RESUMEN
Modern adaptive optics (AO) systems for large telescopes require tomographic techniques to reconstruct the phase aberrations induced by the turbulent atmosphere along a line of sight to a target which is angularly separated from the guide sources that are used to sample the atmosphere. Multi-object adaptive optics (MOAO) is one such technique. Here, we present a method which uses an artificial neural network (ANN) to reconstruct the target phase given off-axis references sources. We compare our ANN method with a standard least squares type matrix multiplication method and to the learn and apply method developed for the CANARY MOAO instrument. The ANN is trained with a large range of possible turbulent layer positions and therefore does not require any input of the optical turbulence profile. It is therefore less susceptible to changing conditions than some existing methods. We also exploit the non-linear response of the ANN to make it more robust to noisy centroid measurements than other linear techniques.