Traditionally, high-accuracy full-sphere polar measurements require dense sampling of the sound field at very-fine angular increments, particularly at high frequencies. The proposed HELS (Helmholtz Equation Least Squares) method allows this restriction to be relaxed significantly. Using this method, far fewer sampling points are needed for full and accurate reconstruction of the radiated sound field. Depending on the required accuracy, sound fields can be reconstructed using only 10 to 20% of the number of sampling points required by conventional techniques. The HELS method allows accurate reconstruction even for sample spacing that violates the Nyquist spatial sampling rate in certain directions. This paper examines the convergence of HELS solutions via theory and simulation for reconstruction of the acoustic radiation patterns generated by a rectangular plate mounted on an infinite rigid flat baffle. In particular, the impact of the numbers of expansion terms and measurement points as well as errors imbedded in the input data on the resultant accuracy of reconstruction is analyzed.
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