Drinkwater, B. W. (2022). The Physical Principles of Arrays for Mid-Air Haptic Applications (pp. 313–334).
Arrays of emitters and receivers are seen in a wide range of applications, from the square kilometre array used in radio astronomy to those used for medical ultrasound imaging. Here, we explore the use of arrays to steer and focus ultrasound for the purposes of mid-air haptics, but many of the basic principles are shared with these other applications. To achieve a mid-air haptic effect, we must use the array to focus ultrasound to a point and thereby create a high-intensity local region. The force then occurs when an object, such as a human hand, is positioned at the focus of the ultrasound beam. Here, the momentum of the sound wave is transferred directly to the object, and the haptic force is proportional to the ultrasonic intensity. High-intensity ultrasound also creates a flow called acoustic streaming, as some of the wave momentum is absorbed by the air causing it to move. These forces and flows interact with the skin where users perceive the presence of a physical object. This chapter will introduce and bring together these ideas to provide an understanding of how mid-air ultrasonic haptics works and how such systems can be designed.