The invention is directed to a scanning system having one or several deflectable probe tips which are excited to oscillation at or near their resonant frequency. A saturation amplifier (16) is provided for detecting and measuring the phase shift between the excitation signal and the oscillation carried out by the probe tip. The saturation amplifier (16) generates a rectangular signal from the incoming sinusoidally-shaped signal (3e) while exactly maintaining the time-dependent position of the zero crossovers of the signal. The detection system, which is required for each probe tip, thereby acquires a very simple configuration of few commercially available components. Saturation amplified rectangular signals exclusively form the basis for the further evaluation. For this reason, a substantial independence of the signal intensity of the oscillation signal is ensured.