Abstract. We present the results of a statistical study of the magnetic structure of upper main sequence chemically peculiar stars. We have modelled a sample of 34 stars, assuming that the magnetic morphology is described by the superposition of a dipole and a quadrupole field, arbitrarily oriented. In order to interpret the modelling results, we have introduced a novel set of angles that provides one with a convenient way to represent the mutual orientation of the quadrupolar component, the dipolar component, and the rotation axis. Some of our results are similar to what has already been found in previous studies, e.g., that the inclination of the dipole axis to the rotation axis is usually large for short-period stars and small for long-period ones -see Landstreet & Mathys (2000). We also found that for short-period stars (approximately P < 10 days) the plane containing the two unit vectors that characterise the quadrupole is almost coincident with the plane containing the stellar rotation axis and the dipole axis. Long-period stars seem to be preferentially characterised by a quadrupole orientation such that the planes just mentioned are perpendicular. There is also some loose indication of a continuous transition between the two classes of stars with increasing rotational period.

We present a generalized frequency redistribution function for the polarized two-term atom in an arbitrary magnetic field. This result is derived within a new formulation of the quantum problem of coherent scattering of polarized radiation by atoms in the collisionless regime. The general theory, which is based on a diagrammatic treatment of the atom-photon interaction, is still work in progress. However, the results anticipated here are relevant enough for the study of the magnetism of the solar chromosphere and of interest for astrophysics in general.

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A theoretical model of the polarization properties of a 'Zeiss-type' coelostat is presented and discussed in detail. The Muller matrix describing the modification of the Stokes vector of the incident radiation as a result of the multiple reflections on the coelostat mirrors is derived as a function of the solar coordinates, the geometrical configuration of the coelostat, and the parameters defining the optical properties of the mirrors. These parameters, or more particularly, the index of refraction n and the extinction coefficient k, have been evaluated by means of laboratory measurements performed on a series of specimens having characteristics similar to those of the coelostat mirrors. The geometry of the coelostat configuration is described in full detail. The theoretical model has been then particularized to the case of the Donati Solar Tower in Arcetri, and some experimental measurements have been performed to check the correctness of the mode1. These measurements show the basic adequacy of the mathematical model, although some offset terms are found in the Stokes parameters U and V.

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