Paraxial Ocular Measurements and Entries in Spectral and Modal Matrices: Analogy and Application

Figure 1

Eigenvectors 𝐮 and 𝐯 of 𝐀 multiplied by 𝐀 yield 𝐀𝐮and 𝐀𝐯 that are parallel to 𝐮 and to 𝐯, respectively since 𝜆𝐮=𝐀𝐮 and 𝜇𝐯=𝐀𝐯. The upper central figure is analogous to an optical cross if we represent principal powers of a lens or corneal surface by 𝜆 and 𝜇 and the directions of principal meridians by 𝐮 and 𝐯, respectively. Components in 𝐮=^𝑢||_𝑢⟂ and 𝐯=^𝑣||_𝑣⟂ placed along meridians are processed to yield angles 𝛼 and 𝛽 at O in (a) and (b). The plane of the figure is tangent to an optical surface at its vertex O.