  We present preliminary results from a programme aimed at acquiring linear
spectropolarimetry of magnetic A and B stars. Linear polarization in the
spectral lines of these objects is due to the Zeeman effect, and should provide
detailed new information regarding the structure of their strong magnetic
fields. To illustrate the impact of these new data, we compare observed
circular and linear polarization line profiles of 53 Cam with the profiles
predicted by the magnetic model by Landstreet (1988).
  Linear polarization in the spectral lines of all stars studied is extremely
weak; in most cases, below the threshold of detectability even for very high
SNRs. In order to overcome this problem, we employ the Least-Squares
Deconvolution (LSD) multi-line analysis technique in order to extract low-noise
mean line profiles and polarization signatures from our echelle spectra. Tests
show that these mean signatures can be modelled as real spectral lines, and
have the potential to lead to high-resolution maps of the magnetic and chemical
abundance surface distributions.
