Access Type

Open Access Dissertation

Date of Award


Degree Type


Degree Name



Mechanical Engineering

First Advisor

Sean Wu


The dissertation investigates the reconstruction of coherent point sources using Helmholtz Equation Least Squares (HELS) method based on measurements in violation of Nearfield Acoustical Holography (NAH) resolution guidelines. In HELS, the Helmholtz equation is solved by matching a series of localized spherical expansion functions to the measured pressures in the field. Expansion coefficients are solved for by least squares and used to reconstruct pressures at the source surface. By approximating the pressure radiation with expansion functions, field and surface pressures can be synthesized, resulting in the possibility of higher spatial resolution than previous generation NAH methods such as Fourier Acoustics and Inverse Boundary Element Methods. The NAH guidelines dictate that spatial resolution decreases with increasing stand-off distance and decreasing Signal to Noise Ratio (SNR). Also, in methods other than HELS, measurement spacing must exceed the spacing derived from the Nyquist rate to mitigate the risk of aliasing. HELS is not limited by the Nyquist rate due to its ability to synthesize field and surface points.

The resolution capability of HELS is tested through numerical simulation and experimental testing. Besides HELS, a weighted variant of HELS, termed "Modified HELS" is tested. For comparison, Fourier Acoustics is used as a baseline with measurement spacing equal to and finer than the measurement spacing used in the HELS simulations. Results show that both HELS and Fourier Acoustics reconstruct point sources at finer resolution than the NAH guidelines predict. The increased resolution is likely due to the use of point sources and its affect on the definition of SNR and the angular spectrum. However, HELS, and in particular Modified HELS, show a significant increase in accuracy in comparison to Fourier Acoustics for the parameters tested.

The main conclusion of this dissertation is that Standard and Modified HELS are better tools than traditional NAH methods when reconstructing coherent point sources in violation of the NAH spatial resolution guidelines.