Comment on A.-P. Calderón’s paper: “On an inverse boundary value problem” [in Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980), 65–73, Soc. Brasil. Mat., Rio de Janeiro, 1980; MR0590275 (81k:35160)]

Calderón determined a method to approximate the conductivity σ σ of a conducting body in R n {R^n} (for n ≥ 2 n ≥ 2 ) based on measurements of boundary data. The approximation is good in the L ∞ {L_∞ } norm provided that the conductivity is a small perturbation from a constant. We calculate the approximation exactly for the case of homogeneous concentric conducting disks in R 2 {R^2} with different conductivities. Here, the difference in the conductivities is the perturbation. We show that the approximation yields precise information about the spatial variation of σ σ , even when the perturbation is large. This ability to distinguish spatial regions with different conductivities is important for clinical monitoring applications.