# Practical Method for Evaluating the Element Sensitivity Variation of an Ultrasonic Annular Phased Array Transducer

## TL;DR

This paper introduces a new method to accurately evaluate sensitivity consistency in annular phased array transducers, improving their reliability in practical applications.

## Contribution

A novel algorithm is proposed to evaluate element sensitivity in annular array transducers by using response voltage per unit width.

## Key findings

- The response amplitude of ring-shaped elements is linearly correlated with radial width, confirmed by numerical simulations.
- The new algorithm reduced sensitivity variation from 25 dB to 6 dB in a 32-element transducer.
- The central element cannot be evaluated using the proposed method due to its distinct geometry.

## Abstract

The unique features of annular phased array transducers, such as ring-shaped elements and the concentric configuration, cause them to behave differently from commonly used linear array transducers, in terms of sound field distribution and pulse–echo response. Consequently, standard techniques for assessing linear array transducers can introduce significant errors when applied to annular array transducers, especially concerning element-to-element sensitivity variance. This study investigates the consistency of element sensitivity in annular phased array transducers. Through theoretical analysis, a Long-Belt source assumption model was developed based on the Rayleigh integral to characterize the responses of ring-shaped elements in an analytical and explicit form. The model suggests that the response amplitude is linearly correlated with the radial width of the element, which was validated by subsequent numerical simulations. Based on these findings, a modified sensitivity evaluation algorithm for annular array transducers is presented. The response voltage per unit width, rather than the total response voltage, is used to eliminate the influence of varying geometries and sizes across elements. The sensitivity variation of a 32-element annular array transducer was evaluated using the new algorithm. Compared to the uncorrected measurement, the maximum sensitivity variation was reduced significantly from 25 dB to 6 dB, revealing the transducer’s intrinsic consistency despite the different geometric features of each element. Due to its distinct geometry compared to the ring-shaped elements, the central element cannot be corrected or evaluated using this method. These results suggest that the proposed algorithm enables the more accurate evaluation of sensitivity consistency for annular phased array transducers, thereby improving measurement reliability in practical applications.