Reconstructing the electric field from the measured voltages in an antenna, unfolding the antenna response, comes with several problems. Due to the noisiness of the signal it is often necessary to disregard part of the bandwidth of the antenna. It is also not guaranteed, that this system of equations can be inverted at all. In any case, the noise of the measurement will be converted into noise on the electric field.

This could be solved by Bayesian inference, however, the electric field is continuous, which would lead to an infinite-dimensional latent space. Information field theory (IFT) has been developed to deal with this problem and allow for Bayesian reasoning on fields. It provides a theoretical backbone and effective tools to approach the inference as a discrete problem in the continuum limit, taking the continuous nature of fields into account.

We will present a first working signal model that can be used with IFT-based inference algorithms, which can successfully reconstruct the electric field. The model is based on the current understanding of air shower emission physics, modelling geomagnetic and charge-excess emission and their respective polarisation and spectra separately. Since Bayesian inference provides the posterior distribution, this method also gives an estimate on the uncertainty of the measured field. The performance of this method will be demonstrated with Monte-Carlo simulations of air shower radio signals.