Radiation Pressure Field Reconstruction for Ultrasound Midair Haptics by Greedy Algorithm With Brute-Force Search

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%.