Two-Scale Sparse Spiral Array Design for 3D Ultrasound Imaging in Air

Sparse array designs are a promising approach to improve the beam pattern and imaging quality, especially for applications, where hardware resources are severely limited. In particular, spiral sunflower arrays become increasingly popular due to their excellent point-spread-function (PSF) characteristics and their simple, deterministic and scalable design. Therefore, several sunflower modifications for further improvement have been investigated, e.g. density tapering based on window functions adapted from apodization techniques. In this article, we introduce a two-scale spiral array design concept, which exploits the specific PSF structure of the sunflower geometry, instead of relying on window functions. The modification proposed combines two nested sunflower sub-arrays featuring two different spatial element densities such that the locations of their respective main, side and grating lobe zones differ, resulting in a balanced and improved composite one-way PSF in terms of main lobe width (MLW) and maximum side lobe level (MSLL) under far-field and narrow-band conditions. First, we provide an analysis of the unmodified classic sunflower geometry, describe its PSF zones and show how their locations in the PSF can be estimated based on the array design parameters, which finally leads to the two-scale concept. Second, we examine a specific well-matching combination of nested sub-arrays to discuss the advantages and limitations of the resulting PSF. Third, we benchmark the respective optimum arrays of the classic sunflower and density tapering strategies with the two-scale method, where the latter shows an improved performance of the one-way PSF in terms of MLW and MSLL. Fourth, the two-scale design strategy is validated using a real-world 64-element prototype for narrow-band ultrasound imaging in air. We conduct two experiments to analyze the resulting PSF and angular resolution. Overall, the results demonstrate that the proposed flexible four-parameter concept is particularly valuable for high frame rate imaging as well as for transmit-only and receive-only applications.