Point spread function of electrical probe for measuring induced charge on surface of piezoelectric vibrator

Electrical probe method developed by Fukuyo is an excellent tool to identify various vibration modes of a piezoelectric vibrator. Piezoelectrically induced charge of a mode is picked up by a small needle probe embedded in the lower electrode. Mechanical scanning of the vibrator by an X-Y stage allowed to obtain a distribution of induced charge over the surface. Fukuyo measured only the amplitude of induced charge. Ya. Watanabe, et al. introduced a network analyzer, which allowed the measurement of phase as well as amplitude and the scanning of frequency. Their works, however, were limited to qualitative observation of distribution pattern. This paper presents more quantitative characterization of a probe. An observed value of the input to the network analyzer by electrical probe consists of a desired piezoelectrically induced part and an undesired part caused mainly by stray capacitances. On a circle diagram (vector) plot as a function of frequency, the former part at a resonance is essentially a circle, whereas the latter part is essentially constant, which we call here "reference origin". A reference origin can be directly determined from observed values obtained by a frequency scanning in a narrow range around a resonance itself. A probe picks up surface charge not only at an infinitesimal point but also at surrounding points due to fringing in electrical field. Its characteristics can be expressed by a spatial point spread function similar to an optical point spread function of a lens. Spatial distribution of surface charge of a main thickness-shear mode usually contains components of high spatial frequency due to effects of high overtones of contour modes, of which observed amplitude are much reduced due to a spread function. In previous papers, an estimation of reference origin were refined and distributions of surface charge analytically obtained were compared with experiments. A good agreement is obtained, when a spread function is taking into an account. Th- is paper presents a further refinement of the estimation of reference origin and also details of both theoretical and experimental characterization of point spread function.