A method for operating a scanning probe microscope having a probe, adapted to be associated with a specimen to be imaged, equipped with a scanning element carried by a piezo-electric support member arranged for performing distance regulation between the scanning element and the surface of the specimen under investigation and for moving the scanning element in directions parallel to the surface of the specimen for achieving the scanning of the said surface, the method including: - driving the scanning element along at least a scanning trajectory over the surface of the specimen; - acquiring an electric signal (I n) indicative of a predetermined reading parameter representative of the interaction between the scanning element and the specimen at each scanning position; and - possibly adjusting the height of the scanning element over the specimen as a function of the acquired signal (I n) wherein the method comprises: i) a characterization stage, including: sweeping a plurality of excitation frequencies of the vertical displacement of the scanning element, i.e. the variation of the distance between the scanning element and the surface of the specimen; measuring the value attained by the reading parameter at the excitation frequencies; characterized in that the characterization stage further comprises the step of identifying plateau regions of the response spectrum of the reading parameter, where the reading parameter variation is limited within a predetermined range over a predefined frequency interval, thereby defining corresponding fast scanning frequency windows, and in that the method further comprises ii) a measurement stage, including driving the scanning element along at least a scanning trajectory over the surface of the specimen at a frequency selected among the frequencies included in a fast scanning frequency window. - driving the scanning element along at least a scanning trajectory over the surface of the specimen; - acquiring an electric signal (I n) indicative of a predetermined reading parameter representative of the interaction between the scanning element and the specimen at each scanning position; and - possibly adjusting the height of the scanning element over the specimen as a function of the acquired signal (I n) i) a characterization stage, including: sweeping a plurality of excitation frequencies of the vertical displacement of the scanning element, i.e. the variation of the distance between the scanning element and the surface of the specimen; measuring the value attained by the reading parameter at the excitation frequencies; characterized in that the characterization stage further comprises the step of identifying plateau regions of the response spectrum of the reading parameter, where the reading parameter variation is limited within a predetermined range over a predefined frequency interval, thereby defining corresponding fast scanning frequency windows, and in that the method further comprises sweeping a plurality of excitation frequencies of the vertical displacement of the scanning element, i.e. the variation of the distance between the scanning element and the surface of the specimen; measuring the value attained by the reading parameter at the excitation frequencies; characterized in that the characterization stage further comprises the step of identifying plateau regions of the response spectrum of the reading parameter, where the reading parameter variation is limited within a predetermined range over a predefined frequency interval, thereby defining corresponding fast scanning frequency windows, ii) a measurement stage, including driving the scanning element along at least a scanning trajectory over the surface of the specimen at a frequency selected among the frequencies included in a fast scanning frequency window.