The present invention relates to an apparatus (100) for influencing and/or detecting magnetic particles in a field of view (28), in particular an MPI apparatus. The apparatus comprises selection field elements (116) for generating a magnetic selection field (50), drive field coils (124; 125, 126, 127) for changing the position in space of the two sub-zones (52, 54) by means of a magnetic drive field, focus field elements (116) for changing the position in space of the field of view (28) by means of a magnetic focus field, and receiving elements (148) for acquiring detection signals. A static system function of the apparatus is obtained in the absence of a magnetic focus field, from which an extended system function is generated by shifting a time-domain representation of said static system function proportional to the changes of the position of the field of view caused by appliance of the magnetic focus field. Said extended system function is then used for reconstructing the spatial distribution of the magnetic particles in the field of view from the detection signals.