A differential approach is proposed for tomographic rain field reconstruction using the estimated signal-to-noise ratio of microwave signals from low earth orbit satellites at the ground receivers, with the unknown baseline values eliminated before using least squares to reconstruct the attenuation field. Simulations are done when the baseline is modelled by an autoregressive process and when the baseline is assumed fixed. Comparisons between the reconstruction results for the differential and non-differential approaches suggest that the differential approach performs better in both scenarios. For high correlation coefficient and low model noise in the autoregressive process, the differential approach surpasses the non-differential approach significantly.