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Ultrasound emitted from an array of transducers can produce various tactile sensations by temporally controlling the phase and amplitude of the transducers. However, the controllability in haptic applications has not been well examined. This article clarifies a phase shift of the driving signal causes amplitude fluctuation of emitted ultrasound, even under a constant driving amplitude. We demonstrate theoretically that this problem exists in general resonant systems with various quality factors, and point out that it produces radiation force decrease and audible noise. We also show a method to reduce the fluctuation and quantitatively evaluate the effectiveness. The results provide the measure of the displayed force fluctuation by a fast focus movement and enable silent haptic stimulation.

Reducing Amplitude Fluctuation by Gradual Phase Shift in Midair Ultrasound Haptics