  Determination of solar magnetic fields with a spatial resolution set by the
diffraction limit of a telescope is difficult because the time required to
measure the Stokes vector with sufficient signal-to-noise is long compared to
the solar evolution timescale. This difficulty gets worse with increasing
telescope size as the photon flux per diffraction-limited resolution element
remains constant but the evolution timescale decreases linearly with the
diffraction-limited resolution. We aim to improve magnetic field reconstruction
at the diffraction limit without averaging the observations in time or space,
and without applying noise filtering. The magnetic field vector tends to evolve
slower than the temperature, velocity and microturbulence. We exploit this by
adding temporal regularisation terms for the magnetic field to the linear
least-squares fitting used in the weak-field approximation, as well as to the
Levenberg-Marquardt algorithm used in inversions. The other model parameters
are allowed to change in time without constraints. We infer the chromospheric
magnetic field from Ca II 854.2 nm observations using the weak field
approximation and the photospheric magnetic field from Fe I 617.3 nm
observations using Milne-Eddington inversions, both with and without temporal
regularisation. Temporal regularisation reduce the noise in the reconstructed
maps of the magnetic field and provides a better coherency in time in both the
weak-field approximation and Milne-Eddington inversions. Temporal
regularisation markedly improves magnetic field determination from spatially
and temporally resolved observations.
