Spherical monopoles and holomorphic functions

We show that any gauge-equivalence class of solutions (del, phi) of the mon opole equation F-del = *d(del)phi, defined on an open set Omega of S-3 (equ ipped with its standard metric), induces canonically a holomorphic function on the complex 2-dimensional space of all geodesics on S-3 entirely contai ned in Omega.