# Generating Airborne Ultrasonic Amplitude Patterns Using an Open Hardware Phased Array
## 2 Related Work  
Our review of related work gives an overview of projects that designed and built ultrasonic arrays that typically operate at 40 kHz. Additionally, we provide a review of algorithms for creating an arbitrary pressure field. An ultrasonic phased array consists of a collection of elements that can transmit or receive ultrasonic waves with specific time delays (phases offsets) and amplitudes. This technology enables the generation of arbitrary pressure fields by controlling the phases and amplitudes of each emitter. Moreover, it provides an interesting setup for a wide spectrum of novel applications, such as mid-air displays [22], wireless power transfer [23], acoustic imaging [24], or delivering food through acoustic levitation [25], to mention a few. [PERSON] et al. first demonstrated ultrasonic mid-air haptic feedback [26], who developed a prototype consisting of 12 annular channels with a total of 91 ultrasound transducers in a hexagonal arrangement, a single focal point could be refocused along the central axis perpendicular to the array. [PERSON]'s group [27; 28; 29; 30] developed a more sophisticated system that was capable of controlling individually 249 transducers, being able to focus at different 3D positions in space, their boards have the capability to be chained to operate as a larger array system. [PERSON] et al. [6] developed a phased array that can produce multi-point haptic feedback. Ultraleap (Bristol, UK) is a company that commercializes ultrasonic phased arrays for haptic applications related to automotive [31], digital signage [32], and AR/VR [33] applications. The company has also been exploring the effects on humans of high intensity ultrasound exposure [34] and has been releasing multiple prototypes that explore optimized array designs [35; 36]. For example, transducer array in a Fibonacci spiral arrangement can suppress unwanted secondary focal points [37]. Pixe Dist Technologies (Tokyo, Japan) provides a parametric speaker [10] and an acoustic levitator [38] based on ultrasound phased arrays. The parametric prototype array has 269 transducers populating a circular array, \(\pi/32\) phase resolution, and can be refreshed at 1 kHz. Their levitator prototype has four orthogonally placed arrays with 285 transducers with a phase resolution of \(\pi/8\) and it is updated at 1 kHz. These ultrasound phased arrays have a fast update rate, high-power output, and sufficient phase and amplitude resolution; however, they are comparatively expensive, the software is closed, and the hardware cannot be easily modified. Some researchers have developed open platforms of acoustic phased arrays operating at 40 kHz in air. These platforms allow developers to create their own low-cost array [39; 40; 41]. For example, TinyLev [42] is a single-axis acoustic levitator that uses two ultrasonic arrays facing each other, reducing the number of independent channels by arranging transducers within the same distance to the trapping positions. [PERSON] et al. [9] presented an acoustic levitator display with two opposed arrays that was capable of creating and modulating a large number of focal points at high speeds (20 kHz update rate) for delivering tactile feedback and parametric audio at the same time. While some part of the code is public, the hardware was not provided. Other projects have released both the hardware and software. For example, Ultraino [41] is a multi-purpose phased array that is accompanied by a platform that helps designers to build small phased arrays. The hardware is based on an Arduino MEGA microcontroller and provides 64 channels with \(\pi\)/5 phase resolution. Furthermore, multiple boards can be chained together, expanding the number of individual controlled channels. The software is capable of customising phased array arrangements and visualising the pressure field in real-time. Despite the advantage of being a low-cost platform, the operating voltage is limited, reaching a large number of channels is cumbersome, and the transducers need to be wired to the boards.