This paper is concerned with studies of birefringence and optical activity of the twisted nematic mixture 5CB/CB15 confined to cylindrical pores of ANOPORE (AP) membranes. Both birefringence and optical activity of the liquid crystal (LC) filled membranes exhibit unusual properties. The sign of the optical activity is reversed with respect to the bulk LC phase. Measurements have been performed using polarizing microscopy and generalized transmission ellipsometry. By means of C-13-NMR and FTIR experiments an increase of the tilt angle between local director and membrane normal with raising chiral dopant concentration could be proved. However, an unambiguous model for the structure of the chiral director field inside the pores could not be established up to now.