matrices C and E are

\[E_{ij}= 1/(2𝜈_i w_i) 𝛿_{ij}\]

\[C_{ij}= 2𝜈_i w_i 𝛿_{ij}\]