# The Effects of Manufacturing Errors on the Performance of Acoustic Metamaterial Lenses Operating in the MHz Regime

## TL;DR

This paper studies how manufacturing errors affect the performance of acoustic metamaterial lenses used in medical imaging and nondestructive testing.

## Contribution

A new method is proposed to evaluate manufacturing errors' impact on acoustic metamaterial lenses during the design phase.

## Key findings

- Silicone–resin layered unit cells are less affected by manufacturing errors compared to other unit cell types.
- Monte Carlo simulations show how manufacturing errors influence focal length and focal spot size.
- The proposed procedure helps select suitable unit cells and manufacturing methods for better lens performance.

## Abstract

This article explores the use of acoustical metamaterials to design lenses in the megahertz frequency range of relevance to applications in nondestructive testing and medical imaging. In particular, the effect of manufacturing errors on their focusing performance is quantified. A rapid method for including manufacturing errors is described and this is used to perform Monte Carlo simulations of wave pressure fields from lenses with manufacturing errors. In this process, the required time delay distribution for a target focal length is calculated and the acoustical lenses with a chosen unit cell type are designed. Manufacturing errors of the unit cells are then added, considering their statistical properties and a large number of realizations. As an example, an acoustical lens with a focal length of 76 mm at a frequency of 1 MHz is designed using three different unit cell types: steel cross unit cell, resin circular void unit cell, and silicone–resin layered unit cell. Finally, the resulting acoustic pressure fields are computed using a Huygens’ principle model to assess the effects of manufacturing errors on lens performance, i.e., the focal length and the size of the focal spot. It is shown that the performance of lenses consisting of silicone–resin layered units is less affected by the manufacturing errors than for lenses constructed with the other unit cells. This study paves the way for selecting a suitable combination of metamaterial unit cell and manufacturing method to enable acceptable lens imaging performance.

Herein, a procedure is proposed for evaluating the impact of manufacturing errors on the performance of acoustic metamaterial lenses during the design process. This procedure employs the accumulated delay method and Huygens’ principle to access the performance variations caused by manufacturing errors. Three types of unit cells are used to investigate the versatility of this procedure.© 2024 WILEY‐VCH GmbH