A system includes an apparatus having at least one permanent magnet and at least one magnetic field sensor at a pole of the at least one permanent magnet and configured to be positioned relative to a surface of a membrane containing immobilized magnetic particles selectively bound to an analyte such that the magnetic particles are magnetized by the at least one permanent magnet. The system further includes a stage configured to move at least one of the apparatus and the membrane relative to one another with an oscillatory movement parallel to the surface of the membrane, at least one controller configured to control the oscillatory movement, and a data acquisition unit configured to receive signals from the at least one magnetic field sensor and the at least one controller method.