Abstract
Non-contact tactile presentation using ultrasound phased arrays is becoming a powerful method for providing haptic feedback on bare skin without restricting the user's movement. In such ultrasonic mid-air haptics, it is often necessary to generate multiple ultrasonic foci simultaneously, which requires solving the inverse problem of amplitudes and phases of the transducers in a phased array. Conventionally, matrix calculation methods have been used to solve this inverse problem. However, a matrix calculation requires a non-negligible amount of time when the number of control points and the number of transducers in the array are large. In this article, we propose a simple method based on a greedy algorithm and brute-force search to solve the field reconstruction problem. The proposed method directly optimizes the desired field without matrix calculation or target field phase optimization. The empirical results indicate that the proposed method can reproduce the target sound with an accuracy of more than 80%.
Highlights
A IRBORNE ultrasound phased arrays [1]–[3] have been a typical non-contact stimulator in haptics [4]
Sound field reconstruction a) Experiments: First, we evaluated the performance of a sound field reconstruction
We used a phased array consisting of 36 × 36 transducers arranged in a grid pattern with 10 mm spacing; the wavelength of the ultrasound was set to 8.5 mm
Summary
A IRBORNE ultrasound phased arrays [1]–[3] have been a typical non-contact stimulator in haptics [4]. For scientific studies on haptics, this non-contact method can create stable forces on the skin with good reproducibility and the spatial and temporal pattern can be freely designed. In such ultrasonic mid-air haptics, it is often necessary to solve the inverse problem to obtain transducers’ inputs from the desired radiation pressure pattern, typically with multiple foci. Matsubayashi et al proposed a midair haptic system where a user can pinch and handle a virtual object [6], [7] In these systems, it is needed to calculate the optimal phase and amplitude of each transducer in the array, desirably in real time
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