抄録
A new method of measuring the distribution of vibration amplitude on an ultrasonic transducer has been developed by using the concept of ultrasonic holography. The basic idea is to measure the complex amplitude of a sound field at some distance apart from the transducer, and to reconstruct the vibration amplitude on the transducer by using the holographic reconstruction formula with the aid of a computer. If the complex amplitude of the sound field (denoted by P(γ, θ)) generated by the ultrasonic transducer is measured for a fixed value of the distance γand for the angle between O to θ_0 (see Fig. 1), then the vibration amplitude on the surface of the transducer can be calculated by using Eq. (12), where V_c(ρ) is the reconstructed vibration amplitude on the transducer and ρis the radial component of a polar coordinate system taken on the transducer. However, it is necessary to satisfy Eqs. (8) and (10) in order to use Eq. (12), whereγ', γ'_0 and ρ' show γ/λ, γ_0 /λand ρ/λrespectively, in which λis the wavelength of ultrasonic waves and γ_0 is the radius of curvature of the transducer. Results of analysis of the resolving power of this method are shown in Figs. 2 and 3. In Fig. 2, the half-power width of the reconstructed line source is shown as a function of maximum scanning angle θ_0. It is seen that a linear relation exists between 1 / sin θ_0 and half-width. Fig. 3 shows the relation between the radius of transducer and the distance between transducer and measuring point. The parameters in the figure show the half-width required for the measurement. Experimental apparatus is shown in Fig. 4, where the transducer to be measured is mounted on a rotating table and scanning of the angle is performed by rotating the transducer. Consequently, only a small water tank is required for the measurement. For experiments, a P. Z. T. ultrasonic transducer of radius 25 mm was divided into four rings concentrically whose radii were given by 12. 5 mm, 17. 7 mm, 21. 7 mm, and 25. 0 mm from inner to outer. But this division was made for the electrode only and the ceramic portion of the transducer was not divided at all. The driving high-voltage signal was applied to the central and second electrodes independently, and in each case the vibration amplitude on the whole circular transducer was examined. In Fig. 5, the amplitude and phase of the measured ultrasonic field are shown where the central and second rings are excited. In Fig. 6, the reconstructed amplitude and phase of the vibration amplitude on the transducer are shown where only the central rings is excited. The dotted lines in Figs. 6 show the calculated curves on the assumption that the excited region of the transducer vibrates uniformly and the other part of the transducer does not vibrate at all. In Fig. 7, the reconstructed amplitude and phase are shown when the second ring is excited. The dotted lines in Fig. 7, also show the calculated curves for the ideal case. By comparing these curves it can be said that the amplitude and phase of the excited region is almost uniform and the other part of the transducer radiates a considerable amount of sound energy.
